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Title: A Course of Mechanical, Magnetical, Optical, Hydrostatical and Pneumatical Experiments - perform'd by Francis Hauksbee, and the Explanatory Lectures - read by William Whiston, M.A.
Author: Francis Hauksbee (the Younger)
Language: English
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team at DP-test Italia, http://dp-test.dm.unipi.it



                                    A
                                  COURSE
                                    OF
             Mechanical, Magnetical, Optical, Hydrostatical,
                                   AND
                         Pneumatical EXPERIMENTS.

To be perform'd by FRANCIS HAUKSBEE; and the Explanatory Lectures read by
                          WILLIAM WHISTON, M. A.


                               MECHANICKS.

1st Day. SIR _ISAAC NEWTON_'s Three Laws of Motion, or Nature,
demonstrated by Experiments.

That the Velocity of Falling Bodies is as the Times of Falling, and the
Lines of Descent in the Duplicate Proportion of those Times.

An Instrument to measure the Force of Falling Bodies.

Experiments concerning the Sliding, Rolling, and Falling of Bodies.

That Bodies will ascend as high, as whence they fall by the last Velocity
impress'd, when all Obstacles are removed.

That Bodies by a compound Force move in a Diagonal Line.

2d—The Balance and Stilyard, with all their Properties and Uses shewn and
explain'd.

The Method of estimating the _Momentum_, or Quantity of Motion in any
given Body.

The general Principle of Mechanicks established upon this Method.

Experiments to demonstrate the different Effects of the same Weight of
Power acting in different Directions at the same Point of any Engine.

The Resolution of Forces into those of other Directions.

All the various Kinds of Levers explain'd.

3d—All the Phænomena of Pulleys, both single and in all their possible
Combinations explain'd.

The Power of the Wheel or Axis in Peritrochio explain'd.

The Wedge, with the Method of comparing its Force, deduced from
Experiments.

The Screw, with the manner of computing its Force.

A Compound Engine.

4th—An Experiment of Lifting a Weight by a Chain of Inflated Bladders,
with its Application to Muscular Motion.

_Galilæo_'s Demonstration concerning the Strength of the Bones, Timber,
_&c._ reduced to Experiment.

The Method of computing the Force of the Air on the Sails of Windmills,
and of Ships; and of Water on Water-Wheels, and on the Rudder of a Ship.

Experiments to shew the proportional Advantages of large and small Wheels,
in all Sorts of Carriages, as Couches, Waggons, Carts, _&c._

5th—An Experiment to shew, that the lateral Motion compounded with the
perpendicular Projection, does not alter the Line of Ascent or Descent in
the projected Body.

The most considerable Objections against the Motion of the Earth, answered
from this Experiment.

That the Line described by a Projectile is a Parabola.

The Experiments upon which the Art of Gunnery does depend, most exactly
perform'd.

6th—Experiments concerning Pendulums.

The Description and chief Properties of the Cycloid, and the Application
of Cycloidal Cheeks for regulating the Vibrations of Pendulums.

An Experiment to shew the Analogy between the Swings of a Pendulum and the
Waves of the Sea.

Experiments concerning the Expansion of Metals by Heat.

7th—The Laws of Motion in the Collision of Hard and Elastick Bodies.

Experiments concerning the Centrifugal and Centripetal Forces of Solid and
Fluid Bodies in Motion.

Experiments in order to estimate the Centrifugal Forces of Solid Bodies.


                               MAGNETICKS.

8th Day. Attractive and Directive Powers of Loadstones.

The Form or Position of Filings of Iron at the Poles and Equator of a
Loadstone.

Magnetick Power acts thro' all Bodies but Iron.

The Attraction of different, and Repulse of corresponding Poles.

The manner of touching and untouching of Needles.

The Law of Magnetick Attraction discover'd.

9th—The Phænomena of _Terrella_, or Spherical Loadstones.

The Direction of Magnetick Needles on the Surfaces of _Terrella_ nearly
towards the Poles.

Their Variation _East_ and _West_.

The Inclinatory or Dipping-Needle, with the Law of the Alteration of that
Inclination on the Surface of a _Terrella_.

The Terrestrial Magnetism consider'd.

The Application of the Dipping-Needle to the Discovery of the Longitude
and Latitude of Places by Land and Sea.


                                 OPTICKS.

10th Day. Experiments to demonstrate, that in the Rays of Light the Angle
of Incidence is equal to the Angle of Reflection in all Sorts of Surfaces.

The Method of tracing the reflected Rays of Light from Plain, Convex,
Concave, and Cylindrical Superficies, with all their wonderful Properties
and Uses, shew'd and explain'd.

11th—Sir _Is. Newton_'s Reflecting Telescope exhibited, and its
Construction explained; together with some Specimens of its Uses in
observing the Planets and Fixed Stars.

12th—Experiments to shew the Manner of Refraction.

The Sines of the Angles of Incidence and Refraction, shewn to be (at all
Degrees of Incidence) in a constant Proportion to each other.

An Instrument to measure the Refraction of Fluids.

The Method of tracing the Refracted Rays of Light thro' Plain, Convex, and
Concave Superficies.

13th—An artificial Eye, in which all the Coats and Humours are curiously
represented.

The Dissection of the Eye.

The Explication of Vision by the naked Eye, deduced from Experiments.

14th—All the Effects, Properties, and Uses of Plain, Convex, and Concave
Glasses, both single and combin'd in Telescopes and Microscopes, shew'd
and explain'd.

Several Kinds of Microscopes and Telescopes, with the Manner of applying
them to their respective Objects; together with a Specimen of the Uses of
such Microscopes and Telescopes.

A Multiplying Glass.

The Magick Lanthorn.

15th—A particular _Apparatus_ to manifest and measure the Refraction of
Air.

The _Camera Obscura_.

The Theory of Light and Colours, as delivered by Sir _Isaac Newton_,
demonstrated by several of his principal Experiments.

The Archbishop of _Spalato_'s Experiment, which discovered the Cause of
the Rainbow.

Monsieur _Hugen_'s Experiments, which discover the Causes of Halo's, of
the Mock Suns and Moons, and of inverted Rainbows.

Experiments concerning the blending and Production of Colours by Motion.


                              HYDROSTATICKS.

16th Day. That Fluids gravitate _in proprio loco_, the upper Parts
continually pressing upon the lower: That this Pressure is not only
propagated Downwards, but even Upwards, and Sideways, according to all
possible Directions; That a lighter Fluid may gravitate upon a heavier,
and an heavier upon a lighter; That a Fluid may sustain a Body heavier _in
Specie_ than it self, and even raise it up; That a Fluid may detain a Body
lighter _in Specie_ than it self, and even depress it. A general
Experiment to prove, that a competent Pressure of a Fluid may produce the
remarkable Phænomena of the Torricellian Tube, the Pump, Syringe, Syphon,
polished Plates, and other Effects of the like Nature.

17th—That Fluids press according to their perpendicular Altitudes,
whatever be their Quantities, or however the containing Vessels be
figured. The exact Estimate of all manner of Pressures. That the Velocity
and Quantity of Fluids running out at a given Hole, is in the subduplicate
Proportion of their perpendicular Altitudes. Several Sorts of Pumps. Of
the sinking and floating of Bodies immers'd in Fluids; their relative
Gravities and Levities; their Situations and Positions. The Phænomena of
Glass Bubbles and Images accounted for.

18th—An Instrument to find out the Specifick Gravity of all Liquors. The
Hydrostatical Balance explain'd, with the Methods of determining the
Specifick Gravities of all Sorts of Bodies, whether Solid or Fluid,
thereby. The Praxis of the Hydrostatical Balance, whereby the Specifick
Gravities of several particular Bodies are actually found out. Some
Account of the various Uses of such Enquiries.


PNEUMATICKS _illustrated by Experiments for the most part Tubular,
being such as were wont to be made before the Air-Pump was invented._

19th Day. The several Phænomena of the Torricellian Experiment exhibited
and explained. Other Experiments of the like Nature, with Fluids variously
combin'd. Several Sorts of Barometers, Thermometers, and Hygroscopes. The
Pressure of the Air shewn by Experiment to be different at different
Altitudes from the Surface of the Earth.

20th—The Density and Spring of the Air proved by several ways to be as the
Force which compresses it, and reciprocally as the Spaces into which it is
compress'd. From hence an Enquiry is made into the Limits and State of the
Atmosphere.

21st—The Effects of the Weight and Spring of the Air in Syringes, Pumps,
Siphons, polished Plates, Cupping-Glasses, Suction: Respiration explained
by artificial Lungs; That the Air may be so disorder'd by a violent
Impulse, as to require Time to recover its Strength and Elasticity again.


_The more known Properties of the Air established by the Air-Pump, and
                            other Engines._

22d Day. The Air-Pump; the Instruments for Condensing and Transferring of
Air; their Fabrick, Operation, and Gages explained.

23d—A Parcel of Air weighed in the Balance; its Specifick Gravity to that
of Water determined thereby; an artificial Storm, shewing that high Winds
may make the Barometer sink much and suddenly.

24th—The Weight, Pressure, and Spring of the Air prov'd several ways; by
the Sense of Feeling; by breaking Glass Vials; the Phænomena of Bladders,
Glass-bubbles, Fountains; the Gardiner's Watering-Pot; the Diving-Bell,
_&c._

25th—The Torricellian Tube _in Vacuo_; Quicksilver raised to the usual
Height of the Weather-Glass, by the bare Spring of a little included Air;
_Otto Gerick_'s Hemispheres; and that dense Air has the same Advantage
over common Air, as that has over a _Vacuum_.

