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Title: Letters of a Radio-Engineer to His Son
Author: Mills, John, 1880-
Language: English
As this book started as an ASCII text book there are no pictures available.
Copyright Status: Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook. See comments about copyright issues at end of book.

*** Start of this Doctrine Publishing Corporation Digital Book "Letters of a Radio-Engineer to His Son" ***

This book is indexed by ISYS Web Indexing system to allow the reader find any word or number within the document.

[Transcriber's Note: An underscore character "_" is used around
text to signify italics in the _original_ text, as illustrated.
It also is used to signify a subscript, used frequently in technical
descriptions. For example _E_{C}_ would have been originally typeset
as a capital E followed by a smaller C subscript, and both would
have been in an italic typeface.]

[Illustration: Pl. I.--One of the Lines of Towers at Radio Central
(Courtesy of Radio Corporation of America).]




Engineering Department, Western Electric Company, Inc.,

Author of "Radio-Communication," "The Realities of
Modern Science," and "Within the Atom"









J. M., Jr.


        1  Electricity and Matter                        3

        2  Why a Copper Wire Will Conduct
           Electricity                                   9

        3  How a Battery Works                          16

        4  The Batteries in Your Radio Set              27

        5  Getting Electrons from a Heated Wire         34

        6  The Audion                                   40

        7  How to Measure an Electron Stream            48

        8  Electron-Moving-Forces                       57

        9  The Audion-Characteristic                    66

       10  Condensers and Coils                         77

       11  A "C-W" Transmitter                          86

       12  Inductance and Capacity                      96

       13  Tuning                                      112

       14  Why and How to Use a Detector               124

       15  Radio-Telephony                             140

       16  The Human Voice                             152

       17  Grid Batteries and Grid Condensers for
           Detectors                                   165

       18  Amplifiers and the Regenerative Circuit     176

       19  The Audion Amplifier and Its Connections    187

       20  Telephone Receivers and Other
           Electromagnetic Devices                     199

       21  Your Receiving Set and How to Experiment    211

       22  High-Powered Radio-Telephone
           Transmitters                                230

       23  Amplification at Intermediate
           Frequencies                                 242

       24  By Wire and by Radio                        251

           Index                                       263


        I  One of the Lines of Towers at Radio Central

       II  Bird's-Eye View of Radio Central             10

      III  Dry Battery for Use in Audion Circuits,
           and also Storage Battery                     27

       IV  Radiotron                                    42

        V  Variometer and Variable Condenser of
           the General Radio Company. Voltmeter
           and Ammeter of the Weston Instrument
           Company                                      91

       VI  Low-Power Transmitting Tube, U V 202        106

      VII  Photographs of Vibrating Strings            155

     VIII  To Illustrate the Mechanism for the
           Production of the Human Voice               170

       IX  Western Electric Loud Speaking
           Receiver. Crystal Detector Set of the
           General Electric Co. Audibility Meter
           of General Radio Co.                        203

        X  Audio-Frequency Transformer and
           Banked-Wound Coil                           218

       XI  Broadcasting Equipment, Developed by
           the American Telephone and Telegraph
           Company and the Western Electric Company    235

      XII  Broadcasting Station of the American
           Telephone and Telegraph Company on the
           Roof of the Walker-Lispenard Bldg. in
           New York City where the Long-distance
           Telephone Lines Terminate                   250





You are interested in radio-telephony and want me to explain it to you.
I'll do so in the shortest and easiest way which I can devise. The
explanation will be the simplest which I can give and still make it
possible for you to build and operate your own set and to understand the
operation of the large commercial sets to which you will listen.

I'll write you a series of letters which will contain only what is
important in the radio of to-day and those ideas which seem necessary if
you are to follow the rapid advances which radio is making. Some of the
letters you will find to require a second reading and study. In the case
of a few you might postpone a second reading until you have finished
those which interest you most. I'll mark the letters to omit in this

All the letters will be written just as I would talk to you, for I shall
draw little sketches as I go along. One of them will tell you how to
experiment for yourself. This will be the most interesting of all. You
can find plenty of books to tell you how radio sets operate and what to
do, but very few except some for advanced students tell you how to
experiment for yourself. Not to waste time in your own experiments,
however, you will need to be quite familiar with the ideas of the other

What is a radio set? Copper wires, tinfoil, glass plates, sheets of
mica, metal, and wood. Where does it get its ability to work--that is,
where does the "energy" come from which runs the set? From batteries or
from dynamos. That much you know already, but what is the real reason
that we can use copper wires, metal plates, audions, crystals, and
batteries to send messages and to receive them?

The reason is that all these things are made of little specks, too tiny
ever to see, which we might call specks of electricity. There are only
two kinds of specks and we had better give them their right names at
once to save time. One kind of speck is called "electron" and the other
kind "proton." How do they differ? They probably differ in size but we
don't yet know so very much about their sizes. They differ in laziness a
great deal. One is about 1845 times as lazy as the other. That is, it
has eighteen hundred and forty-five times as much inertia as the other.
It is harder to get it started but it is just as much harder to get it
to stop after it is once started or to change its direction and go a
different direction. The proton has the larger inertia. It is the
electron which is the easier to start or stop.

How else do they differ? They differ in their actions. Protons don't
like to associate with other protons but take quite keenly to electrons.
And electrons--they go with protons but they won't associate with each
other. An electron always likes to be close to a proton. Two is company
when one is an electron and the other a proton but three is a crowd

It doesn't make any difference to a proton what electron it is keeping
company with provided only it is an electron and not another proton. All
electrons are alike as far as we can tell and so are all protons. That
means that all the stuff, or matter, of our world is made up of two
kinds of building blocks, and all the blocks of each kind are just
alike. Of course you mustn't think of these blocks as like bricks, for
we don't know their shapes.

Then there is another reason why you must not think of them as bricks
and that is because when you build a house out of bricks each brick must
rest on another. Between an electron and any other electron or between
two protons or between an electron and a proton there is usually a
relatively enormous distance. There is enough space so that lots of
other electrons or protons could be fitted in between if only they were
willing to get that close together.

Sometimes they do get very close together. I can tell you how if you
will imagine four small boys playing tag. Suppose Tom and Dick don't
like to play with each other and run away from each other if they can.
Now suppose that Bill and Sam won't play with each other if they can
help it but that either of them will play with Tom or Dick whenever
there is a chance. Now suppose Tom and Bill see each other; they start
running toward each other to get up some sort of a game. But Sam sees
Tom at the same time, so he starts running to join him even though Bill
is going to be there too. Meanwhile Dick sees Bill and Sam running along
and since they are his natural playmates he follows them. In a minute
they are all together, and playing a great game; although some of the
boys don't like to play together.

Whenever there is a group of protons and electrons playing together we
have what we call an "atom." There are about ninety different games
which electrons and protons can play, that is ninety different kinds of
atoms. These games differ in the number of electrons and protons who
play and in the way they arrange themselves. Larger games can be formed
if a number of atoms join together. Then there is a "molecule." Of
molecules there are as many kinds as there are different substances in
the world. It takes a lot of molecules together to form something big
enough to see, for even the largest molecule, that of starch, is much
too small to be seen by itself with the best possible microscope.

What sort of a molecule is formed will depend upon how many and what
kinds of atoms group together to play the larger game. Whenever there is
a big game it doesn't mean that the little atomic groups which enter
into it are all changed around. They keep together like a troop of boy
scouts in a grand picnic in which lots of troops are present. At any
rate they keep together enough so that we can still call them a group,
that is an atom, even though they do adapt their game somewhat so as to
fit in with other groups--that is with other atoms.

What will the kind of atom depend upon? It will depend upon how many
electrons and protons are grouped together in it to play their little
game. How any atom behaves so far as associating with other groups or
atoms will depend upon what sort of a game its own electrons and protons
are playing.

Now the simplest kind of a game that can be played, and the one with the
smallest number of electrons and protons, is that played by a single
proton and a single electron. I don't know just how it is played but I
should guess that they sort of chase each other around in circles. At
any rate I do know that the atom called "hydrogen" is formed by just one
proton and one electron. Suppose they were magnified until they were as
large as the moon and the earth. Then they would be just about as far
apart but the smaller one would be the proton.

That hydrogen atom is responsible for lots of interesting things for it
is a great one to join with other atoms. We don't often find it by
itself although we can make it change its partners and go from one
molecule to another very easily. That is what happens every time you
stain anything with acid. A hydrogen atom leaves a molecule of the acid
and then it isn't acid any more. What remains isn't a happy group either
for it has lost some of its playfellows. The hydrogen goes and joins
with the stuff which gets stained. But it doesn't join with the whole
molecule; it picks out part of it to associate with and that leaves the
other part to take the place of the hydrogen in the original molecule of
acid from which it came. Many of the actions which we call chemistry are
merely the result of such changes of atoms from one molecule to another.

Not only does the hydrogen atom like to associate in a larger game with
other kinds of atoms but it likes to do so with one of its own kind.
When it does we have a molecule of hydrogen gas, the same gas as is used
in balloons.

We haven't seemed to get very far yet toward radio but you can see how
we shall when I tell you that next time I shall write of more
complicated games such as are played in the atoms of copper which form
the wires of radio sets and of how these wires can do what we call
"carrying an electric current."




You have learned that the simplest group which can be formed by protons
and electrons is one proton and one electron chasing each other around
in a fast game. This group is called an atom of hydrogen. A molecule of
hydrogen is two of these groups together.

All the other possible kinds of groups are more complicated. The next
simplest is that of the atom of helium. Helium is a gas of which small
quantities are obtained from certain oil wells and there isn't very much
of it to be obtained. It is an inert gas, as we call it, because it
won't burn or combine with anything else. It doesn't care to enter into
the larger games of molecular groups. It is satisfied to be as it is, so
that it isn't much use in chemistry because you can't make anything else
out of it. That's the reason why it is so highly recommended for filling
balloons or airships, because it cannot burn or explode. It is not as
light as hydrogen but it serves quite well for making balloons buoyant
in air.

This helium atom is made up of four electrons and four protons. Right at
the center there is a small closely crowded group which contains all the
protons and two of the electrons. The other two electrons play around
quite a little way from this inner group. It will make our explanations
easier if we learn to call this inner group "the nucleus" of the atom.
It is the center of the atom and the other two electrons play around
about it just as the earth and Mars and the other planets play or
revolve about the sun as a center. That is why we shall call these two
electrons "planetary electrons."

There are about ninety different kinds of atoms and they all have names.
Some of them are more familiar than hydrogen and helium. For example,
there is the iron atom, the copper atom, the sulphur atom and so on.
Some of these atoms you ought to know and so, before telling you more of
how atoms are formed by protons and electrons, I am going to write down
the names of some of the atoms which we have in the earth and rocks of
our world, in the water of the oceans, and in the air above.

Start first with air. It is a mixture of several kinds of gases. Each
gas is a different kind of atom. There is just a slight trace of
hydrogen and a very small amount of helium and of some other gases which
I won't bother you with learning. Most of the air, however, is nitrogen,
about 78 percent in fact and almost all the rest is oxygen. About 20.8
percent is oxygen so that all the gases other than these two make up
only about 1.2 percent of the atmosphere in which we live.

[Illustration: Pl. II.--Bird's-eye View of Radio Central
(Courtesy of Radio Corporation of America).]

The earth and rocks also contain a great deal of oxygen; about 47.3
percent of the atoms which form earth and rocks are oxygen atoms. About
half of the rest of the atoms are of a kind called silicon. Sand is made
up of atoms of silicon and oxygen and you know how much sand there is.
About 27.7 percent of the earth and its rocks is silicon. The next most
important kind of atom in the earth is aluminum and after that iron and
then calcium. Here is the way they run in percentages: Aluminum 7.8
percent; iron 4.5 percent; calcium 3.5 percent; sodium 2.4 percent;
potassium 2.4 percent; magnesium 2.2 percent. Besides these which are
most important there is about 0.2 percent of hydrogen and the same
amount of carbon. Then there is a little phosphorus, a little sulphur, a
little fluorine, and small amounts of all of the rest of the different
kinds of atoms.

Sea water is mostly oxygen and hydrogen, about 85.8 percent of oxygen
and 10.7 percent of hydrogen. That is what you would expect for water is
made up of molecules which in turn are formed by two atoms of hydrogen
and one atom of oxygen. The oxygen atom is about sixteen times as heavy
as the hydrogen atom. However, for every oxygen atom there are two
hydrogen atoms so that for every pound of hydrogen in water there are
about eight pounds of oxygen. That is why there is about eight times as
high a percentage of oxygen in sea water as there is of hydrogen.

Most of sea water, therefore, is just water, that is, pure water. But it
contains some other substances as well and the best known of these is
salt. Salt is a substance the molecules of which contain atoms of sodium
and of chlorine. That is why sea water is about 1.1 percent sodium and
about 2.1 percent chlorine. There are some other kinds of atoms in sea
water, as you would expect, for it gets all the substances which the
waters of the earth dissolve and carry down to it but they are
unimportant in amounts.

Now we know something about the names of the important kinds of atoms
and can take up again the question of how they are formed by protons and
electrons. No matter what kind of atom we are dealing with we always
have a nucleus or center and some electrons playing around that nucleus
like tiny planets. The only differences between one kind of atom and any
other kind are differences in the nucleus and differences in the number
and arrangement of the planetary electrons which are playing about the

No matter what kind of atom we are considering there is always in it
just as many electrons as protons. For example, the iron atom is formed
by a nucleus and twenty-six electrons playing around it. The copper atom
has twenty-nine electrons as tiny planets to its nucleus. What does that
mean about its nucleus? That there are twenty-nine more protons in the
nucleus than there are electrons. Silver has even more planetary
electrons, for it has 47. Radium has 88 and the heaviest atom of all,
that of uranium, has 92.

We might use numbers for the different kinds of atoms instead of names
if we wanted to do so. We could describe any kind of atom by telling how
many planetary electrons there were in it. For example, hydrogen would
be number 1, helium number 2, lithium of which you perhaps never heard,
would be number 3, and so on. Oxygen is 8, sodium is 11, chlorine is 17,
iron 26, and copper 29. For each kind of atom there is a number. Let's
call that number its atomic number.

Now let's see what the atomic number tells us. Take copper, for example,
which is number 29. In each atom of copper there are 29 electrons
playing around the nucleus. The nucleus itself is a little inner group
of electrons and protons, but there are more protons than electrons in
it; twenty-nine more in fact. In an atom there is always an extra proton
in the nucleus for each planetary electron. That makes the total number
of protons and electrons the same.

About the nucleus of a copper atom there are playing 29 electrons just
as if the nucleus was a teacher responsible for 29 children who were out
in the play yard. There is one very funny thing about it all, however,
and that is that we must think of the scholars as if they were all just
alike so that the teacher couldn't tell one from the other. Electrons
are all alike, you remember. All the teacher or nucleus cares for is
that there shall be just the right number playing around her. You could
bring a boy in from some other play ground and the teacher couldn't tell
that he was a stranger but she would know that something was the matter
for there would be one too many in her group. She is responsible for
just 29 scholars, and the nucleus of the copper atom is responsible for
just 29 electrons. It doesn't make any difference where these electrons
come from provided there are always just 29 playing around the nucleus.
If there are more or less than 29 something peculiar will happen.

We shall see later what might happen, but first let's think of an
enormous lot of atoms such as there would be in a copper wire. A small
copper wire will have in it billions of copper atoms, each with its
planetary electrons playing their invisible game about their own
nucleus. There is quite a little distance in any atom between the
nucleus and any of the electrons for which it is responsible. There is
usually a greater distance still between one atomic group and any other.

On the whole the electrons hold pretty close to their own circles about
their own nuclei. There is always some tendency to run away and play in
some other group. With 29 electrons it's no wonder if sometimes one goes
wandering off and finally gets into the game about some other nucleus.
Of course, an electron from some other atom may come wandering along and
take the place just left vacant, so that nucleus is satisfied.

We don't know all we might about how the electrons wander around from
atom to atom inside a copper wire but we do know that there are always a
lot of them moving about in the spaces between the atoms. Some of them
are going one way and some another.

It's these wandering electrons which are affected when a battery is
connected to a copper wire. Every single electron which is away from its
home group, and wandering around, is sent scampering along toward the
end of the wire which is connected to the positive plate or terminal of
the battery and away from the negative plate. That's what the battery
does to them for being away from home; it drives them along the wire.
There's a regular stream or procession of them from the negative end of
the wire toward the positive. When we have a stream of electrons like
this we say we have a current of electricity.

We'll need to learn more later about a current of electricity but one of
the first things we ought to know is how a battery is made and why it
affects these wandering electrons in the copper wire. That's what I
shall tell you in my next letter.[1]

[Footnote 1: The reader who wishes the shortest path to the construction
and operation of a radio set should omit the next two letters.]



(This letter may be omitted on the first reading.)


When I was a boy we used to make our own batteries for our experiments.
That was before storage batteries became as widely used as they are
to-day when everybody has one in the starting system of his automobile.
That was also before the day of the small dry battery such as we use in
pocket flash lights. The batteries which we made were like those which
they used on telegraph systems, and were sometimes called "gravity"
batteries. Of course, we tried several kinds and I believe I got quite a
little acid around the house at one time or another. I'll tell you about
only one kind but I shall use the words "electron," "proton," "nucleus,"
"atom," and "molecule," about some of which nothing was known when I was
a boy.

We used a straight-sided glass jar which would hold about a gallon. On
the bottom we set a star shaped arrangement made of sheets of copper
with a long wire soldered to it so as to reach up out of the jar. Then
we poured in a solution of copper sulphate until the jar was about half
full. This solution was made by dissolving in water crystals of "blue
vitriol" which we bought at the drug store.

Blue vitriol, or copper sulphate as the chemists would call it, is a
substance which forms glassy blue crystals. Its molecules are formed of
copper atoms, sulphur atoms, and oxygen atoms. In each molecule of it
there is one atom of copper, one of sulphur and four of oxygen.

When it dissolves in water the molecules of the blue vitriol go
wandering out into the spaces between the water molecules. But that
isn't all that happens or the most important thing for one who is
interested in making a battery.

Each molecule is formed by six atoms, that is by six little groups of
electrons playing about six little nuclei. About each nucleus there is
going on a game but some of the electrons are playing in the game about
their own nucleus and at the same time taking some part in the game
which is going on around one of the other nuclei. That's why the groups
or atoms stay together as a molecule. When the molecules wander out into
the spaces between the water molecules something happens to this
complicated game.

It will be easiest to see what sort of thing happens if we talk about a
molecule of ordinary table salt, for that has only two atoms in it. One
atom is sodium and one is chlorine. The sodium molecule has eleven
electrons playing around its nucleus. Fairly close to the nucleus there
are two electrons. Then farther away there are eight more and these are
having a perfect game. Then still farther away from the nucleus there is
a single lonely electron.

The atom of chlorine has seventeen electrons which play about its
nucleus. Close to the nucleus there are two. A little farther away there
are eight just as there are in the sodium atom. Then still farther away
there are seven.

I am going to draw a picture (Fig. 1) to show what I mean, but you must
remember that these electrons are not all in the same plane as if they
lay on a sheet of paper, but are scattered all around just as they would
be if they were specks on a ball.

[Illustration: Fig. 1]

You see that the sodium atom has one lonely electron which hasn't any
play fellows and that the chlorine atom has seven in its outside circle.
It appears that eight would make a much better game. Suppose that extra
electron in the sodium atom goes over and plays with those in the
chlorine atom so as to make eight in the outside group as I have shown
Fig. 2. That will be all right as long as it doesn't get out of sight of
its own nucleus because you remember that the sodium nucleus is
responsible for eleven electrons. The lonely electron of the sodium atom
needn't be lonely any more if it can persuade its nucleus to stay so
close to the chlorine atom that it can play in the outer circle of the
chlorine atom.

[Illustration: Fig. 2]

The outer circle of the chlorine atom will then have a better game, for
it will have just the eight that makes a perfect game. This can happen
if the chlorine atom will stay close enough to the sodium atom so that
the outermost electron of the sodium atom can play in the chlorine
circle. You see everything will be satisfactory if an electron can be
shared by the two atoms. That can happen only if the two atoms stay
together; that is, if they form a molecule. That's why there are
molecules and that's what I meant when I spoke of the molecule as a big
game played by the electrons of two or more atoms.

This molecule which is formed by a sodium atom and a chlorine atom is
called a molecule of sodium chloride by chemists and a molecule of salt
by most every one who eats it. Something strange happens when it
dissolves. It wanders around between the water molecules and for some
reason or other--we don't know exactly why--it decides to split up again
into sodium and chlorine but it can't quite do it. The electron which
joined the game about the chlorine nucleus won't leave it. The result is
that the nucleus of the sodium atom gets away but it leaves this one
electron behind.

What gets away isn't a sodium atom for it has one too few electrons; and
what remains behind isn't a chlorine atom for it has one too many
electrons. We call these new groups "ions" from a Greek word which means
"to go" for they do go, wandering off into the spaces between the water
molecules. Fig. 3 gives you an idea of what happens.

You remember that in an atom there are always just as many protons as
electrons. In this sodium ion which is formed when the nucleus of the
sodium atom breaks away but leaves behind one planetary electron, there
is then one more proton than there are electrons. Because it has an
extra proton, which hasn't any electron to associate with, we call it a
plus ion or a "positive ion." Similarly we call the chlorine ion, which
has one less proton than it has electrons, a minus or "negative ion."

[Illustration: Fig. 3]

Now, despite the fact that these ions broke away from each other they
aren't really satisfied. Any time that the sodium ion can find an
electron to take the place of the one it lost it will welcome it. That
is, the sodium ion will want to go toward places where there are extra
electrons. In the same way the chlorine ion will go toward places where
electrons are wanted as if it could satisfy its guilty conscience by
giving up the electron which it stole from the sodium atom, or at least
by giving away some other electron, for they are all alike anyway.

Sometimes a positive sodium ion and a negative chlorine ion meet in
their wanderings in the solution and both get satisfied by forming a
molecule again. Even so they don't stay together long before they split
apart and start wandering again. That's what goes on over and over
again, millions of times, when you dissolve a little salt in a glass of

Now we can see what happens when copper sulphate dissolves. The copper
atom has twenty-nine electrons about its nucleus and all except two of
these are nicely grouped for playing their games about the nucleus. Two
of the electrons are rather out of the game, and are unsatisfied. They
play with the electrons of the part of the molecule which is called
"sulphate," that is, the part formed by the sulphur atom and the four
oxygen atoms. These five atoms of the sulphate part stay together very
well and so we treat them as a group.

The sulphate group and the copper atom stay together as long as they are
not in solution but when they are, they act very much like the sodium
and chlorine which I just described. The molecule splits up into two
ions, one positive and one negative. The positive ion is the copper part
except that two of the electrons which really belong to a copper atom
got left behind because the sulphate part wouldn't give them up. The
rest of the molecule is the negative ion.

The copper ion is a copper atom which has lost two electrons. The
sulphate ion is a combination of one sulphur atom, four oxygen atoms and
two electrons which it stole from the copper atom. Just as the sodium
ion is unsatisfied because in it there is one more proton than there are
electrons, so the copper ion is unsatisfied. As a matter of fact it is
twice as badly unsatisfied. It has two more protons than it has
electrons. We say it has twice the "electrical charge" of the sodium

Just like a sodium ion the copper ion will tend to go toward any place
where there are extra electrons which it can get to satisfy its own
needs. In much the same way the sulphate ion will go toward places where
it can give up its two extra electrons. Sometimes, of course, as ions of
these two kinds wander about between the water molecules, they meet and
satisfy each other by forming a molecule of copper sulphate. But if they
do they will split apart later on; that is, they will "dissociate" as we
should say.

Now let's go on with the kind of batteries I used to make as a boy. You
can see that in the solution of copper sulphate at the bottom of the jar
there was always present a lot of positive copper ions and of negative
sulphate ions.

On top of this solution of copper sulphate I poured very carefully a
weak solution of sulphuric acid. As I told you, an acid always has
hydrogen in its molecules. Sulphuric acid has molecules formed by two
hydrogen atoms and one of the groups which we decided to call sulphate.
A better name for this acid would be hydrogen sulphate for that would
imply that its molecule is the same as one of copper sulphate, except
that the place of the copper is taken by two atoms of hydrogen. It takes
two atoms of hydrogen because the copper atom has two lonely electrons
while a hydrogen atom only has one. It takes two electrons to fill up
the game which the electrons of the sulphate group are playing. If it
can get these from a single atom, all right; but if it has to get one
from each of two atoms, it will do it that way.

I remember when I mixed the sulphuric acid with water that I learned to
pour the acid into the water and not the other way around. Spatterings
of sulphuric acid are not good for hands or clothes. With this solution
I filled the jar almost to the top and then hung over the edge a sort of
a crow's foot shape of cast zinc. The zinc reached down into the
sulphuric acid solution. There was a binding post on it to which a wire
could be connected. This wire and the one which came from the plate of
copper at the bottom were the two terminals of the battery. We called
the wire from the copper "positive" and the one from the zinc

Now we shall see why and how the battery worked. The molecules of
sulphuric acid dissociate in solution just as do those of copper
sulphate. When sulphuric acid molecules split, the sulphate part goes
away with two electrons which don't belong to it and each of the
hydrogen atoms goes away by itself but without its electron. We call
each a "hydrogen ion" but you can see that each is a single proton.

In the two solutions are pieces of zinc and copper. Zinc is like all the
rest of the metals in one way. Atoms of metals always have lonely
electrons for which there doesn't seem to be room in the game which is
going on around their nuclei. Copper as we saw has two lonely electrons
in each atom. Zinc also has two. Some metals have one and some two and
some even more lonely electrons in each atom.

What happens then is this. The sulphate ions wandering around in the
weak solution of sulphuric acid come along beside the zinc plate and
beckon to its atoms. The sulphate ions had a great deal rather play the
game called "zinc sulphate" than the game called "hydrogen sulphate." So
the zinc atoms leave their places to join with the sulphate ions. But
wait a minute! The sulphate ions have two extra electrons which they
kept from the hydrogen atoms. They don't need the two lonely electrons
which each zinc atom could bring and so the zinc atom leaves behind it
these unnecessary electrons.

Every time a zinc atom leaves the plate it fails to take all its
electrons with it. What leaves the zinc plate, therefore, to go into
solution is really not a zinc atom but is a zinc ion; that is, it is the
nucleus of a zinc atom and all except two of the planetary electrons.

Every time a zinc ion leaves the plate there are left behind two
electrons. The plate doesn't want them for all the rest of its atoms
have just the same number of protons as of electrons. Where are they to
go? We shall see in a minute.

Sometimes the zinc ions which have got into solution meet with sulphate
ions and form zinc sulphate molecules. But if they do these molecules
split up sooner or later into ions again. In the upper part of the
liquid in the jar, therefore, there are sulphate ions which are negative
and two kinds of positive ions, namely, the hydrogen ions and the zinc

Before the zinc ions began to crowd in there were just enough hydrogen
ions to go with the sulphate ions. As it is, the entrance of the zinc
ions has increased the number of positive ions and now there are too
many. Some of the positive ions, therefore, and particularly the
hydrogen ions, because the sulphate prefers to associate with the zinc
ions, can't find enough playfellows and so go down in the jar.

Down in the bottom of the jar the hydrogen ions find more sulphate ions
to play with, but that leaves the copper ions which used to play with
these sulphate ions without any playmates. So the copper ions go still
further down and join with the copper atoms of the copper plate. They
haven't much right to do so, for you remember that they haven't their
proper number of electrons. Each copper ion lacks two electrons of being
a copper atom. Nevertheless they join the copper plate. The result is a
plate of copper which has too few electrons. It needs two electrons for
every copper ion which joins it.

How about the zinc plate? You remember that it has two electrons more
than it needs for every zinc ion which has left it. If only the extra
electrons on the negative zinc plate could get around to the positive
copper plate. They can if we connect a wire from one plate to the other.
Then the electrons from the zinc stream into the spaces between the
atoms of the wire and push ahead of them the electrons which are
wandering around in these spaces. At the other end an equal number of
electrons leave the wire to satisfy the positive copper plate. So we
have a stream of electrons in the wire, that is, a current of
electricity and our battery is working.

That's the sort of a battery I used to play with. If you understand it
you can get the general idea of all batteries. Let me express it in
general terms.

At the negative plate of a battery ions go into solution and electrons
are left behind. At the other end of the battery positive ions are
crowded out of solution and join the plate where they cause a scarcity
of electrons; that is, make the plate positive. If a wire is connected
between the two plates, electrons will stream through it from the
negative plate to the positive; and this stream is a current of

[Illustration: Pl. III.--Dry Battery for Use in Audion Circuits
(Courtesy of National Carbon Co., Inc.). Storage Battery (Courtesy of
the Electric Storage Battery Co.).]



(This letter may be omitted on the first reading.)


You will need several batteries when you come to set up your radio
receiver but you won't use such clumsy affairs as the gravity cell which
I described in my last letter. Some of your batteries will be dry
batteries of the size used in pocket flash lights.

These are not really dry, for between the plates they are filled with a
moist paste which is then sealed in with wax to keep it from drying out
or from spilling. Instead of zinc and copper these batteries use zinc
and carbon. No glass jar is needed, for the zinc is formed into a jar
shape. In this is placed the paste and in the center of the paste a rod
or bar of carbon. The paste doesn't contain sulphuric acid, but instead
has in it a stuff called sal ammoniac; that is, ammonium chloride.

The battery, however, acts very much like the one I described in my last
letter. Ions of zinc leave the zinc and wander into the moist paste.
These ions are positive, just as in the case of the gravity battery. The
result is that the electrons which used to associate with a zinc ion to
form a zinc atom are left in the zinc plate. That makes the zinc
negative for it has more electrons than protons. The zinc ions take the
place of the positive ions which are already in the paste. The positive
ions which originally belonged with the paste, therefore, move along to
the carbon rod and there get some electrons. Taking electrons away from
the carbon leaves it with too many protons; that is, leaves it positive.
In the little flash light batteries, therefore, you will always find
that the round carbon rod, which sticks out of the center, is positive
and the zinc casing is negative.

The trouble with the battery like the one I used to make is that the
zinc plate wastes away. Every time a zinc ion leaves it that means that
the greater part of an atom is gone. Then when the two electrons which
were left behind get a chance to start along a copper wire toward the
positive plate of the battery there goes the rest of the atom. After a
while there is no more zinc plate. It is easy to see what has happened.
All the zinc has gone into solution or been "eaten away" as most people
say. Dry batteries, however, don't stop working because the zinc gets
used up, but because the active stuff in the paste, the ammonium
chloride, is changed into something else.

There's another kind of battery which you will need to use with your
radio set; that is the storage battery. Storage batteries can be used
over and over again if they are charged between times and will last for
a long time if properly cared for. Then too, they can give a large
current, that is, a big swift-moving stream of electrons. You will need
that when you wish to heat the filament of the audion in your receiving

The English call our storage batteries by the name "accumulators." I
don't like that name at all, but I don't like our name for them nearly
as well as I do the name "reversible batteries." Nobody uses this last
name because it's too late to change. Nevertheless a storage battery is
reversible, for it will work either way at an instant's notice.

A storage battery is something like a boy's wagon on a hill side. It
will run down hill but it can be pushed up again for another descent.
You can use it to send a stream of electrons through a wire from its
negative plate to its positive plate. Then if you connect these plates
to some other battery or to a generator, (that is, a dynamo) you can
make a stream of electrons go in the other direction. When you have done
so long enough the battery is charged again and ready to discharge.

I am not going to tell you very much about the storage battery but you
ought to know a little about it if you are to own and run one with your
radio set. When it is all charged and ready to work, the negative plate
is a lot of soft spongy lead held in place by a frame of harder lead.
The positive plate is a lead frame with small squares which are filled
with lead peroxide, as it is called. This is a substance with molecules
formed of one lead atom and two oxygen atoms. Why the chemists call it
lead peroxide instead of just lead oxide I'll tell you some other time,
but not in these letters.

Between the two plates is a wood separator to keep pieces of lead from
falling down between and touching both plates. You know what would
happen if a piece of metal touched both plates. There would be a short
circuit, that is, a sort of a short cut across lots by which some of the
electrons from the negative plate could get to the positive plate
without going along the wires which we want them to travel. That's why
there are separators.

The two plates are in a jar of sulphuric acid solution. The sulphuric
acid has molecules which split up in solution, as you remember, into
hydrogen ions and the ions which we called "sulphate." In my gravity
battery the sulphate ions used to coax the zinc ions away into the
solution. In the storage battery on the other hand the sulphate ions can
get to most of the lead atoms because the lead is so spongy. When they
do, they form lead sulphate right where the lead atoms are. They don't
really need whole lead atoms, because they have two more electrons than
they deserve, so there are two extra electrons for every molecule of
lead sulphate which is formed. That's why the spongy lead plate is

The lead sulphate won't dissolve, so it stays there on the plate as a
whitish coating. Now see what that means. What are the hydrogen ions
going to do? As long as there was sulphuric acid in the water there was
plenty of sulphate ions for them to associate with as often as they met;
and they would meet pretty often. But if the sulphate ions get tied up
with the lead of the plate there will be too many hydrogen ions left in
the solution. Now what are the hydrogen ions to do? They are going to
get as far away from each other as they can, for they are nothing but
protons; and protons don't like to associate. They only stayed around in
the first place because there was always plenty of sulphate ions with
whom they liked to play.

When the hydrogen ions try to get away from each other they go to the
other plate of the battery, and there they will get some electrons, if
they have to steal in their turn.

I won't try to tell you all that happens at the other plate. The
hydrogen ions get the electrons which they need, but they get something
more. They get some of the oxygen away from the plate and so form
molecules of water. You remember that water molecules are made of two
atoms of hydrogen and one of oxygen. Meanwhile, the lead atoms, which
have lost their oxygen companions, combine with some of the sulphate
ions which are in that neighborhood. During the mix-up electrons are
carried away from the plate and that leaves it positive.

The result of all this is a little lead sulphate on each plate, a
negative plate where the spongy lead was, and a positive plate where the
lead peroxide was.

Notice very carefully that I said "a little lead sulphate on each
plate." The sort of thing I have been describing doesn't go on very
long. If it did the battery would run down inside itself and then when
we came to start our automobile we would have to get out and crank.

How long does it go on? Answer another question first. So far we haven't
connected any wire between the two plates of the battery, and so none of
the electrons on the negative plate have any way of getting around to
the positive plate where electrons are badly needed. Every time a
negative sulphate ion combines with the spongy lead of the negative
plate there are two more electrons added to that plate. You know how
well electrons like each other. Do they let the sulphate ions keep
giving that plate more electrons? There is the other question; and the
answer is that they do not. Every electron that is added to that plate
makes it just so much harder for another sulphate ion to get near enough
to do business at all. That's why after a few extra electrons have
accumulated on the spongy lead plate the actions which I was describing
come to a stop.

Do they ever begin again? They do just as soon as there is any reduction
in the number of electrons which are hopping around in the negative
plate trying to keep out of each other's way. When we connect a wire
between the plates we let some of these extra electrons of the negative
plate pass along to the positive plate where they will be welcome. And
the moment a couple of them start off on that errand along comes another
sulphate ion in the solution and lands two more electrons on the plate.
That's how the battery keeps on discharging.

We mustn't let it get too much discharged for the lead sulphate is not
soluble, as I just told you, and it will coat up that plate until there
isn't much chance of getting the process to reverse. That's why we are
so careful not to let the discharge process go on too long before we
reverse it and charge. That's why, when the car battery has been used
pretty hard to start the car, I like to run quite a while to let the
generator charge the battery again. When the battery charges, the
process reverses and we get spongy lead on the negative plate and lead
peroxide on the positive plate.

You've learned enough for one day. Write me your questions and I'll
answer and then go on in my next letter to tell how the audion works.
You know about conduction of electricity in wires; that is, about the
electron stream, and about batteries which can cause the stream. Now you
are ready for the most wonderful little device known to science: the




I was pleased to get your letter and its questions. Yes, a proton is a
speck of electricity of the kind we call positive and an electron is of
the kind we call negative. You might remember this simple law; "Like
kinds of electricity repel, and unlike attract."

The word ion[2] is used to describe any atom, or part of a molecule
which can travel by itself and has more or less than its proper number
of electrons. By proper number of electrons I mean proper for the number
of protons which it has. If an ion has more electrons than protons it is
negative; if the inequality is the other way around it is positive. An
atom or molecule has neither more nor less protons than electrons. It is
neutral or "uncharged," as we say.

No, not every substance which will dissolve will dissociate or split up
into positive and negative ions. The salt which you eat will, but the
sugar will not. If you want a name for those substances which will
dissociate in solution, call them "electrolytes." To make a battery we
must always use an electrolyte.

Yes, it is hard to think of a smooth piece of metal or a wire as full
of holes. Even in the densest solids like lead the atoms are quite far
apart and there are large spaces between the nuclei and the planetary
electrons of each atom.

I hope this clears up the questions in your mind for I want to get along
to the vacuum tube. By a vacuum we mean a space which has very few atoms
or molecules in it, just as few as we can possibly get, with the best
methods of pumping and exhausting. For the present let's suppose that we
can get all the gas molecules, that is, all the air, out of a little
glass bulb.

The audion is a glass bulb like an electric light bulb which has in it a
thread, or filament, of metal. The ends of this filament extend out
through the glass so that we may connect a battery to them and pass a
current of electricity through the wire. If we do so the wire gets hot.

What do we mean when we say "the wire gets hot?" We mean that it feels
hot. It heats the glass bulb and we can feel it. But what do we mean in
words of electrons and atoms? To answer this we must start back a little

In every bit of matter in our world the atoms and molecules are in very
rapid motion. In gases they can move anywhere; and do. That's why odors
travel so fast. In liquids most of the molecules or atoms have to do
their moving without getting out of the dish or above the surface. Not
all of them stay in, however, for some are always getting away from the
liquid and going out into the air above. That is why a dish of water
will dry up so quickly. The faster the molecules are going the better
chance they have of jumping clear away from the water like fish jumping
in the lake at sundown. Heating the liquid makes its molecules move
faster and so more of them are able to jump clear of the rest of the
liquid. That's why when we come in wet we hang our clothes where they
will get warm. The water in them evaporates more quickly when it is
heated because all we mean by "heating" is speeding up the molecules.

In a solid body the molecules can't get very far away from where they
start but they keep moving back and forth and around and around. The
hotter the body is, the faster are its molecules moving. Generally they
move a little farther when the body is hot than when it is cold. That
means they must have a little more room and that is why a body is larger
when hot than when cold. It expands with heating because its molecules
are moving more rapidly and slightly farther.

When a wire is heated its molecules and atoms are hurried up and they
dash back and forth faster than before. Now you know that a wire, like
the filament of a lamp, gets hot when the "electricity is turned on,"
that is, when there is a stream of electrons passing through it. Why
does it get hot? Because when the electrons stream through it they bump
and jostle their way along like rude boys on a crowded sidewalk. The
atoms have to step a bit more lively to keep out of the way. These more
rapid motions of the atoms we recognize by the wire growing hotter.

That is why an electric current heats a wire through which it is
flowing. Now what happens to the electrons, the rude boys who are
dodging their way along the sidewalk? Some of them are going so fast and
so carelessly that they will have to dodge out into the gutter and off
the sidewalk entirely. The more boys that are rushing along and the
faster they are going the more of them will be turned aside and plunge
off the sidewalks.

The greater and faster the stream of electrons, that is the more current
which is flowing through the wire, the more electrons will be "emitted,"
that is, thrown out of the wire. If you could watch them you would see
them shooting out of the wire, here, there, and all along its length,
and going in every direction. The number which shoot out each second
isn't very large until they have stirred things up so that the wire is
just about red hot.

What becomes of them? Sometimes they don't get very far away from the
wire and so come back inside again. They scoot off the sidewalk and on
again just as boys do in dodging their way along. Some of them start
away as if they were going for good.

If the wire is in a vacuum tube, as it is in the case of the audion,
they can't get very far away. Of course there is lots of room; but they
are going so fast that they need more room just as older boys who run
fast need a larger play ground than do the little tots. By and by there
gets to be so many of them outside that they have to dodge each other
and some of them are always dodging back into the wire while new
electrons are shooting out from it.

When there are just as many electrons dodging back into the wire each
second as are being emitted from it the vacuum in the tube has all the
electrons it can hold. We might say it is "saturated" with electrons,
which means, in slang, "full up." If any more electrons are to get out
of the filament just as many others which are already outside have to go
back inside. Or else they have got to be taken away somewhere else.

What I have just told you about electrons getting away from a heated
wire is very much like what happens when a liquid is heated. The
molecules of the liquid get away from the surface. If we cover a dish of
liquid which is being heated the liquid molecules can't get far away and
very soon the space between the surface of the liquid and the cover gets
saturated with them. Then every time another molecule escapes from the
surface of the liquid there must be some molecule which goes back into
the liquid. There is then just as much condensation back into liquid as
there is evaporation from it. That's why in cooking they put covers over
the vessels when they don't want the liquid all to "boil away."

Sometimes we speak of the vacuum tube in the same words we would use in
describing evaporation of a liquid. The molecules of the liquid which
have escaped form what is called a "vapor" of the liquid. As you know
there is usually considerable water vapor in the air. We say then that
electrons are "boiled out" of the filament and that there is a "vapor of
electrons" in the tube.

That is enough for this letter. Next time I shall tell you how use is
made of these electrons which have been boiled out and are free in the
space around the filament.

[Footnote 2: If the reader has omitted Letters 3 and 4 he should omit
this paragraph and the next.]




In my last letter I told how electrons are boiled out of a heated
filament. The hotter the filament the more electrons are emitted each
second. If the temperature is kept steady, or constant as we say, then
there are emitted each second just the same number of electrons. When
the filament is enclosed in a vessel or glass bulb these electrons which
get free from it cannot go very far away. Some of them, therefore, have
to come back to the filament and the number which returns each second is
just equal to the number which is leaving. You realize that this is what
is happening inside an ordinary electric light bulb when its filament is
being heated.

[Illustration: Fig 4]

An ordinary electric light bulb, however, is not an audion although it
is like one in the emission of electrons from its filament. That reminds
me that last night as I was waiting for a train I picked up one of the
Radio Supplements which so many newspapers are now running. There was a
column of enquiries. One letter told how its writer had tried to use an
ordinary electric light bulb to receive radio signals.

He had plenty of electrons in it but no way to control them and make
their motions useful. In an audion besides the filament there are two
other things. One is a little sheet or plate of metal with a connecting
wire leading out through the glass walls and the other is a little wire
screen shaped like a gridiron and so called a "grid." It also has a
connecting wire leading through the glass. Fig. 4 shows an audion. It
will be most convenient, however, to represent an audion as in Fig. 5.
There you see the filament, _F_, with its two terminals brought out
from the tube, the plate, _P_, and between these the grid,

[Illustration: Fig 5]

These three parts of the tube are sometimes called "elements." Usually,
however, they are called "electrodes" and that is why the audion is
spoken of as the "three-electrode vacuum tube." An electrode is what we
call any piece of metal or wire which is so placed as to let us get at
electrons (or ions) to control their motions. Let us see how it does so.

To start with, we shall forget the grid and think of a tube with only a
filament and a plate in it--a two-electrode tube. We shall represent it
as in Fig. 6 and show the battery which heats the filament by some lines
as at _A_. In this way of representing a battery each cell is
represented by a short heavy line and a longer lighter line. The heavy
line stands for the negative plate and the longer line for the positive
plate. We shall call the battery which heats the filament the "filament
battery" or sometimes the "A-battery." As you see, it is formed by
several battery cells connected in series.

[Illustration: Fig 6]

Sometime later I may tell you how to connect battery cells together and
why. For the present all you need to remember is that two batteries are
in series if the positive plate of one is connected to the negative
plate of the other. If the batteries are alike they will pull an
electron just twice as hard as either could alone.

[Illustration: Pl. IV.--Radiotron (Courtesy of Radio Corporation of

To heat the filament of an audion, such as you will probably use in your
set, will require three storage-battery cells, like the one I described
in my fourth letter, all connected in series. We generally use storage
batteries of about the same size as those in the automobile. If you will
look at the automobile battery you will see that it is made of three
cells connected in series. That battery would do very well for the
filament circuit.

By the way, do you know what a "circuit" is? The word comes from the
same Latin word as our word "circus." The Romans were very fond of
chariot racing at their circuses and built race tracks around which the
chariots could go. A circuit, therefore, is a path or track around which
something can race; and an electrical circuit is a path around which
electrons can race. The filament, the A-battery and the connecting wires
of Fig. 6 form a circuit.

[Illustration: Fig 7]

Let us imagine another battery formed by several cells in series which
we shall connect to the tube as in Fig. 7. All the positive and negative
terminals of these batteries are connected in pairs, the positive of one
cell to the negative of the next, except for one positive and one
negative. The remaining positive terminal is the positive terminal of
the battery which we are making by this series connection. We then
connect this positive terminal to the plate and the negative terminal to
the filament as shown in the figure. This new battery we shall call the
"plate battery" or the "B-battery."

Now what's going to happen? The B-battery will want to take in electrons
at its positive terminal and to send them out at its negative terminal.
The positive is connected to the plate in the vacuum tube of the figure
and so draws some of the electrons of the plate away from it. Where do
these electrons come from? They used to belong to the atoms of the plate
but they were out playing in the space between the atoms, so that they
came right along when the battery called them. That leaves the plate
with less than its proper number of electrons; that is, leaves it
positive. So the plate immediately draws to itself some of the electrons
which are dodging about in the vacuum around it.

Do you remember what was happening in the tube? The filament was
steadily going on emitting electrons although there were already in the
tube so many electrons that just as many crowded back into the filament
each second as the filament sent out. The filament was neither gaining
nor losing electrons, although it was busy sending them out and
welcoming them home again.

When the B-battery gets to work all this is changed. The B-battery
attracts electrons to the plate and so reduces the crowd in the tube.
Then there are not as many electrons crowding back into the filament as
there were before and so the filament loses more than it gets back.

Suppose that, before the B-battery was connected to the plate, each tiny
length of the filament was emitting 1000 electrons each second but was
getting 1000 back each second. There was no net change. Now, suppose
that the B-battery takes away 100 of these each second. Then only 900
get back to the filament and there is a net loss from the filament of
100. Each second this tiny length of filament sends into the vacuum 100
electrons which are taken out at the plate. From each little bit of
filament there is a stream of electrons to the plate. Millions of
electrons, therefore, stream across from filament to plate. That is,
there is a current of electricity between filament and plate and this
current continues to flow as long as the A-battery and the B-battery do
their work.

The negative terminal of the B-battery is connected to the filament.
Every time this battery pulls an electron from the plate its negative
terminal shoves one out to the filament. You know from my third and
fourth letters that electrons are carried through a battery from its
positive to its negative terminal. You see, then, that there is the same
stream of electrons through the B-battery as there is through the vacuum
between filament and plate. This same stream passes also through the
wires which connect the battery to the tube. The path followed by the
stream of electrons includes the wires, the vacuum and the battery in
series. We call this path the "plate circuit."

We can connect a telephone receiver, or a current-measuring instrument,
or any thing we wish which will pass a stream of electrons, so as to let
this same stream of electrons pass through it also. All we have to do is
to connect the instrument in series with the other parts of the plate
circuit. I'll show you how in a minute, but just now I want you to
understand that we have a stream of electrons, for I want to tell you
how it may be controlled.

Suppose we use another battery and connect it between the grid and the
filament so as to make the grid positive. That would mean connecting the
positive terminal of the battery to the grid and the negative to the
filament as shown by the C-battery of Fig. 8. This figure also shows a
current-measuring instrument in the plate circuit.

What effect is this C-battery, or grid-battery, going to have on the
current in the _plate circuit_? Making the grid positive makes it
want electrons. It will therefore act just as we saw that the plate did
and pull electrons across the vacuum towards itself.

[Illustration: Fig 8]

What happens then is something like this: Electrons are freed at the
filament; the plate and the grid both call them and they start off in a
rush. Some of them are stopped by the wires of the grid but most of them
go on by to the plate. The grid is mostly open space, you know, and the
electrons move as fast as lightning. They are going too fast in the
general direction of the grid to stop and look for its few and small

When the grid is positive the grid helps the plate to call electrons
away from the filament. Making the grid positive, therefore, increases
the stream of electrons _between filament and plate_; that is,
increases the current in the plate circuit.

We could get the same effect so far as concerns an increased plate
current by using more batteries in series in the plate circuit so as to
pull harder. But the grid is so close to the filament that a single
battery cell in the grid circuit can call electrons so strongly that it
would take several extra battery cells in the plate circuit to produce
the same effect.

[Illustration: Fig 9]

If we reverse the grid battery, as in Fig. 9, so as to make the grid
negative, then, instead of attracting electrons the grid repels them.
Nowhere near as many electrons will stream across to the plate when the
grid says, "No, go back." The grid is in a strategic position and what
it says has a great effect.

When there is no battery connected to the grid it has no possibility of
influencing the electron stream which the plate is attracting to itself.
We say, then, that the grid is uncharged or is at "zero potential,"
meaning that it is zero or nothing in possibility. But when the grid is
charged, no matter how little, it makes a change in the plate current.
When the grid says "Come on," even though very softly, it has as much
effect on the electrons as if the plate shouted at them, and a lot of
extra electrons rush for the plate. But when the grid whispers "Go
back," many electrons which would otherwise have gone streaking off to
the plate crowd back toward the filament. That's how the audion works.
There is an electron stream and a wonderfully sensitive way of
controlling the stream.



(This letter may be omitted on the first reading.)


If we are to talk about the audion and how its grid controls the current
in the plate circuit we must know something of how to measure currents.
An electric current is a stream of electrons. We measure it by finding
the rate at which electrons are traveling along through the circuit.

What do we mean by the word "rate?" You know what it means when a
speedometer says twenty miles an hour. If the car should keep going just
as it was doing at the instant you looked at the speedometer it would go
twenty miles in the next hour. Its rate is twenty miles an hour even
though it runs into a smash the next minute and never goes anywhere
again except to the junk heap.

It's the same when we talk of electric currents. We say there is a
current of such and such a number of electrons a second going by each
point in the circuit. We don't mean that the current isn't going to
change, for it may get larger or smaller, but we do mean that if the
stream of electrons keeps going just as it is there will be such and
such a number of electrons pass by in the next second.

In most of the electrical circuits with which you will deal you will
find that electrons must be passing along in the circuit at a most
amazing rate if there is to be any appreciable effect. When you turn on
the 40-watt light at your desk you start them going through the filament
of the lamp at the rate of about two and a half billion billion each
second. You have stood on the sidewalk in the city and watched the
people stream past you. Just suppose you could stand beside that narrow
little sidewalk which the filament offers to the electrons and count
them as they go by. We don't try to count them although we do to-day
know about how many go by in a second if the current is steady.

If some one asks you how old you are you don't say "About five hundred
million seconds"; you tell him in years. When some one asks how large a
current is flowing in a wire we don't tell him six billion billion
electrons each second; we tell him "one ampere." Just as we use years as
the units in which to count up time so we use amperes as the units in
which to count up streams of electrons. When a wire is carrying a
current of one ampere the electrons are streaming through it at the rate
of about 6,000,000,000,000,000,000 a second.

Don't try to remember this number but do remember that an ampere is a
unit in which we measure currents just as a year is a unit in which we
measure time. An ampere is a unit in which we measure streams of
electrons just as "miles per hour" is a unit in which we measure the
speed of trains or automobiles.

If you wanted to find the weight of something you would take a scale and
weigh it, wouldn't you? You might take that spring balance which hangs
out in the kitchen. But if the spring balance said the thing weighed
five pounds how would you know if it was right? Of course you might take
what ever it was down town and weigh it on some other scales but how
would you know those scales gave correct weight?

The only way to find out would be to try the scales with weights which
you were sure were right and see if the readings on the scale correspond
to the known weights. Then you could trust it to tell you the weight of
something else. That's the way scales are tested. In fact that's the way
that the makers know how to mark them in the first place. They put on
known weights and marked the lines and figures which you see. What they
did was called "calibrating" the scale. You could make a scale for
yourself if you wished, but if it was to be reliable you would have to
find the places for the markings by applying known weights, that is, by

How would you know that the weights you used to calibrate your scale
were really what you thought them to be? You would have to find some
place where they had a weight that everybody would agree was correct and
then compare your weight with that. You might, for example, send your
pound weight to the Bureau of Standards in Washington and for a small
payment have the Bureau compare it with the pound which it keeps as a

That is easy where one is interested in a pound. But it is a little
different when one is interested in an ampere. You can't make an ampere
out of a piece of platinum as you can a standard pound weight. An ampere
is a stream of electrons at about the rate of six billion billion a
second. No one could ever count anywhere near that many, and yet
everybody who is concerned with electricity wants to be able to measure
currents in amperes. How is it done?

First there is made an instrument which will have something in it to
move when electrons are flowing through the instrument. We want a meter
for the flow of electrons. In the basement we have a meter for the flow
of gas and another for the flow of water. Each of these has some part
which will move when the water or the gas passes through. But they are
both arranged with little gear wheels so as to keep track of all the
water or gas which has flowed through; they won't tell the rate at which
the gas or water is flowing. They are like the odometer on the car which
gives the "trip mileage" or the "total mileage." We want a meter like
the speedometer which will indicate at each instant just how fast the
electrons are streaming through it.

There are several kinds of meters but I shall not try to tell you now of
more than one. The simplest to understand is called a "hot-wire meter."
You already know that an electron stream heats a wire. Suppose a piece
of fine wire is fastened at the two ends and that there are binding
posts also fastened to these ends of the wire so that the wire may be
made part of the circuit where we want to know the electron stream. Then
the same stream of electrons will flow through the fine wire as through
the other parts of the circuit. Because the wire is fine it acts like a
very narrow sidewalk for the stream of electrons and they have to bump
and jostle pretty hard to get through. That's why the wire gets heated.

You know that a heated wire expands. This wire expands. It grows longer
and because it is held firmly at the ends it must bow out at the center.
The bigger the rate of flow of electrons the hotter it gets; and the
hotter it gets the more it bows out. At the center we might fasten one
end--the short end--of a little lever. A small motion of this short end
of the lever will mean a large motion of the other end, just like a
"teeter board" when one end is longer than the other; the child on the
long end travels further than the child on the short end. The lever
magnifies the motion of the center of the hot wire part of our meter so
that we can see it easier.

[Illustration: Fig 10]

There are several ways to make such a meter. The one shown in Fig. 10 is
as easy to understand as any. We shape the long end of the lever like a
pointer. Then the hotter the wire the farther the pointer moves.

If we could put this meter in an electric circuit where we knew one
ampere was flowing we could put a numeral "1" opposite where the pointer
stood. Then if we could increase the current until there were two
amperes flowing through the meter we could mark that position of the
pointer "2" and so on. That's the way we would calibrate the meter.
After we had done so we would call it an "ammeter" because it measures
amperes. Years ago people would have called it an "amperemeter" but no
one who is up-to-date would call it so to-day.

[Illustration: Fig 11]

If we had a very carefully made ammeter we would send it to the Bureau
of Standards to be calibrated. At the Bureau they have a number of
meters which they know are correct in their readings. They would put one
of their meters and ours into the same circuit so that both carry the
same stream of electrons as in Fig. 11. Then whatever the reading was on
their meter could be marked opposite the pointer on ours.

Now I want to tell you how the physicists at the Bureau know what is an
ampere. Several years ago there was a meeting or congress of physicists
and electrical engineers from all over the world who discussed what they
thought should be the unit in which to measure current. They decided
just what they would call an ampere and then all the countries from
which they came passed laws saying that an ampere should be what these
scientists had recommended. To-day, therefore, an ampere is defined by

To tell when an ampere of current is flowing requires the use of two
silver plates and a solution of silver nitrate. Silver nitrate has
molecules made up of one atom of silver combined with a group of atoms
called "nitrate." You remember that the molecule of copper sulphate,
discussed in our third letter, was formed by a copper atom and a group
called sulphate. Nitrate is another group something like sulphate for it
has oxygen atoms in it, but it has three instead of four, and instead of
a sulphur atom there is an atom of nitrogen.

When silver nitrate molecules go into solution they break up into ions
just as copper sulphate does. One ion is a silver atom which has lost
one electron. This electron was stolen from it by the nitrate part of
the molecule when they dissociated. The nitrate ion, therefore, is
formed by a nitrogen atom, three oxygen atoms, and one extra electron.

If we put two plates of silver into such a solution nothing will happen
until we connect a battery to the plates. Then the battery takes
electrons away from one plate and gives electrons to the other. Some of
the atoms in the plate which the battery is robbing of electrons are
just like the silver ions which are moving around in the solution.
That's why they can go out into the solution and play with the nitrate
ions each of which has an extra electron which it stole from some silver
atom. But the moment silver ions leave their plate we have more silver
ions in the solution than we do sulphate ions.

The only thing that can happen is for some of the silver ions to get out
of the solution. They aren't going back to the positive silver plate
from which they just came. They go on toward the negative plate where
the battery is sending an electron for every one which it takes away
from the positive plate. There start off towards the negative plate, not
only the ions which just came from the positive plate, but all the ions
that are in the solution. The first one to arrive gets an electron but
it can't take it away from the silver plate. And why should it? As soon
as it has got this electron it is again a normal silver atom. So it
stays with the other atoms in the silver plate. That's what happens
right along. For every atom which is lost from the positive plate there
is one added to the negative plate. The silver of the positive plate
gradually wastes away and the negative plate gradually gets an extra
coating of silver.

Every time the battery takes an electron away from the positive plate
and gives it to the negative plate there is added to the negative plate
an atom of silver. If the negative plate is weighed before the battery
is connected and again after the battery is disconnected we can tell how
much silver has been added to it. Suppose the current has been perfectly
steady, that is, the same number of electrons streaming through the
circuit each second. Then if we know how long the current has been
running we can tell how much silver has been deposited each second.

The law says that if silver is being deposited at the rate of 0.001118
gram each second then the current is one ampere. That's a small amount
of silver, only about a thousandth part of a gram, and you know that it
takes 28.35 grams to make an ounce. It's a very small amount of silver
but it's an enormous number of atoms. How many? Six billion billion, of
course, for there is deposited one atom for each electron in the stream.

In my next letter I'll tell you how we measure the pull which batteries
can give to electrons, and then we shall be ready to go on with more
about the audion.



(This letter may be omitted on the first reading.)


I trust you have a fairly good idea that an ampere means a stream of
electrons at a certain definite rate and hence that a current of say 3
amperes means a stream with three times as many electrons passing along
each second.

In the third and fourth letters you found out why a battery drives
electrons around a conducting circuit. You also found that there are
several different kinds of batteries. Batteries differ in their
abilities to drive electrons and it is therefore convenient to have some
way of comparing them. We do this by measuring the electron-moving-force
or "electromotive force" which each battery can exert. To express
electromotive force and give the results of our measurements we must
have some unit. The unit we use is called the "volt."

The volt is defined by law and is based on the suggestions of the same
body of scientists who recommended the ampere of our last letter. They
defined it by telling how to make a particular kind of battery and then
saying that this battery had an electromotive force of a certain number
of volts. One can buy such standard batteries, or standard cells as they
are called, or he can make them for himself. To be sure that they are
just right he can then send them to the Bureau of Standards and have
them compared with the standard cells which the Bureau has.

I don't propose to tell you much about standard cells for you won't have
to use them until you come to study physics in real earnest. They are
not good for ordinary purposes because the moment they go to work
driving electrons the conditions inside them change so their
electromotive force is changed. They are delicate little affairs and are
useful only as standards with which to compare other batteries. And even
as standard batteries they must be used in such a way that they are not
required to drive any electrons.

[Illustration: Fig 12]

Let's see how it can be done. Suppose two boys sit opposite each other
on the floor and brace their feet together. Then with their hands they
take hold of a stick and pull in opposite directions. If both have the
same stick-motive-force the stick will not move.

Now suppose we connect the negative feet--I mean negative terminals--of
two batteries together as in Fig. 12. Then we connect their positive
terminals together by a wire. In the wire there will be lots of free
electrons ready to go to the positive plate of the battery which pulls
the harder. If the batteries are equal in electromotive force these
electrons will stay right where they are. There will be no stream of
electrons and yet we'll be using one of the batteries to compare with
the other.

That is all right, you think, but what are we to do when the batteries
are not just equal in e. m. f.? (e. m. f. is code for electromotive
force). I'll tell you, because the telling includes some other ideas
which will be valuable in your later reading.

[Illustration: Fig 13]

Suppose we take batteries which aren't going to be injured by being made
to work--storage batteries will do nicely--and connect them in series as
in Fig. 13. When batteries are in series they act like a single stronger
battery, one whose e. m. f. is the sum of the e. m. f.'s of the separate
batteries. Connect these batteries to a long fine wire as in Fig. 14.
There is a stream of electrons along this wire. Next connect the
negative terminal of the standard cell to the negative terminal of the
storage batteries, that is, brace their feet against each other. Then
connect a wire to the positive terminal of the standard cell. This wire
acts just like a long arm sticking out from the positive plate of this

[Illustration: Fig 14]

Touch the end of the wire, which is _p_ of Fig. 14, to some point
as _a_ on the fine wire. Now what do we have? Right at _a_, of
course, there are some free electrons and they hear the calls of both
batteries. If the standard battery, _S_ of the figure, calls the
stronger they go to it. In that case move the end _p_ nearer the
positive plate of the battery _B_, so that it will have a chance to
exert a stronger pull. Suppose we try at _c_ and find the battery
_B_ is there the stronger. Then we can move back to some point, say
_b_, where the pulls are equal.

To make a test like this we put a sensitive current-measuring instrument
in the wire which leads from the positive terminal of the standard cell.
We also use a long fine wire so that there can never be much of an
electron stream anyway. When the pulls are equal there will be no
current through this instrument.

As soon as we find out where the proper setting is we can replace
_S_ by some other battery, say _X_, which we wish to compare
with _S_. We find the setting for that battery in the same way as
we just did for _S_. Suppose it is at _d_ in Fig. 14 while the
setting for _S_ was at _b_. We can see at once that _X_
is stronger than _S_. The question, however, is how much stronger.

Perhaps it would be better to try to answer this question by talking
about e. m. f.'s. It isn't fair to speak only of the positive plate
which calls, we must speak also of the negative plate which is shooing
electrons away from itself. The idea of e. m. f. takes care of both
these actions. The steady stream of electrons in the fine wire is due to
the e. m. f. of the battery _B_, that is to the pull of the
positive terminal and the shove of the negative.

If the wire is uniform, that is the same throughout its length, then
each inch of it requires just as much e. m. f. as any other inch. Two
inches require twice the e. m. f. which one inch requires. We know how
much e. m. f. it takes to keep the electron stream going in the part of
the wire from _n_ to _b_. It takes just the e. m. f. of the
standard cell, _S_, because when that had its feet braced at
_n_ it pulled just as hard at _b_ as did the big battery

Suppose the distance _n_ to _d_ (usually written _nd_) is
twice as great as that from _n_ to _b_ (_nb_). That means
that battery _X_ has twice the e. m. f. of battery _S_. You
remember that _X_ could exert the same force through the length of
wire _nd_, as could the large battery. That is twice what cell
_S_ can do. Therefore if we know how many volts to call the e. m.
f. of the standard cell we can say that _X_ has an e. m. f. of
twice as many volts.

If we measured dry batteries this way we should find that they each had
an e. m. f. of about 1.46 volts. A storage battery would be found to
have about 2.4 volts when fully charged and perhaps as low as 2.1 volts
when we had run it for a while.

That is the way in which to compare batteries and to measure their e. m.
f.'s, but you see it takes a lot of time. It is easier to use a
"voltmeter" which is an instrument for measuring e. m. f.'s. Here is how
one could be made.

First there is made a current-measuring instrument which is quite
sensitive, so that its pointer will show a deflection when only a very
small stream of electrons is passing through the instrument. We could
make one in the same way as we made the ammeter of the last letter but
there are other better ways of which I'll tell you later. Then we
connect a good deal of fine wire in series with the instrument for a
reason which I'll tell you in a minute. The next and last step is to

We know how many volts of e. m. f. are required to keep going the
electron stream between _n_ and _b_--we know that from the e.
m. f. of our standard cell. Suppose then that we connect this new
instrument, which we have just made, to the wire at _n_ and
_b_ as in Fig. 15. Some of the electrons at _n_ which are so
anxious to get away from the negative plate of battery _B_ can now
travel as far as _b_ through the wire of the new instrument. They
do so and the pointer swings around to some new position. Opposite that
we mark the number of volts which the standard battery told us there was
between _n_ and _b_.

[Illustration: Fig 15]

If we move the end of the wire from _b_ to _d_ the pointer
will take a new position. Opposite this we mark twice the number of
volts of the standard cell. We can run it to a point _e_ where the
distance _ne_ is one-half _nb_, and mark our scale with half
the number of volts of the standard cell, and so on for other positions
along the wire. That's the way we calibrate a sensitive
current-measuring instrument (with its added wire, of course) so that it
will read volts. It is now a voltmeter.

If we connect a voltmeter to the battery _X_ as in Fig. 16 the
pointer will tell us the number of volts in the e. m. f. of _X_,
for the pointer will take the same position as it did when the voltmeter
was connected between _n_ and _d_.

There is only one thing to watch out for in all this. We must be careful
that the voltmeter is so made that it won't offer too easy a path for
electrons to follow. We only want to find how hard a battery can pull an
electron, for that is what we mean by e. m. f. Of course, we must let a
small stream of electrons flow through the voltmeter so as to make the
pointer move. That is why voltmeters of this kind are made out of a long
piece of fine wire or else have a coil of fine wire in series with the
current-measuring part. The fine wire makes a long and narrow path for
the electrons and so there can be only a small stream. Usually we
describe this condition by saying that a voltmeter has a high

[Illustration: Fig 16]

Fine wires offer more resistance to electron streams than do heavy wires
of the same length. If a wire is the same diameter all along, the longer
the length of it which we use the greater is the resistance which is
offered to an electron stream.