The Ebullition of Liquors _in Vacuo_; the Quantity of Air contain'd in
them; the Sustentation of Fumes and Vapours; the Descent of Bodies _in
Vacuo_.


_The more hidden Properties of the Air consider'd by the help of the like
                                Engines._

26th Day. The Influence of the Air examin'd as to the Causes of Magnetism;
the Elasticity of Springs; the Cohæsion of the Parts of Matter; the
Sphericity of the Drops of Fluids; the Ascent of Liquors in capillary
Tubes, and between Glass-Planes in the Curve of the Hyperbola, both by the
Attractive and Repulsive Power of the Glass.

27th—The Influence of the Air, as to Sounds, Fire, and Flame; the
Consumption of Fuel; the firing of Gunpowder; the Effects of rarified,
condensed, and burnt Air upon the Life of Animals.

28th—A Piece of Phosphorus _in Vacuo_; new Experiments concerning the
Mercurial Phosphori; Experiments concerning the Electricity of Bodies.

--------------------------------------------------------------------------

   _Every SUBSCRIBER is to pay Three Guineas; One Guinea at the Time of
      Subscription, and the Remainder, the First Day of the Course._

SUBSCRIPTIONS _are taken in at Mr. Whiston's, in Great Russel-Street; and
 at Mr. Hauksbee's, in Crane-Court in Fleetstreet; where the Course is to
                              be perform'd._



                              Advertisement.


Air-Pumps, or Engines for Exhausting the Air from proper Vessels, with all
their Appurtenances; whereby the various Properties and Uses of that Fluid
are discover'd and demonstrated by undeniable Experiments. Engines for the
Compression of the Air: Fountains, in which the Water, or other Liquor, is
made to ascend by the Force of the Air's Spring. Syringes and Blow-Pipes,
with Valves for Anatomical Injections. Hydrostatical Balances, for
determining the Specifick Gravity of Fluids and Solids. The Engine and
Glasses for the New Way of Cupping without Fire. Scarificators, which at
once make either 10, 13, or 16 Incisions. Weather-Glasses of all Sorts, as
Barometers, Thermometers, _&c._ Reflecting Telescopes, by which in so
short a Length as Six Feet, all that has hitherto been discovered in the
Heavens (by the longest Telescopes of the common Construction) may be
observed.

All the above-mention'd Instruments, according to their Latest and Best
Improvements, are made and sold by FRANCIS HAUKSBEE, in _Crane-Court_ in
_Fleetstreet, London_.



             [[Mechanicks Plate I. ― Sutton Nicholls sculp:]]



                                    1
                               MECHANICKS.

                    An Explication of the First PLATE.


Figure. 1. This belongs to _Galilæo's_ famous Demonstration of the
Velocities and Times of Bodies descending by an uniform Force, such is
that of Gravity here below: And shews that they will ever fall in equal
Times, 1, 2, 3, 4, _&c._ according to the odd Numbers, 1, 3, 5, 7, _&c._
or the Trapezia B C D E, D E F G, F G H I, _&c._ and by consequence, that
their Velocity will increase uniformly in Proportion to the Lines B C,
D E, F G, H I, _&c._ or to the Times of Descent. And that the entire Lines
of their Descent will be as the Triangles A B C, A D E, A F G, A H I,
_&c._ or as the Squares of those Times, 1, 4, 9, 16, _&c._

_Fig. 2._ This is a strong Balance for an Experiment to prove the former
Proposition, by shewing that any Bullet or Ball, when it falls from four
Times the Height, has twice, from nine Times the Height has thrice its
former Velocity or Force; and will accordingly raise a double or triple
Weight in the opposite Scale, to the same Height, and no more; and so for
ever.

_Fig. 3._ This shews how Bodies upon an inclin'd Plane will _slide_, if
the Perpendicular through the Center of their Gravity falls _within_; and
will _rowl_, if that Perpendicular fall _without_ their common Section.

_Fig. 4._ This shews that an oblique Body will stand, if the Perpendicular
through its Center of Gravity cut the Base; and that it will fall, if it
cut not the Base: As accordingly we stand when the Perpendicular through
the Center of Gravity of our Bodies falls within the Base of our Feet; and
we are ready to tumble when it falls without the same.

_Fig. 5._ This is a Conick Rhombus, or two right Cones, with a common
Base, rowling upwards to Appearance, or from E towards F and G: Which
Points are set higher by Screws than the Point E. But so that the
Declivity from C towards A and B is greater than the Aclivity from E
towards F and G. Whence it is plain, that the Axis and Center of Gravity
do really descend all the Way.

_Fig. 6._ Is a Balance, in an horizontal Posture, with weights at
Distances from the Center reciprocally proportional to themselves; and
thereby _in Æquilibrio_.

_Fig. 7. and 8._ Are two other Balances in an horizontal Posture, with
several Weights on each Side, so adjusted, that the Sum of the Motion on
one Side, made by multiplying each Weight by its Velocity, or Distance
from the Center, and so added together, is equal to that on the other: And
so all still _in Æquilibrio_.

_Fig. 9._ Belongs to the Laws of Motion, in the Collision of Bodies to be
tried with Pendulums, or otherwise, both as to Elastical Bodies, and to
those which are not Elastical.

_Fig. 10._ Belongs to that Famous and Fundamental Law of Motion, that if a
Body be impell'd by two distinct Forces in an Proportion, it will in the
same Time move along the Diagonal of that Parallelogram, whose Sides would
have been describ'd by those distinct Forces; and that accordingly all
Lines, in which Bodies move, be consider'd as Diagonals of Parallelograms;
and so may be resolved into those two Forces, which would have been
necessary for the distinct Motions along their two Sides respectively:
Which grand Law includes the Composition and Resolution of all Motions
whatsoever, and is of the greatest Use in Mechanical and Natural
Philosophy.

_Fig. 11._ Are two polite Plains inclined to one another, to shew that the
Descent down one Plain will elevate a Ball almost to an equal Height on
the other.



                  [[Plate II. ― Sutton Nicholls sculp:]]



                              MECHANICKS. 2

                   An Explication of the Second PLATE.


Figure 1. Is the deceitful Balance; which yet is _in Æquilibrio_ because
the Weights 23 and 24 are reciprocally proportional to their Distances
from the Center of Motion. Now this Cheat is easily discover'd by changing
the Position of the Weights, and putting each of them into the other
Scale, which will then be very unequal, or nearly as 11 to 12.

_Fig. 2._ Is that sort of Balance which is called a Stiliard, and of
frequent Use among us. It is only a Common Balance, with Weights at
Distances from the Center of Motion reciprocally Proportionable to
themselves: Only here the Length of Part of the Beam is compensated by a
large Ball or Weight B, fixed to the shorter Beam; and one Weight as w
removed along equal Divisions is made use of to weigh several others, as
6 w. _&c._

_Fig. 3_. Is design'd to shew how any Force is diminish'd by its
Obliquity; and that a Weight hung obliquely at 3, 2, 1, in the
Circumference of a Circle or Wheel, is of no more Efficacy, as to the
turning of the Wheel round, than if it were hung perpendicularly at the
corresponding Points 3, 2, 1, in the Semidiameter of the same Circle.

_Fig. 4._ Is the Demonstration of the former Case, by shewing that in
those Circumstances the Force P B is resolved into two B F and B G, of
which B F pulls directly from the Center, and is of no Use to the turning
the Wheel round: And so all the remaining Force is represented by the
perpendicular Force B G, which is wholly spent in turning it round. So
that as B P is to B G, so is the whole oblique Force, to the real or
direct Force: Or so, in the similar Triangle B E C, is B C the whole
oblique Radius, to C E the Perpendicular: Or so in the foregoing Figure is
O 1, O 2, O 3, the common Hypotenuse or entire Radius, to O 1, O 2, O 3,
the Bases or shorter Radij, where the String cuts the entire Radius
perpendicularly.

_Fig. 5._ Is the first Sort of Lever, where C the Prop is between the
Resistance to be overcome, or Weight to be moved 5 w, and w 1 the Power or
Weight to move the other by: And is so like the Case of the Balance or
Stiliard, that it needs no particular Explication. A Crow of Iron is of
this Sort.

_Fig. 6._ Is the second Sort of Lever, where the Resistance to be
overcome, or Weight to be moved w 3, is between the Prop C and the Point
A, to which by the means of the Pulley P, the Power or Weight to move the
other by, is applied. Bakers Knives for cutting Bread are commonly of this
Sort.

_Fig. 7._ Is the third Sort of Lever, where the Resistance to be overcome,
or Weight to be moved, w 2 is at one End, the Prop at the other, and the
Power or Weight w 3 between them. A Ladder lifted up by the Middle, in
order to be rear'd, where one End is fixed, is of this Sort. Only the
Force being in this Case nearer the Prop than the Resistance to be
overcome, or Weight to be moved, this Sort of Lever diminishes Force
instead of increasing it, and is therefore of little Use.

_Fig. 8._ Is a common Lever of the first Sort, with its Prop and equal
Divisions, fit to be used as the Stiliard.

_Fig. 9._ Is a compound Lever of the first Sort, as long as the single one
just above it, where a Weight at G, by being doubled three several Times,
will raise eight Times its own Weight at A, as well as the other does it
at once. This last is therefore of the same Force as the former, and no
more; and by being compounded, is less considerable than the other.

_N. B._ Had the Proportion in the Compound Lever, _Fig. 9._ been
otherwise, as suppose the Part B C on one Side of the Prop B three Times
the Length of A B on the other Side, and the same in the other two Levers
C E and E G; then the Weight G being but the 27th Part of the Weight at A,
will be in _Æquilibrio_ with it.