You will need to know how to describe the resistance of a wire or of any
part of an electric circuit. To do so you tell how many "ohms" of
resistance it has. The ohm is the unit in which we measure the
resistance of a circuit to an electron stream.

I can show you what an ohm is if I tell you a simple way to measure a
resistance. Suppose you have a wire or coil of wire and want to know its
resistance. Connect it in series with a battery and an ammeter as shown
in Fig. 17. The same electron stream passes through all parts of this
circuit and the ammeter tells us what this stream is in amperes. Now
connect a voltmeter to the two ends of the coil as shown in the figure.
The voltmeter tells in volts how much e. m. f. is being applied to force
the current through the coil. Divide the number of volts by the number
of amperes and the quotient (answer) is the number of ohms of resistance
in the coil.

[Illustration: Fig 17]

Suppose the ammeter shows a current of one ampere and the voltmeter an
e. m. f. of one volt. Then dividing 1 by 1 gives 1. That means that the
coil has a resistance of one ohm. It also means one ohm is such a
resistance that one volt will send through it a current of one ampere.
You can get lots of meaning out of this. For example, it means also that
one volt will send a current of one ampere through a resistance of one

How many ohms would the coil have if it took 5 volts to send 2 amperes
through it. Solution: Divide 5 by 2 and you get 2.5. Therefore the coil
would have a resistance of 2.5 ohms.

Try another. If a coil of resistance three ohms is carrying two amperes
what is the voltage across the terminals of the coil? For 1 ohm it would
take 1 volt to give a current of 1 ampere, wouldn't it? For 3 ohms it
takes three times as much to give one ampere. To give twice this current
would take twice 3 volts. That is, 2 amperes in 3 ohms requires 2x3

Here's one for you to try by yourself. If an e. m. f. of 8 volts is
sending current through a resistance of 2 ohms, how much current is
flowing? Notice that I told the number of ohms and the number of volts,
what are you going to tell? Don't tell just the number; tell how many
and what.




Although there is much in Letters 7 and 8 which it is well to learn and
to think about, there are only three of the ideas which you must have
firmly grasped to get the most out of this letter which I am now going
to write you about the audion.

First: Electric currents are streams of electrons. We measure currents
in amperes. To measure a current we may connect into the circuit an

Second: Electrons move in a circuit when there is an
electron-moving-force, that is an electromotive force or e. m. f. We
measure e. m. f.'s in volts. To measure an e. m. f. we connect a
voltmeter to the two points between which the e. m. f. is active.

Third: What current any particular e. m. f. will cause depends upon the
circuit in which it is active. Circuits differ in the resistance which
they offer to e. m. f.'s. For any particular e. m. f. (that is for any
given e. m. f.) the resulting current will be smaller the greater the
resistance of the circuit. We measure resistance in ohms. To measure it
we find the quotient of the number of volts applied to the circuit by
the number of amperes which flow.

In my sixth letter I told you something of how the audion works. It
would be worth while to read again that letter. You remember that the
current in the plate circuit can be controlled by the e. m. f. which is
applied to the grid circuit. There is a relationship between the plate
current and the grid voltage which is peculiar or characteristic to the
tube. So we call such a relationship "a characteristic." Let us see how
it may be found and what it will be.

Connect an ammeter in the plate- or B-circuit, of the tube so as to
measure the plate-circuit current. You will find that almost all books
use the letter "_I_" to stand for current. The reason is that
scientists used to speak of the "intensity of an electric current" so
that "_I_" really stands for intensity. We use _I_ to stand
for something more than the word "current." It is our symbol for
whatever an ammeter would read, that is for the amount of current.

[Illustration: Fig 18]

Another convenience in symbols is this: We shall frequently want to
speak of the currents in several different circuits. It saves time to
use another letter along with the letter _I_ to show the circuit to
which we refer. For example, we are going to talk about the current in
the B-circuit of the audion, so we call that current _I_{B}_. We
write the letter _B_ below the line on which _I_ stands. That
is why we say the _B_ is subscript, meaning "written below." When
you are reading to yourself be sure to read _I_{B}_ as "eye-bee" or
else as "eye-subscript-bee." _I_{B}_ therefore will stand for the
number of amperes in the plate circuit of the audion. In the same way
_I_{a}_ would stand for the current in the filament circuit.

We are going to talk about e. m. f.'s also. The letter "_E_" stands
for the number of volts of e. m. f. in a circuit. In the filament
circuit the battery has _E_{A}_ volts. In the plate circuit the e.
m. f. is _E_{B}_ volts. If we put a battery in the grid circuit we
can let _E_{C}_ represent the number of volts applied to the
grid-filament or C-circuit.

The characteristic relation which we are after is one between grid
voltage, that is _E_{C}_, and plate current, that is _I_{B}_.
So we call it the _E_{C}_--_I_{B}_ characteristic. The dash
between the letters is not a subtraction sign but merely a dash to
separate the letters. Now we'll find the "ee-see-eye-bee"

Connect some small dry cells in series for use in the grid circuit. Then
connect the filament to the middle cell as in Fig. 19. Take the wire
which comes from the grid and put a battery clip on it, then you can
connect the grid anywhere you want along this series of batteries. See
Fig. 18. In the figure this movable clip is represented by an arrow
head. You can see that if it is at _a_ the battery will make the
grid positive. If it is moved to _b_ the grid will be more
positive. On the other hand if the clip is at _o_ there will be no
e. m. f. applied to the grid. If it is at _c_ the grid will be made

Between grid and filament there is placed a voltmeter which will tell
how much e. m. f. is applied to the grid, that is, tell the value of
_E_{C}_, for any position whatever of the clip.

We shall start with the filament heated to a deep red. The manufacturers
of the audion tell the purchaser what current should flow through the
filament so that there will be the proper emission of electrons. There
are easy ways of finding out for one's self but we shall not stop to
describe them. The makers also tell how many volts to apply to the
plate, that is what value _E_{B}_ should have. We could find this
out also for ourselves but we shall not stop to do so.

[Illustration: Fig 19]

Now we set the battery clip so that there is no voltage applied to the
grid; that is, we start with _E_{C}_ equal to zero. Then we read the
ammeter in the plate circuit to find the value of _I_{B}_ which
corresponds to this condition of the grid.

Next we move the clip so as to make the grid as positive as one battery
will make it, that is we move the clip to _a_ in Fig. 19. We now
have a different value of _E_{C}_ and will find a different value
of _I_{B}_ when we read the ammeter. Next move the clip to apply
two batteries to the grid. We get a new pair of values for _E_{C}_
and _I_{B}_, getting _E_{C}_ from the voltmeter and _I_{B}_ from the
ammeter. As we continue in this way, increasing _E_{C}_, we find that
the current _I_{B}_ increases for a while and then after we have
reached a certain value of _E_{C}_ the current _I_{B}_ stops
increasing. Adding more batteries and making the grid more positive
doesn't have any effect on the plate current.

[Illustration: Fig 20]

Before I tell you why this happens I want to show you how to make a
picture of the pairs of values of _E_{C}_ and _I_{B}_ which we
have been reading on the voltmeter and ammeter.

Imagine a city where all the streets are at right angles and the north
and south streets are called streets and numbered while the east and
west thorofares are called avenues. I'll draw the map as in Fig. 20.
Right through the center of the city goes Main Street. But the people
who laid out the roads were mathematicians and instead of calling it
Main Street they called it "Zero Street." The first street east of Zero
St. we should have called "East First Street" but they called it
"Positive 1 St." and the next beyond "Positive 2 St.," and so on. West
of the main street they called the first street "Negative 1 St." and so

When they came to name the avenues they were just as precise and
mathematical. They called the main avenue "Zero Ave." and those north of
it "Positive 1 Ave.," "Positive 2 Ave." and so on. Of course, the
avenues south of Zero Ave. they called Negative.

The Town Council went almost crazy on the subject of numbering; they
numbered everything. The silent policeman which stood at the corner of
"Positive 2 St." and "Positive 1 Ave." was marked that way. Half way
between Positive 2 St. and Positive 3 St. there was a garage which set
back about two-tenths of a block from Positive 1 Ave. The Council
numbered it and called it "Positive 2.5 St. and Positive 1.2 Ave." Most
of the people spoke of it as "Plus 2.5 St. and Plus 1.2 Ave."

Sometime later there was an election in the city and a new Council was
elected. The members were mostly young electricians and the new Highway
Commissioner was a radio enthusiast. At the first meeting the Council
changed the names of all the avenues to "Mil-amperes"[3] and of all the
streets to "Volts."

Then the Highway Commissioner who had just been taking a set of
voltmeter and ammeter readings on an audion moved that there should be a
new road known as "Audion Characteristic." He said the road should pass
through the following points:

    Zero Volt and Plus 1.0 Mil-ampere
    Plus 2.0 Volts and Plus 1.7 Mil-amperes
    Plus 4.0 Volts and Plus 2.6 Mil-amperes
    Plus 6.0 Volts and Plus 3.4 Mil-amperes
    Plus 8.0 Volts and Plus 4.3 Mil-amperes

And so on. Fig. 21 shows the new road.

[Illustration: Fig 21]

One member of the Council jumped up and said "But what if the grid is
made negative?" The Commissioner had forgotten to see what happened so
he went home to take more readings.

He shifted the battery clip along, starting at _c_ of Fig. 22. At
the next meeting of the Council he brought in the following list of
readings and hence of points on his proposed road.

    Minus 1.0 Volts and Plus 0.6 Mil-ampere
      "   2.0   "    "    "  0.4  "     "
      "   3.0   "    "    "  0.2  "     "
      "   4.0   "    "    "  0.1  "     "
      "   5.0   "    "    "  0.0  "     "

Then he showed the other members of the Council on the map of Fig. 23
how the Audion Characteristic would look.

[Illustration: Fig 22]

There was considerable discussion after that and it appeared that
different designs and makes of audions would have different
characteristic curves. They all had the same general form of curve but
they would pass through different sets of points depending upon the
design and upon the B-battery voltage. It was several meetings later,
however, before they found out what effects were due to the form of the
curve. Right after this they found that they could get much better
results with their radio sets.

Now look at the audion characteristic. Making the grid positive, that is
going on the positive side of the zero volts in our map, makes the plate
current larger. You remember that I told you in Letter 6 how the grid,
when positive, helped call electrons away from the filament and so made
a larger stream of electrons in the plate circuit. The grid calls
electrons away from the filament. It can't call them out of it; they
have to come out themselves as I explained to you in the fifth letter.

[Illustration: Fig 23]

You can see that as we make the grid more and more positive, that is,
make it call louder and louder, a condition will be reached where it
won't do it any good to call any louder, for it will already be getting
all the electrons away from the filament just as fast as they are
emitted. Making the grid more positive after that will not increase the
plate current any. That's why the characteristic flattens off as you see
at high values of grid voltage.

The arrangement which we pictured in Fig. 22 for making changes in the
grid voltage is simple but it doesn't let us change the voltage by less
than that of a single battery cell. I want to show you a way which will.
You'll find it very useful to know and it is easily understood for it is
something like the arrangement of Fig. 14 in the preceding letter.

[Illustration: Fig 24]

Connect the cells as in Fig. 24 to a fine wire. About the middle of this
wire connect the filament. As before use a clip on the end of the wire
from the grid. If the grid is connected to _a_ in the figure there
is applied to the grid circuit that part of the e. m. f. of the battery
which is active in the length of wire between _o_ and _a_. The
point _a_ is nearer the positive plate of the battery than is the
point _o_. So the grid will be positive and the filament negative.

On the other hand, if the clip is connected at _b_ the grid will be
negative with respect to the filament. We can, therefore, make the grid
positive or negative depending on which side of _o_ we connect the
clip. How large the e. m. f. is which will be applied to the grid
depends, of course, upon how far away from _o_ the clip is

Suppose you took the clip in your hand and slid it along in contact with
the wire, first from _o_ to _a_ and then back again through
_o_ to _b_ and so on back and forth. You would be making the
grid _alternately_ positive and negative, wouldn't you? That is,
you would be applying to the grid an e. m. f. which increases to some
positive value and then, decreasing to zero, _reverses_, and
increases just as much, only to decrease to zero, where it started. If
you do this over and over again, taking always the same time for one
round trip of the clip you will be impressing on the grid circuit an
"_alternating e. m. f._"

What's going to happen in the plate circuit? When there is no e. m. f.
applied to the grid circuit, that is when the grid potential
(possibilities) is zero, there is a definite current in the plate
circuit. That current we can find from our characteristic of Fig. 23 for
it is where the curve crosses Zero Volts. As the grid becomes positive
the current rises above this value. When the grid is made negative the
current falls below this value. The current, _I_{B}_, then is made
alternately greater and less than the current when _E_{C}_ is zero.

You might spend a little time thinking over this, seeing what happens
when an alternating e. m. f. is applied to the grid of an audion, for
that is going to be fundamental to our study of radio.

[Footnote 3: A mil-ampere is a thousandth of an ampere just as a
millimeter is a thousandth of a meter.]




In the last letter we learned of an alternating e. m. f. The way of
producing it, which I described, is very crude and I want to tell how to
make the audion develop an alternating e. m. f. for itself. That is what
the audion does in the transmitting set of a radio telephone. But an
audion can't do it all alone. It must have associated with it some coils
and a condenser. You know what I mean by coils but you have yet to learn
about condensers.

A condenser is merely a gap in an otherwise conducting circuit. It's a
gap across which electrons cannot pass so that if there is an e. m. f.
in the circuit, electrons will be very plentiful on one side of the gap
and scarce on the other side. If there are to be many electrons waiting
beside the gap there must be room for them. For that reason we usually
provide waiting-rooms for the electrons on each side of the gap. Metal
plates or sheets of tinfoil serve nicely for this purpose. Look at Fig.
25. You see a battery and a circuit which would be conducting except for
the gap at _C_. On each side of the gap there is a sheet of metal.
The metal sheets may be separated by air or mica or paraffined paper.
The combination of gap, plates, and whatever is between, provided it is
not conducting, is called a condenser.

Let us see what happens when we connect a battery to a condenser as in
the figure. The positive terminal of the battery calls electrons from
one plate of the condenser while the negative battery-terminal drives
electrons away from itself toward the other plate of the condenser. One
plate of the condenser, therefore, becomes positive while the other
plate becomes negative.

[Illustration: Fig 25]

You know that this action of the battery will go on until there are so
many electrons in the negative plate of the condenser that they prevent
the battery from adding any more electrons to that plate. The same thing
happens at the other condenser plate. The positive terminal of the
battery calls electrons away from the condenser plate which it is making
positive until so many electrons have left that the protons in the atoms
of the plate are calling for electrons to stay home just as loudly and
effectively as the positive battery-terminal is calling them away.

When both these conditions are reached--and they are both reached at the
same time--then the battery has to stop driving electrons around the
circuit. The battery has not enough e. m. f. to drive any more
electrons. Why? Because the condenser has now just enough e. m. f. with
which to oppose the battery.

It would be well to learn at once the right words to use in describing
this action. We say that the battery sends a "charging current" around
its circuit and "charges the condenser" until it has the same e. m. f.
When the battery is first connected to the condenser there is lots of
space in the waiting-rooms so there is a great rush or surge of
electrons into one plate and away from the other. Just at this first
instant the charging current, therefore, is large but it decreases
rapidly, for the moment electrons start to pile up on one plate of the
condenser and to leave the other, an e. m. f. builds up on the
condenser. This e. m. f., of course, opposes that of the battery so that
the net e. m. f. acting to move electrons round the circuit is no longer
that of the battery, but is the difference between the e. m. f. of the
battery and that of the condenser. And so, with each added electron, the
e. m. f. of the condenser increases until finally it is just equal to
that of the battery and there is no net e. m. f. to act.

What would happen if we should then disconnect the battery? The
condenser would be left with its extra electrons in the negative plate
and with its positive plate lacking the same number of electrons. That
is, the condenser would be left charged and its e. m. f. would be of
the same number of volts as the battery.

[Illustration: Fig 26]

Now suppose we connect a short wire between the plates of the condenser
as in Fig. 26. The electrons rush home from the negative plate to the
positive plate. As fast as electrons get home the e. m. f. decreases.
When they are all back the e. m. f. has been reduced to zero. Sometimes
we say that "the condenser discharges." The "discharge current" starts
with a rush the moment the conducting path is offered between the two
plates. The e. m. f. of the condenser falls, the discharge current grows
smaller, and in a very short time the condenser is completely

[Illustration: Fig 27]

That's what happens when there is a short conducting path for the
discharge current. If that were all that could happen I doubt if there
would be any radio communication to-day. But if we connect a coil of
wire between two plates of a charged condenser, as in Fig. 27, then
something of great interest happens. To understand you must know
something more about electron streams.

Suppose we should wind a few turns of wire on a cylindrical core, say on
a stiff cardboard tube. We shall use insulated wire. Now start from one
end of the coil, say _a_, and follow along the coiled wire for a
few turns and then scratch off the insulation and solder onto the coil
two wires, _b_, and _c_, as shown in Fig. 28. The further end
of the coil we shall call _d_. Now let's arrange a battery and
switch so that we can send a current through the part of the coil
between _a_ and _b_. Arrange also a current-measuring instrument so as
to show if any current is flowing in the part of the coil between _c_
and _d_. For this purpose we shall use a kind of current-measuring
instrument which I have not yet explained. It is different from the
hot-wire type described in Letter 7 for it will show in which direction
electrons are streaming through it.

The diagram of Fig. 28 indicates the apparatus of our experiment. When
we close the switch, _S_, the battery starts a stream of electrons
from _a_ towards _b_. Just at that instant the needle, or
pointer, of the current instrument moves. The needle moves, and thus
shows a current in the coil _cd_; but it comes right back again,
showing that the current is only momentary. Let's say this again in
different words. The battery keeps steadily forcing electrons through
the circuit _ab_ but the instrument in the circuit _cd_ shows
no current in that circuit except just at the instant when current
starts to flow in the neighboring circuit _ab_.

[Illustration: Fig 28]

One thing this current-measuring instrument tells us is the direction of
the electron stream through itself. It shows that the momentary stream
of electrons goes through the coil from _d_ to _c_, that is in
the opposite direction to the stream in the part _ab_.

Now prepare to do a little close thinking. Read over carefully all I
have told you about this experiment. You see that the moment the battery
starts a stream of electrons from _a_ towards _b_, something causes
a momentary, that is a temporary, movement of electrons from _d_ to
_c_. We say that starting a stream of electrons from _a_ to _b_ sets
up or "induces" a stream of electrons from _d_ to _c_.

What will happen then if we connect the battery between _a_ and _d_
as in Fig. 29? Electrons will start streaming away from _a_ towards
_b_, that is towards _d_. But that means there will be a momentary
stream from _d_ towards _c_, that is towards _a_. Our stream from
the battery causes this oppositely directed stream. In the usual
words we say it "induces" in the coil an opposing stream of electrons.
This opposing stream doesn't last long, as we saw, but while it does
last it hinders the stream which the battery is trying to establish.

[Illustration: Fig 29]

The stream of electrons which the battery causes will at first meet an
opposition so it takes a little time before the battery can get the
full-sized stream of electrons flowing steadily. In other words a
current in a coil builds up slowly, because while it is building up it
induces an effect which opposes somewhat its own building up.

Did you ever see a small boy start off somewhere, perhaps where he
shouldn't be going, and find his conscience starting to trouble him at
once. For a time he goes a little slowly but in a moment or two his
conscience stops opposing him and he goes on steadily at his full pace.
When he started he stirred up his conscience and that opposed him.
Nobody else was hindering his going. It was all brought about by his
own actions. The opposition which he met was "self-induced." He was
hindered at first by a self-induced effect of his own conscience. If he
was a stream of electrons starting off to travel around the coil we
would say that he was opposed by a self-induced e. m. f. And any path
in which such an effect will be produced we say has "self-inductance."
Usually we shorten this term and speak of "inductance."

There is another way of looking at it. We know habits are hard to form
and equally hard to break. It's hard to get electrons going around a
coil and the self-inductance of a circuit tells us how hard it is. The
harder it is the more self-inductance we say that the coil or circuit
has. Of course, we need a unit in which to measure self-inductance. The
unit is called the "henry." But that is more self-inductance than we can
stand in most radio circuits, so we find it convenient to measure in
smaller units called "mil-henries" which are thousandths of a henry.

You ought to know what a henry[4] is, if we are to use the word, but it
isn't necessary just now to spend much time on it. The opposition which
one's self-induced conscience offers depends upon how rapidly one
starts. It's volts which make electrons move and so the conscience which
opposes them will be measured in volts. Therefore we say that a coil has
one henry of inductance when an electron stream which is increasing one
ampere's worth each second stirs up in the coil a conscientious
objection of one volt. Don't try to remember this now; you can come back
to it later.

There is one more effect of inductance which we must know before we can
get very far with our radio. Suppose an electron stream is flowing
through a coil because a battery is driving the electrons along. Now let
the battery be removed or disconnected. You'd expect the electron stream
to stop at once but it doesn't. It keeps on for a moment because the
electrons have got the habit.

[Illustration: Fig 28]

If you look again at Fig. 28 you will see what I mean. Suppose the
switch is closed and a steady stream of electrons is flowing through the
coil from _a_ to _b_. There will be no current in the other
part of the coil. Now open the switch. There will be a motion of the
needle of the current-measuring instrument, showing a momentary current.
The direction of this motion, however, shows that the momentary stream
of electrons goes through the coil from _c_ to _d_.

Do you see what this means? The moment the battery is disconnected there
is nothing driving the electrons in the part _ab_ and they slow
down. Immediately, and just for an instant, a stream of electrons starts
off in the part _cd_ in the same direction as if the battery was
driving them along.

Now look again at Fig. 29. If the battery is suddenly disconnected there
is a momentary rush of electrons in the same direction as the battery
was driving them. Just as the self-inductance of a coil opposes the
starting of a stream of electrons, so it opposes the stopping of a
stream which is already going.

[Illustration: Fig 29]

So far we haven't said much about making an audion produce alternating
e. m. f.'s and thus making it useful for radio-telephony. Before radio
was possible all these things that I have just told you, and some more
too, had to be known. It took hundreds of good scientists years of
patient study and experiment to find out those ideas about electricity
which have made possible radio-telephony.

Two of these ideas are absolutely necessary for the student of
radio-communication. First: A condenser is a gap in a circuit where
there are waiting-rooms for the electrons. Second: Electrons form
habits. It's hard to get them going through a coil of wire, harder than
through a straight wire, but after they are going they don't like to
stop. They like it much less if they are going through a coil instead of
a straight wire.

In my next letter I'll tell you what happens when we have a coil and a
condenser together in a circuit.

[Footnote 4: The "henry" has nothing to do with a well-known automobile.
It was named after Joseph Henry, a professor years ago at Princeton




[Illustration: Fig 28]

Let's look again at the coils of Fig. 28 which we studied in the last
letter. I have reproduced them here so you won't have to turn back. When
electrons start from _a_ towards _b_ there is a momentary
stream of electrons from _d_ towards _c_. If the electron
stream through _ab_ were started in the opposite direction, that is
from _b_ to _a_ the induced stream in the coil _cd_ would
be from _c_ towards _d_.

[Illustration: Fig 30]

It all reminds me of two boys with a hedge or fence between them as in
Fig. 30. One boy is after the other. Suppose you were being chased; you
know what you'd do. If your pursuer started off with a rush towards one
end of the hedge you'd "beat it" towards the other. But if he started
slowly and cautiously you would start slowly too. You always go in the
opposite direction, dodging back and forth along the paths which you are
wearing in the grass on opposite sides of the hedge. If he starts to the
right and then slows up and starts back, you will start to your right,
slow up, and start back. Suppose he starts at the center of the hedge.
First he dodges to the right, and then back through the center as far to
the left, then back again and so on. You follow his every change.

[Illustration: Fig 31]

I am going to make a picture of what you two do. Let's start with the
other fellow. He dodges or alternates back and forth. Some persons would
say he "oscillates" back and forth in the same path. As he does so he
induces you to move. I am on your side of the hedge with a
moving-picture camera. My camera catches both of you. Fig. 31 shows the
way the film would look if it caught only your heads. The white circle
represents the tow-head on my side of the hedge and the black circle,
young Brown who lives next door. Of course, the camera only catches you
each time the shutter opens but it is easy to draw a complete picture of
what takes place as time goes on. See Fig. 32.

[Illustration: Fig 32]

Now suppose you are an electron in coil _cd_ of Fig. 33 and
"Brownie" is one in coil _ab_. Your motions are induced by his.
What's true of you two is true of all the other electrons. I have
separated the coils a little in this sketch so that you can think of a
hedge between. I don't know how one electron can affect another on the
opposite side of this hedge but it can. And I don't know anything really
about the hedge, which is generally called "the ether." The hedge isn't
air. The effect would be the same if the coils were in a vacuum. The
"ether" is just a name for whatever is left in the space about us when
we have taken out everything which we can see or feel--every molecule,
every proton and every electron.

[Illustration: Fig 33]

Why and how electrons can affect one another when they are widely
separated is one of the great mysteries of science. We don't know any
more about it than about why there are electrons. Let's accept it as a
fundamental fact which we can't as yet explain.

[Illustration: Fig 34]

And now we can see how to make an audion produce an alternating current
or as we sometimes say "make an audion oscillator." We shall set up an
audion with its A-battery as in Fig. 34. Between the grid and the
filament we put a coil and a condenser. Notice that they are in
parallel, as we say. In the plate-filament circuit we connect the
B-battery and a switch, _S_, and another coil. This coil in the
plate circuit of the audion we place close to the other coil so that the
two coils are just like the coils _ab_ and _cd_ of which I
have been telling you. The moment any current flows in coil _ab_
there will be a current flow in the coil _cd_. (An induced electron
stream.) Of course, as long as the switch in the B-battery is open no
current can flow.

The moment the switch _S_ is closed the B-battery makes the plate
positive with respect to the filament and there is a sudden surge of
electrons round the plate circuit and through the coil from _a_ to
_b_. You know what that does to the coil _cd_. It induces an
electron stream from _d_ towards _c_. Where do these electrons
come from? Why, from the grid and the plate 1 of the condenser. Where do
they go? Most of them go to the waiting-room offered by plate 2 of the
condenser and some, of course, to the filament. What is the result? The
grid becomes positive and the filament negative.

[Illustration: Fig 35]

This is the crucial moment in our study. Can you tell me what is going
to happen to the stream of electrons in the plate circuit? Remember that
just at the instant when we closed the switch the grid was neither
positive nor negative. We were at the point of zero volts on the audion
characteristic of Fig. 35. When we close the switch the current in the
plate circuit starts to jump from zero mil-amperes to the number of
mil-amperes which represents the point where Zero Volt St. crosses
Audion Characteristic. But this jump in plate current makes the grid
positive as we have just seen. So the grid will help the plate call
electrons and that will make the current in the plate circuit still
larger, that is, result in a larger stream of electrons from _a_ to

This increase in current will be matched by an increased effect in the
coil _cd_, for you remember how you and "Brownie" behaved. And that
will pull more electrons away from plate 1 of the condenser and send
them to the waiting-room of 2. All this makes the grid more positive and
so makes it call all the more effectively to help the plate move

[Illustration: Pl. V.--Variometer (top) and Variable Condenser (bottom)
of the General Radio Company. Voltmeter and Ammeter of the Weston
Instrument Company.]

We "started something" that time. It's going on all by itself. The grid
is getting more positive, the plate current is getting bigger, and so
the grid is getting more positive and the plate current still bigger. Is
it ever going to stop? Yes. Look at the audion characteristic. There
comes a time when making the grid a little more positive won't have any
effect on the plate-circuit current. So the plate current stops

There is nothing now to keep pulling electrons away from plate 1 and
crowding them into waiting-room 2. Why shouldn't the electrons in this
waiting-room go home to that of plate 1? There is now no reason and so
they start off with a rush.

Of course, some of them came from the grid and as fast as electrons get
back to the grid it becomes less and less positive. As the grid becomes
less and less positive it becomes less and less helpful to the plate.

If the grid doesn't help, the plate alone can't keep up this stream of
electrons. All the plate can do by itself is to maintain the current
represented by the intersection of zero volts and the audion
characteristic. The result is that the current in the plate circuit,
that is, of course, the current in coil _ab_, becomes gradually less.
About the time all the electrons, which had left the grid and plate 1
of the condenser, have got home the plate current is back to the value
corresponding to _E_{C}_=_0_.

The plate current first increases and then decreases, but it doesn't
stop decreasing when it gets back to zero-grid value. And the reason is
all due to the habit forming tendencies of electrons in coils. To see
how this comes about, let's tell the whole story over again. In other
words let's make a review and so get a sort of flying start.

[Illustration: Fig 34]

When we close the battery switch, _S_ in Fig. 34, we allow a
current to flow in the plate circuit. This current induces a current in
the coil _cd_ and charges the condenser which is across it, making
plate 1 positive and plate 2 negative. A positive grid helps the plate
so that the current in the plate circuit builds up to the greatest
possible value as shown by the audion characteristic. That's the end of
the increase in current. Now the condenser discharges, sending electrons
through the coil _cd_ and making the grid less positive until
finally it is at zero potential, that is neither positive nor negative.

While the condenser is discharging the electrons in the coil _cd_
get a habit of flowing from _c_ toward _d_, that is from plate
2 to plate 1. If it wasn't for this habit the electron stream in
_cd_ would stop as soon as the grid had reduced to zero voltage.
Because of the habit, however, a lot of electrons that ought to stay on
plate 2 get hurried along and land on plate 1. It is a little like the
old game of "crack the whip." Some electrons get the habit and can't
stop quickly enough so they go tumbling into waiting-room 1 and make it

That means that the condenser not only discharges but starts to get
charged in the other direction with plate 1 negative and plate 2
positive. The grid feels the effect of all this, because it gets extra
electrons if plate 1 gets them. In fact the voltage effective between
grid and filament is always the voltage between the plates of the

The audion characteristic tells us what is the result. As the grid
becomes negative it opposes the plate, shooing electrons back towards
the filament and reducing the plate current still further. But you have
already seen in my previous letter what happens when we reduce the
current in coil _ab_. There is then induced in coil _cd_ an
electron stream from _c_ to _d_. This induced current is in
just the right direction to send more electrons into waiting-room 1 and
so to make the grid still more negative. And the more negative the grid
gets the smaller becomes the plate current until finally the plate
current is reduced to zero. Look at the audion characteristic again and
see that making the grid sufficiently negative entirely stops the plate

When the plate current stops, the condenser in the grid circuit is
charged, with plate 1 negative and 2 positive. It was the plate current
which was the main cause of this change for it induced the charging
current in coil _cd_. So, when the plate current becomes zero there
is nothing to prevent the condenser from discharging.

Its discharge makes the grid less and less negative until it is zero
volts and there we are--back practically where we started. The plate
current is increasing and the grid is getting positive, and we're off on
another "cycle" as we say. During a cycle the plate current increases to
a maximum, decreases to zero, and then increases again to its initial

[Illustration: Fig 36]

This letter has a longer continuous train of thought than I usually ask
you to follow. But before I stop I want to give you some idea of what
good this is in radio.

What about the current which flows in coil _cd_? It's an
alternating current, isn't it? First the electrons stream from _d_
towards _c_, and then back again from _c_ towards _d_.

Suppose we set up another coil like _CD_ in Fig. 36. It would have
an alternating current induced in it. If this coil was connected to an
antenna there would be radio waves sent out. The switch _S_ could
be used for a key and kept closed longer or shorter intervals depending
upon whether dashes or dots were being set. I'll tell you more about
this later, but in this diagram are the makings of a "C-W Transmitter,"
that is a "continuous wave transmitter" for radio-telegraphy.

It would be worth while to go over this letter again using a pencil and
tracing in the various circuits the electron streams which I have




In the last letter I didn't stop to draw you a picture of the action of
the audion oscillator which I described. I am going to do it now and you
are to imagine me as using two pencils and drawing simultaneously two
curves. One curve shows what happens to the current in the plate
circuit. The other shows how the voltage of the grid changes. Both
curves start from the instant when the switch is closed; and the two
taken together show just what happens in the tube from instant to

Fig. 37 shows the two curves. You will notice how I have drawn them
beside and below the audion characteristic. The grid voltage and the
plate current are related, as I have told you, and the audion
characteristic is just a convenient way of showing the relationship. If
we know the current in the plate circuit we can find the voltage of the
grid and vice versa.

As time goes on, the plate current grows to its maximum and decreases to
zero and then goes on climbing up and down between these two extremes.
The grid voltage meanwhile is varying alternately, having its maximum
positive value when the plate current is a maximum and its maximum
negative value when the plate current is zero. Look at the two curves
and see this for yourself.