_Fig. 10._ Is a bended Lever of the first Sort, where C the Prop is at an
Angle, and the Force is increas'd with C H, the Distance of the Weight
w 1, which by the means of the Pulley P, is applied to the longer Part of
the Lever; and in this Lever, the Power is to the Resistance reciprocally
as their Distances. An Hammer drawing out a Nail is such a bended Lever.

_Fig. 11, 12._ Shew that Levers or Balances that are even when horizontal,
may be uneven in other Positions; that is, too light when the Center of
Gravity of one Weight is fix'd to the Lever or Balance above, and it is
elevated; or below, and depress'd: Because the Perpendicular cuts the
horizontal Line too near the Center in these Cases.



                 [[Plate III. ― Sutton Nicholls sculp:]]



                              MECHANICKS. 3

                    An Explication of the Third PLATE.


Figure 1. Is a Sort of Compound Lever of the second Kind, where the Weight
H 6 is unequally born by the Weights F 4 and G 2, which are reciprocally
proportional to the Distances C B and C A; and are accordingly _in
Æquilibrio_. Whence we see how two Men may bear unequal Parts of the same
Weight, in Proportion to their Nearness thereto.

_Fig. 2._ Is another Engine of the same Nature with the former; where the
Lines D C, A E, B F, and the Lever A B, are parallel to the Horizon; but
the Lines on which the Weights hang D w 7, E w 5, F w 2, are perpendicular
thereto; and here a Force or Weight pulling at the Point C sustains the
unequal Weights w 5 and w 2 _in Æquilibrio_: Provided the Distances C B
and C A be reciprocally proportional to those Weights. Whence we learn,
how Horses of unequal Strength may be duly fitted to preserve equally in
their Labour; _viz._ by taking care that the Beam by which they both draw
a Weight or Waggon, may be divided at the Point of Traction as C, in
reciprocal Proportion to such their Strength.

_Fig. 3._ A B is an upper Pulley, of no direct Advantage, but for
Readiness of the Motion, as increasing not the Power at all; equal Weights
being ever required to raise others.

_Fig. 4._ Is an upper and an under Pulley connected together; where the
upper being of no Efficacy, the lower does however double the Force, as is
ever the Case in such Pulleys.

_Fig. 5._ Is a Compound Pulley of three upper and three under Pulleys, all
communicating together; where therefore the whole Weight is divided among
6 Strings; and so 1 Pound balances 6 Pound. The last String B M 1, as
passing beyond the last upper Pulley, not being here to be reckon'd of any
Consequence.

_Fig. 6._ and 7. These are Boxes of the same Number of upper and under
Pulleys with the former; only in other Positions, and depend on the same
Principle entirely.



                  [[Plate IV. ― Sutton Nicholls sculp:]]



                              MECHANICKS. 4

                   An Explication of the Fourth PLATE.


Figure 1. Is a System of Pulleys connected together, whereby the Force is
increased by Addition in Proportion to the Number of Cords; so that one
Pound, w 1, sustains five Pounds, w 5, as must happen from the Equality of
the stretching of the whole Cord, and the consequent Division of the whole
Weight into five equal Parts, as equally supported by them all.

_Fig. 2._ Is a System of Pulleys not connected together, whereby the Force
is increas'd, for every lower Pulley; according to the Numbers, 2, 4, 8,
in a double Proportion; because every lower Pulley doubles the Force of
the former; as is evident at the first Sight; since the Velocity of Ascent
or Descent of the greater Weight is every Time but half so great as
before.

_Fig. 3._ Is the Axis in Peritrochio; or Wheel, with its Axel; where any
Weight or Force applied round E F, or C D, or A B, has just so much
greater Power to move the Wheel, or entire Machine about the Axis, as the
Velocity or Distance from the Geometrical Axis it self is greater. Nor is
there any farther Difficulty in this plain Engine.

_Fig. 4._ This is only a Train of Wheel-work; which by Composition of
Wheels vastly increases the Force. Thus suppose the Diameter of the Barrel
E F, be ten times the Diameter of the Pinion G: And the Diameter, or
Number of equal Teeth in G, be one tenth of the Diameter, or Number of
equal Teeth in H I: And the Diameter and Velocity of the Teeth in H I, be
ten times the Diameter and Velocity of the Pinion K; and the Diameter or
Number of equal Teeth in K, be one tenth of the Diameter, or Number of
equal Teeth in L M; And that the Barrel N O, be of the same Diameter with
the Wheel L M. Then a Weight on the Barrel E F will balance a Weight one
hundred times as heavy upon the Barrel N O; which is done by its moving an
hundred Times as swift as the other. For the Velocity in the first Barrel
E F, to that of its Pinion G, is as ten to one; and that in the Wheel H I,
to that in its Pinion K, is also as ten to one. While the Velocities at
each Wheel, and its corresponding Pinion in the other Wheel, as well as at
the Wheel L M, and its Barrel N O, are equal.

_Fig. 5._ Is a compound Engine, to prove that in a Wedge, as E M G,
depress'd by a Weight w, or by its own Weight, or by a Stroke, the Force
is diminished in Proportion to the Sine of its Aperture, compar'd with the
Line of its Depth: So that when the former Sine is double or triple, _&c._
the Force is diminished one half, or one third, _&c._ This is here prov'd
by the Wedges separating two Cylinders, which are drawn together by other
Weights, in the Scales R and S beneath, when its Sides are screw'd nearer
or farther off, to adjust their Distance to those Weights perpetually.

_Fig. 6._ Is a Wedge by it self, where the Force is increas'd in the
Proportion of the Sines of the Angles of Aperture, D F and D E, to the
Radius D B; or is resolv'd into two Forces, the one perpendicular, and the
other parallel to the Plain of the Tree or Timber it is to reeve: And this
because the Velocity downward is ever to the Velocity side-ways in the
Proportion of D B to D F and D E, or to 2 D F. _i. e._ by the Similitude
of Triangles, as A B or C B to A C.

_Fig. 7._ Is a Paper Wedge, H F G coil'd round a Cylinder, and so
representing a Screw; and shews that its Force must be increas'd in
Proportion to the Progress along its Cylinder, when it is compar'd with
the Circumferences on the same Cylindrical Surface, or as H F to H G.

_Fig. 8._ Is a compound Engine to explain and measure the Power of the
Screw: from whence it appears, that the Force of Screws is reciprocally
proportional to the Distance of the _Helix_'s or Threads which compose
them.



               [[Plate V. ― Sutton Nicholls del. & sculp:]]



                              MECHANICKS. 5

                    An Explication of the Fifth PLATE.


Figure 1. Is a Compound Engine in which all the several Mechanical Powers
are combin'd: as the Wheel and Axle G H: The Balance or Lever I K: the
Screw F; which includes the Wedge: and the Pulley L M. The entire Force of
this Engine is to be computed by compounding the separate Forces together.

_Fig. 2._ Is a Windmill; whose Force is here represented, by its raising a
Weight on a Barrel. The Wind is supposed to blow parallel to the Axis,
from E towards D; its several Sails have their Plains nearly 45 Degrees
oblique to the Plain through the middle of those Sails: Two of them
inclining, and two reclining. By this Means the Wind falling at about 45
Degrees obliquity on the Plain of each Sail; the Breadth of each Sail is a
Diagonal of a square, one of whose Sides is parallel to the Direction of
the circular Motion, and has its full Force; and the other is
perpendicular thereto, and so has no Effect as to that circular Motion at
all. And as much as the Side of a Square is lesser than the Diagonal, so
much of the whole Quantity of the Wind is lost on every single Sail. But
then each Pair along the same Line, by the different Situation of those
Sails, agreeing in the same Motion, the whole united Quantity is more than
the single Quantity upon one equal Sail directly expos'd to the same Wind,
as much as two Sides of a Square are greater than the Diagonal. But this
without the Consideration of the weakning of the Force of the Wind by the
Obliquity of Incidence; which alters the former Proportion: for this also
diminishing the Force in the same Proportion with the former Diminution of
the Quantity of the Wind, the whole Diminution will ever be as the Squares
of that Quantity; or as the Squares of the Sines of the Angles of
Incidence: wherefore in this Case of Four oblique Sails of 45 Degrees will
be equivalent to Two direct ones.

_Fig. 3._ Is the elastical spiral Spring of a Watch, out of its Box, and
unwinding it self more weakly, as it is less restrained.

_Fig. 4._ Is the same Spring in its Barrel A B join'd by a Chain to its
Fusee C D, or spiral Line about a Cone, which Cone has the Semidiameter or
Distance from its Axis in the very same Proportion, greater as the Spring
is weaker, and lesser as the Spring is stronger: that so the absolute
Force on the Wheels of the Watch may be ever the same, for the exact
Equality of their Motion in all Cases.

_Fig. 5._ Is an Imitation of a Waggon or Coach, with its fore Wheels E F,
either equal (as here,) or else lesser, or greater, than the hinder G H;
to be drawn by a Weight w in the Scale, either upon an Horizontal, or upon
an Inclined Plain A B, and to get over any Obstacle as C D: The Quadrant
M, and Bullet N, are to shew the Quantity of the Elevation of that Plain,
for the Tryal of Experiments relating to all such Sort of Vehicles.

_Fig. 6._ Is a strong Machine, with a Wheel O P, and its Winch R, and
String O P L K, its lesser Barrel K L, circular Table A B, Scale with a
Weight w, suspended by a String that comes through the hollow Axis C D,
and oblique Tube G C, in which Mercury or a Bullet is included; its Screw
H; its Balls I and B, and their Strings; To shew that Motion once begun
always continues, till some other Cause stops it: That absolute and
respective Motion are entirely different: And to shew withal the Endeavour
of Bodies that move circularly to recede from the Center of their Motion,
on inclined, as well as horizontal Plains, and that in the same Circle in
a duplicate Proportion to their Velocity.