[Illustration: Fig 37]

Now I want to tell you something about how fast these oscillations
occur. We start by learning two words. One is "cycle" with which you are
already partly familiar and the other is "frequency." Take cycle first.
Starting from zero the current increases to a maximum, decreases to
zero, and is ready again for the same series of changes. We say the
current has passed through "a cycle of values." It doesn't make any
difference where we start from. If we follow the current through all its
different values until we are back at the same value as we started with
and ready to start all over, then we have followed through a cycle of

Once you get the idea of a cycle, and the markings on the curves in Fig.
31 will help you to understand, then the other idea is easy. By
"frequency" we mean the number of cycles each second. The electric
current which we use in lighting our house goes through sixty cycles a
second. That means the current reverses its direction 120 times a

In radio we use alternating currents which have very high frequencies.
In ship sets the frequency is either 500,000 or 1,000,000 cycles per
second. Amateur transmitting sets usually have oscillators which run at
well over a million cycles per second. The longer range stations use
lower frequencies.

You'll find, however, that the newspaper announcements of the various
broadcast stations do not tell the frequency but instead tell the "wave
length." I am not going to stop now to explain what that means but I am
going to give you a simple rule. Divide 300,000,000 by the "wave length"
and you'll have the frequency. For example, ships are supposed to use
wave lengths of 300 meters or 600 meters. Dividing three hundred million
by three hundred gives one million and that is one of the frequencies
which I told you were used by ship sets. Dividing by six hundred gives
500,000 or just half the frequency. You can remember that sets
transmitting with long waves have low frequencies, but sets with short
waves have high frequencies. The frequency and the wave length don't
change in the same way. They change in opposite ways or inversely, as we
say. The higher the frequency the shorter the wave length.

I'll tell you about wave lengths later. First let's see how to control
the frequency of an audion oscillator like that of Fig. 38.

[Illustration: Fig 38]

It takes time to get a full-sized stream going through a coil because of
the inductance of the coil. That you have learned. And also it takes
time for such a current to stop completely. Therefore, if we make the
inductance of the coil small, keeping the condenser the same, we shall
make the time required for the current to start and stop smaller. That
will mean a higher frequency for there will be more oscillations each
second. One rule, then, for increasing the frequency of an audion
oscillator is to decrease the inductance.

Later in this letter I shall tell you how to increase or decrease the
inductance of a coil. Before I do so, however, I want to call your
attention to the other way in which we can change the frequency of an
audion oscillator.

Let's see how the frequency will depend upon the capacity of the
condenser. If a condenser has a large capacity it means that it can
accommodate in its waiting-room a large number of electrons before the
e. m. f. of the condenser becomes large enough to stop the stream of
electrons which is charging the condenser. If the condenser in the grid
circuit of Fig. 38 is of large capacity it means that it must receive in
its upper waiting-room a large number of electrons before the grid will
be negative enough to make the plate current zero. Therefore, the
charging current will have to flow a long time to store up the necessary
number of electrons.

You will get the same idea, of course, if you think about the electrons
in the lower room. The current in the plate circuit will not stop
increasing until the voltage of the grid has become positive enough to
make the plate current a maximum. It can't do that until enough
electrons have left the upper room and been stored away in the lower.
Therefore the charging current will have to flow for a long time if the
capacity is large. We have, therefore, the other rule for increasing the
frequency of an audion oscillator, that is, decrease the capacity.

These rules can be stated the other way around. To decrease the
frequency we can either increase the capacity or increase the inductance
or do both.

But what would happen if we should decrease the capacity and increase
the inductance? Decreasing the capacity would make the frequency higher,
but increasing the inductance would make it lower. What would be the net
effect? That would depend upon how much we decreased the capacity and
how much we increased the inductance. It would be possible to decrease
the capacity and then if we increased the inductance just the right
amount to have no change in the frequency. No matter how large or how
small we make the capacity we can always make the inductance such that
there isn't any change in frequency. I'll give you a rule for this,
after I have told you some more things about capacities and inductances.

First as to inductances. A short straight wire has a very small
inductance, indeed. The longer the wire the larger will be the
inductance but unless the length is hundreds of feet there isn't much
inductance anyway. A coiled wire is very different.

A coil of wire will have more inductance the more turns there are to it.
That isn't the whole story but it's enough for the moment. Let's see
why. The reason why a stream of electrons has an opposing conscience
when they are started off in a coil of wire is because each electron
affects every other electron which can move in a parallel path. Look
again at the coils of Figs. 28 and 29 which we discussed in the tenth
letter. Those sketches plainly bring out the fact that the electrons in
part _cd_ travel in paths which are parallel to those of the
electrons in part _ab_.

[Illustration: Fig 39]

If we should turn these coils as in Fig. 39 so that all the paths in
_cd_ are at right angles to those in _ab_ there wouldn't be
any effect in _cd_ when a current in _ab_ started or stopped.
Look at the circuit of the oscillating audion in Fig. 38. If we should
turn these coils at right angles to each other we would stop the
oscillation. Electrons only influence other electrons which are in
parallel paths.

When we want a large inductance we wind the coil so that there are many
parallel paths. Then when the battery starts to drive an electron along,
this electron affects all its fellows who are in parallel paths and
tries to start them off in the opposite direction to that in which it is
being driven. The battery, of course, starts to drive all the electrons,
not only those nearest its negative terminal but those all along the
wire. And every one of these electrons makes up for the fact that the
battery is driving it along by urging all its fellows in the opposite

It is not an exceptional state of affairs. Suppose a lot of boys are
being driven out of a yard where they had no right to be playing.
Suppose also that a boy can resist and lag back twice as much if some
other boy urges him to do so. Make it easy and imagine three boys. The
first boy lags back not only on his own account but because of the
urging of the other boys. That makes him three times as hard to start as
if the other boys didn't influence him. The same is true of the second
boy and also of the third. The result is the unfortunate property owner
has nine times as hard a job getting that gang started as if only one
boy were to be dealt with. If there were two boys it would be four times
as hard as for one boy. If there were four in the group it would be
sixteen times, and if five it would be twenty-five times. The difficulty
increases much more rapidly than the number of boys.

Now all we have to do to get the right idea of inductance is to think of
each boy as standing for the electrons in one turn of the coil. If there
are five turns there will be twenty-five times as much inductance, as
for a single turn; and so on. You see that we can change the inductance
of a coil very easily by changing the number of turns.

I'll tell you two things more about inductance because they will come in
handy. The first is that the inductance will be larger if the turns are
large circles. You can see that for yourself because if the circles were
very small we would have practically a straight wire.

The other fact is this. If that property owner had been an electrical
engineer and the boys had been electrons he would have fixed it so that
while half of them said, "Aw, don't go; he can't put you off"; the other
half would have said "Come on, let's get out." If he did that he would
have a coil without any inductance, that is, he would have only the
natural inertia of the electrons to deal with. We would say that he had
made a coil with "pure resistance" or else that he had made a
"non-inductive resistance."

[Illustration: Fig 40]

How would he do it? Easy enough after one learns how, but quite
ingenious. Take the wire and fold it at the middle. Start with the
middle and wind the coil with the doubled wire. Fig. 40 shows how the
coil would look and you can see that part of the way the electrons are
going around the coil in one direction and the rest of the way in the
opposite direction. It is just as if the boys were paired off, a
"goody-goody" and a "tough nut" together. They both shout at once
opposite advice and neither has any effect.

I have told you all except one of the ways in which we can affect the
inductance of a circuit. You know now all the methods which are
important in radio. So let's consider how to make large or small

First I want to tell you how we measure the capacity of a condenser. We
use units called "microfarads." You remember that an ampere means an
electron stream at the rate of about six billion billion electrons a
second. A millionth of an ampere would, therefore, be a stream at the
rate of about six million million electrons a second--quite a sizable
little stream for any one who wanted to count them as they went by. If a
current of one millionth of an ampere should flow for just one second
six million million electrons would pass along by every point in the
path or circuit.

That is what would happen if there weren't any waiting-rooms in the
circuit. If there was a condenser then that number of electrons would
leave one waiting-room and would enter the other. Well, suppose that
just as the last electron of this enormous number[5] entered its
waiting-room we should know that the voltage of the condenser was just
one volt. Then we would say that the condenser had a capacity of one
microfarad. If it takes half that number to make the condenser oppose
further changes in the contents of its waiting-rooms, with one volt's
worth of opposition, that is, one volt of e. m. f., then the condenser
has only half a microfarad of capacity. The number of microfarads of
capacity (abbreviated mf.) is a measure of how many electrons we can get
away from one plate and into the other before the voltage rises to one

What must we do then to make a condenser with large capacity? Either of
two things; either make the waiting-rooms large or put them close

If we make the plates of a condenser larger, keeping the separation
between them the same, it means more space in the waiting-rooms and
hence less crowding. You know that the more crowded the electrons become
the more they push back against any other electron which some battery is
trying to force into their waiting-room, that is the higher the e. m. f.
of the condenser.

The other way to get a larger capacity is to bring the plates closer
together, that is to shorten the gap. Look at it this way: The closer
the plates are together the nearer home the electrons are. Their home is
only just across a little gap; they can almost see the electronic games
going on around the nuclei they left. They forget the long round-about
journey they took to get to this new waiting-room and they crowd over to
one side of this room to get just as close as they can to their old
homes. That's why it's always easier, and takes less voltage, to get the
same number of electrons moved from one plate to the other of a
condenser which has only a small space between plates. It takes less
voltage and that means that the condenser has a smaller e. m. f. for the
same number of electrons. It also means that before the e. m. f. rises
to one volt we can get more electrons moved around if the plates are
close together. And that means larger capacity.

There is one thing to remember in all this: It doesn't make any
difference how thick the plates are. It all depends upon how much
surface they have and how close together they are. Most of the electrons
in the plate which is being made negative are way over on the side
toward their old homes, that is, toward the plate which is being made
positive. And most of the homes, that is, atoms which have lost
electrons, are on the side of the positive plate which is next to the
gap. That's why I said the electrons could almost see their old homes.

[Illustration: Fig 41]

All this leads to two very simple rules for building condensers. If you
have a condenser with too small a capacity and want one, say, twice as
large, you can either use twice as large plates or bring the plates you
already have twice as close together; that is, make the gap half as
large. Generally, of course, the gap is pretty well fixed. For example,
if we make a condenser by using two pieces of metal and separating them
by a sheet of mica we don't want the job of splitting the mica. So we
increase the size of the plates. We can do that either by using larger
plates or other plates and connecting it as in Fig. 41 so that the total
waiting-room space for electrons is increased.

[Illustration: Pl. VI.--Low-power Transmitting Tube, U V 202
(Courtesy of Radio Corporation of America).]

[Illustration: Fig 42]

If you have got these ideas you can understand how we use both sides of
the same plate in some types of condensers. Look at Fig. 42. There are
two plates connected together and a third between them. Suppose
electrons are pulled from the outside plates and crowded into the middle
plate. Some of them go on one side and some on the other, as I have
shown. The negative signs indicate electrons and the plus signs their
old homes. If we use more plates as in Fig. 43 we have a larger

[Illustration: Fig 43]

[Illustration: Fig 44]

What if we have two plates which are not directly opposite one another,
like those of Fig. 44? What does the capacity depend upon? Imagine
yourself an electron on the negative plate. Look off toward the positive
plate and see how big it seems to you. The bigger it looks the more
capacity the condenser has. When the plates are right opposite one
another the positive plate looms up pretty large. But if they slide
apart you don't see so much of it; and if it is off to one side about
all you see is the edge. If you can't see lots of atoms which have lost
electrons and so would make good homes for you, there is no use of your
staying around on that side of the plate; you might just as well be
trying to go back home the long way which you originally came.

That's why in a variable plate condenser there is very little capacity
when no parts of the plates are opposite each other, and there is the
greatest capacity when they are exactly opposite one another.

[Illustration: Fig 45]

While we are at it we might just as well clean up this whole business of
variable capacities and inductances by considering two ways in which to
make a variable inductance. Fig. 45 shows the simplest way but it has
some disadvantages which I won't try now to explain. We make a long coil
and then take off taps. We can make connections between one end of the
coil and any of the taps. The more turns there are included in the part
of the coil which we are using the greater is the inductance. If we want
to do a real job we can bring each of these taps to a little stud and
arrange a sliding or rotating contact with them. Then we have an
inductance the value of which we can vary "step-by-step" in a convenient

Another way to make a variable inductance is to make what is called a
"variometer." I dislike the name because it doesn't "meter" anything. If
properly calibrated it would of course "meter" inductance, but then it
should be called an "inducto-meter."

Do you remember the gang of boys that fellow had to drive off his
property? What if there had been two different gangs playing there? How
much trouble he has depends upon whether there is anything in common
between the gangs. Suppose they are playing in different parts of his
property and so act just as if the other crowd wasn't also trespassing.
He could just add the trouble of starting one gang to the trouble of
starting the other.

It would be very different if the gangs have anything in common. Then
one would encourage the other much as the various boys of the same gang
encourage each other. He would have a lot more trouble. And this extra
trouble would be because of the relations between gangs, that is,
because of their "mutual inductance."

On the other hand suppose the gangs came from different parts of the
town and disliked each other. He wouldn't have nearly the trouble. Each
gang would be yelling at the other as they went along: "You'd better
beat it. He knows all right, all right, who broke that bush down by the
gate. Just wait till he catches you." They'd get out a little easier,
each in the hope the other crowd would catch it from the owner. There's
a case where their mutual relations, their mutual inductance, makes the
job easier.

That's true of coils with inductance. Suppose you wind two inductance
coils and connect them in series. If they are at right angles to each
other as in Fig. 46a they have no effect on each other. There is no
mutual inductance. But if they are parallel and wound the same way like
the coils of Fig. 46b they will act like a single coil of greater
inductance. If the coils are parallel but wound in opposite directions
as in Fig. 46c they will have less inductance because of their mutual
inductance. You can check these statements for yourself if you'll refer
back to Letter 10 and see what happens in the same way as I told you in
discussing Fig. 28.

[Illustration: Fig 46a]

[Illustration: Fig 46b]

If the coils are neither parallel nor at right angles there will be some
mutual inductance but not as much as if they were parallel. By turning
the coils we can get all the variations in mutual relations from the
case of Fig. 46b to that of Fig. 46c. That's what we arrange to do in a
variable inductance of the variometer type.

[Illustration: Fig 46c]

There is another way of varying the mutual inductance. We can make one
coil slide inside another. If it is way inside, the total inductance
which the two coils offer is either larger than the sum of what they can
offer separately or less, depending upon whether the windings are in the
same direction or opposite. As we pull the coil out the mutual effect
becomes less and finally when it is well outside the mutual inductance
is very small.

Now we have several methods of varying capacity and inductance and
therefore we are ready to vary the frequency of our audion oscillator;
that is, "tune" it, as we say. In my next letter I shall show you why we

Now for the rule which I promised. The frequency to which a circuit is
tuned depends upon the product of the number of mil-henries in the coil
and the number of microfarads in the condenser. Change the coil and the
condenser as much as you want but keep this product the same and the
frequency will be the same.

[Footnote 5: More accurately the number is 6,286,000,000,000.]




I want to tell you about receiving sets and their tuning. In the last
letter I told you what determines the frequency of oscillation of an
audion oscillator. It was the condenser and inductance which you studied
in connection with Fig. 36. That's what determines the frequency and
also what makes the oscillations. All the tube does is to keep them
going. Let's see why this is so.

[Illustration: Fig 47a]

Start first, as in Fig. 47a, with a very simple circuit of a battery and
a non-inductive resistance, that is, a wire wound like that of Fig. 40
in the previous letter, so that it has no inductance. The battery must
do work forcing electrons through that wire. It has the ability, or the
energy as we say.

[Illustration: Fig 47b]

Now connect a condenser to the battery as in Fig. 47b. The connecting
wires are very short; and so practically all the work which the battery
does is in storing electrons in the negative plate of the condenser and
robbing the positive plate. The battery displaces a certain number of
electrons in the waiting-rooms of the condenser. How many, depends upon
how hard it can push and pull, that is on its e. m. f., and upon how
much capacity the condenser has.

[Illustration: Fig 47c]

Remove the battery and connect the charged condenser to the resistance
as in Fig. 47c. The electrons rush home. They bump and jostle their way
along, heating the wire as they go. They have a certain amount of energy
or ability to do work because they are away from home and they use it
all up, bouncing along on their way. When once they are home they have
used up all the surplus energy which the battery gave them.

Try it again, but this time, as in Fig. 47d, connect the charged
condenser to a coil which has inductance. The electrons don't get
started as fast because of the inductance. But they keep going because
the electrons in the wire form the habit. The result is that about the
time enough electrons have got into plate 2 (which was positive), to
satisfy all its lonely protons, the electrons in the wire are streaming
along at a great rate. A lot of them keep going until they land on this
plate and so make it negative.

[Illustration: Fig 47d]

That's the same sort of thing that happens in the case of the inductance
and condenser in the oscillating audion circuit except for one important
fact. There is nothing to keep electrons going to the 2 plate except
this habit. And there are plenty of stay-at-home electrons to stop them
as they rush along. They bump and jostle, but some of them are stopped
or else diverted so that they go bumping around without getting any
nearer plate 2. Of course, they spend all their energy this way, getting
every one all stirred up and heating the wire.

Some of the energy which the electrons had when they were on plate 1 is
spent, therefore, and there aren't as many electrons getting to plate 2.
When they turn around and start back, as you know they do, the same
thing happens. The result is that each successive surge of electrons is
smaller than the preceding. Their energy is being wasted in heating the
wire. The stream of electrons gets smaller and smaller, and the voltage
of the condenser gets smaller and smaller, until by-and-by there isn't
any stream and the condenser is left uncharged. When that happens, we
say the oscillations have "damped out."

[Illustration: Fig 48]

That's one way of starting oscillations which damp out--to start with a
charged condenser and connect an inductance across it. There is another
way which leads us to some important ideas. Look at Fig. 48. There is an
inductance and a condenser. Near the coil is another coil which has a
battery and a key in circuit with it. The coils are our old friends of
Fig. 33 in Letter 10. Suppose we close the switch _S_. It starts a
current through the coil _ab_ which goes on steadily as soon as it
really gets going. While it is starting, however, it induces an electron
stream in coil _cd_. There is only a momentary or transient current
but it serves to charge the condenser and then events happen just as
they did in the case where we charged the condenser with a battery.

[Illustration: Fig 49]

Now take away this coil _ab_ with its battery and substitute the
oscillator of Fig. 36. What's going to happen? We have two circuits in
which oscillations can occur. See Fig. 49. One circuit is associated
with an audion and some batteries which keep supplying it with energy so
that its oscillations are continuous. The other circuit is near enough
to the first to be influenced by what happens in that circuit. We say it
is "coupled" to it, because whatever happens in the first circuit
induces an effect in the second circuit.

Suppose first that in each circuit the inductance and capacity have such
values as to produce oscillations of the same frequency. Then the moment
we start the oscillator we have the same effect in both circuits. Let me
draw the picture a little differently (Fig. 50) so that you can see this
more easily. I have merely made the coil _ab_ in two parts, one of
which can affect _cd_ in the oscillator and the other the coil
_L_ of the second circuit.

But suppose that the two circuits do not have the same natural
frequencies, that is the condenser and inductance in one circuit are so
large that it just naturally takes more time for an oscillation in that
circuit than in the other. It is like learning to dance. You know about
how well you and your partner would get along if you had one frequency
of oscillation and she had another. That's what happens in a case like

[Illustration: Fig 50]

If circuit _L-C_ takes longer for each oscillation than does
circuit _ab_ its electron stream is always working at cross
purposes with the electron stream in _ab_ which is trying to lead
it. Its electrons start off from one condenser plate to the other and
before they have much more than got started the stream in _ab_
tries to call them back to go in the other direction. It is practically
impossible under these conditions to get a stream of any size going in
circuit _L-C_. It is equally hard if _L-C_ has smaller capacity and
inductance than _ab_ so that it naturally oscillates faster.

I'll tell you exactly what it is like. Suppose you and your partner are
trying to dance without any piano or other source of music. She has one
tune running through her head and she dances to that, except as you drag
her around the floor. You are trying to follow another tune. As a couple
you have a difficult time going anywhere under these conditions. But it
would be all right if you both had the same tune.

If we want the electron stream in coil _ab_ to have a large guiding
effect on the stream in coil _L-C_ we must see that both circuits
have the same tune, that is the same natural frequency of oscillation.

[Illustration: Fig 51]

This can be shown very easily by a simple experiment. Suppose we set up
our circuit _L-C_ with an ammeter in it, so as to be able to tell
how large an electron stream is oscillating in that circuit. Let us also
make the condenser a variable one so that we can change the natural
frequency or tune of the circuit. Now let's see what happens to the
current as we vary this condenser, changing the capacity and thus
changing the tune of the circuit. If we use a variable plate condenser
it will have a scale on top graduated in degrees and we can note the
reading of the ammeter for each position of the movable plates. If we
do, we find one position of these plates, that is one setting,
corresponding to one value of capacity in the condenser, where the
current in the circuit is a maximum. This is the setting of the
condenser for which the circuit has the same tune or natural frequency
as the circuit _cd_. Sometimes we say that the circuits are now in
resonance. We also refer to the curve of values of current and condenser
positions as a "tuning curve." Such a curve is shown in Fig. 51.

[Illustration: Fig 52]

That's all there is to tuning--adjusting the capacity and inductance of
a circuit until it has the same natural frequency as some other circuit
with which we want it to work. We can either adjust the capacity as we
just did, or we can adjust the inductance. In that case we use a
variable inductance as in Fig. 52.

If we want to be able to tune to any of a large range of frequencies we
usually have to take out or put into the circuit a whole lot of
mil-henries at a time. When we do we get these mil-henries of inductance
from a coil which we call a "loading coil." That's why your friends add
a loading coil when they want to tune for the long wave-length stations,
that is, those with a low frequency.

When our circuit _L-C_ of Fig. 49 is tuned to the frequency of the
oscillator we get in it a maximum current. There is a maximum stream of
electrons, and hence a maximum number of them crowded first into one and
then into the other plate of the condenser. And so the condenser is
charged to a maximum voltage, first in one direction and then in the

[Illustration: Fig 53]

Now connect the circuit _L-C_ to the grid of an audion. If the
circuit is tuned we'll have the maximum possible voltage applied between
grid and filament. In the plate circuit we'll get an increase and then a
decrease of current. You know that will happen for I prepared you for
this moment by the last page of my ninth letter. I'll tell you more
about that current in the plate circuit in a later letter. I am
connecting a telephone receiver in the plate circuit, and also a
condenser, the latter for a reason to be explained later. The
combination appears then as in Fig. 53. That figure shows a C-W
transmitter and an audion detector. This is the sort of a detector we
would use for radio-telephony, but the transmitter is the sort we would
use for radio-telegraphy. We shall make some changes in them later.

[Illustration: Fig 54]

Whenever we start the oscillating current in the transmitter we get an
effect in the detector circuit, of which I'll tell you more later. For
the moment I am interested in showing you how the transmitter and the
detector may be separated by miles and still there will be an effect in
the detector circuit every time the key in the transmitter circuit is

This is how we do it. At the sending station, that is, wherever we
locate the transmitter, we make a condenser using the earth, or ground,
as one plate. We do the same thing at the receiving station where the
detector circuit is located. To these condensers we connect inductances
and these inductances we couple to our transmitter and receiver as shown
in Fig. 54. The upper plate of the condenser in each case is a few
horizontal wires. The lower plate is the moist earth of the ground and
we arrange to get in contact with that in various ways. One of the
simplest methods is to connect to the water pipes of the city

Now we have our radio transmitting-station and a station for receiving
its signals. You remember we can make dots and dashes by the key or
switch in the oscillator circuit. When we depress the key we start the
oscillator going. That sets up oscillations in the circuit with the
inductance and the capacity formed by the antenna. If we want a
real-sized stream of electrons up and down this antenna lead (the
vertical wire), we must tune that circuit. That is why I have shown a
variable inductance in the circuit of the transmitting antenna.

What happens when these electrons surge back and forth between the
horizontal wires and the ground, I don't know. I do know, however, that
if we tune the antenna circuit at the receiving station there will be a
small stream of electrons surging back and forth in that circuit.

Usually scientists explain what happens by saying that the transmitting
station sends out waves in the ether and that these waves are received
by the antenna system at the distant station. Wherever you put up a
receiving station you will get the effect. It will be much smaller,
however, the farther the two stations are apart.

I am not going to tell you anything about wave motion in the ether
because I don't believe we know enough about the ether to try to
explain, but I shall tell you what we mean by "wave length."

Somehow energy, the ability to do work, travels out from the sending
antenna in all directions. Wherever you put up your receiving station
you get more or less of this energy. Of course, energy is being sent out
only while the key is depressed and the oscillator going. This energy
travels just as fast as light, that is at the enormous speed of 186,000
miles a second. If you use meters instead of miles the speed is
300,000,000 meters a second.

Now, how far will the energy which is sent out from the antenna travel
during the time it takes for one oscillation of the current in the
antenna? Suppose the current is oscillating one million times a second.
Then it takes one-millionth of a second for one oscillation. In that
time the energy will have traveled away from the antenna one-millionth
part of the distance it will travel in a whole second. That is
one-millionth of 300 million meters or 300 meters.

The distance which energy will go in the time taken by one oscillation
of the source of that energy is the wave length. In the case just given
that distance is 300 meters. The wave length, then, of 300 meters
corresponds to a frequency of one million. In fact if we divide 300
million meters by the frequency we get the wave length, and that's the
same rule as I gave you in the last letter.

In further letters I'll tell you how the audion works as a detector and
how we connect a telephone transmitter to the oscillator to make it send
out energy with a speech significance instead of a mere dot and dash
significance, or signal significance. We shall have to learn quite a
little about the telephone itself and about the human voice.




In the last letter we got far enough to sketch, in Fig. 54, a radio
transmitting station and a receiving station. We should never, however,
use just this combination because the transmitting station is intended
to send telegraph signals and the receiving station is best suited to
receiving telephonic transmission. But let us see what happens.

[Illustration: Fig 54]

When the key in the plate circuit of the audion at the sending station
is depressed an alternating current is started. This induces an
alternating current in the neighboring antenna circuit. If this antenna
circuit, which is formed by a coil and a condenser, is tuned to the
frequency of oscillations which are being produced in the audion circuit
then there is a maximum current induced in the antenna.

As soon as this starts the antenna starts to send out energy in all
directions, or "radiate" energy as we say. How this energy, or ability
to do work, gets across space we don't know. However it may be, it does
get to the receiving station. It only takes a small fraction of a second
before the antenna at the receiving station starts to receive energy,
because energy travels at the rate of 186,000 miles a second.

The energy which is received does its work in making the electrons in
that antenna oscillate back and forth. If the receiving antenna is tuned
to the frequency which the sending station is producing, then the
electrons in the receiving antenna oscillate back and forth most widely
and there is a maximum current in this circuit.

The oscillations of the electrons in the receiving antenna induce
similar oscillations in the tuned circuit which is coupled to it. This
circuit also is tuned to the frequency which the distant oscillator is
producing and so in it we have the maximum oscillation of the electrons.
The condenser in that circuit charges and discharges alternately.

The grid of the receiving audion always has the same voltage as the
condenser to which it is connected and so it becomes alternately
positive and negative. This state of affairs starts almost as soon as
the key at the sending station is depressed and continues as long as it
is held down.

Now what happens inside the audion? As the grid becomes more and more
positive the current in the plate circuit increases. When the grid no
longer grows more positive but rather becomes less and less positive the
current in the plate circuit decreases. As the grid becomes of zero
voltage and then negative, that is as the grid "reverses its polarity,"
the plate current continues to decrease. When the grid stops growing
more negative and starts to become less so, the plate current stops
decreasing and starts to increase.

All this you know, for you have followed through such a cycle of changes
before. You know also how we can use the audion characteristic to tell
us what sort of changes take place in the plate current when the grid
voltage changes. The plate current increases and decreases alternately,
becoming greater and less than it would be if the grid were not
interfering. These variations in its intensity take place very rapidly,
that is with whatever high frequency the sending station operates. What
happens to the plate current on the average?

The plate current, you remember, is a stream of electrons from the
filament to the plate (on the inside of the tube), and from the plate
back through the B-battery to the filament (on the outside of the tube).
The grid alternately assists and opposes that stream. When it assists,
the electrons in the plate circuit are moved at a faster rate. When the
grid becomes negative and opposes the plate the stream of electrons is
at a slower rate. The stream is always going in the same direction but
it varies in its rate depending upon the changes in grid potential.

[Illustration: Fig 55]

When the grid is positive, that is for half a cycle of the alternating
grid-voltage, the stream is larger than it would be if the plate current
depended only on the B-battery. For the other half of a cycle it is
less. The question I am raising is this: Do more electrons move around
the plate circuit if there is a signal coming in than when there is no
incoming signal? To answer this we must look at the audion
characteristic of our particular tube and this characteristic must have
been taken with the same B-battery as we use when we try to receive the

There are just three possible answers to this question. The first answer
is: "No, there is a smaller number of electrons passing through the
plate circuit each second if the grid is being affected by an incoming
signal." The second is: "The signal doesn't make any difference in the
total number of electrons which move each second from filament to
plate." And the third answer is: "Yes, there is a greater total number
each second."

[Illustration: Fig 56]

Any one of the three answers may be right. It all depends on the
characteristic of the tube as we are operating it, and that depends not
only upon the type and design of tube but also upon what voltages we are
using in our batteries. Suppose the variations in the voltage of the
grid are as represented in Fig. 55, and that the characteristic of the
tube is as shown in the same figure. Then obviously the first answer is
correct. You can see for yourself that when the grid becomes positive
the current in the plate circuit can't increase much anyway. For the
other half of the cycle, that is, while the grid is negative, the
current in the plate is very much decreased. The decrease in one
half-cycle is larger than the increase during the other half-cycle, so
that on the average the current is less when the signal is coming in.
The dotted line shows the average current.

Suppose that we take the same tube and use a B-battery of lower voltage.
The characteristic will have the same shape but there will not be as
much current unless the grid helps, so that the characteristic will be
like that of Fig. 56. This characteristic crosses the axis of zero volts
at a smaller number of mil-amperes than does the other because the
B-batteries can't pull as hard as they did in the other case.

[Illustration: Fig 57]

You can see the result. When the grid becomes positive it helps and
increases the plate current. When it becomes negative it opposes and
decreases the plate current. But the increase just balances the
decrease, so that on the average the current is unchanged, as shown by
the dotted line.

On the other hand, if we use a still smaller voltage of B-battery we get
a characteristic which shows a still smaller current when the grid is at
zero potential. For this case, as shown in Fig. 57, the plate current is
larger on the average when there is an incoming signal.

If we want to know whether or not there is any incoming signal we will
not use the tube in the second condition, that of Fig. 56, because it
won't tell us anything. On the other hand why use the tube under the
first conditions where we need a large plate battery? If we can get the
same result, that is an indication when the other station is signalling,
by using a small battery let's do it that way for batteries cost money.
For that reason we shall confine ourselves to the study of what takes
place under the conditions of Fig. 57.

We now know that when a signal is being sent by the distant station the
current in the plate circuit of our audion at the receiving station is
greater, on the average. We are ready to see what effect this has on the
telephone receiver. And to do this requires a little study of how the
telephone receiver works and why.

[Illustration: Fig 58]

I shall not stop now to tell you much about the telephone receiver for
it deserves a whole letter all to itself. You know that a magnet
attracts iron. Suppose you wind a coil of insulated wire around a bar
magnet or put the magnet inside such a coil as in Fig. 58. Send a stream
of electrons through the turns of the coil--a steady stream such as
comes from the battery shown in the figure. The strength of the magnet
is altered. For one direction of the electron stream through the coil
the magnet is stronger. For the opposite direction of current the magnet
will be weaker.

[Illustration: Fig 59]

Fig. 59 shows a simple design of telephone receiver. It is formed by a
bar magnet, a coil about it through which a current can flow, and a thin
disc of iron. The iron disc, or diaphragm, is held at its edges so that
it cannot move as a whole toward the magnet. The center can move,
however, and so the diaphragm is bowed out in the form shown in the
smaller sketch.

Now connect a battery to the receiver winding and allow a steady stream
of electrons to flow. The magnet will be either strengthened or
weakened. Suppose the stream of electrons is in the direction to make it
stronger--I'll give you the rule later. Then the diaphragm is bowed out
still more. If we open the battery circuit and so stop the stream of
electrons the diaphragm will fly back to its original position, for it
is elastic. The effect is very much that of pushing in the bottom of a
tin pan and letting it fly back when you remove your hand.

Next reverse the battery. The magnet does not pull as hard as it would
if there were no current. The diaphragm is therefore not bowed out so

Suppose that instead of reversing the current by reversing the battery
we arrange to send an alternating current through the coil. That will
have the same effect. For one direction of current flow, the diaphragm
is attracted still more by the magnet but for the other direction it is
not attracted as much. The result is that the center of the diaphragm
moves back and forth during one complete cycle of the alternating
current in the coil.

The diaphragm vibrates back and forth in tune with the alternating
current in the receiver winding. As it moves away from the magnet it
pushes ahead of it the neighboring molecules of air. These molecules
then crowd and push the molecules of air which are just a little further
away from the diaphragm. These in turn push against those beyond them
and so a push or shove is sent out by the diaphragm from molecule to
molecule until perhaps it reaches your ear. When the molecules of air
next your ear receive the push they in turn push against your eardrum.

In the meantime what has happened? The current in the telephone receiver
has reversed its direction. The diaphragm is now pulled toward the
magnet and the adjacent molecules of air have even more room than they
had before. So they stop crowding each other and follow the diaphragm in
the other direction. The molecules of air just beyond these, on the way
toward your ear, need crowd no longer and they also move back. Of
course, they go even farther than their old positions for there is now
more room on the other side. That same thing happens all along the line
until the air molecules next your ear start back and give your eardrum a
chance to expand outward. As they move away they make a little vacuum
there and the eardrum puffs out.

That goes on over and over again just as often as the alternating
current passes through one cycle of values. And you, unless you are
thinking particularly of the scientific explanations, say that you "hear
a musical note." As a matter of fact if we increase the frequency of the
alternating current you will say that the "pitch" of the note has been
increased or that you hear a note higher in the musical scale.

If we started with a very low-frequency alternating current, say one of
fifteen or twenty cycles per second, you wouldn't say you heard a note
at all. You would hear a sort of a rumble. If we should gradually
increase the frequency of the alternating current you would find that
about sixty or perhaps a hundred cycles a second would give you the
impression of a musical note. As the frequency is made still larger you
have merely the impression of a higher-pitched note until we get up into
the thousands of cycles a second. Then, perhaps about twenty-thousand
cycles a second, you find you hear only a little sound like wind or like
steam escaping slowly from a jet or through a leak. A few thousand
cycles more each second and you don't hear anything at all.

You know that for radio-transmitting stations we use audion oscillators
which are producing alternating currents with frequencies of several
hundred-thousand cycles per second. It certainly wouldn't do any good to
connect a telephone receiver in the antenna circuit at the receiving
station as in Fig. 60. We couldn't hear so high pitched a note.

[Illustration: Fig 60]

Even if we could, there are several reasons why the telephone receiver
wouldn't work at such high frequencies. The first is that the diaphragm
can't be moved so fast. It has some inertia, you know, that is, some
unwillingness to get started. If you try to start it in one direction
and, before you really get it going, change your mind and try to make it
go in the other direction, it simply isn't going to go at all. So even
if there is an alternating current in the coil around the magnet there
will not be any corresponding vibration of the diaphragm if the
frequency is very high, certainly not if it is above about 20,000 cycles
a second.

The other reason is that there will only be a very feeble current in the
coil anyway, no matter what you do, if the frequency is high. You
remember that the electrons in a coil are sort of banded together and
each has an effect on all the others which can move in parallel paths.
The result is that they have a great unwillingness to get started and an
equal unwillingness to stop. Their unwillingness is much more than if
the wire was long and straight. It is also made very much greater by the
presence of the iron core. An alternating e. m. f. of high frequency
hardly gets the electrons started at all before it's time to get them
going in the opposite direction. There is very little movement to the
electrons and hence only a very small current in the coil if the
frequency is high.

If you want a rule for it you can remember that the higher the frequency
of an alternating e. m. f. the smaller the electron stream which it can
set oscillating in a given coil. Of course, we might make the e. m. f.
stronger, that is pull and shove the electrons harder, but unless the
coil has a very small inductance or unless the frequency is very low we
should have to use an e. m. f. of enormous strength to get any
appreciable current.

Condensers are just the other way in their action. If there is a
condenser in a circuit, where an alternating e. m. f. is active, there
is lots of trouble if the frequency is low. If, however, the frequency
is high the same-sized current can be maintained by a smaller e. m. f.
than if the frequency is low. You see, when the frequency is high the
electrons hardly get into the waiting-room of the condenser before it is
time for them to turn around and go toward the other room. Unless there
is a large current, there are not enough electrons crowded together in
the waiting-room to push back very hard on the next one to be sent along
by the e. m. f. Because the electrons do not push back very hard a small
e. m. f. can drive them back and forth.

Ordinarily we say that a condenser impedes an alternating current less
and less the higher is the frequency of the current. And as to
inductances, we say that an inductance impedes an alternating current
more and more the higher is the frequency.

Now we are ready to study the receiving circuit of Fig. 54. I showed you
in Fig. 57 how the current through, the tube will vary as time goes on.
It increases and decreases with the frequency of the current in the
antenna of the distant transmitting station. We have a picture, or
graph, as we say, of how this plate current varies. It will be necessary
to study that carefully and to resolve it into its components, that is
to separate it into parts, which, added together again will give the
whole. To show you what I mean I am going to treat first a very simple
case involving money.

Suppose a boy was started by his father with 50 cents of spending money.
He spends that and runs 50 cents in debt. The next day his father gives
him a dollar. Half of this he has to spend to pay up his yesterday's
indebtedness. This he does at once and that leaves him 50 cents ahead.
But again he buys something for a dollar and so runs 50 cents in debt.
Day after day this cycle is repeated. We can show what happens by the
curve of Fig. 61a.

[Illustration: Fig 61a]

On the other hand, suppose he already had 60 cents which, he was saving
for some special purpose. This he doesn't touch, preferring to run into
debt each day and to pay up the next, as shown in Fig. 61a. Then we
would represent the story of this 60 cents by the graph of Fig. 61b.

[Illustration: Fig 61b]

Now suppose that instead of going in debt each day he uses part of this
60 cents. Each day after the first his father gives him a dollar, just
as before. He starts then with 60 cents as shown in Fig. 61c, increases
in wealth to $1.10, then spends $1.00, bringing his funds down to 10
cents. Then he receives $1.00 from his father and the process is
repeated cyclically.

[Illustration: Fig 61c]

If you saw the graph of Fig. 61c you would be able to say that, whatever
he actually did, the effect was the same as if he had two pockets, in
one of which he kept 60 cents all the time as shown in Fig. 61b. In his
other pocket he either had money or he was in debt as shown in Fig. 61a.
If you did that you would be resolving the money changes of Fig. 61c
into the two components of Figs. 61a and b.

That is what I want you to do with the curve of Fig. 57 which I am
reproducing here, redrawn as Fig. 62a. You see it is really the result
of adding together the two curves of Figs. 62b and c, which are shown on
the following page.

[Illustration: Fig 62a]

We can think, therefore, of the current in the plate circuit as if it
were two currents added together, that is, two electron streams passing
through the same wire. One stream is steady and the other alternates.

[Illustration: Fig 62b]

Now look again at the diagram of our receiving set which I am
reproducing as Fig. 63. When the signal is incoming there flow in the
plate circuit two streams of electrons, one steady and of a value in
mil-amperes corresponding to that of the graph in Fig. 62b, and the
other alternating as shown in Fig. 62c.

The steady stream of electrons will have no more difficulty in getting
through the coiled wire of the receiver than it would through the same
amount of straight wire. On the other hand it cannot pass the gap of the

The alternating-current component can't get along in the coil because
its frequency is so high that the coil impedes the motion of the
electrons so much as practically to stop them. On the other hand these
electrons can easily run into the waiting-room offered by the condenser
and then run out again as soon as it is time.

[Illustration: Fig 62c]

When the current in the plate circuit is large all the electrons which
aren't needed for the steady stream through the telephone receiver run
into one plate of the condenser. Of course, at that same instant an
equal number leave the other plate and start off toward the B-battery
and the filament. An instant later, when the current in the plate
circuit is small, electrons start to come out of the plate and to join
the stream through the receiver so that this stream is kept steady.

[Illustration: Fig 63]

This steady stream of electrons, which is passing through the receiver
winding, is larger than it would be if there was no incoming radio
signal. The result is a stronger pull on the diaphragm of the receiver.
The moment the signal starts this diaphragm is pulled over toward the
magnet and it stays pulled over as long as the signal lasts. When the
signal ceases it flies back. We would hear then a click when the signal
started and another when it stopped.

If we wanted to distinguish dots from dashes this wouldn't be at all
satisfactory. So in the next letter I'll show you what sort of changes
we can make in the apparatus. To understand what effect these changes
will have you need, however, to understand pretty well most of this




Before we start on the important subject matter of this letter let us
make a short review of the preceding two letters.

An oscillating audion at the transmitting station produces an effect on
the plate current of the detector audion at the receiving station. There
is impressed upon the grid of the detector an alternating e. m. f. which
has the same frequency as the alternating current which is being
produced at the sending station. While this e. m. f. is active, and of
course it is active only while the sending key is held down, there is
more current through the winding of the telephone receiver and its
diaphragm is consequently pulled closer to its magnet.

What will happen if the e. m. f. which is active on the grid of the
detector is made stronger or weaker? The pull on the receiver diaphragm
will be stronger or weaker and the diaphragm will have to move
accordingly. If the pull is weaker the elasticity of the iron will move
the diaphragm away from the magnet, but if the pull is stronger the
diaphragm will be moved toward the magnet.

Every time the diaphragm moves it affects the air in the immediate
neighborhood of itself and that air in turn affects the air farther away
and so the ear of the listener. Therefore if there are changes in the
intensity or strength of the incoming signal there are going to be
corresponding motions of the receiver diaphragm. And something to
listen, too, if these changes are frequent enough but not so frequent
that the receiver diaphragm has difficulty in following them.

There are many ways of affecting the strength of the incoming signal.
Suppose, for example, that we arrange to decrease the current in the
antenna of the transmitting station. That will mean a weaker signal and
a smaller increase in current through the winding of the telephone
receiver at the other station. On the other hand if the signal strength
is increased there is more current in this winding.

[Illustration: Fig 64]

Suppose we connect a fine wire in the antenna circuit as in Fig. 64 and
have a sliding contact as shown. Suppose that when we depress the switch
in the oscillator circuit and so start the oscillations that the sliding
contact is at _o_ as shown. Corresponding to that strength of
signal there is a certain value of current through the receiver winding
at the other station. Now let us move the slider, first to _a_ and
then back to _b_ and so on, back and forth. You see what will
happen. We alternately make the current in the antenna larger and
smaller than it originally was. When the slider is at _b_ there is
more of the fine wire in series with the antenna, hence more resistance
to the oscillations of the electrons, and hence a smaller oscillating
stream of electrons. That means a weaker outgoing signal. When the
slider is at _a_ there is less resistance in the antenna circuit
and a larger alternating current.

[Illustration: Fig 65]

[Illustration: Fig 66]

A picture of what happens would be like that of Fig. 65. The signal
varies in intensity, therefore, becoming larger and smaller alternately.
That means the voltage impressed on the grid of the detector is
alternately larger and smaller. And hence the stream of electrons
through the winding of the telephone receiver is alternately larger and
smaller. And that means that the diaphragm moves back and forth in just
the time it takes to move the slider back and forth.

Instead of the slider we might use a little cup almost full of grains of
carbon. The carbon grains lie between two flat discs of carbon. One of
these discs is held fixed. The other is connected to the center of a
thin diaphragm of steel and moves back and forth as this diaphragm is
moved. The whole thing makes a telephone transmitter such as you have
often talked to.

[Illustration: Fig 67a]

Wires connect to the carbon discs as shown in Fig. 66. A stream of
electrons can flow through the wires and from grain to grain through the
"carbon button," as we call it. The electrons have less difficulty if
the grains are compressed, that is the button then offers less
resistance to the flow of current. If the diaphragm moves back, allowing
the grains to have more room, the electron stream is smaller and we say
the button is offering more resistance to the current.

[Illustration: Fig 67b]

You can see what happens. Suppose some one talks into the transmitter
and makes its diaphragm go back and forth as shown in Fig. 67a. Then the
current in the antenna varies, being greater or less, depending upon
whether the button offers less or more resistance. The corresponding
variations in the antenna current are shown in Fig. 67b.

In the antenna at the receiving station there are corresponding
variations in the strength of the signal and hence corresponding
variations in the strength of the current through the telephone
receiver. I shall show graphically what happens in Fig. 68. You see that
the telephone receiver diaphragm does just the same motions as does the
transmitter diaphragm. That means that the molecules of air near the
receiver diaphragm are going through just the same kind of motions as
are those near the transmitter diaphragm. When these air molecules
affect your eardrum you hear just what you would have heard if you had
been right there beside the transmitter.

That's one way of making a radio-telephone. It is not a very efficient
method but it has been used in the past. Before we look at any of the
more recent methods we can draw some general ideas from this method and
learn some words that are used almost always in speaking of

In any system of radio-telephony you will always find that there is
produced at the transmitting station a high-frequency alternating
current and that this current flows in a tuned circuit one part of which
is the condenser formed by the antenna and the ground (or something
which acts like a ground). This high-frequency current, or
radio-current, as we usually say, is varied in its strength. It is
varied in conformity with the human voice. If the human voice speaking
into the transmitter is low pitched there are slow variations in the
intensity of the radio current. If the voice is high pitched there are
more rapid variations in the strength of the radio-frequency current.
That is why we say the radio-current is "modulated" by the human voice.

[Illustration: Fig 68]

The signal which radiates out from the transmitting antenna carries all
the little variations in pitch and loudness of the human voice. When
this signal reaches the distant antenna it establishes in that antenna
circuit a current of high frequency which has just the same variations
as did the current in the antenna at the sending station. The human
voice isn't there. It is not transmitted. It did its work at the sending
station by modulating the radio-signal, "modulating the carrier
current," as we sometimes say. But there is speech significance hidden
in the variations in strength of the received signal.

If a telephone-receiver diaphragm can be made to vibrate in accordance
with the variations in signal intensity then the air adjacent to that
diaphragm will be set into vibration and these vibrations will be just
like those which the human voice set up in the air molecules near the
mouth of the speaker. All the different systems of receiving
radio-telephone signals are merely different methods of getting a
current which will affect the telephone receiver in conformity with the
variations in signal strength. Getting such a current is called
"detecting." There are many different kinds of detectors but the vacuum
tube is much to be preferred.

The cheapest detector, but not the most sensitive, is the crystal. If
you understand how the audion works as a detector you will have no
difficulty in understanding the crystal detector.

The crystal detector consists of some mineral crystal and a fine-wire
point, usually platinum. Crystals are peculiar things. Like everything
else they are made of molecules and these molecules of atoms. The atoms
are made of electrons grouped around nuclei which, in turn, are formed
by close groupings of protons and electrons. The great difference
between crystals and substances which are not crystalline, that is,
substances which don't have a special natural shape, is this: In
crystals the molecules and atoms are all arranged in some orderly
manner. In other substances, substances without special form, amorphous
substances, as we call them, the molecules are just grouped together in
a haphazard way.

[Illustration: Fig 69]

For some crystals we know very closely indeed how their molecules or
rather their individual atoms are arranged. Sometime you may wish to
read how this was found out by the use of X-rays.[6] Take the crystal of
common salt for example. That is well known. Each molecule of salt is
formed by an atom of sodium and one of chlorine. In a crystal of salt
the molecules are grouped together so that a sodium atom always has
chlorine atoms on every side of it, and the other way around, of course.

Suppose you took a lot of wood dumb-bells and painted one of the balls
of each dumb-bell black to stand for a sodium atom, leaving the other
unpainted to stand for a chlorine atom. Now try to pile them up so that
above and below each black ball, to the right and left of it, and also
in front and behind it, there shall be a white ball. The pile which you
would probably get would look like that of Fig. 69. I have omitted the
gripping part of each dumbell because I don't believe it is there. In my
picture each circle represents the nucleus of an atom. I haven't
attempted to show the planetary electrons. Other crystals have more
complex arrangements for piling up their molecules.

Now suppose we put two different kinds of substances close together,
that is, make contact between them. How their electrons will behave will
depend entirely upon what the atoms are and how they are piled up. Some
very curious effects can be obtained.

[Illustration: Fig 70]

The one which interests us at present is that across the contact points
of some combinations of substances it is easier to get a stream of
electrons to flow one way than the other. The contact doesn't have the
same resistance in the two directions. Usually also the resistance
depends upon what voltage we are applying to force the electron stream
across the point of contact.

The one way to find out is to take the voltage-current characteristic of
the combination. To do so we use the same general method as we did for
the audion. And when we get through we plot another curve and call it,
for example, a "platinum-galena characteristic." Fig. 70 shows the
set-up for making the measurements. There is a group of batteries
arranged so that we can vary the e. m. f. applied across the contact
point of the crystal and platinum. A voltmeter shows the value of this
e. m. f. and an ammeter tells the strength of the electron stream. Each
time we move the slider we get a new pair of values for volts and
amperes. As a matter of fact we don't get amperes or even mil-amperes;
we get millionths of an ampere or "microamperes," as we say. We can
plot the pairs of values which we measure and make a curve like that of
Fig. 71.

[Illustration: Fig 71]

When the voltage across the contact is reversed, of course, the current
reverses. Part of the curve looks something like the lower part of an
audion characteristic.

[Illustration: Fig 72]

Now connect this crystal in a receiving circuit as in Fig. 72. We use an
antenna just as we did for the audion and we tune the antenna circuit to
the frequency of the incoming signal. The receiving circuit is coupled
to the antenna circuit and is tuned to the same frequency. Whatever
voltage there may be across the condenser of this circuit is applied to
the crystal detector. We haven't put the telephone receiver in the
circuit yet. I want to wait until you have seen what the crystal does
when an alternating voltage is applied to it.

[Illustration: Fig 73]

We can draw a familiar form of sketch as in Fig. 73 to show how the
current in the crystal varies. You see that there flows through the
crystal a current very much like that of Fig. 62a. And you know that
such a current is really equivalent to two electron streams, one steady
and the other alternating. The crystal detector gives us much the same
sort of a current as does the vacuum tube detector of Fig. 54. The
current isn't anywhere near as large, however, for it is microamperes
instead of mil-amperes.

Our crystal detector produces the same results so far as giving us a
steady component of current to send through a telephone receiver. So we
can connect a receiver in series with the crystal as shown in Fig. 74.
Because the receiver would offer a large impedance to the high-frequency
current, that is, seriously impede and so reduce the high-frequency
current, we connect a condenser around the receiver.

[Illustration: Fig 74]

There is a simple crystal detector circuit. If the signal intensity
varies then the current which passes through the receiver will vary. If
these variations are caused by a human voice at the sending station the
crystal will permit one to hear from the telephone receiver what the
speaker is saying. That is just what the audion detector does very many
times better.

In the letter on how to experiment you'll find details as to the
construction of a crystal-detector set. Excellent instructions for an
inexpensive set are contained in Bull. No. 120 of the Bureau of
Standards. A copy can be obtained by sending ten cents to the
Commissioner of Public Documents, Washington, D. C.

[Footnote 6: Cf. "Within the Atom," Chapter X.]




The radio-telephone does not transmit the human voice. It reproduces
near the ears of the listener similar motions of the air molecules and
hence causes in the ears of the listener the same sensations of sound as
if he were listening directly to the speaker. This reproduction takes
place almost instantaneously so great is the speed with which the
electrical effects travel outward from the sending antenna. If you wish
to understand radio-telephony you must know something of the mechanism
by which the voice is produced and something of the peculiar or
characteristic properties of voice sounds.

[Illustration: Fig 75]

The human voice is produced by a sort of organ pipe. Imagine a long pipe
connected at one end to a pair of fire-bellows, and closed at the other
end by two stretched sheets of rubber. Fig. 75 is a sketch of what I
mean. Corresponding to the bellows there is the human diaphragm, the
muscular membrane separating the thorax and abdomen, which expands or
contracts as one breathes. Corresponding to the pipe is the windpipe.
Corresponding to the two stretched pieces of rubber are the vocal cords,
L and R, shown in cross section in Fig. 77. They are part of the larynx
and do not show in Fig. 76 (Pl. viii) which shows the wind pipe and an
outside view of the larynx.

[Illustration: Fig 77]

When the sides of the bellows are squeezed together the air molecules
within are crowded closer together and the air is compressed. The
greater the compression the greater, of course, is the pressure with
which the enclosed air seeks to escape. That it can do only by lifting
up, that is by blowing out, the two elastic strips which close the end
of the pipe.

The air pressure, therefore, rises until it is sufficient to push aside
the elastic membranes or vocal cords and thus to permit some of the air
to escape. It doesn't force the membranes far apart, just enough to let
some air out. But the moment some air has escaped there isn't so much
inside and the pressure is reduced just as in the case of an automobile
tire from which you let the air escape. What is the result? The
membranes fly back again and close the opening of the pipe. What got
out, then, was just a little puff of air.

The bellows are working all the while, however, and so the space
available for the remaining air soon again becomes so crowded with air
molecules that the pressure is again sufficient to open the membranes.
Another puff of air escapes.

This happens over and over again while one is speaking or singing.
Hundreds of times a second the vocal cords vibrate back and forth. The
frequency with which they do so determines the note or pitch of the
speaker's voice.

What determines the significance of the sounds which he utters? This is
a most interesting question and one deserving of much more time than I
propose to devote to it. To give you enough of an answer for your study
of radio-telephony I am going to tell you first about vibrating strings
for they are easier to picture than membranes like the vocal cords.

Suppose you have a stretched string, a piece of rubber band or a wire
will do. You pluck it, that is pull it to one side. When you let go it
flies back. Because it has inertia[7] it doesn't stop when it gets to
its old position but goes on through until it bows out almost as far on
the other side.

[Illustration: Pl. VII.--Photographs of Vibrating Strings.]

It took some work to pluck this string, not much perhaps; but all the
work which you did in deforming it, goes to the string and becomes its
energy, its ability to do work. This work it does in pushing the air
molecules ahead of it as it vibrates. In this way it uses up its energy
and so finally comes again to rest. Its vibrations "damp out," as we
say, that is die down. Each swing carries it a smaller distance away
from its original position. We say that the "amplitude," meaning the
size, of its vibration decreases. The frequency does not. It takes just
as long for a small-sized vibration as for the larger. Of course, for
the vibration of large amplitude the string must move faster but it has
to move farther so that the time required for a vibration is not

First the string crowds against each other the air molecules which are
in its way and so leads to crowding further away, just as fast as these
molecules can pass along the shove they are receiving. That takes place
at the rate of about 1100 feet a second. When the string swings back it
pushes away the molecules which are behind it and so lets those that
were being crowded follow it. You know that they will. Air molecules
will always go where there is the least crowding. Following the shove,
therefore, there is a chance for the molecules to move back and even to
occupy more room than they had originally.

The news of this travels out from the string just as fast as did the
news of the crowding. As fast as molecules are able they move back and
so make more room for their neighbors who are farther away; and these in
turn move back.

Do you want a picture of it? Imagine a great crowd of people and at the
center some one with authority. The crowd is the molecules of air and
the one with authority is one of the molecules of the string which has
energy. Whatever this molecule of the string says is repeated by each
member of the crowd to his neighbor next farther away. First the string
says: "Go back" and each molecule acts as soon as he gets the word. And
then the string says: "Come on" and each molecule of air obeys as soon
as the command reaches him. Over and over this happens, as many times a
second as the string makes complete vibrations.

[Illustration: Fig 78]

If we should make a picture of the various positions of one of these air
molecules much as we pictured "Brownie" in Letter 9 it would appear as
in Fig. 78a where the central line represents the ordinary position of
the molecule.

That's exactly the picture also of the successive positions of an
electron in a circuit which is "carrying an alternating current." First
it moves in one direction along the wire and then back in the opposite
direction. The electron next to it does the same thing almost
immediately for it does not take anywhere near as long for such an
effect to pass through a crowd of electrons. If we make the string
vibrate twice as fast, that is, have twice the frequency, the story of
an adjacent particle of air will be as in Fig. 78b. Unless we tighten
the string, however, we can't make it vibrate as a whole and do it twice
as fast. We can make it vibrate in two parts or even in more parts, as
shown in Fig. 79 of Pl. VII. When it vibrates as a whole, its frequency
is the lowest possible, the fundamental frequency as we say. When it
vibrates in two parts each part of the string makes twice as many
vibrations each second. So do the adjacent molecules of air and so does
the eardrum of a listener.

The result is that the listener hears a note of twice the frequency that
he did when the string was vibrating as a whole. He says he hears the
"octave" of the note he heard first. If the string vibrates in three
parts and gives a note of three times the frequency the listener hears a
note two octaves above the "fundamental note" of which the string is

It is entirely possible, however, for a string to vibrate simultaneously
in a number of ways and so to give not only its fundamental note but
several others at the same time. The photographs[8] of Fig. 80 of Pl.
VII illustrate this possibility.

What happens then to the molecules of air which are adjacent to the
vibrating string? They must perform quite complex vibrations for they
are called upon to move back and forth just as if there were several
strings all trying to push them with different frequencies of vibration.
Look again at the pictures, of Fig. 80 and see that each might just as
well be the picture of several strings placed close together, each
vibrating in a different way. Each of the strings has a different
frequency of vibration and a different maximum amplitude, that is,
greatest size of swing away from its straight position.

[Illustration: Fig 81]

Suppose instead of a single string acting upon the adjacent molecules we
had three strings. Suppose the first would make a nearby molecule move
as in Fig. 81A, the second as in Fig. 81B, and the third as in Fig. 81C.
It is quite evident that the molecule can satisfy all three if it will
vibrate as in Fig. 81D.

Now take it the other way around. Suppose we had a picture of the motion
of a molecule and that it was not simple like those shown in Fig. 78 but
was complex like that of Fig. 81D. We could say that this complex motion
was made up of three parts, that is, had three component simple motions,
each represented by one of the three other graphs of Fig. 81. That means
we can resolve any complex vibratory motion into component motions which
are simple.

It means more than that. It means that the vibrating string which makes
the neighboring molecules of air behave as shown in Fig. 81D is really
acting like three strings and is producing simultaneously three pure
musical notes.

Now suppose we had two different strings, say a piano string in the
piano and a violin string on its proper mounting. Suppose we played both
instruments and some musician told us they were in tune. What would he
mean? He would mean that both strings vibrated with the same fundamental

They differ, however, in the other notes which they produce at the same
time that they produce their fundamental notes. That is, they differ in
the frequencies and amplitudes of these other component vibrations or
"overtones" which are going on at the same time as their fundamental
vibrations. It is this difference which lets us tell at once which
instrument is being played.

That brings us to the main idea about musical sounds and about human
speech. The pitch of any complex sound is the pitch of its fundamental
or lowest sound; but the character of the complex sound depends upon all
the overtones or "harmonics" which are being produced and upon their
relative frequencies and amplitudes.

[Illustration: Fig 82]

The organ pipe which ends in the larynx produces a very complex sound. I
can't show you how complex but I'll show you in Fig. 82 the complicated
motion of an air molecule which is vibrating as the result of being near
an organ pipe. (Organ pipes differ--this is only one case.) You can see
that there are a large number of pure notes of various intensities, that
is, strengths, which go to make up the sound which a listener to this
organ pipe would hear. The note from the human pipe is much more

When one speaks there are little puffs of air escaping from his larynx.
The vocal cords vibrate as I explained. And the molecules of air near
the larynx are set into very complex vibrations. These transmit their
vibrations to other molecules until those in the mouth are reached. In
the mouth, however, something very important happens.

Did you ever sing or howl down a rain barrel or into a long pipe or
hallway and hear the sound? It sounds just about the same no matter who
does it. The reason is that the long column of air in the pipe or barrel
is set into vibration and vibrates according to its own ideas of how
fast to do it. It has a "natural frequency" of its own. If in your voice
there is a note of just that frequency it will respond beautifully. In
fact it "resonates," or sings back, when it hears this note.

The net result is that it emphasizes this note so much that you don't
hear any of the other component notes of your voice--all you hear is the
rain barrel. We say it reinforces one of the component notes of your
voice and makes it louder.

That same thing happens in the mouth cavity of a speaker. The size and
shape of the column of air in the mouth can be varied by the tongue and
lip positions and so there are many different possibilities of
resonance. Depending on lip and tongue, different frequencies of the
complex sound which comes from the larynx are reinforced. You can see
that for yourself from Fig. 83 which shows the tongue positions for
three different vowel sounds. You can see also from Fig. 84, which shows
the mouth positions for the different vowels, how the size and shape of
the mouth cavity is changed to give different sounds. These figures are
in Pl. VIII.

The pitch of the note need not change as every singer knows. You can try
that also for yourself by singing the vowel sound of "ahh" and then
changing the shape of your mouth so as to give the sound
"ah--aw--ow--ou." The pitch of the note will not change because the
fundamental stays the same. The speech significance of the sound,
however, changes completely because the mouth cavity resonates to
different ones of the higher notes which come from the larynx along with
the fundamental note.

Now you can see what is necessary for telephonic transmission. Each and
every component note which enters into human speech must be transmitted
and accurately reproduced by the receiver. More than that, all the
proportions must be kept just the same as in the original spoken sound.
We usually say that there must be reproduced in the air at the receiver
exactly the same "wave form" as is present in the air at the
transmitter. If that isn't done the speech won't be natural and one
cannot recognize voices although he may understand pretty well. If there
is too much "distortion" of the wave form, that is if the relative
intensities of the component notes of the voice are too much altered,
then there may even be a loss of intelligibility so that the listener
cannot understand what is being said.

What particular notes are in the human voice depends partly on the
person who is speaking. You know that the fundamental of a bass voice is
lower than that of a soprano. Besides the fundamental, however, there
are a lot of higher notes always present. This is particularly true when
the spoken sound is a consonant, like "s" or "f" or "v." The particular
notes, which are present and are important, depend upon what sound one
is saying.

Usually, however, we find that if we can transmit and reproduce exactly
all the notes which lie between a frequency of about 200 cycles a second
and one of about 2000 cycles a second the reproduced speech will be
quite natural and very intelligible. For singing and for transmitting
instrumental music it is necessary to transmit and reproduce still
higher notes.

What you will have to look out for, therefore, in a receiving set is
that it does not cut out some of the high notes which are necessary to
give the sound its naturalness. You will also have to make sure that
your apparatus does not distort, that is, does not receive and reproduce
some notes or "voice frequencies" more efficiently than it does some
others which are equally necessary. For that reason when you buy a
transformer or a telephone receiver it is well to ask for a
characteristic curve of the apparatus which will show how the action
varies as the frequency of the current is varied. The action or response
should, of course, be practically the same at all the frequencies within
the necessary part of the voice range.

[Footnote 7: Cf. Chap. VI of "The Realities of Modern Science."]

[Footnote 8: My thanks are due to Professor D. C. Miller and to the
Macmillan Company for permission to reproduce Figs. 79 to 83 inclusive
from that interesting book, "The Science of Musical Sounds."]




You remember the audion characteristics which I used in Figs. 55, 56 and
57 of Letter 14 to show you how an incoming signal will affect the
current in the plate circuit. Look again at these figures and you will
see that these characteristics all had the same general shape but that
they differed in their positions with reference to the "main streets" of
"zero volts" on the grid and "zero mil-amperes" in the plate circuit.
Changing the voltage of the B-battery in the plate circuit changed the
position of the characteristic. We might say that changing the B-battery
shifted the curve with reference to the axis of zero volts on the grid.

[Illustration: Fig 56]

[Illustration: Fig 63]

In the case of the three characteristics which we are discussing the
shift was made by changing the B-battery. Increasing B-voltage shifts
characteristic to the left. It is possible, however, to produce such a
shift by using a C-battery, that is, a battery in the grid circuit,
which makes the grid permanently negative (or positive, depending upon
how it is connected). This battery either helps or hinders the plate
battery, and because of the strategic position of the grid right near
the filament one volt applied to the grid produces as large an effect as
would several volts in the plate battery. Usually, therefore, we arrange
to shift the characteristic by using a C-battery.

[Illustration: Fig 85]

Suppose for example that we had an audion in the receiving circuit of
Fig. 63 and that its characteristic under these conditions is given by
Fig. 56. I've redrawn the figures to save your turning back. The audion
will not act as a detector because an incoming signal will not change
the average value of the current in the plate circuit. If, however, we
connect a C-battery so as to make the grid negative, we can shift this
characteristic so that the incoming signal will be detected. We have
only to make the grid sufficiently negative to reduce the plate current
to the value shown by the line _oa_ in Fig. 85. Then the signal
will be detected because, while it makes the plate current alternately
larger and smaller than this value _oa_, it will result, on the
average, in a higher value of the plate current.

[Illustration: Fig 86]

You see that what we have done is to arrange the point on the audion
characteristic about which the tube is to work by properly choosing the
value of the grid voltage _E_{C}_.

There is an important method of using an audion for a detector where we
arrange to have the grid voltage change steadily, getting more and more
negative all the time the signal is coming in. Before I tell how it is
done I want to show you what will happen.

Suppose we start with an audion detector, for which the characteristic
is that of Fig. 56, but arranged as in Fig. 86 to give the grid any
potential which we wish. The batteries and slide wire resistance which
are connected in the grid circuit are already familiar to you.

When the slider is set as shown in Fig. 86 the grid is at zero potential
and we are at the point 1 of the characteristic shown in Fig. 87. Now
imagine an incoming signal, as shown in that same figure, but suppose
that as soon as the signal has stopped making the grid positive we shift
the slider a little so that the C-battery makes the grid slightly
negative. We have shifted the point on the characteristic about which
the tube is being worked by the incoming signal from point 1 to point 2.