                  [[Plate VI. ― Sutton Nicholls sculp:]]



                              MECHANICKS. 6

                    An Explication of the Sixth PLATE.


Figure 1. Is an Instrument to shew the various Parabola's that are made by
Projectils, and particularly the Truth of the several Rules in the Art of
Gunnery. Wherein A B is a Tunnel full of Quicksilver, D K is a Glass Tube,
let into a Groove or Frame of Wood for its Support, and at K is a fine
Stem, accommodated to the Arch of a Quadrant L M, and turning upon its
Center, to direct the projected Quicksilver to any Angle; while the Tube's
perpendicular Altitude, or the Force that produces the Projection, is
either the same, or altered by a different Inclination at Pleasure,
according to the Nature of the several Experiments.

_Fig. 2._ Is a Cycloid with its equal Sides A B, A C, and pendulous Body
E, oscillating therein. And, _Note_, That by the Make of the Figure, the
Line B C is equal to the Circumference of the Circle D G F, by which it
was describ'd; that the Length of the Cycloid it self is four times that
Circle's Diameter; that every Part of it from F the _Vertex_ is still
double to the Chord of the Correspondent circular Arch G F; that its
included Area B D C F, is Three times the Area of the former Circle; that
the Force upon the Pendulum at any Point E, is exactly proportional to the
Distance along the Cycloid of the Point from the _Vertex_, as E F; and
that therefore the Time of every Oscillation, in all Angles whatsoever, is
always equal.

_Fig. 3._ A C B is a Syphon with Quicksilver from A to C, and a Pendulum
of half that Length; to shew here also that the Force is as the Line to be
describ'd, and that by Consequence the Vibrations in the Syphon are all
equal: as also to shew that they are equal to those of a Pendulum, of half
the same Length: As is plain from the former Case of the Cycloid, where
the Length of the Pendulum is half that of the Cycloid in which the Body
moves.

_Fig. 4._ A B are two Spheres, to denote the several Laws of Motion in the
Collision of Bodies, whether Elastical or not Elastical, to be tried in
the Cycloid, or in a Circle, with proper Corrections: Which Experiments
yet are most of them too difficult for such a Course as this is.

_Fig. 5._ Is an Instrument to explain muscular Motion; supposing the
Muscles to be some way like a String of Bladders; by shewing that a
smaller Quantity of an elastical Fluid may equally raise equal Weights
with a larger; and to shew exactly what Quantity is necessary for any
particular Effect. For thus will the lesser Quantity of Air, (measured in
both Cases by the Gage C A K, as condens'd by the Syringe H A) equally
raise an equal Weight to the same Height by the lesser three Bladders,
that the greater Quantity raises the same by the one larger Bladder.

_Fig. 6._ Are several Pendulums of several Sorts of Matter, heavy and
light; where the Centers of Suspension and Oscillation are equally
distant, and the Times of those Oscillations are all equal. This also
hints the other remarkable Phænomena of Pendulums; _viz._ that the
Semicircular and Cycloidal Times of Oscillation are to each other as 34 to
29: That in both the Length of the Strings of Pendulums are in a duplicate
Proportion to their Times of Oscillation; and that the Heights of Roofs,
_&c._ may be found from the Times of the Oscillations of Pendulous Bodies
fixed to them, on the known Hypothesis that a Pendulum of 39.2 Inches
vibrates in one Second of Time.

_Fig. 7._ Is a Fountain running on Wheels, and made by Air condens'd on
the Surface of Quicksilver, and so forcing the Quicksilver to ascend
through the Pipe G: And is to shew that the Lines of Projectils, or other
Bodies, are not alter'd by the common Motion of the whole Instrument or
Floor on which they are plac'd; and that all Motions on the Earth, if it
move, will be the same as if it stand still.

_Fig. 8._ Is a Parabola with the several Lines belonging to it, in order
to demonstrate the Doctrine of Projectils; and particularly the Art of
Gunnery.

_Fig. 9._ Is an Engine moving on Wheels, that lets a Ball fall down from a
Groove through a Hole, as it is in Motion; to shew that it will then fall
on the same Point of the Frame that it falls upon when it is at rest; as
does a Stone let fall from the Top of the Mast of a Ship under Sail: and
that all respective Motions on the Earth must be the very same, while it
self moves as if it were at rest.

_Fig. 10._ Is a Cylindrical Iron A B, swinging on a Pin E F, in the very
same time that a pendulous Body D of two thirds of its Length C D does; to
shew that two thirds is the Center of Oscillation or Percussion in all
such prismatick or cylindrical Bodies.



              [[Opticks Plate I. ― Sutton Nicholls sculp:]]



                                    7
                                 OPTICKS.

                    An Explication of the First PLATE.


Figure 1. Represents the Foundation of Vision, and of all Opticks
whatsoever, by exhibiting to the Eye a Specimen how the Rays of Light do
as well originally, as after Reflection or Refraction, spread themselves
in right Lines from each Point in every visible Object, as P, to each
other Point, as R, R, R, R, R, every way, to be receiv'd by the Eye in any
direct Position whatsoever.

_Fig. 2._ Represents the known Law of Reflection; that the Angle of
Incidence C P D, is equal to that of Reflection C P E, or that the Angle
of Inclination D P A is equal to the other E P B.

_Fig. 3._ Shews the Reason why a plain Looking-Glass, as A E F B, exhibits
the Object C D by the Image _c d_, which is equal to C D, and equidistant
from the Glass A _c_ = A C: And in an erect Posture; all depending only on
the Equality of the Triangles, whose Vertices are C _c_ : D _d_, and have
their common Bases below E and above F, which Glass by forming the same
Image _c d_, so to the Eye, as if the real Object C D was at _c d_, must
needs shew that Picture in the Place assign'd, without any Inequality of
Distance or Magnitude, or any Inversion.

_Fig. 4._ Shews the Reason why the same or equal Object, as A B, C D, E F,
appears larger when it is nearer, and smaller when farther off: _viz._ on
account of the Inequality of the Angles A G B, or M G N, and C G D, or
K G L, and E G F or H G I, and the consequent Inequality of the Pictures
made by the Rays at the Bottom of the Eye.

_Fig. 5._ Shews the Reason why a Convex Looking-Glass, as A E F B,
exhibits Object C D by the Image _c d_, both nearer to the Glass, and
lesser than it self; but still in an erect Posture. All depending only on
the different Bend of the Circle between E and its lower Point, between F
and its upper Point; which cannot make the Angles of Reflection or
Inclination equal, as they must needs be in all such Reflections, without
making the Vertices of the Angles, as _c_ and _d_, nearer the Glass than C
and D: And so the apparent Picture or Diameter _c d_ lesser than that of
the Object C D, though without any Inversion.

_Fig. 6._ Shews the Reason why a Concave Glass, as A E F B, exhibits an
Object plac'd nearer the Glass than the Center, as C D by the Image _c d_,
remoter from the Glass, and larger than it self, _viz._ for Reasons just
contrary to those under the fifth Figure foregoing.

_Fig. 7._ Shews the Reason why a Concave Glass, as C D E F, exhibits an
Object, if it be plac'd remoter than the Center, as A B, inverted, and at
different Distances between the Eye and the Glass; according to the Length
or Shortness of its own Distance, as B C or A D, _viz._ Because the Rays
from the same Point still cross one another, as at G and H, before they
fall upon the Eye; and so by forming an inverted Image make it impossible
for the Eye to see the Object in any other Position than that the Image
has; which Image indeed it self is the only proper Object of the Eye, in
all such Cases whatsoever.

_Fig. 8._ Is a Picture in Confusion; but rectified by a Convex Cylinder,
and thereby brought into exact Order again.

_Fig. 9._ Represents an Image in a Cylindrical Concave Surface, when the
Eye is in a Plain perpendicular to its Axis; so that lengthways it is as a
Plain, and breadthways as a Concave _Speculum_: Which therefore makes the
Picture longer, but not wider. The contrary will happen in a Convex
_Speculum_, which will make it shorter but not narrower, for the like
Reason.



                  [[Plate II. ― Sutton Nicholls sculp.]]



                                OPTICKS. 8

                   An Explication of the Second PLATE.


Figure 1. Shews that an Object, as K, seen through a plain Glass, whose
Sides A B, C D, are parallel, by the Eye at G, appears out of its true
Place; and this so much the more as the Glass is thicker: While at the
same time the two Surfaces do exactly balance each other's Refraction, and
make the two Rays H K, G F exactly parallel.

_Fig. 2._ Exhibits a plain Method of measuring the Refraction of Fluids at
all Angles, and of proving thereby that it is always in one fixed
Proportion of the Sines, as the next Figure will explain it. For if the
moveable Rule K C L, with its measuring Circle A B D E fix'd by the Prop
E, to a heavy Pedestal F G, in a large Glass A H I D, be so far immers'd
in the Fluid, that the Center C may be in the Surface of the Fluid, and
one of its Legs C L be so far bent from a rectilinear Position, that the
Refraction of the Fluid can just make it appear as if it were in a strait
Line, the Angle B C K, or its equal M C E, is the Angle of Incidence: And
L C E the Angle of Refraction: And L C M the Difference, or the refracted
Angle.

_Fig. 3._ Is for the Illustration of the former Proposition, and shews the
Sines afore-mentioned; as A D or G N (for they are suppos'd equal, and the
Line A C N one strait Line,) is the Sine of the Angle of Incidence, and
F E the Sine of the Angle of Refraction, which Sines do in the same Fluid
at all Angles bear one and the same Proportion to each other; till at
last, if the Refraction be out of a thick Medium into a thin one, and
makes the second Sine equal to the Radius, that Ray cannot emerge at all,
but will be reflected back by the Surface into the same Medium whence it
came, along the Line C R.

_Fig. 4._ Is a Bason of Water, or other Fluid; to shew the common
Experiment of Refraction; where a Shilling, or other Object at A, (which
is so plac'd that it cannot be seen by the Eye at O, the Side of the Bason
C interposing) is readily seen there, as soon as the Water or other Fluid
is put in to the same Bason, and appears to be remov'd to the Point B.

_Fig. 5._ Is the Alteration of a round white Object D, as seen through a
Triangular Glass Prism A B C, by the Eye at G, where the double Refraction
of the Glass at E and F makes the Object appear at _d_; and that as an
oblong colour'd Image; wherein the upper Part is made by the violet Rays,
which are most refrangible; and the lower by the red Rays, which are least
so; and the intermediate Parts by those that are refrangible in a mean
Degree; after the Order of the Colours of the Rainbow.

_Fig. 6._ Shews the Nature of a multiplying Glass A D, and its Plains A B,
B C, C D, _&c._ and the Reason why the different Refraction of every
oblique Plain, as A B, C D, _&c._ exhibits the same Object K as a
different Object k, k, _&c._ according to the Number of the oblique
Plains: While the direct Plain B C shews it still in its own Place: And
while the Convolution of the Glass on the Axis K L removes all the oblique
Images, but does not remove the direct one, on Account of the Change of
the Position of those oblique Plains, and of the unchanged Position of the
direct Plain.

_Fig. 7._ Shews the Effect of the Lens, or double Convex Glass, in
gathering parallel Rays, as G L, H M, A B, I N, K O, _&c._ towards a
Point, as D; because, as in the Case of the Prism above, the Refraction
_to_ the perpendicular in the Entrance, and _from_ it in the Exit of those
Rays, do still, by the different Position of that Perpendicular, conspire
to unite the same Rays.

_Fig. 8._ Shews the contrary Effect of the double Concave Glass, in
scattering the parallel Rays; and that exactly on the like Account; and so
this needs no new Explication.

_Fig. 9._ Shews the Reason why a Lens, or double Convex, shews a near
Object at Q, as more remote at _q_, because it refracts it so that the
Rays from the same Point meet more backward than before: And why it shews
the same Object larger also: Which must needs be, because every Point in
the Object appearing so much more backward, and yet in the same apparent
Angle, its Length and Breadth must every where be proportionably enlarg'd.

_Fig. 10._ Shews how such a Lens inverts Objects, as A, B, _b a_, which it
does on Account of the Intersection of the Rays from each Point, in or
near the Lens it self: Which necessarily infers such an Alteration: just
as the Images of all Objects are in the Eye in an inverted Position, on
the like Account.

_Fig. 11._ Shews how a Lens does so refract the Rays from every Point of
an Object, that is in its Focus C, and B, and A, that the Rays from each
of those Points do become parallel afterward; and also how parallel Rays
of different Positions are gather'd in that Focus.

_Fig. 12._ Is the Nature of direct Vision by the Eye, in some Conformity
to the 10th Figure: only in this Case the Crystalline Humour is the Lens.

_Fig. 13._ Is the Case of a Concavo-convex Glass, with its parallel
Surfaces, as in _Fig. 1_.



                 [[Plate III. ― Sutton Nicholls sculp:]]



                                OPTICKS. 9

                    An Explication of the Third PLATE.


Figure 1. Is a Telescope, with two Convex Glasses, the one towards the
Object and the Segments of a great Sphere, the other near the Eye, the
Segments of a small Sphere _g h i_, and they are to be so placed that the
distinct Base or Image may, by the Collection of the Rays, be in the
common Focus of both the Glasses _f e d_. By these two Glasses the
parallel Rays, or those nearly so, as proceeding from the same Point of
the Object A B C, (which is to be suppos'd considerably remote) are made
to meet in the intermediate Image _f e d_, at _f_, and _e_, and _d_; and
again at the Bottom of the Eye, at _r_, and _s_, and _t_; but in an erect
Position; and therefore so as to shew the Object inverted.

_Fig. 2._ Is a Telescope with four Convex Glasses, the one towards the
Object, and three nearer the Eye: Whose Images are made in the common
Focus of two Glasses, as before. This is like the former; but only that
two of the Eye Glasses serve merely to reinvert, or to erect the Image,
that so it may be inverted at the Bottom of the Eye; and therefore may
shew the Object in its true or erect Position.

_Fig. 3._ Is a Telescope, with a Convex Object Glass, and a Concave Eye
Glass; which last, by scattering the Rays, as if they came from a nearer
Point, makes the Image inverted in the Bottom of the Eye, and therefore
shews the Object in its true or erect Position. Only this takes in but a
small Part of an Object, an so is less used than the two former
Telescopes.

_Fig. 4._ Is a Telescope with a Triangular Prism D B in its Axis; and that
Prism's Gage F G for the Demonstration of the Refraction out of _Vacuum_
into Air, and out of thinner Air into thicker; and both by the Means of an
Object seen through the Prism, as well when the Air is condensed, as when
it is exhausted. Where in the first Case the Object is seen higher, and in
the other lower than in its natural Situation; as the two following
Figures demonstrate.

_Fig. 5._ Shews how the Object or Circle which was low at first, is to
Appearance _rais'd_ as it passes through condens'd Air; by being refracted
towards the perpendicular, in its Ingress into a Glass Prism, and from it
in its Egress into the common Air again.

_Fig. 6._ Shews how the same Object or Circle, which was high at first, is
to Appearance _depress'd_, as it passes through the _Vacuum_; by being
refracted from the Perpendicular, in its Ingress into the Prism, and
towards it, in its Egress into the common Air again.

_Fig. 7._ Is a Triangular Glass Prism, fitted to receive all sorts of
Fluids, and when rightly apply'd to the Semi-circle of the next Figure,
does exactly measure the refractive Power of all those Fluids. Where the
vertical Angle G D H is 45 Degrees; and by consequence the half Angles
C D H, C D G, C H G, are 22° 30′, and where all is to be so contriv'd,
that the Rays within the Glass may be parallel to G H, and perpendicular
to C D, and may fall on each side Plain of the Glass Prism in an Angle of
22° 30′ from their Perpendiculars; that so the Refractions at the Ingress
and Egress may be equal, and the Computations easy.

_Fig. 8._ Is the Semicircle, with the Glass Prism full of its Liquor
rightly apply'd thereto; and both Arms of the Index E D, F D, equally
elevated above the horizontal Line A C. This shews the Proportion of the
Sine of the Angle of Incidence to that of Refraction, in this Incidence of
22° 30′; which Proportion of Sines being the same in all other Angles, we
hence learn that Proportion accurately and universally.



                 [[Plate IIII. ― Sutton Nicholls sculp:]]



                               OPTICKS. 10

                   An Explication of the Fourth PLATE.


Figure 1. Is the Apparatus for Microscopes: Containing A C a Cylinder of
Brass or Ivory; to which, near the Eye at K, the Microscope it self, or
very small Sphere of Glass set Ivory, is apply'd; G H a small Slice of
Ivory, and its _Muscovy_ Glass Circles, with the fine Objects upon them,
inserted in their true Place; E F a Convex Glass, screwed into the former
Cylinder, and at a due Distance casting Light on the Objects; with I L,
the Handle of the Microscope.

_Fig. 2._ Is only one of the Slices of Ivory A B, like G H
before-mentioned, set by it self; with the double Circles of _Muscovy_
Glass, and kept down by circular Wire; between which, on one of those
Glasses, the small Objects are commonly plac'd.

_Fig. 3._ Is a Scheme to demonstrate how the double Microscope comes to
magnify so much. Where G is the small Object; which, if there be Light
sufficient, may by the small Microscope Glass E F, placed very near the
Object, be cast into a larger Image H I: Which by the Means of the two Eye
Glasses, are reduc'd into a Compass fit to enter into the Eye. And here by
the way it is to be noted that die small Glasses, whereby single
Microscope do magnify so much, and whereby the Magnitude is in Part
increas'd in this double Microscope, is only a very small spherical Glass,
or Segment of it, which does so suddenly reduce distant Rays to
Parallelism, or nearly to it, that a small Object, which by its great
Nearness could not be otherwise seen, is hereby made visible.

_Fig. 4._ Is the double Microscope, with all its Apparatus and
Contrivances, as to the Position of the Object, the Light to be thrown
upon it, and the Elevation and Depression of the Instrument it self, as
the Case requires, _&c._ all which the Figure does plainly shew to the
Eye.

_Fig 5._ Is a circular Plate of Ivory, with a small Sphere of Glass in its
Center, and a Screw round the Center, to be put upon the first Figure at
B C, as a single Microscope.

_Fig. 6._ Is a small Fish, represented in a Cylindrical hollow Glass, so
as it is to be placed when the Circulation of Blood in its Tail is to be
seen by the single Microscope.

_Fig. 7._ Is the Magick Lanthorn, with its Pedestal T: its Lamp W; its
double Convex Glass X Y; its Pictures inverted upon the Plate E F; and its
large or gygantick Images at B A projected upon the white Wall, to the
Surprize of the Spectators.