[Illustration: Fig 87]

Every time the incoming signal makes one complete cycle of changes we
shift the slider a little further and make the grid permanently more
negative. You can see what happens. As the grid becomes more negative
the current in the plate circuit decreases on the average. Finally, of
course, the grid will become so negative that the current in the plate
circuit will be reduced to zero. Under these conditions an incoming
signal finally makes a large change in the plate current and hence in
the current through the telephone.

The method of shifting a slider along, every time the incoming signal
makes a complete cycle, is impossible to accomplish by hand if the
frequency of the signal is high. It can be done automatically, however,
no matter how high the frequency if we use a condenser in the grid
circuit as shown in Fig. 88.

[Illustration: Fig 88]

When the incoming signal starts a stream of electrons through the coil
_L_ of Fig. 88 and draws them away from plate 1 of the condenser
_C_ it is also drawing electrons away from the 1 plate of the
condenser _C_{g}_ which is in series with the grid. As electrons
leave plate 1 of this condenser others rush away from the grid and enter
plate 2. This means that the grid doesn't have its ordinary number of
electrons and so is positive.

If the grid is positive it will be pleased to get electrons; and it can
do so at once, for there are lots of electrons streaming past it on
their way to the plate. While the grid is positive, therefore, there is
a stream of electrons to it from the filament. Fig. 89 shows this

All this takes place during the first half-cycle of the incoming signal.
During the next half-cycle electrons are sent into plate 1 of the
condenser _C_ and also into plate 1 of the grid condenser
_C_{g}_. As electrons are forced into plate 1 of the grid condenser
those in plate 2 of that condenser have to leave and go back to the grid
where they came from. That is all right, but while they were away the
grid got some electrons from the filament to take their places. The
result is that the grid has now too many electrons, that is, it is
negatively charged.

[Illustration: Fig 89]

An instant later the signal e. m. f. reverses and calls electrons away
from plate 1 of the grid condenser. Again electrons from the grid rush
into plate 2 and again the grid is left without its proper number and so
is positive. Again it receives electrons from the filament. The result
is still more electrons in the part of the grid circuit which is formed
by the grid, the plate 2 of the grid condenser and the connecting wire.
These electrons can't get across the gap of the condenser _C_{g}_
and they can't go back to the filament any other way. So there they are,
trapped. Finally there are so many of these trapped electrons that the
grid is so negative all the time as almost entirely to oppose the
efforts of the plate to draw electrons away from the filament.

[Illustration: Pl. VIII.--To Illustrate the Mechanism for the Production
of the Human Voice.]

Then the plate current is reduced practically to zero.

That's the way to arrange an audion so that the incoming signal makes
the largest possible change in plate current. We can tell if there is an
incoming signal because it will "block" the tube, as we say. The
plate-circuit current will be changed from its ordinary value to almost
zero in the short time it takes for a few cycles of the incoming signal.

We can detect one signal that way, but only one because the first signal
makes the grid permanently negative and blocks the tube so that there
isn't any current in the plate circuit and can't be any. If we want to
put the tube in condition to receive another signal we must allow these
electrons, which originally came from the filament, to get out of their
trapped position and go back to the filament.

[Illustration: Fig 90]

To do so we connect a very fine wire between plates 1 and 2 of the grid
condenser. We call that wire a "grid-condenser leak" because it lets the
electrons slip around past the gap. By using a very high resistance, we
can make it so hard for the electrons to get around the gap that not
many will do so while the signal is coming in. In that case we can leave
the leak permanently across the condenser as shown in Fig. 90. Of
course, the leak must offer so easy a path for the electrons that all
the trapped electrons can get home between one incoming signal and the

One way of making a high resistance like this is to draw a heavy pencil
line on a piece of paper, or better a line with India ink, that is ink
made of fine ground particles of carbon. The leak should have a very
high resistance, usually one or two million ohms if the condenser is
about 0.002 microfarad. If it has a million ohms we say it has a
"megohm" of resistance.

This method of detecting with a leaky grid-condenser and an audion is
very efficient so far as telling the listener whether or not a signal is
coming into his set. It is widely used in receiving radio-telephone
signals although it is best adapted to receiving the telegraph signals
from a spark set.

I don't propose to stop to tell you how a spark-set transmitter works.
It is sufficient to say that when the key is depressed the set sends out
radio signals at the rate usually of 1000 signals a second. Every time a
signal reaches the receiving station the current in the telephone
receiver is sudden reduced; and in the time between signals the leak
across the grid condenser brings the tube back to a condition where it
can receive the next signal. While the sending key is depressed the
current in the receiver is decreasing and increasing once for every
signal which is being transmitted. For each decrease and increase in
current the diaphragm of the telephone receiver makes one vibration.
What the listener then hears is a musical note with a frequency
corresponding to that number of vibrations a second, that is, a note
with a frequency of one thousand cycles per second. He hears a note of
frequency about that of two octaves above middle _C_ on the piano.
There are usually other notes present at the same time and the sound is
not like that of any musical instrument.

[Illustration: Fig 91]

If the key is held down a long time for a dash the listener hears this
note for a corresponding time. If it is depressed only about a third of
that time so as to send a dot, the listener hears the note for a
shorter time and interprets it to mean a dot.

In Fig. 91 I have drawn a sketch to show the e. m. f. which the signals
from a spark set impress on the grid of a detector and to show how the
plate current varies if there is a condenser and leak in the grid
circuit. I have only shown three signals in succession. If the operator
sends at the rate of about twenty words a minute a dot is formed by
about sixty of these signals in succession.

The frequency of the alternations in one of the little signals will
depend upon the wave length which the sending operator is using. If he
uses the wave length of 600 meters, as ship stations do, he will send
with a radio frequency of 500,000 cycles a second. Since the signals are
at the rate of a thousand a second each one is made up of 500 complete
cycles of the current in the antenna. It would be impracticable
therefore to show you a complete picture of the signal from a spark set.
I have, however, lettered the figure quite completely to cover what I
have just told you.

If the grid-condenser and its leak are so chosen as to work well for
signals from a 500-cycle spark set they will also work well for the
notes in human speech which are about 1000 cycles a second in frequency.
The detecting circuit will not, however, work so well for the other
notes which are in the human voice and are necessary to speech. For
example, if notes of about 2000 cycles a second are involved in the
speech which is being transmitted, the leak across the condenser will
not work fast enough. On the other hand, for the very lowest notes in
the voice the leak will work too fast and such variations in the signal
current will not be detected as efficiently as are those of 1000 cycles
a second.

You can see that there is always a little favoritism on the part of the
grid-condenser detector. It doesn't exactly reproduce the variations in
intensity of the radio signal which were made at the sending station. It
distorts a little. As amateurs we usually forgive it that distortion
because it is so efficient. It makes so large a change in the current
through the telephone when it receives a signal that we can use it to
receive much weaker signals, that is, signals from smaller or more
distant sending stations, than we can receive with the arrangement
described in Letter 14.




There is one way of making an audion even more efficient as a detector
than the method described in the last letter. And that is to make it
talk to itself.

Suppose we arrange a receiving circuit as in Fig. 92. It is exactly like
that of Fig. 90 of the previous letter except for the fact that the
current in the plate circuit passes through a little coil, _L_{t}_,
which is placed near the coil _L_ and so can induce in it an e. m.
f. which will correspond in intensity and wave form to the current in
the plate circuit.

If we should take out the grid condenser and its leak this circuit would
be like that of Fig. 54 in Letter 13 which we used for a generator of
high-frequency alternating currents. You remember how that circuit
operates. A small effect in the grid circuit produces a large effect in
the plate circuit. Because the plate circuit is coupled to the grid
circuit the grid is again affected and so there is a still larger effect
in the plate circuit. And so on, until the current in the plate circuit
is swinging from zero to its maximum possible value.

What happens depends upon how closely the coils _L_ and
_L_{t}_ are coupled, that is, upon how much the changing current in
one can affect the other. If they are turned at right angles to each
other, so that there is no possible mutual effect we say there is "zero

Start with the coils at right angles to each other and turn _L_{t}_
so as to bring its windings more and more parallel to those of _L_.
If we want _L_{t}_ to have a large effect on _L_ its windings
should be parallel and also in the same direction just as they were in
Fig. 54 of Letter 13 to which we just referred. As we approach nearer to
that position the current in _L_{t}_ induces more and more e. m. f.
in coil _L_. For some position of the two coils, and the actual
position depends on the tube we are using, there will be enough effect
from the plate circuit upon the grid circuit so that there will be
continuous oscillations.

[Illustration: Fig 92]

We want to stop just short of this position. There will then be no
continuous oscillations; but if any changes do take place in the plate
current they will affect the grid. And these changes in the grid voltage
will result in still larger changes in the plate current.

Now suppose that there is coming into the detector circuit of Fig. 92 a
radio signal with, speech significance. The current in the plate circuit
varies accordingly. So does the current in coil _L_{t}_ which is in
the plate circuit. But this current induces an e. m. f. in coil _L_
and this adds to the e. m. f. of the incoming signal so as to make a
greater variation in the plate current. This goes on as long as there is
an incoming signal. Because the plate circuit is coupled to the grid
circuit the result is a larger e. m. f. in the grid circuit than the
incoming signal could set up all by itself.

You see now why I said the tube talked to itself. It repeats to itself
whatever it receives. It has a greater strength of signal to detect than
if it didn't repeat. Of course, it detects also just as I told you in
the preceding letter.

In adjusting the coupling of the two coils of Fig. 92 we stopped short
of allowing the tube circuit to oscillate and to generate a high
frequency. If we had gone on increasing the coupling we should have
reached a position where steady oscillations would begin. Usually this
is marked by a little click in the receiver. The reason is that when the
tube oscillates the average current in the plate circuit is not the same
as the steady current which ordinarily flows between filament and plate.
There is a sudden change, therefore, in the average current in the plate
circuit when the tube starts to oscillate. You remember that what
affects the receiver is the average current in the plate circuit. So the
receiver diaphragm suddenly changes position as the tube starts to
oscillate and a listener hears a little click.

The frequency of the alternating current which the tube produces depends
upon the tuned circuit formed by _L_ and _C_. Suppose that
this frequency is not the same as that to which the receiving antenna is
tuned. What will happen?

There will be impressed on the grid of the tube two alternating e. m.
f.'s, one due to the tube's own oscillations and the other incoming from
the distant transmitting station. The two e. m. f. 's are both active at
once so that at each instant the e. m. f. of the grid is really the sum
of these two e. m. f.'s. Suppose at some instant both e. m.
f.'s are acting to make the grid positive. A little later one of them
will be trying to make the grid negative while the other is still trying
to make it positive. And later still when the first e. m. f. is ready
again to make the grid positive the second will be trying to make it

It's like two men walking along together but with different lengths of
step. Even if they start together with their left feet they are soon so
completely out of step that one is putting down his right foot while the
other is putting down his left. A little later, but just for an instant,
they are in step again. And so it goes. They are in step for a moment
and then completely out of step. Suppose one of them makes ten steps in
the time that the other makes nine. In that time they will be once in
step and once completely out of step. If one makes ten steps while the
other does eight this will happen twice.

The same thing happens in the audion detector circuit when two e. m.
f.'s which differ slightly in frequency are simultaneously impressed on
the grid. If one e. m. f. passes through ten complete cycles while the
other is making eight cycles, then during that time they will twice be
exactly in step, that is, "in phase" as we say. Twice in that time they
will be exactly out of step, that is, exactly "opposite in phase." Twice
in that time the two e. m. f.'s will aid each other in their effects on
the grid and twice they will exactly oppose. Unless they are equal in
amplitude there will still be a net e. m. f. even when they are exactly
opposed. The result of all this is that the average current in the plate
circuit of the detector will alternately increase and decrease twice
during this time.

The listener will then hear a note of a frequency equal to the
difference between the frequencies of the two e. m. f.'s which are being
simultaneously impressed on the grid of the detector. Suppose the
incoming signal has a frequency of 100,000 cycles a second but that the
detector tube is oscillating in its own circuit at the rate of 99,000
cycles per second, then the listener will hear a note of 1000 cycles per
second. One thousand times each second the two e. m. f.'s will be
exactly in phase and one thousand times each second they will be exactly
opposite in phase. The voltage applied to the grid will be a maximum one
thousand times a second and alternately a minimum. We can think of it,
then, as if there were impressed on the grid of the detector a
high-frequency signal which varied in intensity one thousand times a
second. This we know will produce a corresponding variation in the
current through the telephone receiver and thus give rise to a musical
note of about two octaves above middle _C_ on the piano.

This circuit of Fig. 92 will let us detect signals which are not varying
in intensity. And consequently this is the method which we use to detect
the telegraph signals which are sent out by such a "continuous wave
transmitter" as I showed you at the end of Letter 13.

When the key of a C-W transmitter is depressed there is set up in the
distant receiving-antenna an alternating current. This current doesn't
vary in strength. It is there as long as the sender has his key down.
Because, however, of the effect which I described above there will be an
audible note from the telephone receiver if the detector tube is
oscillating at a frequency within two or three thousand cycles of that
of the transmitting station.

This method of receiving continuous wave signals is called the
"heterodyne" method. The name comes from two Greek words, "dyne" meaning
"force" and the other part meaning "different." We receive by combining
two different electron-moving-forces, one produced by the distant
sending-station and the other produced locally at the receiving station.
Neither by itself will produce any sound, except a click when it starts.
Both together produce a musical sound in the telephone receiver; and the
frequency of that note is the difference of the two frequencies.

There are a number of words used to describe this circuit with some of
which you should be familiar. It is sometimes called a "feed-back"
circuit because part of the output of the audion is fed back into its
input side. More generally it is known as the "regenerative circuit"
because the tube keeps on generating an alternating current. The little
coil which is used to feed back into the grid circuit some of the
effects from the plate circuit is sometimes called a "tickler" coil.

It is not necessary to use a grid condenser in a feed-back circuit but
it is perhaps the usual method of detecting where the regenerative
circuit is used. The whole value of the regenerative circuit so far as
receiving is concerned is in the high efficiency which it permits. One
tube can do the work of two.

We can get just as loud signals by using another tube instead of making
one do all the work. In the regenerative circuit the tube is performing
two jobs at once. It is detecting but it is also amplifying.[9] By
"amplifying" we mean making an e. m. f. larger than it is without
changing the shape of its picture, that is without changing its "wave

To show just what we mean by amplifying we must look again at the audion
and see how it acts. You know that a change in the grid potential makes
a change in the plate current. Let us arrange an audion in a circuit
which will tell us a little more of what happens. Fig. 93 shows the

This circuit is the same as we used to find the audion characteristic
except that there is a clip for varying the number of batteries in the
plate circuit and a voltmeter for measuring their e. m. f. We start with
the grid at zero potential and the usual number of batteries in the
plate circuit. The voltmeter tells us the e. m. f. We read the ammeter
in the plate circuit and note what that current is. Then we shift the
slider in the grid circuit so as to give the grid a small potential. The
current in the plate circuit changes. We can now move the clip on the
B-batteries so as to bring the current in this circuit back to its
original value. Of course, if we make the grid positive we move the clip
so as to use fewer cells of the B-battery. On the other hand if we make
the grid negative we shall need more e. m. f. in the plate circuit. In
either case we shall find that we need to make a very much larger change
in the voltage of the plate circuit than we have made in the voltage of
the grid circuit.

[Illustration: Fig 93]

Usually we perform the experiment a little differently so as to get more
accurate results. We read the voltmeter in the plate circuit and the
ammeter in that circuit. Then we change the number of batteries which we
are using in the plate circuit. That changes the plate current. The next
step is to shift the slider in the grid circuit until we have again the
original value of current in the plate circuit. Suppose that the tube is
ordinarily run with a plate voltage of 40 volts and we start with that
e. m. f. on the plate. Suppose that we now make it 50 volts and then
vary the position of the slider in the grid circuit until the ammeter
reads as it did at the start. Next we read the voltage impressed on the
grid by reading the voltmeter in the grid circuit. Suppose it reads 2
volts. What does that mean?

[Illustration: Fig 94]

It means that two volts in the grid circuit have the same effect on the
plate current as ten volts in the plate circuit. If we apply a volt to
the grid circuit we get five times as large an effect in the plate
circuit as we would if the volt were applied there. We get a greater
effect, the effect of more volts, by applying our voltage to the grid.
We say that the tube acts as an "amplifier of voltage" because we can
get a larger effect than the number of volts which we apply would
ordinarily entitle us to.

Now let's take a simple case of the use of an audion as an amplifier.
Suppose we have a receiving circuit with which we find that the signals
are not easily understood because they are too weak. Let this be the
receiving circuit of Fig. 88 which I am reproducing here as part of Fig.

We have replaced the telephone receiver by a "transformer." A
transformer is two coils, or windings, coupled together. An alternating
current in one will give rise to an alternating current in the other.
You are already familiar with the idea but this is our first use of the
word. Usually we call the first coil, that is the one through which the
alternating current flows, the "primary" and the second coil, in which a
current is induced, the "secondary."

The secondary of this transformer is connected to the grid circuit of
another vacuum tube, to the plate circuit of which is connected another
transformer and the telephone receiver. The result is a detector and
"one stage of amplification."

The primary of the first transformer, so we shall suppose, has in it the
same current as would have been in the telephone. This alternating
current induces in the secondary an e. m. f. which has the same
variations as this current. This e. m. f. acts on the grid of the second
tube, that is on the amplifier. Because the audion amplifies, the e. m.
f. acting on the telephone receiver is larger than it would have been
without the use of this audion. And hence there is a greater response on
the part of its diaphragm and a louder sound.

In setting up such a circuit as this there are several things to watch.
For some of these you will have to rely on the dealer from whom you buy
your supplies and for the others upon yourself. But it will take another
letter to tell you of the proper precautions in using an audion as an

[Illustration: Fig 95]

In the circuit which I have just described an audion is used to amplify
the current which comes from the detector before it reaches the
telephone receiver. Sometimes we use an audion to amplify the e. m. f.
of the signal before impressing it upon the grid of the detector. Fig.
95 shows a circuit for doing that. In the case of Fig. 94 we are
amplifying the audio-frequency current. In that of Fig. 95 it is the
radio-frequency effect which is amplified. The feed-back or regenerative
circuit of Fig. 92 is a one-tube circuit for doing the same thing as is
done with two tubes in Fig 95.

[Footnote 9: There is always some amplification taking place in an
audion detector but the regenerative circuit amplifies over and over
again until the signal is as large as the tube can detect.]




In our use of the audion we form three circuits. The first or A-circuit
includes the filament. The B-circuit includes the part of the tube
between filament and plate. The C-circuit includes the part between
filament and grid. We sometimes speak of the C-circuit as the "input"
circuit and the B-circuit as the "output" circuit of the tube. This is
because we can put into the grid-filament terminals an e. m. f. and
obtain from the plate-filament circuit an effect in the form of a change
of current.

[Illustration: Fig 96]

Suppose we had concealed in a box the audion and circuit of Fig. 96 and
that only the terminals which are shown came through the box. We are
given a battery and an ammeter and asked to find out all we can as to
what is between the terminals _F_ and _G_. We connect the
battery and ammeter in series with these terminals. No current flows
through the circuit. We reverse the battery but no current flows in the
opposite direction. Then we reason that there is an open-circuit between
_F_ and _G_.

As long as we do not use a higher voltage than that of the C-battery
which is in the box no current can flow. Even if we do use a higher
voltage than the "negative C-battery" of the hidden grid-circuit there
will be a current only when the external battery is connected so as to
make the grid positive with respect to the filament.

Now suppose we take several cells of battery and try in the same way to
find what is hidden between the terminals _P_ and _F_. We
start with one battery and the ammeter as before and find that if this
battery is connected so as to make _P_ positive with respect to
_F_, there is a feeble current. We increase the battery and find
that the current is increased. Two cells, however, do not give exactly
twice the current that one cell does, nor do three give three times as
much. The current does not increase proportionately to the applied
voltage. Therefore we reason that whatever is between _P_ and
_F_ acts like a resistance but not like a wire resistance.

Then, we try another experiment with this hidden audion. We connect a
battery to _G_ and _F_, and note what effect it has on the
current which our other battery is sending through the box between
_P_ and _F_. There is a change of current in this circuit,
just as if our act of connecting a battery to _G-F_ had resulted in
connecting a battery in series with the _P-F_ circuit. The effect
is exactly as if there is inside the box a battery which is connected
into the hidden part of the circuit _P-F_. This concealed battery,
which now starts to act, appears to be several times stronger than the
battery which is connected to _G-F_.

Sometimes this hidden battery helps the B-battery which is on the
outside; and sometimes it seems to oppose, for the current in the
_P-F_ circuit either increases or decreases, depending upon how we
connect the battery to _G_ and _F_. The hidden battery is
always larger than our battery connected to _G_ and _F_. If we
arrange rapidly to reverse the battery connected to _G-F_ it
appears as if there is inside the box in the _P-F_ circuit an
alternator, that is, something which can produce an alternating e. m. f.

All this, of course, is merely a review statement of what we already
know. These experiments are interesting, however, because they follow
somewhat those which were performed in studying the audion and finding
out how to make it do all the wonderful things which it now can.

As far as we have carried our series of experiments the box might
contain two separate circuits. One between _G_ and _F_ appears
to be an open circuit. The other appears to have in it a resistance and
a battery (or else an alternator). The e. m. f. of the battery, or
alternator, as the case may be, depends on what source of e. m. f. is
connected to _G-F_. Whatever that e. m. f. is, there is a
corresponding kind of e. m. f. inside the box but one several times

[Illustration: Fig 97]

We might, therefore, pay no further attention to what is actually inside
the box or how all these effects are brought about. We might treat the
entire box as if it was formed by two separate circuits as shown in Fig.
97. If we do so, we are replacing the box by something which is
equivalent so far as effects are concerned, that is we are replacing an
actual audion by two circuits which together are equivalent to it.

The men who first performed such experiments wanted some convenient way
of saying that if an alternator, which has an e. m. f. of _V_
volts, is connected to _F_ and _G_, the effect is the same as
if a much stronger alternator is connected between _F_ and
_P_. How much stronger this imaginary alternator is depends upon
the design of the audion. For some audions it might be five times as
strong, for other designs 6.5 or almost any other number, although
usually a number of times less than 40. They used a little Greek letter
called "mu" to stand for this number which depends on the design of the
tube. Then they said that the hidden alternator in the output circuit
was mu times as strong as the actual alternator which was applied
between the grid and the filament. Of course, instead of writing the
sound and name of the letter they used the letter [Greek: m] itself. And
that is what I have done in the sketch of Fig. 97.

Now we are ready to talk about the audion as an amplifier. The first
thing to notice is the fact that we have an open circuit between
_F_ and _G_. This is true as long as we don't apply an e. m.
f. large enough to overcome the C-battery of Fig. 96 and thus let the
grid become positive and attract electrons from the filament. We need
then spend no further time thinking about what will happen in the
circuit _G-F_, for there will be no current.

As to the circuit _F-P_, we can treat it as a resistance in series
with which there is a generator [Greek: m] times as strong as that which
is connected to _F_ and _G_. The next problem is how to get
the most out of this hidden generator. We call the resistance which the
tube offers to the passage of electrons between _P_ and _F_
the "internal resistance" of the plate circuit of the tube. How large it
is depends upon the design of tube. In some tubes it may be five or six
thousand ohms, and in others several times as high. In the large tubes
used in high-powered transmitting sets it is much less. Since it will be
different in different cases we shall use a symbol for it and say that
it is _R_{p}_ ohms.

Then one rule for using an audion as an amplifier is this: To get the
most out of an audion see that the telephone, or whatever circuit or
piece of apparatus is connected to the output terminals, shall have a
resistance of _R_{p}_ ohms. When the resistance of the circuit,
which an audion is supplying with current, is the same as the internal
resistance of the output side of the tube, then the audion gives its
greatest output. That is the condition for the greatest "amount of
energy each second," or the "greatest power" as we say.

That rule is why we always select the telephone receivers which we use
with an audion and always ask carefully as to their resistance when we
buy. Sometimes, however, it is not practicable to use receivers of just
the right resistance. Where we connect the output side of an audion to
some other circuit, as where we let one audion supply another, it is
usually impossible to follow this rule without adding some special

This leads to the next rule: If the telephone receiver, or the circuit,
which we wish to connect to the output of an audion, does not have quite
nearly a resistance of _R_{p}_ ohms we use a properly designed
transformer as we have already done in Figs. 94 and 95.

A transformer is two separate coils coupled together so that an
alternating current in the primary will induce an alternating current in
the secondary. Of course, if the secondary is open-circuited then no
current can flow but there will be induced in it an e. m. f. which is
ready to act if the circuit is closed. Transformers have an interesting
ability to make a large resistance look small or vice versa. To show you
why, I shall have to develop some rules for transformers.

Suppose you have an alternating e. m. f. of ten volts applied to the
primary of an iron-cored transformer which has ten turns. There is one
volt applied to each turn. Now, suppose the secondary has only one turn.
That one turn has induced in it an alternating e. m. f. of one volt. If
there are more turns of wire forming the secondary, then each turn has
induced in it just one volt. But the e. m. f.'s of all these turns add
together. If the secondary has twenty turns, there is induced in it a
total of twenty volts. So the first rule is this: In a transformer the
number of volts in each turn of wire is just the same in the secondary
as in the primary.

If we want a high-voltage alternating e. m. f. all we have to do is to
send an alternating current through the primary of a transformer which
has in the secondary, many times more turns of wire than it has in the
primary. From the secondary we obtain a higher voltage than we impress
on the primary.

You can see one application of this rule at once. When we use an audion
as an amplifier of an alternating current we send the current which is
to be amplified through the primary of a transformer, as in Fig. 94. We
use a transformer with many times more turns on the secondary than on
the primary so as to apply a large e. m. f. to the grid of the
amplifying tube. That will mean a large effect in the plate circuit of
the amplifier.

You remember that the grid circuit of an audion with a proper value of
negative C-battery is really open-circuited and no current will flow in
it. For that case we get a real gain by using a "step-up" transformer,
that is, one with more turns in the secondary than in the primary.

It looks at first as if a transformer would always give a gain. _If we
mean a gain in energy it will not_ although we may use it, as we
shall see in a minute, to permit a vacuum tube to work into an output
circuit more efficiently than it could without the transformer. We
cannot have any more energy in the secondary circuit of a transformer
than we give to the primary.

Suppose we have a transformer with twice as many turns on the secondary
as on the primary. To the primary we apply an alternating e. m. f. of a
certain number of volts. In the secondary there will be twice as many
volts because it has twice as many turns. The current in the secondary,
however, will be only half as large as is the current in the primary. We
have twice the force in the secondary but only half the electron stream.

It is something like this: You are out coasting and two youngsters ask
you to pull them and their sleds up hill. You pull one of them all the
way and do a certain amount of work. On the other hand suppose you pull
them both at once but only half way up. You pull twice as hard but only
half as far and you do the same amount of work as before.

[Illustration: Fig 98]

We can't get more work out of the secondary of a transformer than we do
in the primary. If we design the transformer so that there is a greater
pull (e. m. f.) in the secondary the electron stream in the secondary
will be correspondingly smaller.

You remember how we measure resistance. We divide the e. m. f. (number
of volts) by the current (number of amperes) to find the resistance
(number of ohms). Suppose we do that for the primary and for the
secondary of the transformer of Fig. 98 which we are discussing. See
what happens in the secondary. There is only half as much voltage but
twice as much current. It looks as though the secondary had one-fourth
as much resistance as the primary. And so it has, but we usually call it
"impedance" instead of resistance because straight wires resist but
coils or condensers impede alternating e. m. f.'s.

[Illustration: Fig 99]

Before we return to the question of using a transformer in an audion
circuit let us turn this transformer around as in Fig. 99 and send the
current through the side with the larger number of windings. Let's talk
of "primary" and "secondary" just as before but, of course, remember
that now the primary has twice the turns of the secondary. On the
secondary side we shall have only half the current, but there will be
twice the e. m. f. The resistance of the secondary then is four times
that of the primary.

Now return to the amplifier of Fig. 94 and see what sort of a
transformer should be between the plate circuit of the tube and the
telephone receivers. Suppose the internal resistance of the tube is
12,000 ohms and the resistance of the telephones is 3,000 ohms. Suppose
also that the resistance (really impedance) of the primary side of the
transformer which we just considered is 12,000 ohms. The impedance of
its secondary will be a quarter of this or 3,000 ohms. If we connect
such a transformer in the circuit, as shown, we shall obtain the
greatest output from the tube.

In the first place the primary of the transformer has a number of ohms
just equal to the internal resistance of the tube. The tube, therefore,
will give its best to that transformer. In the second place the
secondary of the transformer has a resistance just equal to the
telephone receivers so it can give its best to them. The effect of the
transformer is to make the telephones act as if they had four times as
much resistance and so were exactly suited to be connected to the

This whole matter of the proper use of transformers is quite simple but
very important in setting up vacuum-tube circuits. To overlook it in
building or buying your radio set will mean poor efficiency. Whenever
you have two parts of a vacuum-tube circuit to connect together be sure
and buy only a transformer which is designed to work between the two
impedances (or resistances) which you wish to connect together.

There is one more precaution in connection with the purchase of
transformers. They should do the same thing for all the important
frequencies which they are to transmit. If they do not, the speech or
signals will be distorted and may be unintelligible.

If you take the precautions which I have mentioned your radio receiving
set formed by a detector and one amplifier will look like that of Fig.
94. That is only one possible scheme of connections. You can use any
detector circuit which you wish,[10] one with a grid condenser and leak,
or one arranged for feed-back In either case your amplifier may well be
as shown in the figure.

[Illustration: Fig 100]

The circuit I have described uses an audion to amplify the
audio-frequency currents which come from the detector and are capable of
operating the telephones. In some cases it is desirable to amplify the
radio signals before applying them to the detector. This is especially
true where a "loop antenna" is being used. Loop antennas are smaller and
more convenient than aërials and they also have certain abilities to
select the signals which they are to receive because they receive best
from stations which lie along a line drawn parallel to their turns.
Unfortunately, however, they are much less efficient and so require the
use of amplifiers.

With a small loop made by ten turns of wire separated by about a quarter
of an inch and wound on a square mounting, about three feet on a side,
you will usually require two amplifiers. One of these might be used to
amplify the radio signals before detection and the other to amplify
after detection. To tune the loop for broadcasts a condenser of about
0.0005 mf. will be needed. The diagram of Fig. 100 shows the complete
circuit of a set with three stages of radio-amplification and none of

[Footnote 10: Except for patented circuits. See p. 224.]




In an earlier letter when we first introduced a telephone receiver into
a circuit I told you something of how it operates. I want now to tell
why and also of some other important devices which operate for the same

You remember that a stream of electrons which is starting or stopping
can induce the electrons of a neighboring parallel circuit to start off
in parallel paths. We do not know the explanation of this. Nor do we
know the explanation of another fact which seems to be related to this
fact of induction and is the basis for our explanations of magnetism.

[Illustration: Fig 101]

If two parallel wires are carrying steady electron streams in the same
general direction the wires attract each other. If the streams are
oppositely directed the wires repel each other. Fig. 101 illustrates
this fact. If the streams are not at all in the same direction, that is,
if they are at right angles, they have no effect on each other.

[Illustration: Fig 102]

These facts, of the attraction of electron streams which are in the same
direction and repulsion of streams in opposite directions, are all that
one need remember to figure out for himself what will happen under
various conditions. For example, if two coils of wire are carrying
currents what will happen is easily seen. Fig. 102 shows the two coils
and a section through them.

[Illustration: Fig 103]

Looking at this cross section we seem to have four wires, _1_ and
_2_ of coil _A_ and _3_ and _4_ of coil _B_. You see at once that
if the coils are free to move they will move into the dotted positions
shown in Fig 102, because wire _1_ attracts wire _3_ and repels wire
_4_, while wire _2_ attracts wire _4_ and repels wire _3_. If
necessary, and if they are free to move, the coils will turn
completely around to get to this position. I have shown such a case
in Fig. 103.

Wires which are not carrying currents do not behave in this way. The
action is due, but how we don't yet know, to the motions of the
electrons. As far as we can explain it to-day, the attraction of two
wires which are carrying currents is due to the attraction of the two
streams of electrons. Of course these electrons are part of the wires.
They can't get far away from the stay-at-home electrons and the nuclei
of the atoms which form the wires. In fact it is these nuclei which keep
the wandering electrons within the wires. The result is that if the
streams of electrons are to move toward each other the wires must go
along with them.

If the wires are held firmly the electron streams cannot approach one
another for they must stay in the wires. Wires, therefore, perform the
important service of acting as paths for electrons which are traveling
as electric currents. There are other ways in which electrons can be
kept in a path, and other means beside batteries for keeping them going.
It doesn't make any difference so far as the attraction or the repulsion
is concerned why they are following a certain path or why they stay in
it. So far as we know two streams of electrons, following parallel
paths, will always, behave just like the two streams of Fig. 101.

[Illustration: Fig 104]

Suppose, for example, there were two atoms which were each formed by a
nucleus and a number of electrons swinging around about the nucleus as
pictured in Fig. 104. The electrons are going of their own accord and
the nucleus keeps them from flying off at a tangent, the way mud flies
from the wheel of an automobile. Suppose these two atoms are free to
turn but not to move far from their present positions. They will turn so
as to make their electron paths parallel just as did the loops of Fig.

[Illustration: Fig 105]

Now, I don't say that there are any atoms at all like the ones I have
pictured. There is still a great deal to be learned about how electrons
act inside different kinds of atoms. We do know, however, that the atoms
of iron act just as if they were tiny loops with electron streams.

[Illustration: Fig 106]

Suppose we had several loops and that they were lined up like the three
loops in Fig. 105. You can see that they would all attract the other
loop, on the right in the figure. On the other hand if they were grouped
in the triangle of Fig. 106 they would barely affect the loop because
they would be pulling at cross purposes. If a lot of the tiny loops of
the iron atoms are lined up so as to act together and attract other
loops, as in the first figure, we say the iron is magnetized and is a
magnet. In an ordinary piece of iron, however, the atoms are so grouped
that they don't pull together but like the loops of our second figure
pull in different directions and neutralize each other's efforts so that
there is no net effect.

[Illustration: Pl. IX.--Western Electric Loud Speaking Receiver.
Crystal Detector Set of the General Electric Co. Audibility Meter of
General Radio Co.]

And like the loops of Fig. 106 the atoms in an unmagnetized piece of
iron are pretty well satisfied to stay as they are without all lining up
to pull together. To magnetize the iron we must force some of these
atomic loops to turn part way around. That can be done by bringing near
them a strong magnet or a coil of wire which is carrying a current. Then
the atoms are forced to turn and if enough turn so that there is an
appreciable effect then the iron is magnetized. The more that are
properly turned the stronger is the magnet. One end or "pole" we call
north-seeking and the other south-seeking, because a magnetized bar of
iron acts like a compass needle.

[Illustration: Fig 107]

A coil of wire, carrying a current, acts just like a magnet because its
larger loops are all ready to pull together. I have marked the coil of
Fig. 107 with _N_ and _S_ for north and south. If the electron
stream in it is reversed the "polarity" is reversed. There is a simple
rule for this. Partially close your left hand so that the fingers form
loops. Let the thumb stick out at right angles to these loops. If the
electron streams are flowing around the loops of a coil in the same
direction as your fingers point then your thumb is the _N_ pole and
the coil will repel the north poles of other loops or magnets in the
direction in which your thumb points. If you know the polarity already
there is a simple rule for the repulsion or attraction. Like poles
repel, unlike poles attract.

From what has been said about magnetism you can now understand why in a
telephone receiver the current in the winding can make the magnet
stronger. It does so because it makes more of the atomic loops of the
iron turn around and help pull. On the other hand if the current in the
winding is reversed it will turn some of the loops which are already
helping into other positions where they don't help and may hinder. If
the current in the coil is to help, the electron stream in it must be so
directed that the north pole of the coil is at the same end as the north
pole of the magnet.

This idea of the attraction or repulsion of electron streams, whether in
coils of wire or in atoms of iron and other magnetizable substances, is
the fundamental idea of most forms of telephone receivers, of electric
motors, and of a lot of other devices which we call "electromagnetic."

The ammeters and voltmeters which we use for the measurement of audion
characteristics and the like are usually electromagnetic instruments.
Ammeters and voltmeters are alike in their design. Both are sensitive
current-measuring instruments. In the case of the voltmeter, as you
know, we have a large resistance in series with the current-measuring
part for the reason of which I told in Letter 8. In the case of ammeters
we sometimes let all the current go through the current-measuring part
but generally we let only a certain fraction of it do so. To pass the
rest of the current we connect a small resistance in parallel with the
measuring part. In both types of instruments the resistances are
sometimes hidden away under the cover. Both instruments must, of course,
be calibrated as I have explained before.

In the electromagnetic instruments there are several ways of making the
current-measuring part. The simplest is to let the current, or part of
it, flow through a coil which is pivoted between the _N_ and
_S_ poles of a strong permanent magnet. A spring keeps the coil in
its zero position and if the current makes the coil turn it must do so
against this spring. The stronger the current in the coil the greater
the interaction of the loops of the coil and those of the iron atoms and
hence the further the coil will turn. A pointer attached to the coil
indicates how far; and the number of volts or amperes is read off from
the calibrated scale.

Such instruments measure direct-currents, that is, steady streams of
electrons in one direction. To measure an alternating current or voltage
we can use a hot-wire instrument or one of several different types of
electromagnetic instruments. Perhaps the simplest of these is the
so-called "plunger type." The alternating current flows in a coil; and a
piece of soft iron is so pivoted that it can be attracted and moved into
the coil. Soft iron does not make a good permanent magnet. If you put a
piece of it inside a coil which is carrying a steady current it becomes
a magnet but about as soon as you interrupt the current the atomic loops
of the iron stop pulling together. Almost immediately they turn into all
sorts of positions and form little self-satisfied groups which don't
take any interest in the outside world. (That isn't true of steel, where
the atomic loops are harder to turn and to line up, but are much more
likely to stay in their new positions.)

Because the plunger in an alternating-current ammeter is soft iron its
loops line up with those of the coil no matter which way the electron
stream happens to be going in the coil. The atomic magnets in the iron
turn around each time the current reverses and they are always,
therefore, lined up so that the plunger is attracted. If the plunger has
much inertia or if the oscillations of the current are reasonably
frequent the plunger will not move back and forth with each reversal of
the current but will take an average position. The stronger the a-c
(alternating current) the farther inside the coil will be this position
of the plunger. The position of the plunger becomes then a measure of
the strength of the alternating current.

Instruments for measuring alternating e. m. f.'s and currents, read in
volts and in amperes. So far I haven't stopped to tell what we mean by
one ampere of alternating current. You know from Letter 7 what we mean
by an ampere of d-c (direct current). It wasn't necessary to explain
before because I told you only of hot-wire instruments and they will
read the same for either d-c or a-c.

When there is an alternating current in a wire the electrons start, rush
ahead, stop, rush back, stop, and do it all over again and again. That
heats the wire in which it happens. If an alternating stream of
electrons, which are doing this sort of thing, heats a wire just exactly
as much as would a d-c of one ampere, then we say that the a-c has an
"effective value" of one ampere. Of course part of the time of each
cycle the stream is larger than an ampere but for part it is less. If
the average heating effect is the same the a-c is said to be one ampere.

In the same way, if a steady e. m. f. (a d-c e. m. f.) of one volt will
heat a wire to which it is applied a certain amount and if an
alternating e. m. f. will have the same heating effect in the same time,
then the a-c e. m. f. is said to be one volt.

Another electromagnetic instrument which we have discussed but of which
more should be said is the iron-cored transformer. We consider first
what happens in one of the coils of the transformer.

The inductance of a coil is very much higher if it has an iron core. The
reason is that then the coil acts as if it had an enormously larger
number of turns. All the atomic loops of the core add their effects to
the loops of the coil. When the current starts it must line up a lot of
these atomic loops. When the current stops and these loops turn back
into some of their old self-satisfied groupings, they affect the
electrons in the coil. Where first they opposed the motion of these
electrons, now they insist on its being continued for a moment longer.
I'll prove that by describing two simple experiments; and then we'll
have the basis for understanding the effect of an iron core in a

[Illustration: Fig 33]

Look again at Fig. 33 of Letter 9 which I am reproducing for
convenience. We considered only what would happen in coil _cd_ if a
current was started in coil _ab_. Suppose instead of placing the
coils as shown in that figure they are placed as in Fig. 108. Because
they are at right angles there will be no effect in _cd_ when the
current is started in _ab_. Let the current flow steadily through
_ab_ and then suddenly turn the coils so that they are again
parallel as shown by the dotted positions. We get the same temporary
current in _cd_ as we would if we should place the coils parallel
and then start the current in _ab_.

[Illustration: Fig 108]

The other experiment is this: Starting with the coils lined up as in the
dotted position of Fig. 108 and the current steadily flowing in
_ab_, we suddenly turn them into positions at right angles to each
other. There is the same momentary current in _cd_ as if we had
left them lined up and had opened the switch in the circuit of

[Illustration: Fig 109]

Now we know that the atomic loops of iron behave in the same general way
as do loops of wire which are carrying currents. Let us replace the coil
_ab_ by a magnet as shown in Fig. 109. First we start with the
magnet at right angles to the coil _cd_. Suddenly we turn it into
the dotted position of that figure. There is the same momentary current
in _cd_ as if we were still using the coil _ab_ instead of a
magnet. If now we turn the magnet back to a position at right angles to
_cd_, we observe the opposite direction of current in _cd_.
These effects are more noticeable the more rapidly we turn the magnet.
The same is true of turning the coil.

The experiment of turning the magnet illustrates just what happens in
the case of a transformer with, an iron core except that instead of
turning the entire magnet the little atomic loops do the turning inside
the core. In the secondary of an iron-cored transformer the induced
current is the sum of two currents both in the same direction at each
instant. One current is caused by the starting or stopping of the
current in the primary. The other current is due to the turning of the
atomic loops of the iron atoms so that more of them line up with the
turns of the primary. These atomic loops, of course, are turned by the
current in the primary. There are so many of them, however, that the
current due to their turning is usually the more important part of the
total current.

In all transformers the effect is greater the more rapidly the current
changes direction and the atomic loops turn around. For the same size of
electron stream in the primary, therefore, there is induced in the
secondary a greater e. m. f. the greater is the frequency with which the
primary current alternates.

Where high frequencies are dealt with it isn't necessary to have iron
cores because the effect is large enough without the help of the atomic
loops. And even if we wanted their help it wouldn't be easy to obtain,
for they dislike to turn so fast and it takes a lot of power to make
them do so. We know that fact because we know that an iron core
increases the inductance and so chokes the current. For low frequencies,
however, that is those frequencies in the audio range, it is usually
necessary to have iron cores so as to get enough effect without too many
turns of wire.

The fact that iron decreases the inductance and so seriously impedes
alternating currents leads us to use iron-core coils where we want high
inductance. Such coils are usually called "choke coils" or "retard
coils." Of their use we shall see more in a later letter where we study
radio-telephone transmitters.




In this letter I want to tell you how to experiment with radio
apparatus. The first rule is this: Start with a simple circuit, never
add anything to it until you know just why you are doing so, and do not
box it up in a cabinet until you know how it is working and why.

Your antenna at the start had better be a single wire about 25 feet high
and about 75 feet long. This antenna will have capacity of about 0.0001
m. f. If you want an antenna of two wires spaced about three feet apart
I would make it about 75 feet long. Bring down a lead from each wire,
twisting them into a pigtail to act like one wire except near the
horizontal part of the antenna.

[Illustration: Fig 110]

Your ground connection can go to a water pipe. To protect the house and
your apparatus from lightning insert a fuse and a little carbon block
lightning arrester such as are used by the telephone company in their
installations of house phones. You can also use a so-called "vacuum
lightning arrester." In either case the connections will be as shown in
Fig. 111. If you use a loop antenna, of course, no arrester is needed.

At first I would plan to receive signals between 150 meters and 360
meters. This will include the amateurs who work between 160 and 200 m.,
the special amateurs who send C-W telegraph at 275 m., and the
broadcasting stations which operate at 360 m. This range will give you
plenty to listen to while you are experimenting. In addition you will
get some ship signals at 300 m.

[Illustration: Fig 111]

To tune the antenna to any of the wave lengths in this range you can use
a coil of 75 turns wound on a cardboard tube of three and a half inches
in diameter. You can wind this coil of bare wire if you are careful,
winding a thread along with the wire so as to keep the successive turns
separated. In that case you will need to construct a sliding contact for
it. That is the simplest form of tuner.

On the other hand you can wind with single silk covered wire and bring
out taps at the 0, 2, 4, 6, 8, 10, 14, 20, 28, 36, 44, 56, 66, and 75th
turns. To make a tap drill a small hole through the tube, bend the wire
into a loop about a foot long and pull this loop through the hole as
shown in Fig. 110. Then give the wire a twist, as shown, so that it
can't pull out, and proceed with your winding.

Use 26 s. s. c. wire. You will need about 80 feet and might buy 200 to
have enough for the secondary coil. Make contacts to the taps by two
rotary switches as shown in Fig. 112. You can buy switch arms and
contacts studs or a complete switch mounted on a small panel of some
insulating compound. Let switch _s_{1}_ make the contacts for taps
between 14 and 75 turns, and let switch _s_{2}_ make the other

For the secondary coil use the same size of wire and of core. Wind 60
turns, bringing out a tap at the middle. To tune the secondary circuit
you will need a variable condenser. You can buy one of the small ones
with a maximum capacity of about 0.0003 mf., one of the larger ones with
a maximum capacity of 0.0005 mf., or even the larger size which has a
maximum capacity of 0.001 mf. I should prefer the one of 0.0005 mf.

You will need a crystal detector--I should try galena first--and a
so-called "cat's whisker" with which to make contact with the galena.
For these parts and for the switch mentioned above you can shop around
to advantage. For telephone receivers I would buy a really good pair
with a resistance of about 2500 ohms. Buy also a small mica condenser of
0.002 mf. for a blocking condenser. Your entire outfit will then look as
in Fig. 112. The switch _S_ is a small knife switch.

To operate, leave the switch _S_ open, place the primary and
secondary coils near together as in the figure and listen. The tuning is
varied, while you listen, by moving the slider of the slide-wire tuner
or by moving the switches if you have connected your coil for that
method. Make large changes in the tuning by varying the switch
_s_{1}_ and then turn slowly through all positions of _s_{2}_,
listening at each position.

[Illustration: Fig 112]

When a signal is heard adjust to the position of _s_{1}_ and
_s_{2}_ which gives the loudest signal and then closing _S_
start to tune the secondary circuit. To do this, vary the capacity of
the condenser in the secondary circuit. Don't change the primary tuning
until you have tuned the secondary and can get the signal with good
volume, that is loud. You will want to vary the position of the primary
and secondary coils, that is, vary their coupling, for you will get
sharper tuning as they are drawn farther apart. Sharper tuning means
less interference from other stations which are sending on wave lengths
near that which you wish to receive. Reduce the coupling, therefore, and
then readjust the tuning. It will usually be necessary to make a slight
change in both circuits, in one case with switch _s_{1}_ and in the
other with the variable condenser.

As soon as you can identify any station which you hear sending make a
note of the position of the switches _s_{1}_ and _s_{2}_, and
of the setting of the condenser in the secondary circuit. In that way
you will acquire information as to the proper adjustments to receive
certain wave-lengths. This is calibrating your set by the known
wave-lengths of distant stations.

After learning to receive with this simple set I should recommend buying
a good audion tube. Ask the seller to supply you with a blue print of
the characteristic[11] of the tube taken under the conditions of filament
current and plate voltage which he recommends for its use. Buy a storage
battery and a small slide-wire rheostat, that is variable resistance, to
use in the filament circuit. Buy also a bank of dry batteries of the
proper voltage for the plate circuit of the tube. At the same time you
should buy the proper design of transformer to go between the plate
circuit of your tube and the pair of receivers which you have. It will
usually be advisable to ask the dealer to show you a characteristic
curve for the transformer, which will indicate how well the transformer
operates at the different frequencies in the audio range. It should
operate very nearly the same for all frequencies between 200 and 2500

The next step is to learn to use the tube as a detector. Connect it
into your secondary circuit instead of the crystal detector. Use the
proper value of C-battery as determined from your study of the
characteristic of the tube. One or two small dry cells, which have
binding-post terminals are convenient C-batteries. If you think you
will need a voltage much different from that obtained with a whole
number of batteries you can arrange to supply the grid as we did in
Fig. 86 of Letter 18. In that case you can use a few feet of 30
German-silver wire and make connections to it with a suspender clip.
Learn to receive with the tube and be particularly careful not to let
the filament have too much current and burn out.

Now buy some more apparatus. You will need a grid condenser of about
0.0002 mf. The grid leaks to go with it you can make for yourself. I
would use a piece of brown wrapping paper and two little metal eyelets.
The eyelets can be punched into the paper. Between them coat the paper
with carbon ink, or with lead pencil marks. A line about an inch long
ought to serve nicely. You will probably wish to make several grid leaks
to try. When you get satisfactory operation in receiving by the
grid-condenser method the leak will probably be somewhere between a
megohm and two megohms.

For this method you will not want a C-battery, but you will wish to
operate the detector with about as high a voltage as the manufacturers
will recommend for the plate circuit. In this way the incoming signal,
which decreases the plate current, can produce the largest decrease. It
is also possible to start with the grid slightly positive instead of
being as negative as it is when connected to the negative terminal of
the A-battery. There will then be possible a greater change in grid
voltage. To do so connect the grid as in Fig. 115 to the positive
terminal of the A-battery.

[Illustration: Fig 113]

About this time I would shop around for two or three small double-pole
double-throw switches. Those of the 5-ampere size will do. With these
you can arrange to make comparisons between different methods of
receiving. Suppose, for example, you connect the switches as shown in
Fig. 113 so that by throwing them to the left you are using the audion
and to the right the crystal as a detector. You can listen for a minute
in one position and then switch and listen for a minute in the other
position, and so on back and forth. That way you can tell whether or not
you really are getting better results.

If you want a rough measure of how much better the audion is than the
crystal you might see, while you are listening to the audion, how much
you can rob the telephone receiver of its current and still hear as well
as you do when you switch back to the crystal. The easiest way to do
this is to put a variable resistance across the receiver as shown in
Fig. 113. Adjust this resistance until the intensity of the signal when
detected by the audion is the same as for the crystal. You adjust this
variable resistance until it by-passes so much of the current, which
formerly went through the receiver, that the "audibility" of the signal
is reduced until it is the same as for the crystal detector. Carefully
made resistances for such a purpose are sold under the name of
"audibility meters." You can assemble a resistance which will do fairly
well if you will buy a small rheostat which will give a resistance
varying by steps of ten ohms from zero to one hundred ohms. At the same
time you can buy four resistance spools of one hundred ohms each and
perhaps one of 500 ohms. The spools need not be very expensive for you
do not need carefully adjusted resistances. Assemble them so as to make
a rheostat with a range of 0-1000 ohms by steps of 10 ohms. The cheapest
way to mount is with Fahnestock clips as illustrated in Fig. 114. After
a while, however, you will probably wish to mount them in a box with a
rotary switch on top.

[Illustration: Fig 114]

To study the effect of the grid condenser you can arrange switches so as
to insert this condenser and its leak and at the same time to cut out
the C-battery. Fig. 115 shows how. You can measure the gain in
audibility at the same time.

[Illustration: Pl. X.--Audio-frequency Transformer and Banked-wound Coil.
(Courtesy of Pacent Electric Co.)]

[Illustration: Fig 115]

After learning to use the audion as a detector, both by virtue of its
curved characteristic and by the grid-condenser method, I would suggest
studying the same tube as an amplifier. First I would learn to use it as
an audio-frequency amplifier. Set up the crystal detector circuit. Use
your audio-frequency transformer the other way around so as to step up
to the grid. Put the telephone in the plate circuit. Choose your
C-battery for amplification and _not detection_ and try to receive.

You will get better results if you can afford another iron-core
transformer. If you can, buy one which will work between the plate
circuit of one vacuum tube and the grid circuit of another similar tube.
Then you will have the right equipment when you come to make a two-stage
audio-frequency amplifier. If you buy such a transformer use the other
transformer between plate and telephones as you did before and insert
the new one as shown in Fig. 116. This circuit also shows how you can
connect the switches so as to see how much the audion is amplifying.

[Illustration: Fig 116]

The next step is to use the audion as an amplifier of the radio-signal
before its detection. Use the proper C-battery for an amplifier, as
determined from the blue print of the tube characteristic. Connect the
tube as shown in Fig. 117. You will see that in this circuit we are
using a choke coil to keep the radio-frequency current out of the
battery part of the plate circuit and a small condenser, another one of
0.002 mf., to keep the battery current from the crystal detector. You
can see from the same figure how you can arrange the switches so as to
find whether or not you are getting any gain from the amplifier.

Now you are ready to receive those C-W senders at 275 meters. You will
need to wind another coil like the secondary coil you already have. Here
is where you buy another condenser. You will need it later. If before
you bought the 0.0005 size, this time buy the 0.001 size or vice versa.
Wind also a small coil for a tickler. About 20 turns of 26 wire on a
core of 3-1/2 in. diameter will do. Connect the tickler in the plate
circuit of the audion. Connect to the grid your new coil and condenser
and set the audion circuit so that it will induce a current in the
secondary circuit which supplies the crystal. Fig. 118 shows the

[Illustration: Fig 117]

You will see that you are now supplying the crystal with current from
two sources, namely the distant source of the incoming signals and the
local oscillator which you have formed. The crystal will detect the
"beat note" between these two currents.

To receive the 275 meters signals you will need to make several
adjustments at the same time. In the first place I would set the tuning
of the antenna circuit and of the crystal circuit about where you think
right because of your knowledge of the settings for other wave lengths.
Then I would get the local oscillator going. You can tell whether or not
it is going if you suddenly increase or decrease the coupling between
the tickler coil and the input circuit of the audion. If this motion is
accompanied by a click in the receivers the tube is oscillating.

[Illustration: Fig 118]

Now you must change the frequency at which it is oscillating by slowly
changing the capacity in the tuned input circuit of the tube. Unless the
antenna circuit is properly tuned to the 275 meter signal you will get
no results. If it is, you will hear an intermittent musical note for
some tune of your local oscillator. This note will have the duration of
dots and dashes.

You will have to keep changing the tuning of your detector circuit and
of the antenna. For each new setting very slowly swing the condenser
plates in the oscillator circuit and see if you get a signal. It will
probably be easier to use the "stand-by position," which I have
described, with switch _S_ open in the secondary circuit of Fig.
118. In that case you have only to tune your antenna to 275 meters and
then you will pick up a note when your local oscillator is in tune.
After you have done so you can tune the secondary circuit which supplies
the crystal.

If you adopt this method you will want a close coupling between the
antenna and the crystal circuit. You will always want a very weak
coupling between the oscillator circuit and the detector circuit. You
will also probably want a weaker coupling between tickler and tube input
than you are at first inclined to believe will be enough. Patience and
some skill in manipulation is always required for this sort of

When you have completed this experiment in heterodyne receiving, using a
local oscillator, you are ready to try the regenerative circuit. This
has been illustrated in Fig. 92 of Letter 18 and needs no further
description. You will have the advantage when you come to this of
knowing very closely the proper settings of the antenna circuit and the
secondary tuned circuit. You will need then only to adjust the coupling
of the tickler and make finer adjustments in your tuning.

After you have completed this series of experiments you will be
something of an adept at radio and are in a position to plan your final
set. For this set you will need to purchase certain parts complete from
reputable dealers because many of the circuits which I have described
are patented and should not be used except as rights to use are obtained
by the purchase of licensed apparatus which embodies the patented
circuits. Knowing how radio receivers operate and why, you are now in a
good condition to discuss with dealers the relative merits and costs of
receiving sets.

[Illustration: Fig 119]

Before you actually buy a completed set you may want to increase the
range of frequency over which you are carrying out your experiments. To
receive at longer wave-lengths you will need to increase the inductance
of your antenna so that it will be tuned to a lower frequency. This is
usually called "loading" and can be done by inserting a coil in the
antenna. To obtain smaller wave-lengths decrease the effective capacity
of the antenna circuit by putting another condenser in series with the
antenna. Usually, therefore, one connects into his antenna circuit both
a condenser and a loading coil. By using a variable condenser the
effective capacity of the antenna system may be easily changed. The
result is that this series condenser method becomes the easiest method
of tuning and the slide wire tuner is not needed. Fig. 119 shows the

For quite a range of wave-lengths we may use the same loading coil and
tune the antenna circuit entirely by this series condenser. For some
other range of wave-lengths we shall then need a different loading coil.
In a well-designed set the wave-length ranges overlap. The calculation
of the size of loading coil is quite easy but requires more arithmetic
than I care to impose on you at present. I shall therefore merely give
you illustrations based on the assumption that your antenna has a
capacity of 0.0001 or of 0.0002 mf. and that the condensers which you
have bought are 0.0005 and 0.001 for their maxima.

In Table I there is given, for each of several values of the inductance
of the primary coil, the shortest and the longest wave-lengths which you
can expect to receive. The table is in two parts, the first for an
antenna of capacity 0.0001 mf. and the second for one of 0.0002 mf.
Yours will be somewhere between these two limits. The shortest
wave-length depends upon the antenna and not upon the condenser which
you use in series with it for tuning. It also depends upon how much
inductance there is in the coil which you have in the antenna circuit.
The table gives values of inductance in the first column, and of minimum
wave-length in the second. The third column shows what is the greatest
wave-length you may expect if you use a tuning condenser of 0.0005 mf.;
and the fourth column the slightly large wave-length which is possible
with the larger condenser.

                               TABLE I

       Part 1. (For antenna of 0.0001 mf.)

    Inductance in  Shortest wave-length   Longest wave-length in meters
    mil-henries.        in meters.       with 0.0005 mf.   with 0.001 mf.

        0.10               103                  169             179
        0.20               146                  238             253
        0.40               207                  337             358
        0.85               300                  490             515
        1.80               400                  700             760
        2.00               420                  750             800
        4.00               600                 1080            1130
        5.00               660                 1200            1260
       10.00               900                 1700            1790
       30.00              1600                 2900            3100

                   Part 2. (For antenna of 0.0002 mf.)

        0.10               169                  225             240
        0.16               210                  285             305
        0.20               240                  320             340
        0.25               270                  355             380
        0.40               340                  450             480
        0.60               420                  550             590
        0.80               480                  630             680
        1.20               585                  775             840
        1.80               720                  950            1020
        3.00               930                 1220            1320
        5.00              1200                 1600            1700
        8.00              1500                 2000            2150
       12.00              1850                 2400            2650
       16.00              2150                 2800            3050

From Table I you can find how much inductance you will need in the
primary circuit. A certain amount you will need to couple the antenna
and the secondary circuit. The coil which you wound at the beginning of
your experiments will do well for that. Anything more in the way of
inductance, which the antenna circuit requires to give a desired
wave-length, you may consider as loading. In Table II are some data as
to winding coils on straight cores to obtain various values of
inductance. Your 26 s. s. c. wire will wind about 54 turns to the inch.
I have assumed that you will have this number of turns per inch on your
coils and calculated the inductance which you should get for various
numbers of total turns. The first part of the table is for a core of 3.5
inches in diameter and the second part for one of 5 inches. The first
column gives the inductance in mil-henries. The second gives number of
turns. The third and fourth are merely for convenience and give the
approximate length in inches of the coil and the approximate total
length of wire which is required to wind it. I have allowed for bringing
out taps. In other words 550 feet of the wire will wind a coil of 10.2
inches with an inductance of 8.00 mil-henries, and permit you to bring
out taps at all the lower values of inductance which are given in the

                               Table II

                   Part 1. (For a core of 3.5 in. diam.)

    Inductance in       Number              Length         Feet of wire
    mil-henries.       of turns.           in inches.       required.
        0.10               25                 0.46             25
        0.16               34                 0.63             36
        0.20               39                 0.72             42
        0.25               44                 0.81             49
        0.40               58                 1.07             63
        0.60               75                 1.38             80
        0.80               92                 1.70            100
        0.85               96                 1.78            104
        1.00              108                 2.00            118
        1.20              123                 2.28            133
        1.80              164                 3.03            176
        2.00              180                 3.33            190
        3.00              242                 4.48            250
        4.00              304                 5.62            310
        5.00              366                 6.77            370
        8.00              550                10.20            550

                   Part 2. (For core of 5.0 in. diam.)

        2.00              120                 2.22            160
        3.00              158                 2.93            215
        4.00              194                 3.58            265
        5.00              228                 4.22            310
        8.00              324                 6.00            450
       10.00              384                 7.10            530
       12.00              450                 8.30            625

The coil which you wound at the beginning of your experiment had only 75
turns and was tapped so that you could, by manipulating the two switches
of Fig. 112, get small variations in inductance. In Table III is given
the values of the inductance which is controlled by the switches of that
figure, the corresponding number of turns, and the wave-length to which
the antenna should then be tuned. I am giving this for two values of
antenna capacity, as I have done before. By the aid of these three
tables you should have small difficulty in taking care of matters of
tuning for all wave-lengths below about 3000 meters. If you want to get
longer waves than that you had better buy a few banked-wound coils.
These are coils in which the turns are wound over each other but in such
a way as to avoid in large part the "capacity effects" which usually
accompany such winding. You can try winding them for yourself but I
doubt if the experience has much value until you have gone farther in
the study of the mathematical theory of radio than this series of
letters will carry you.

                           TABLE III
                                     Circuit of Fig. 112
    Number      Inductance in     Wave length with antenna of
    of turns.    mil-henries.      0.0001 mf.      0.0002 mf.
      14            0.04            120              170
      20            0.07            160              220
      28            0.12            210              290
      36            0.18            250              360
      44            0.25            300              420
      56            0.38            370              520
      75            0.60            460              650

In the secondary circuit there is only one capacity, that of the
variable condenser. If it has a range of values from about 0.00005 mf.
to 0.0005 mf. your coil of 60 turns and 0.42 mf. permits a range of
wave-lengths from 270 to 860 m. Using half the coil the range is 150 to
480 m. With the larger condenser the ranges are respectively 270 to 1220
and 270 to 670. For longer wave-lengths load with inductance. Four times
the inductance will tune to double these wave-lengths.

[Footnote 11: If you can afford to buy, or if you can borrow, ammeters
and voltmeters of the proper range you should take the characteristic




This letter is to summarize the operations which must be performed in
radio-telephone transmission and reception; and also to describe the
circuit of an important commercial system.

To transmit speech by radio three operations are necessary. First, there
must be generated a high-frequency alternating current; second, this
current must be modulated, that is, varied in intensity in accordance
with the human voice; and third, the modulated current must be supplied
to an antenna. For efficient operation, of course, the antenna must be
tuned to the frequency which is to be transmitted. There is also a
fourth operation which is usually performed and that is amplification.
Wherever the electrical effect is smaller than desired, or required for
satisfactory transmission, vacuum tubes are used as amplifiers. Of this
I shall give you an illustration later.

Three operations are also essential in receiving. First, an antenna must
be so arranged and tuned as to receive energy from the distant
transmitting station. There is then in the receiving antenna a current
similar in wave form to that in the transmitting antenna. Second, the
speech significance of this current must be detected, that is, the
modulated current must be demodulated. A current is then obtained which
has the same wave form as the human voice which was the cause of the
modulation at the distant station. The third operation is performed by a
telephone receiver which makes the molecules of air in its neighborhood
move back and forth in accordance with the detected current. As you
already know a fourth operation may be carried on by amplifiers which
give on their output sides currents of greater strength but of the same
forms as they receive at their input terminals.

In transmitting and in receiving equipment two or more of these
operations may be performed by the same vacuum tube as you will remember
from our discussion of the regenerative circuit for receiving. For
example, also, in any receiving set the vacuum tube which detects is
usually amplifying. In the regenerative circuit for receiving continuous
waves by the heterodyne method the vacuum tube functions as a generator
of high-frequency current and as a detector of the variations in current
which occur because the locally-generated current does not keep in step
with that generated at the transmitting station.

Another example of a vacuum tube performing simultaneously two different
functions is illustrated in Fig. 120 which shows a simple
radio-telephone transmitter. The single tube performs in itself both the
generation of the radio-frequency current and its modulation in
accordance with the output of the carbon-button transmitter. This audion
is in a feed-back circuit, the oscillation frequency of which depends
upon the condenser _C_ and the inductance _L_. The voice
drives the diaphragm of the transmitter and thus varies the resistance
of the carbon button. This varies the current from the battery,
_B_{a}_, through the primary, _T_{1}_, of the transformer
_T_. The result is a varying voltage applied to the grid by the
secondary _T_{2}_. The oscillating current in the plate circuit of
the audion varies accordingly because it is dependent upon the grid
voltage. The condenser _C_{r}_ offers a low impedance to the
radio-frequency current to which the winding _T_{2}_ of
audio-frequency transformer offers too much.

[Illustration: Fig 120]

In this case the tube is both generator and "modulator." In some cases
these operations are separately performed by different tubes. This was
true of the transmitting set used in 1915 when the engineers of the Bell
Telephone System talked by radio from Arlington, near Washington, D. C.,
to Paris and Honolulu. I shall not draw out completely the circuit of
their apparatus but I shall describe it by using little squares to
represent the parts responsible for each of the several operations.

First there was a vacuum tube oscillator which generated a small current
of the desired frequency. Then there was a telephone transmitter which
made variations in a direct-current flowing through the primary of a
transformer. The e. m. f. from the secondary of this transformer and the
e. m. f. from the radio-frequency oscillator were both impressed upon
the grid of an audion which acted as a modulator. The output of this
audion was a radio-frequency current modulated by the voice. The output
was amplified by a two-stage audion amplifier and supplied through a
coupling coil to the large antenna of the U. S. Navy Station at
Arlington. Fig. 121 shows the system.