_Fig. 8._ Is the Demonstration of the _Camera obscura_, or dark Chamber;
which will shew the Object as A B erect. Where C D is the double Convex
Glass, ready to form an inverted Picture _b a_: Which by the Reflection of
the plain Speculum E F, plac'd obliquely in an Angle of 4°, is formed in
an erect Position at _a b_, for the View of the Spectator.



                  [[Plate V. ― Sutton Nicholls sculp:]]



                               OPTICKS. 11

                    An Explication of the Fifth PLATE.


Figure 1. Is one of Sir _Isaac Newton_'s Experiments, to shew the
different Refrangibility of the Rays of Light, of the different Colours,
Red, Orange, Yellow, Green, Blue, Indigo, Violet. Where D E is a
Parallelogram of Pastboard, having the one half D G blue, and the other
half F E red; both strongly illuminated by the same Candle: and having
black Silk wrapped several times round it. M N is a Lens or double Convex
Glass interpos'd, which gathers upon white Paper the blue Rays sooner at
_h i_ than the Red at H I: As appears by the Distinctness of the Colours
and of the Silk at those and only those Distances. Where also at somewhat
above 12 Feet from the Colours to the Images, the Distance between _h i_
and H I is no less than an Inch and half.

_Fig. 2._ Is another of Sir _Isaac_'s Experiments to the same Purpose:
Where X Y represents the Sun: E G, a Window, with a small round Hole at F:
within which is a Triangular Glass Prism A B C, by which the Rays of the
Sun are differently refracted upon a white Wall or Paper M N; and become
an Oblong Image P T; the Violet seen at P as most refracted; and the Red
at T, as least refracted: And the intermediate Colours seen in
intermediate Places, according to the different Degrees of their
Refraction.

_Fig. 3._ Is another of his Experiments, to shew that White is a Mixture
of all Sorts of colour'd Rays; where D C is a Hole in the Window, which
admits the Sun's Rays. E F G a Prism, casting its oblong colour'd Image
upon a Lens, or double Convex Glass; which collects all those Rays into
its Focus. In which Case, the Point of Concourse exhibits a perfect White
Colour; tho' upon their Separation again, the oblong colour'd Image
appears again, only in an inverted Position: as the crossing of the Rays
in the Focus must of Necessity occasion.

_Fig. 4._ Is the last Experiment improv'd; by shewing that the White Light
made by the Mixture of all the Colours is but imperfectly so, when any of
the several Colours are intercepted in their Passage to their Focus, or
Place of Mixture.

_Fig. 5._ Is the _Experimentum Crucis_, or determining Experiment. Where
B F is the Hole that lets in a large Ray of Light: whose middle Part,
after it has pass'd through the Prism A B C, is let through a lesser Hole
at G, and forms an oblong colour'd Image at _d e_: where another small
Hole lets thro' one Colour only; which passing through the Second Prism
_a b c_ it is refracted again, and cast upon N M. And here it is most
remarkable, that the two Holes and second Prism are kept immoveable; and
so the Rays G _g_ fall upon the second Prism in the very same Angle,
whatever Colour they are of, and that by the Motion of the first Prism,
all the Colours may successfully pass through the same Holes. Yet is the
Refraction by the second Prism never then able to produce any Variety of
Colours; but exhibits the Image always of that Colour alone, which falls
upon it before the second Refraction.

_Fig. 6._ Is a Figure for the Explication of the several Refractions and
Reflections of Light, which cause the _Phænomena_ of the Rainbow. Thus if
the greatest Crowd of Rays enter in Parallel to B Q along or near to A N,
the round Drop of Water L B G Q will refract Part of those Rays to F,
whence Part of them will be reflected to G: And going there out of the
Drop, will be thereby refracted to R, which double Refraction will so
separate the several Colours, and make them go out in Angles so sensibly
different, that as the Eye is placed a little higher or lower, it will see
a different Colour; and that in Angles as A X R, of about 41 Degrees; and
this is the Case of the primary Rainbow, which appears in about that Angle
from the Axis B Q, or its Parallel A X. Thus also, if the same Line A N be
now suppos'd to represent another Drop, and that some of the Rays at G are
reflected a second time, and so pass out at H, and are there refracted to
S; here will be a weaker Impression, but a like Refraction and Separation
of the Colours as before; and the Eye placed a little higher or lower will
also see different Colours, tho' in a contrary Order to the former; and
that in an Angle, as A Y S, of about 52 Degrees and a half; which is the
Case of the secondary Rainbow.

_Fig. 7._ Are the two Rainbows themselves, r presented as they appear in
Nature. Where A E B F represents the Air full of spherical Drops of Rain,
in such Parts as the Angles E O P, F O P are about 41 Degrees from the
Axis O P, which Axis is the Line from the Sun's Center, through the Eye of
the Spectator, to the Center of the Rainbow: And where C G D H represents
the same Air, full of the like Drops, in such Parts where the Angles
G O P, H O P are about 52 Degr. and a half. Where also the Rays S E, S F,
S G, S H, coming from the Sun's Center, are represented as parallel, by
reason of its vast Distance. These Rays, when they fall upon the higher
Quadrant of the Drop, as at S E, S F, come to the Eye at O in about an
Angle of 41 Degrees, after two Refractions, and one Reflection; and so
cause the primary Rainbow: the Red is without, by the least refrangible
Rays at F: and the blue within, by the more refrangible Rays at E. But
when they fall upon the lower Quadrant of the Drop, as at S G, S H, they
come to the same Eye at O, but in an Angle of about 52 Degrees and a half,
after two Refractions, and two Reflections, and so cause the secondary
Rainbow. Which is Blue without, by the more refrangible Rays at H; and Red
within by the least at G. Where note, that because the Angles F O P,
E O P, as well as those H O P, G O P, are ever the same, the same Colours
must still be circular, or appear in the Surface of a right Cone, whose
Axis is O P, and whose Sides are the Lines turned round thereon, as O E
O F, and O G O H.



              [[Hydrostaticks Plate I. ― I. Senex sculp.^t]]



                                    12
                              HYDROSTATICKS.

                    An Explication of the First PLATE.


Figure 1. Is a Balance, to weigh Water in its own Element, and in the Air;
and to prove that its Weight is the very same in the former Case as in the
latter. For when the Glass Bottle F is exhausted of Air, it will indeed
require much more Weight to counterpoise it in the Air, than in the Water;
by Reason of the much greater Weight of the Water thrust out by it, than
of the Air; yet when upon the Admission of Water within, you weigh it
again in the Air, and then in the Water, the additional Counterpoise now
necessary is the very same; and shews that the real Weight of the Water
admitted, is the same in both Elements. This Figure does also shew how
Trials may be made to shew the respective Weight of those Bodies in Fluids
that sink in them.

_Fig. 2._ Is an inverted Syphon, to shew why Fluids ever press according
to perpendicular Altitude, and not according to Quantity of Matter: As the
small Quantity of Water in the smaller Tube is a Balance for the great
Quantity in the greater, and stands upon the same Level C D E G; because
in all possible Motions and Vibrations of the Fluid, the Velocity in the
smaller must, by the Make of the Syphon, compensate the Quantity in the
larger; the one ascending or descending as far as B D, while the other
ascends only as far as E H, and so the Force is equal on both Sides, as is
the known Case in the Stiliard also.

_Fig. 3._ Is to shew the same equal perpendicular Height or Level in a
common Syphon inverted.

_Fig. 4._ Is a Number of hollow Tubes, of all Shapes and Directions, to
shew that if their lower Orifices be put under tinged Water, and Oil be
poured on the Surface of that Water, from G H to E F, the tinged Water
will equally be pressed upwards through all the Tubes, according to all
Directions; and will stand upon a common Level; tho' somewhat under the
Surface of the Oil, because Oil is lighter than Water.

_Fig. 5._ Is for the same Experiment with Water on the Surface of
Quicksilver; into which Quicksilver a hollow Tube is inserted before the
pourings in of the Water. For the Water will press upon the Quicksilver,
and raise it in the small Tube, till it bears the same Proportion to the
Height of the Water, that the Specifick Gravity of Water bears to that of
Quicksilver, or about a fourteenth Part so high. Which, by the by, is one
ready Way also of finding the Specifick Gravity of Quicksilver to Water,
by measuring their several Altitudes.

_Fig. 6._ Is to shew how Water in a very small Tube may elevate
Quicksilver it self, when it is thrust more below the Surface of the
Water, than the Difference of their Specifick Gravity requires; and that
it will rise or fall as you thrust it lower, or raise it higher; and will
at last fall out at the Bottom, if you raise it too high.

_Fig. 7._ Is to shew that Fluids of different Specifick Gravities, as
Water A B, and Oil A C, will stand at unequal perpendicular Altitudes, in
Proportion to their Quantities, and Difference of Specifick Gravities.

_Fig. 8._ Is a Part of a Compound Balance, to be joined to that of
_Fig. 1._ for the weighing of Levity, or of the Power of Ascent in a Body,
as F, lighter than the Fluid wherein it is; and will shew that that Levity
is the Difference of the Weight of that Body, and of an equal Bulk of the
Fluid: Which is also the respective Gravity of those Bodies which are
heavier than their Fluids, as may be tried by the same Balance of
_Fig. 1._ alone.



                    [[Plate II. ― I. Senex sculp.^t]]



                            HYDROSTATICKS. 13

                   An Explication of the Second PLATE.