[Illustration: Fig 121]

The audion amplifiers each consisted of a number of tubes operating in
parallel. When tubes are operated in parallel they are connected as
shown in Fig. 122 so that the same e. m. f. is impressed on all the
grids and the same plate-battery voltage on all the plates. As the grids
vary in voltage there is a corresponding variation of current in the
plate circuit of each tube. The total change of the current in the
plate-battery circuit is, then, the sum of the changes in all the
plate-filament circuits of the tubes. This scheme of connections gives a
result equivalent to that of a single tube with a correspondingly larger
plate and filament.

[Illustration: Fig 122]

Parallel connection is necessary because a single tube would be
overheated in delivering to the antenna the desired amount of power. You
remember that when the audion is operated as an amplifier the resistance
to which it supplies current is made equal to its own internal
resistance of _R_{p}_. That means that there is in the plate
circuit just as much resistance inside the tube as outside. Hence there
is the same amount of work done each second in forcing the current
through the tube as through the antenna circuit, if that is what the
tube supplies. "Work per second" is power; the plate battery is spending
energy in the tube at the same rate as it is supplying it to the antenna
where it is useful for radiation.

[Illustration: Pl. XI.--Broadcasting Equipment, Developed by the American
Telephone and Telegraph Company and the Western Electric Company.]

All the energy expended in the tube appears as heat. It is due to the
blows which the electrons strike against the plate when they are drawn
across from the filament. These impacts set into more rapid motion the
molecules of the plate; and the temperature of the tube rises. There is
a limit to the amount the temperature can rise without destroying the
tube. For that reason the heat produced inside it must not exceed a
certain limit depending upon the design of the tube and the method of
cooling it as it is operated. In the Arlington experiments, which I
mentioned a moment ago, the tubes were cooled by blowing air on them
from fans.

We can find the power expended in the plate circuit of a tube by
multiplying the number of volts in its battery by the number of amperes
which flows. Suppose the battery is 250 volts and the current 0.02
amperes, then the power is 5 watts. The "watt" is the unit for measuring
power. Tubes are rated by the number of watts which can be safely
expended in them. You might ask, when you buy an audion, what is a safe
rating for it. The question will not be an important one, however,
unless you are to set up a transmitting set since a detector is usually
operated with such small plate-voltage as not to have expended in it an
amount of power dangerous to its life.

In recent transmitting sets the tubes are used in parallel for the
reasons I have just told, but a different method of modulation is used.
The generation of the radio-frequency current is by large-powered tubes
which are operated with high voltages in their plate circuits. The
output of these oscillators is supplied to the antenna. The intensity of
the oscillations of the current in these tubes is controlled by changing
the voltage applied in their plate circuits. You can see from Fig. 123
that if the plate voltage is changed the strength of the alternating
current is changed accordingly. It is the method used in changing the
voltage which is particularly interesting.

[Illustration: Fig 123]

The high voltages which are used in the plate circuits of these
high-powered audions are obtained from generators instead of batteries.
You remember from Letter 20 that an e. m. f. is induced in a coil when
the coil and a magnet are suddenly changed in their positions, one being
turned with reference to the other. A generator is a machine for turning
a coil so that a magnet is always inducing an e. m. f. in it. It is
formed by an armature carrying coils and by strong electromagnets. The
machine can be driven by a steam or gas engine, by a water wheel, or by
an electric motor. Generators are designed either to give steady streams
of electrons, that is for d-c currents, or to act as alternators.

[Illustration: Fig 124]

Suppose we have, as shown in Fig. 124, a d-c generator supplying
current to a vacuum tube oscillator. The current from the generator
passes through an iron-cored choke coil, marked _L_{a}_ in the figure.
Between this coil and the plate circuit we connect across the line a
telephone transmitter. To make a system which will work efficiently we
shall have to suppose that this transmitter has a high resistance, say
about the same as the internal resistance, _R_{p}_, of the tube and
also that it can carry as large a current.

Of the current which comes from the generator about one-half goes to
the tube and the rest to the transmitter. If the resistance of the
transmitter is increased it can't take as much current. The coil,
_L_{a}_, however, because of its inductance, tends to keep the same
amount of current flowing through itself. For just an instant then the
current in _L_{a}_ keeps steady even though the transmitter doesn't
take its share. The result is more current for the oscillating tube. On
the other hand if the transmitter takes more current, because its
resistance is decreased, the choke coil, _L_{a}_, will momentarily tend
to keep the current steady so that what the transmitter takes must be
at the expense of the oscillating tube.

That's one way of looking at what happens. We know, however, from Fig.
123 that to get an increase in the amplitude of the current in the
oscillating tube we must apply an increased voltage to its plate
circuit. That is what really happens when the transmitter increases in
resistance and so doesn't take its full share of the current. The
reason is this: When the transmitter resistance is increased the
current in the transmitter decreases. Just for a moment it looks as
though the current in _L_{a}_ is going to decrease. That's the way it
looks to the electrons; and you know what electrons do in an inductive
circuit when they think they shall have to stop. They induce each other
to keep on for a moment. For a moment they act just as if there was
some extra e. m. f. which was acting to keep them going. We say,
therefore, that there is an extra e. m. f., and we call this an e. m.
f. of self-induction. All this time there has been active on the plate
circuit of the tube the e. m. f. of the generator. To this there is
added at the instant when the transmitter resistance increases, the e.
m. f. of self-induction in the coil, _L_{a}_ and so the total e. m. f.
applied to the tube is momentarily increased. This increased e. m. f.,
of course, results in an increased amplitude for the alternating
current which the oscillator is supplying to the transmitting antenna.

When the transmitter resistance is decreased, and a larger current
should flow through the choke coil, the electrons are asked to speed up
in going through the coil. At first they object and during that instant
they express their objection by an e. m. f. of self-induction which
opposes the generator voltage. For an instant, then, the voltage of the
oscillating tube is lowered and its alternating-current output is

[Illustration: Fig 125]

For the purpose of bringing about such threatened changes in current,
and hence such e. m. f.'s of self-induction, the carbon transmitter is
not suitable because it has too small a resistance and too small a
current carrying ability. The plate circuit of a vacuum tube will serve
admirably. You know from the audion characteristic that without changing
the plate voltage we can, by applying a voltage to the grid, change the
current through the plate circuit. Now if it was a wire resistance with
which we were dealing and we should be able to obtain a change in
current without changing the voltage acting on this wire we would say
that we had changed the resistance. We can say, therefore, that the
internal resistance of the plate circuit of a vacuum tube can be changed
by what we do to the grid.

In Fig. 125 I have substituted the plate circuit of an audion for the
transmitter of Fig. 124 and arranged to vary its resistance by changing
the potential of the grid. This we do by impressing upon the grid the e.
m. f. developed in the secondary of a transformer, to the primary of
which is connected a battery and a carbon transmitter. The current
through the primary varies in accordance with the sounds spoken into the
transmitter. And for all the reasons which we have just finished
studying there are similar variations in the output current of the
oscillating tube in the transmitting set of Fig. 125.

In this latter figure you will notice a small air-core coil,
_L_{R}_, between the oscillator and the modulator tube. This coil
has a small inductance but it is enough to offer a large impedance to
radio-frequency currents. The result is, it does not let the alternating
currents of the oscillating tube flow into the modulator. These currents
are confined to their own circuit, where they are useful in establishing
similar currents in the antenna. On the other hand, the coil _L_{R}_
doesn't seriously impede low-frequency currents and therefore it does
not prevent variations in the current which are at audio-frequency. It
does not interfere with the changes in current which accompany the
variations in the resistance of the plate circuit of the modulator.
That is, it has too little impedance to act like _L_{a}_ and so it
permits the modulator to vary the output of the oscillator.

[Illustration: Fig 126]

The oscillating circuit of Fig. 125 includes part of the antenna. It
differs also from the others I have shown in the manner in which grid
and plate circuits are coupled. I'll explain by Fig. 126.

The transmitting set which I have just described involves many of the
principles of the most modern sets. If you understand its operation you
can probably reason out for yourself any of the other sets of which you
will hear from time to time.




In the matter of receiving I have already covered all the important
principles. There is one more system, however, which you will need to
know. This is spoken of either as the "super-heterodyne" or as the
"intermediate-frequency amplification" method of reception.

The system has two important advantages. First, it permits sharper
tuning and so reduces interference from other radio signals. Second, it
permits more amplification of the incoming signal than is usually

First as to amplification: We have seen that amplification can be
accomplished either by amplifying the radio-frequency current before
detection or by amplifying the audio-frequency current which results
from detection. There are practical limitations to the amount of
amplification which can be obtained in either case. An efficient
multi-stage amplifier for radio-frequencies is difficult to build
because of what we call "capacity effects."

Consider for example the portion of circuit shown in Fig. 127. The wires
_a_ and _b_ act like small plates of condensers. What we
really have, is a lot of tiny condensers which I have shown in the
figure by the light dotted-lines. If the wires are transmitting
high-frequency currents these condensers offer tiny waiting-rooms where
the electrons can run in and out without having to go on to the grid of
the next tube. There are other difficulties in high-frequency
amplifiers. This one of capacity effects between parallel wires is
enough for the present. It is perhaps the most interesting because it is
always more or less troublesome whenever a pair of wires is used to
transmit an alternating current.

[Illustration: Fig 127]

In the case of a multi-stage amplifier of audio-frequency current there
is always the possibility of the amplification of any small variations
in current which may naturally occur in the action of the batteries.
There are always small variations in the currents from batteries, due to
impurities in the materials of the plates, air bubbles, and other
causes. Ordinarily we don't observe these changes because they are too
small to make an audible sound in the telephone receivers. Suppose,
however, that they take place in the battery of the first tube of a
series of amplifiers. Any tiny change of current is amplified many times
and results in a troublesome noise in the telephone receiver which is
connected to the last tube.

In both types of amplifiers there is, of course, always the chance that
the output circuit of one tube may be coupled to and induce some effect
in the input circuit of one of the earlier tubes of the series. This
will be amplified and result in a greater induction. In other words, in
a circuit where there is large amplification, there is always the
difficulty of avoiding a feed-back of energy from one tube to another so
that the entire group acts like an oscillating circuit, that is
"regeneratively." Much of this difficulty can be avoided after

If a multi-stage amplifier is to be built for a current which does not
have too high a frequency the "capacity effects" and the other
difficulties due to high-frequency need not be seriously troublesome. If
the frequency is not too high, but is still well above the audible
limit, the noises due to variations in battery currents need not bother
for they are of quite low frequency. Currents from 20,000 to 60,000
cycles a second are, therefore, the most satisfactory to amplify.

Suppose, however, one wishes to amplify the signals from a
radio-broadcasting station. The wave-length is 360 meters and the
frequency is about 834,000 cycles a second. The system of
intermediate-frequency amplification solves the difficulty and
we shall see how it does so.

[Illustration: Fig 128]

At the receiving station a local oscillator is used. This generates a
frequency which is about 30,000 cycles less than that of the incoming
signal. Both currents are impressed on the grid of a detector. The
result is, in the output of the detector, a current which has a
frequency of 30,000 cycles a second. The intensity of this detected
current depends upon the intensity of the incoming signal. The "beat
note" current of 30,000 cycles varies, therefore, in accordance with the
voice which is modulating at the distant sending station. The speech
significance is now hidden in a current of a frequency intermediate
between radio and audio. This current may be amplified many times and
then supplied to the grid of a detector which obtains from it a current
of audio-frequency which has a speech significance. In Fig. 128 I have
indicated the several operations.

We can now see why this method permits sharper tuning. The whole idea
of tuning, of course, is to arrange that the incoming signal shall cause
the largest possible current and at the same time to provide that any
signals at other wave-lengths shall cause only negligible currents. What
we want a receiving set to do is to distinguish between two signals
which differ slightly in wave-length and to respond to only one of them.

Suppose we set up a tuned circuit formed by a coil and a condenser and
try it out for various frequencies of signals. You know how it will
respond from our discussion in connection with the tuning curve of Fig.
51 of Letter 13. We might find from a number of such tests that the best
we can expect any tuned circuit to do is to discriminate between signals
which differ about ten percent in frequency, that is, to receive well
the desired signal and to fail practically entirely to receive a signal
of a frequency either ten percent higher or the same amount lower.

For example, if the signal is at 30,000 cycles a tuned circuit might be
expected to discriminate against an interfering signal of 33,000. If the
signal is at 300,000 cycles a tuned circuit might discriminate against
an interfering signal of 330,000 cycles, but an interference at 303,000
cycles would be very troublesome indeed. It couldn't be "tuned out" at

Now suppose that the desired signal is at 300,000 cycles and that there
is interference at 303,000 cycles. We provide a local oscillator of
270,000 cycles a second, receive by this "super-heterodyne" method which
I have just described, and so obtain an intermediate frequency. In the
output of the first detector we have then a current of 300,000--270,000
or 30,000 cycles due to the desired signal and also a current of
303,000--270,000 or 33,000 cycles due to the interference. Both these
currents we can supply to another tuned circuit which is tuned for
30,000 cycles a second. It can receive the desired signal but it can
discriminate against the interference because now the latter is ten
percent "off the tune" of the signal.

You see the question is not one of how far apart two signals are in
number of cycles per second. The question always is: How large in
percent is the difference between the two frequencies? The matter of
separating two effects of different frequencies is a question of the
"interval" between the frequencies. To find the interval between two
frequencies we divide one by the other. You can see that if the quotient
is larger than 1.1 or smaller than 0.9 the frequencies differ by ten
percent or more. The higher the frequency the larger the number of
cycles which is represented by a given size of interval.

While I am writing of frequency intervals I want to tell you one thing
more of importance. You remember that in human speech there may enter,
and be necessary, any frequency between about 200 and 2000 cycles a
second. That we might call the range of the necessary notes in the
voice. Whenever we want a good reproduction of the voice we must
reproduce all the frequencies in this range.

Suppose we have a radio-current of 100,000 cycles modulated by the
frequencies in the voice range. We find in the output of our
transmitting set not only a current of 100,000 cycles but currents in
two other ranges of frequencies. One of these is above the signal
frequency and extends from 100,200 to 102,000 cycles. The other is the
same amount below and extends from 98,000 to 99,800 cycles. We say there
is an upper and a lower "band of frequencies."

All these currents are in the complex wave which comes from the
radio-transmitter. For this statement you will have to take my word
until you can handle the form of mathematics known as "trigonometry."
When we receive at the distant station we receive not only currents of
the signal frequency but also currents whose frequencies lie in these

No matter what radio-frequency we may use we must transmit and receive
side-bands of this range if we use the apparatus I have described in
the past letters. You can see what that means. Suppose we transmit at a
radio-frequency of 50,000 cycles and modulate that with speech. We
shall really need all the range from 48,000 cycles to 52,000 cycles for
one telephone message. On the other hand if we modulated a 500,000
cycle wave by speech the side-bands are from 498,000 to 499,800 and
500,200 to 502,000 cycles. If we transmit at 50,000 cycles, that is, at
6000 meters, we really need all the range between 5770 meters and 6250
meters, as you can see by the frequencies of the side-bands. At 100,000
cycles we need only the range of wave-lengths between 2940 m. and 3060
m. If the radio-frequency is 500,000 cycles we need a still smaller
range of wave-lengths to transmit the necessary side-bands. Then the
range is from 598 m. to 603 m.

In the case of the transmission of speech by radio we are interested in
having no interference from other signals which are within 2000 cycles
of the frequency of our radio-current no matter what their wave-lengths
may be. The part of the wave-length range which must be kept clear from
interfering signals becomes smaller the higher the frequency which is
being modulated.

You can see that very few telephone messages can be sent in the
long-wave-length part of the radio range and many more, although not
very many after all, in the short wave-length part of the radio range.
You can also see why it is desirable to keep amateurs in the short
wave-length part of the range where more of them can transmit
simultaneously without interfering with each other or with commercial
radio stations.

There is another reason, too, for keeping amateurs to the shortest
wave-lengths. Transmission of radio signals over short distances is best
accomplished by short wave-lengths but over long distances by the longer
wave-lengths. For trans-oceanic work the very longest wave-lengths are
best. The "long-haul" stations, therefore, work in the frequency range
immediately above 10,000 cycles a second and transmit with wave lengths
of 30,000 m. and shorter.

[Illustration: Pl. XII.--Broadcasting Station of the American Telephone
and Telegraph Company on the Roof of the Walker-Lispenard Bldg. in New
York City Where the Long-distance Telephone Lines Terminate.]




The simplest wire telephone-circuit is formed by a transmitter, a
receiver, a battery, and the connecting wire. If two persons are to
carry on a conversation each must have this amount of equipment. The
apparatus might be arranged as in Fig. 129. This set-up, however,
requires four wires between the two stations and you know the telephone
company uses only two wires. Let us find the principle upon which its
system operates because it is the solution of many different problems
including that of wire-to-radio connections.

[Illustration: Fig 129]

Imagine four wire resistances connected together to form a square as in
Fig. 130. Suppose there are two pairs of equal resistances, namely
_R_{1}_ and _R_{2}_, and _Z_{1}_ and _Z_{2}_. If we connect a
generator, _G_, between the junctions _a_ and _b_ there will be two
separate streams of electrons, one through the R-side and the other
through the Z-side of the circuit. These streams, of course, will not
be of the same size for the larger stream will flow through the side
which offers the smaller resistance.

[Illustration: Fig 130]

Half the e. m. f. between _a_ and _b_ is used up in sending the
stream half the distance. Half is used between _a_ and the points _c_
and _d_, and the other half between _c_ and _d_ and the other end. It
doesn't make any difference whether we follow the stream from _a_ to
_c_ or from _a_ to _d_, it takes half the e. m. f. to keep this
stream going. Points _c_ and _d_, therefore, are in the same condition
of being "half-way electrically" from _a_ to _b_. The result is that
there can be no current through any wire which we connect between
_c_ and _d_.

Suppose, therefore, that we connect a telephone receiver between
_c_ and _d_. No current flows in it and no sound is emitted by
it. Now suppose the resistance of _Z_{2}_ is that of a telephone
line which stretches from one telephone station to another. Suppose also
that _Z_{1}_ is a telephone line exactly like _Z_{2}_ except
that it doesn't go anywhere at all because it is all shut up in a little
box. We'll call _Z_{1}_ an artificial telephone line. We ought to
call it, as little children would say, a "make-believe" telephone line.
It doesn't fool us but it does fool the electrons for they can't tell
the difference between the real line _Z_{2}_ and the artificial
line _Z_{1}_. We can make a very good artificial line by using a
condenser and a resistance. The condenser introduces something of the
capacity effects which I told you were always present in a circuit
formed by a pair of wires.

[Illustration: Fig 131]

At the other telephone station let us duplicate this apparatus, using
the same real line in both cases. Instead of just any generator of an
alternating e. m. f. let us use a telephone transmitter. We connect the
transmitter through a transformer. The system then looks like that of
Fig. 131. When some one talks at station 1 there is no current through
his receiver because it is connected to _c_ and _d_, while the
e. m. f. of the transmitter is applied to _a_ and _b_. The transmitter
sets up two electron streams between _a_ and _b_, and the stream which
flows through the Z-side of the square goes out to station 2. At this
station the electrons have three paths between _d_ and _b_. I have
marked these by arrows and you see that one of them is through the
receiver. The current which is started by the transmitter at station 1
will therefore operate the receiver at station 2 but not at its own
station. Of course station 2 can talk to 1 in the same way.

The actual set-up used by the telephone company is a little different
from that which I have shown because it uses a single common battery at
a central office between two subscribers. The general principle,
however, is the same.

[Illustration: Fig 132]

It won't make any difference if we use equal inductance coils, instead
of the R-resistances, and connect the transmitter to them inductively as
shown in Fig. 132. So far as that is concerned we can also use a
transformer between the receiver and the points _c_ and _d_,
as shown in the same figure.

[Illustration: Fig 133]

We are now ready to put in radio equipment at station 2. In place of the
telephone receiver at station 2 we connect a radio transmitter. Then
whatever a person at station 1 says goes by wire to 2 and on out by
radio. In place of the telephone transmitter at station 2 we connect a
radio receiver. Whatever that receives by radio is detected and goes by
wire to the listener at station 1. In Fig. 133 I have shown the
equipment of station 2. There you have the connections for wire to radio
and vice versa.

One of the most interesting developments of recent years is that of
"wired wireless" or "carrier-current telephony" over wires. Suppose that
instead of broadcasting from the antenna at station 2 we arrange to have
its radio transmitter supply current to a wire circuit. We use this same
pair of wires for receiving from the distant station. We can do this if
we treat the radio transmitter and receiver exactly like the telephone
instruments of Fig. 132 and connect them to a square of resistances. One
of these resistances is, of course, the line between the stations. I
have shown the general arrangement in Fig. 134.

You see what the square of resistances, or "bridge" really does for us.
It lets us use a single pair of wires for messages whether they are
coming or going. It does that because it lets us connect a transmitter
and also a receiver to a single pair of wires in such a way that the
transmitter can't affect the receiver. Whatever the transmitter sends
out goes along the wires to the distant receiver but doesn't affect the
receiver at the sending station. This bridge permits this whether the
transmitter and receiver are radio instruments or are the ordinary
telephone instruments.

[Illustration: Fig 134]

By its aid we may send a modulated high-frequency current over a pair of
wires and receive from the same pair of wires the high-frequency current
which is generated and modulated at the distant end of the line. It lets
us send and receive over the same pair of wires the same sort of a
modulated current as we would supply to an antenna in radio-telephone
transmitting. It is the same sort of a current but it need not be
anywhere near as large because we aren't broadcasting; we are sending
directly to the station of the other party to our conversation.

If we duplicate the apparatus we can use the same pair of wires for
another telephone conversation without interfering with the first. Of
course, we have to use a different frequency of alternating current for
each of the two conversations. We can send these two different modulated
high-frequency currents over the same pair of wires and separate them by
tuning at the distant end just as well as we do in radio. I won't sketch
out for you the tuned circuits by which this separation is made. It's
enough to give you the idea.

In that way, a single pair of wires can be used for transmitting,
simultaneously and without any interference, several different telephone
conversations. It takes very much less power than would radio
transmission and the conversations are secret. The ordinary telephone
conversation can go on at the same time without any interference with
those which are being carried by the modulations in high-frequency
currents. A total of five conversations over the same pair of wires is
the present practice.

This method is used between many of the large cities of the U. S.
because it lets one pair of wires do the work of five. That means a
saving, for copper wire costs money. Of course, all the special
apparatus also costs money. You can see, therefore, that this method
wouldn't be economical between cities very close together because all
that is saved by not having to buy so much wire is spent in building
special apparatus and in taking care of it afterwards. For long lines,
however, by not having to buy five times as much wire, the Bell Company
saves more than it costs to build and maintain the extra special

I implied a moment ago why this system is called a "carrier-current"
system; it is because "the high-frequency currents carry in their
modulations the speech significance." Sometimes it is called a system of
"multiplex" telephony because it permits more than one message at a

This same general principle is also applied to the making of a multiplex
system of telegraphy. In the multiplex telephone system we pictured
transmitting and receiving sets very much like radio-telephone sets. If
instead of transmitting speech each transmitter was operated as a C-W
transmitter then it would transmit telegraph messages. In the same
frequency range there can be more telegraph systems operated
simultaneously without interfering with each other, for you remember how
many cycles each radio-telephone message requires. For that reason the
multiplex telegraph system which operates by carrier-currents permits as
many as ten different telegraph messages simultaneously.

You remember that I told you how capacity effects rob the distant end of
a pair of wires of the alternating current which is being sent to them.
That is always true but the effect is not very great unless the
frequency of the alternating current is high. It's enough, however, so
that every few hundred miles it is necessary to connect into the circuit
an audion amplifier. This is true of carrier currents especially, but
also true of the voice-frequency currents of ordinary telephony. The
latter, however, are not weakened, that is, "attenuated," as much and
consequently do not need to be amplified as much to give good
intelligibility at the distant receiver.

[Illustration: Fig 135]

In a telephone circuit over such a long distance as from New York City
to San Francisco it is usual to insert amplifiers at about a dozen
points along the route. Of course, these amplifiers must work for
transmission in either direction, amplifying speech on its way to San
Francisco or in the opposite direction. At each of the amplifying
stations, or "repeater stations," as they are usually called, two vacuum
tube amplifiers are used, one for each direction. To connect these with
the line so that each may work in the right direction there are used two
of the bridges or resistance squares. You can see from the sketch of
Fig. 135 how an alternating current from the east will be amplified and
sent on to the west, or vice versa.

[Illustration: Fig 136]

There are a large number of such repeater stations in the United States
along the important telephone routes. In Fig. 136 I am showing you the
location of those along the route of the famous "transcontinental
telephone-circuit." This shows also a radio-telephone connection between
the coast of California and Catalina Island. Conversations have been
held between this island and a ship in the Atlantic Ocean, as shown in
the sketch. The conversation was made possible by the use of the vacuum
tube and the bridge circuit. Part of the way it was by wire and part by
radio. Wire and radio tie nicely together because both operate on the
same general principles and use much of the same apparatus.

[Blank Page]


    A-battery for tubes, 42

    Accumulator, 29

    Acid, action of hydrogen in, 7

    Air, constitution of, 10

    Ammeter, alternating current, 206;
      calibration of, 53;
      construction of, 205

    Ampere, 49, 54

    Amplification, 182; one stage of, 185

    Amplitude of vibration, 155

    Antenna current variation, 141

    Arlington tests, 233

    Artificial telephone line, 252

    Atom, conception of, 6;
      nucleus of, 10;
      neutral, 34

    Atomic number, 13

    Atoms, difference between, 12;
      kinds of, 6, 10;
      motion of, 35

    Attenuation of current in wires, 259

    Audibility meter, 218

    Audio-frequency amplifier, 185;
      limitations of, 185

    Audion, 35, 40, 42

    Audion, amplifier, 182;
      detector, theory of, 126;
      modulator, 232;
      oscillator, theory of, 89;
      frequency control of, 99

    B-battery for tubes, 43;
      effect upon characteristic, 128

    Banked wound coils, 228

    Battery, construction of gravity, 16;
      dry, 27;
      reversible or storage, 29

    Band of frequencies, 249

    Beat note, detection of, 221, 245

    Bell system, Arlington transmitter, 249

    Blocking of tube, reason for, 171

    Blue vitriol, 16

    Bridge circuit, 255

    Bureau of Standards, 50

    C-battery for tubes, 46, 166;
      variation of, 75;
      for detection, 66

    Calibration of a receiver, 214

    Capacity, effect upon frequency, 100;
      measurement of, 104;
      unit of, 104;
      variable, 107

    Capacity effects, 243;
      elimination of, 228

    Carrier current, modulation of, 146;
      telephony, 255

    Characteristic, of vacuum tube, 68, 74;
      effect of B-battery upon, 128;
      how to plot a, 70

    Characteristic curve of transformer, 64

    Chemistry, 8

    Choke coils, 210, 221

    Circuit, A, B, C, 187;
      coupled, 115;
      defined, 43;
      oscillating, 113;
      plate, 45;
      short, 30;
      tune of a, 117

    Condenser, defined, 77;
      charging current of, 78;
      discharge current of, 80;
      impedance of, 135;
      theory of, 78;
      tuning, 224

    Common battery system, 254

    Connection for wire to radio, 254

    Continuous waves, 86

    Copper, atomic number of, 13

    Copper sulphate, in solution, 21

    Crystals, atomic structure, 147

    Crystal detectors, 146;
      characteristic of, 148;
      circuit of, 150;
      theory of, 147

    Current, transient, 114;
      radio, 144

    Cycle, 94, 97

    Damped oscillations, 114

    Demodulation, 231

    Detection, explained, 146

    Detectors, audion, 126;
      crystal, 146

    Direct currents, 205

    Dissociation, 22

    Distortion, of wave form, 163

    Dry battery, 27

    Earth, atomic constitution, 11

    Effective value, of ampere, 207;
      of volt, 207

    Efficiency, of regenerative circuit, 182

    Electrical charge, 22

    Electricity, current of, 15, 16

    Electrodes, of vacuum tube, 41;
      definition of, 41

    Electrolyte, definition of, 34

    Electrons, properties of, 4;
      planetary, 10, 12;
      rate of flow, 48;
      vapor of, 39;
      wandering of, 14

    Electron streams, laws of attraction, 200

    E. M. F., 59;
      alternating, 76;
      of self-induction, 238

    Energy, expended in tube, 235;
      of electrons, 113;
      radiation of, 125

    Ether, 88

    Feed-back circuit, 182

    Frequency, 98, 158;
      effect upon pitch, 133;
      interval, 247;
      natural, 117;
      of voice, 163

    Fundamental note, of string, 157

    Gravity battery, theory of, 23

    Grid, action of, 47;
      condenser, 169;
      current, 173;
      leak, 171;
      leak, construction, 172, 216;
      of audion, 41

    Harmonics, 160

    Helium, properties of, 9

    Henry, 83

    Heterodyne, 181

    Hot-wire ammeter, 51

    Human voice, mechanism of, 152

    Hydrogen, action of in acid, 7;
      atom of, 7

    Impedance, of coil, 136;
      of condenser, 136;
      of transformer, 195;
      effect of iron core upon, 207;
      matching of, 196

    Intermediate-frequency amplification, 242

    Inductance, defined, 83;
      effect upon frequency, 100;
      impedance of, 135;
      mutual, 109;
      of coils, 101;
      self, 83;
      table of values, 227;
      unit of, 83;
      variable, 108

    Induction, principle of, 208

    Inducto-meter, 109

    Input circuit, 187

    Interference, 249

    Internal resistance, 191

    Ion, definition of, 19;
      positive and negative, 20, 21

    Ionization, 20

    Larynx, 153

    Laws of attraction, 204

    Loading coil, 224

    Loop antenna, 198

    Magnet, pole of, 203;
      of soft iron, 205;
      of steel, 205

    Magnetism, 202

    Matter, constitution of, 5

    Megohm, 172

    Microfarad, 104

    Mil-ampere, 71

    Mil-henry, 83

    Modulation, 145, 230, 237, 239

    Molecule, kinds of, 6;
      motion of, 35

    [Greek: mu], 190

    Multiplex telegraphy, 258;
      telephony, 258

    Mutual inductance, 109;
      variation of, 110

    Natural frequency, 161

    Nitrogen, 10

    Nucleus of atom, 10, 12

    Ohm, defined, 64

    Organ pipe, 160

    Oscillations, 87;
      damped, 114;
      to start, 114;
      intensity of, 236;
      natural frequency of, 117

    Output circuit, 187

    Overtones, 159

    Oxygen, percentage in air, 10

    Phase, 180

    Plate, of an audion, 41

    Plunger type of instrument, 205

    Polarity of a coil, 204

    Power, defined, 234;
      electrical unit of, 235

    Proton, properties of, 4

    Radio current, modulation of, 145

    Radio-frequency  amplification, 243;
      limitations, 243

    Radio-frequency amplifier, 186, 198

    Radio station connected to land line, 254

    Rating of tubes, 235

    Reception, essential operations in, 235

    Regenerative circuit, 176;
      frequency of, 179

    Repeater stations, 261

    Resistance, measurement of, 64;
      non-inductive, 103;
      square, 251

    Resonance, 161

    Resonance curve, 117

    Retard coils, 210

    Salt, atomic construction of, 17;
      crystal structure, 147;
      molecule in solution, 19;
      percentage in sea water, 11

    Saturation, 38

    Sea water, atomic constitution of, 11

    Self-inductance, 83;
      unit of, 83

    Side bands, 248;
      relation to wave lengths, 249

    Silicon, percentage in earth, 11

    Sodium chloride, in solution, 19

    Sound, production of, 152

    Speech, to transmit by radio, 230

    Speed of light, 122

    Standard cell, 58

    Storage battery, 28, 30

    Sulphuric acid, 22

    Super-heterodyne, 242;
      advantages of, 242

    Telephone receiver, 130;
      theory of, 131

    Telephone transmitter, 142

    Telephony, by wire, 253

    Tickler coil, 182

    Transcontinental telephone line, 261

    Transmission, essential operations in, 230

    Transmitter, Arlington, 233;
      continuous wave, 94, 119;
      for high power, 233

    Transformer, 185;
      step-up, 193

    Tubes, connected in parallel, 234

    Tuning, curve, 117;
      sharp, 214;
      with series condenser, 224

    Undamped waves (see continuous waves), 86

    Vacuum tube, 35, 40;
      characteristics of, 67;
      construction of, 205;
      modulator, 239;
      three-electrode, 41;
      two-electrode, 42

    Variometer, 108

    Vibrating string, study of, 154

    Vocal cords, 153

    Voice frequencies, 163

    Volt, definition of, 57;
      measurement of, 61

    Voltmeter, calibration of, 62;
      construction of, 205

    Watt, 235

    Wave form, 182

    Wave length, relation to frequency, 98, 122;
      defined, 122

    Wire, inductance of, 104

    Wire, movement of electrons in, 14;
      emission of electrons from, 37

    Wire telephony, 253

    Wired wireless, 255;
      advantages of, 257

    X-rays, 147

    Zero coupling, 177

    Zinc, electrode for battery, 23

*** End of this Doctrine Publishing Corporation Digital Book "Letters of a Radio-Engineer to His Son" ***

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