Figure 1. Is a large Glass Vessel A D full of Water as high as E F. Within
this is a lesser Glass Vessel P H, open at both Ends, but somewhat
narrower at the Bottom. Through the middle of this goes a strong Wire M N,
to which is fixed at the lower End a Plate of Lead G H, with wet Leather
to its upper Surface, to be applied to the large lower Orifice of the
lesser Glass I K, to keep out the Water from entring into the same any
otherwise than by a slow Insinuation. This is to shew that a Plate of
Lead, or other Metal, may be supported by Water, and not sink in it, where
the Water is kept from pressing on its upper Surface, so long as its Depth
under the Water is greater than its Specifick Gravity requires; and that
by Consequence while Water is gradually admitted over it, it will not sink
till the perpendicular Height of the Column of Air between E F and R S
bears no greater Proportion to the Thickness of the metalline Plate (with
what is annexed to it) than the Specifick Gravity of the Metal bears to
Water.

_Fig. 2._ Is a cylindrical Vial or Glass A D, with a small Cylinder of
Wood below G H fixed to its Bottom, and made very smooth at Top; and
another like Cylinder of Wood above G H, made equally smooth on the lower
Side, that it may as exactly as possible fit the other; with a strong Pin
I, fixed in its Axis. Upon these Two, when laid close, is pour'd
Quicksilver, till it covers them both as far as E F. This is to shew, that
there is no such thing as positive Levity; but that Wood is so far from
rising in Quicksilver of it self, that till a sufficient Force pulls it
up, and permits the Quicksilver to insinuate between the two Plates, the
upper is fastned to the lower by that Quicksilver: Tho' upon the first
Insinuation of the same it immediately and violently emerges of it self:
As Dr. _Moor_'s Famous Trencher did in his Bucket, to his great Surprize;
till he was forc'd to solve it by the Introduction of his Spirit of
Nature.

_Fig. 3_, and _4_. Are Vessels of equal Altitude, but unequal Bases, and
of the same Quantity of Water; to shew that Fluids ever press according to
their Bases, if their perpendicular Height be equal; and according to
their perpendicular Height, if their Bases be equal, whatever Figure they
are of.

_Fig. 5._ Is a cubical Vessel full of Water, in order to compute the
entire Quantity of the Pressure its Sides and Bottom sustain. And that the
Bottom alone sustains the whole Weight of the Water; as is most evident.

_Fig. 6._ Is to shew that each Side of the same Vessel sustains a Pressure
equal to half the Weight of the same Water. For since the Pressure at
every point, as L, M, N, C, is equal to the Altitude of the Water above
it, A L, A M, A N, A C, by erecting equal Perpendiculars L O, M P, N Q,
C D, and so at all the intermediate Points, and summing them up, we shall
have the Triangle A C D as the Sum of all the Pressures; which being half
the Square A C D B, made by as many Perpendiculars equal to the longest
C D, and bearing the whole Weight of the Square over it A C D B, shews
that the Pressure on every physical Line, as A C of a triangular Prism,
and so on the whole Side represented by it, is one half of the whole
Water. So that since each of the four Sides sustain half, and the Bottom
the whole Weight notwithstanding, the entire Pressure is three times the
Weight.

_Fig. 7._ Is a like Method of Computation for an inclined Plain's
Pressure, and how to estimate it; _viz._ by the Weight of Water equal to
the Prism represented by the Triangle A R C, where the Lines L O, M P,
N Q, C R, are erected perpendicular to A C, and equal to L G, M T, N V,
C X, respectively.

_Fig. 8._ Is to determine the Center of Pressure Z against such a Plain;
at which if an equal Weight W directly pulls along Z P over the Pulley P,
it will just balance the Water, and evenly sustain its Pressure.

_Fig. 9._ Is to shew that this Center of Pressure is no other than the
Center of Percussion or Oscillation about an Axis, as D. For the Pressures
being as the Perpendiculars E A, F B, G C; and the Percussions, as D A,
D B, D C, the Radij of the Circles of Motion; and E A being to F B, as D A
to D B; and F B to G C, as D B to D C: The Percussions are still as the
Pressures; and so the Center of Percussion, the same with the Center of
Pressure.

_Fig. 10._ Is for the Computation of the Quantity and Center of the
Pressure on any erect Rectangle under Water; according to that Rule, that
the Depth of any Bodies or Surfaces Center of Gravity is to be taken for
the perpendicular Altitude of all the Pressures, as a Mean between them.

_Fig. 11._ Is a large Glass Vessel A D, containing Water near the Bottom;
with another smaller Vessel F K with Water almost to its Top. There is
also a Syphon B H K, with an hollow Stem G H, communicating with both its
Legs. To shew that if you stop the Top of the Stem of the Syphon while you
pour Oil into both Vessels, a considerable Height above the Bend of the
Syphon, and then unstop it, the Oil will press upon the Water in both
Vessels, and force it to ascend in each Leg; till meeting at the Bend, it
run down the longer Leg, out of the higher Water into the lower. This is
to shew how the Air pressing upon Water may raise it up, and cause the
known Effects of Syphon, Pumps, Syringes, _&c._ Which used to be ascribed
to Nature's Abhorrence of a _Vacuum_.

_Fig. 12._ Is a Cube at different Depths of the same Water; to shew how it
must have the same Weight in one Place that it has in another, because the
Water and Cube have ever the same Proportion of Bulk and Gravity to one
another.

_Fig. 13._ Is a Bucket under Water; to shew it can have there no
respective Gravity, or cannot preponderate; tho' it has ever the same
absolute Gravity.

_Fig. 14._ Are a Bubble and Images of the same Nature, made of Glass, Air,
and Water; all so nicely pois'd, that by the Pressure or Relaxation of the
Air included, which is done at the Bladder A D, the Bubble and Images rise
and fall after a surprizing Manner.



                 [[Plate III. ― Sutton Nicholls sculp.]]



                            HYDROSTATICKS. 14

                    An Explication of the Third PLATE.


Figure 1. Is a Tube full of Water, with Two Holes E, F, for the Water to
run out at, the one F four times as much below the Surface of the Water
A B as the other; (the Vessel to be still kept equally full all along:) to
shew that the Velocity and Quantity of Fluids that run out, are in only a
subduplicate Proportion of the Altitude of the Fluids, or twice so much in
a Fourfold Altitude. Not can it be otherwise: For twice the Quantity
running out, with twice the Velocity, implies the Force or Pressure to be
Fourfold, as the Fourfold Altitude requires; and so for ever.

_Fig. 2._ Is a Pump; where G M is a hollow Cylinder, reaching to the Water
below, with a Valve G, which will be lift up by the ascending Water, and
permit its Entrance into the Body of the Pump; but will not permit its
Return when it is attempting to descend. D is the Sucker, with its hollow
Cylinder, and a like Valve: which Sucker is pulled upward or thrust
downward by the Handle I L K. When it is pulled upward, it leaves the Body
of the Pump a Vacuum: whence the Air's Pressure on the Water's Surface
below raises it up into that Space, and fills it; and when it is thrust
down, the Water, which is stopp'd by the lower Valve from going back, is
forc'd through the Valve in the Sucker D, into the Cistern above; whence
by its own Gravity it runs out at the Canal A C.

_Fig. 3._ Is a Forcing Pump, in the main made like the other, only without
a Cistern; and the Exit is out of the Side through a Hole, with a Valve
opening outward, but shutting inward, in which the Sucker when thrust
downwards forces the Water out sideways with great Violence.

_Fig. 4._ Is _Archimedes_'s Spiral Pump C D, made of only a Cylinder, with
a hollow Spiral Tube wreath'd about it; where the Fluid partly descending,
and partly ascending, all the way, makes its flowing along the more easy,
till upon its Arrival at the Top it runs out at C.

_Fig. 5._ Is the whole Apparatus of the Hydrostatical Balance. The Glass
Bubble G is heavier than all Fluids but Quicksilver, and is to be put into
all those Fluids: The Bulk of Water in ours is 830 Grains _Troy_. If when
pois'd in Water it sink more by any Number of Grains, that Number of
Grains substracted from; if less, added to those 830, do by their
Proportion to 830 give the Specifick Gravity of all such Fluids to Water.
I K is the Glass Bucket, which in Air is in Æquilibrio with the Scale E:
And because when it is let into Water, it will be no longer an Equipoise
to the opposite Scale, but lighter; the Scale R is to be added to the Part
H, by which the Bucket is suspended, and that will restore the Æquilibrium
in Water. By this Solids and Quicksilver are weighed first in Air, and
then in Water: The Difference of which Weights being the Weight of an
equal Bulk of Water, by its Proportion to the first Weight in Air, gives
the Specifick Gravity of the Solid compared with Water: And if that
Difference still divide the Weight in Air, for all sort of Bodies, we may
have a Table of the Specifick Gravities of the Solids; as by dividing 830
by the Sum or Difference of the other Fluids, we may have a like Table of
the Specifick Gravity of Fluids, such an one as here presented the Reader.



                              HYDROSTATICKS.

  A TABLE of the Specifick Gravities of several Solid and Fluid Bodies.


    Fine Gold               19,640   Calculus Humanus         1,700
    Standard Gold           18,888   Oyl of Vitriol           1,700
    Quicksilver             14,000   Oyl of Tartar            1,550
    Lead                    11,325   Bezoar                   1,500
    Fine Silver             11,091   Honey                    1,450
    Standard Silver         10,535   Gum Arabick              1,375
    Bismuth                  9,700   Spirit of Nitre          1,315
    Copper                   9,000   Aqua Fortis              1,300
    Cast Brass               8,000   Serum of Human Blood     1,190
    Steel    } Soft          7,738   Pitch                    1,150
    the same } Hard          7,704   Spirit of Salt           1,130
    Piece    } Spring Temper 7,809   Spirit of Urine          1,120
    Iron                     7,645   Human Blood              1,040
    Tin                      7,320   Amber                    1,040
    Glass of Antimony        5,280   Milk                     1,030
    A Pseudo Topaz           4,270   Urine                    1,030
    A Diamond                3,400   Dry Box-Wood             1,030
    Clear Crystal Glass      3,150   Sea-Water                1,030
    Iceland Crystal          2,720   Common Water             1,000
    Fine Marble              2,700   Camphire                 0,996
    Rock Crystal             2,650   Bees-Wax                 0,955
    Common Green Glass       2,620   Lynseed Oyl              0,932
    Stone of a mean Gravity  2,500   Dry Oak                  0,925
    Sal Gemmæ                2,143   Oyl Olive                0,913
    Brick                    2,000   Spirit of Turpentine     0,874
    Nitre                    1,900   Rectified Spirit of Wine 0,866
    Alabaster                1,875   Dry Ash                  0,800
    Dry Ivory                1,825   Dry Maple                0,755
    Brimstone                1,800   Dry Elm                  0,600
    _Dantzick_ Vitriol       1,715   Dry Firr                 0,550
    Allom                    1,714   Cork                     0,240
    Borax                    1,714   Air                      0,001 ¼



                         [[Plate I. Pneumaticks]]



                                    15
                               PNEUMATICKS.

                    An Explication of the First PLATE.


Figure 1. Are several Torricellian Tubes or Barometers of different
Shapes, Bores, and Positions; but where the perpendicular Altitude of the
Quicksilver in the Tubes, above the Level of the Surface of that in the
Bason, is ever the same, or between 28 and 31 inches high; which is the
known Counterpoise between 32 and 36 Feet of Water; and to the entire
Atmosphere in its several States and Elevations, where the Bases or the
several Tubes are supposed equal.

_Fig. 2._ Is a Diagonal Barometer, where the Alteration of the
Perpendicular Altitude of 3 Inches, by the Obliquity of that Part B C of
the Tube A B C, (as a Diagonal is oblique to the Sides of its
Parallelogram,) is increas'd to 20 or 30 Inches Sideways, for more Nicety
of Observation.

_Fig. 3._ Is a Wheel Barometer, where by two Weights G and H on a Pulley,
by which a Hand is turned, the one of which plays freely in the Air, and
the other rises and falls with the Quicksilver in the Tube, the Divisions
are larger and more obvious than in the ordinary Barometer: as they are in
the Diagonal one; for the like greater Nicety of Observation.

_Fig. 4._ Is a common Thermometer, to determine the Quantity of the Heat
of the Air, or of any Liquor, by the Rarefraction of Spirit of Wine
contain'd in the hollow Ball at the Bottom, and its consequent ascending
to the several Divisions on the small Tube.

_Fig. 5_, and _12_. Are to shew that the Air's Density is as its
Compression, the former upon a greater Compression, and the latter upon a
greater Rarefraction; and that accordingly, in the first Case, B D the
Standard Altitude, or about 29½ Inches, and L M the Additional Altitude of
Quicksilver pour'd in higher than the Level H, taken together, is to B D
the Standard Altitude alone, as I G the inverted Part of the Tube when
full of common Air, to H G the Part full of condens'd Air: And in the
Second Case, B D the Standard Altitude, is to D C the Depression by the
Air, as E C the Part of the Tube full of the expanded Air, to E F the Part
at first left full of common Air.

_Fig. 6._ Is Monsieur _Azout_'s noble Experiment, to determine, that 'tis
certainly the Air's Pressure that raises the Quicksilver in the Barometer.
The Instrument is nothing but a double Barometer communicating together,
by the Means of a small hollow Pipe in the Middle: Its lower Tube is
stopp'd at the Bottom with a Bladder; and when the entire Cavities are
full of Quicksilver, the Bladder is prick'd or cut, and the Quicksilver
runs out: Hereupon the upper Barometer's Tube, and Part of its Bason,
becomes empty; while the lower is yet full: But upon the unscrewing a
Screw, and letting Air in above the upper Bason, that Air presses on the
Quicksilver's Surface, and raises it into its Tube; while the same Air
pressing down the upper Part of the under Tube, depresses the Quicksilver
therein at the same time.

_Fig. 7._ Is a Hygrometer, or Cord, with a Needle or Index in a Circle, to
measure the Air's Moisture by its shrinking up, and consequent Revolution
one way; and the Air's Dryness, by its Extension down, and consequent
Revolution the contrary way; and both measured by the Degrees of the
Bottom Circle.

_Fig. 8._ Is a Syphon above 29½ Inches high, along where no Suction nor
Art can make the Quicksilver run, as it uses to do when it is of any less
Altitude.

_Fig. 9._ Is the new Sort of Cupping-Glass, whence the Air is suck'd out
by a Syringe, and where by a Valve it is hindred from returning.

_Fig. 10._ Is an Example of Suction; and will shew that Quicksilver can
thereby never be rais'd to 29½ Inches.

_Fig. 11._ Is an Example of a Weight raised by a Syringe, as Water uses to
be; and still shews, that all is proportionable to the Power of the Air's
Pressure, and is limited thereby.



                    [[Plate II. ― I. Senex sculp.^t]]



                             PNEUMATICKS. 16

                   An Explication of the Second PLATE.


Figure 1. Is the Air-Pump, with its Receiver and Gage, as ready for Use;
_a a_, _a a_ are two strong hollow Cylindrical Barrels, in which are
suppos'd to be Suckers, with their Handles _c c_, _c c_ notched; into
which Notches a Cog-wheel falls, which Cog-wheel moves upon the Axis _f_,
when the Engine is put into Motion by the Winch _b b_. _g g_, _g g_ are
two Cylinders of Wood, fixed to the Frame of the Air-Pump, with Screws at
the Top, on which the Nuts _e_, _e e_ do run, and press down the upper
Piece _f f_ upon the Tops of the Brass Barrels, to fix them both at Top
and Bottom. _h h_ is a Swan-neck'd, or small bended hollow Brass Pipe,
leading from the Top-Plate _i i i i_, or rather from the Brass hollow
Piece above _n n_, which communicates through that Top-Plate with the
Cavity of the Receiver. This Pipe is screwed to a bottom Brass Piece,
included in the Box _d d_; which is perforated not only lengthways, but
also upwards, in three Places: The Middle one for a Communication with
this Swan-neck'd Pipe, and at the two Ends through small Cylinders;
inserted into the two Brass Barrels _a a a a_; and 'tis by this Threefold
Communication, that the Air is pump'd out of the Receiver. _l l l_ is the
Gage; which is no other than a common Barometer, or Weather-Glass; with
its Bason of Mercury _m m_, fix'd to the Engine by a particular
Contrivance, and its Index or Boxen Receptacle, with Inches, and its Cork
to support that Index upon the Surface of the Mercury, and to rise and
fall with it; for the Exactness of measuring the Height of the Mercury
from that Surface. Only this Barometer is open at the Top, and
communicates, as does the Swan-neck'd Pipe, with the Cavity of the
Receiver. _n n_ is a Stop-cock, that communicates also with the Cavity of
the Receiver, and either excludes or readmits the Air, as you see
convenient. _k_ is the Bottom of the Receiver, ground true to fit the
Brass Circle below it; to which it is affixed by the Hand at first, and
afterward by the Pressure of the Air, with wet Leather instead of Cement.

_Fig. 2._ Is a Barometer Tube, open at the Top H, and included in such a
Receiver G B, as gives room for it to stand upright, and yet permits the
Air to go backward or forward on its Surface, according as you pump the
same out of or readmit the same into that Receiver. And this is done so,
that the included Air C D, which supports the Mercury, by pressing on the
Surface of that in its Bason E D, is confin'd within. This small Quantity
of Air, on the Extraction of that in the Receiver, will, by its
Elasticity, raise the Mercury almost as high as the usual Standard: And
thereby shews, that the Spring of any small Part of common Air presses
equally with the whole correspondent Column of the Atmosphere.

_Fig. 3._ Is a Contrivance to make an Explosion of Gunpowder in Vacuo:
Where H D is a red hot Iron, standing on its Pedestal E, within a Receiver
G C; and F is a Cock made above like a Dish, to contain the Gunpowder;
which by the pulling up and thrusting down a strong Wire, with a Hole like
the Eye of a Needle, is in a certain Quantity let fall every time upon the
hot Iron; and on the Explosion produces Flame, and fictitious Air; but
very little Sound, by reason of the Absence of the Air that should convey
it.

_Fig. 4._ Is a Syringe, which will suck up the Water in the Glass C D,
when it is in the open Air; but will not do the same under the Exhausted
Receiver E F, unless for so small an Altitude as the remaining Air can
sustain.



                    [[Plate III. ― I. Senex sculp.^t]]



                             PNEUMATICKS. 17

                    An Explication of the Third PLATE.


Figure 1. Is a large strong Glass Receiver, or Condenser, Arm'd with Brass
Circles at both Ends, and fit to receive and bear the Pressure of Air
considerably condens'd, when crouded into it by a Syringe fitted for that
Purpose. It has also annexed to it a Gage C D, to determine the Quantity
of the condens'd Air within. This Gage consists of a hollow Tube,
Hermetically seal'd at D, with another smaller included, open towards D,
and Hermetically seal'd at the other End. In this smaller Tube is left a
little Quicksilver: This Quicksilver is by the Air at D in the larger
Tube, which communicates with the condens'd Air in the Receiver it self,
and so is of the same Density with it, crouded inwards towards C every
time of the Admission of new Air; and by its whole Length from the End
near D, compar'd with its Distance from the End near C, it determines the
Proportion of the Density of the included Air to that of the common Air.
_Note_, That the Syringe to be made use of with the Receiver, is the same
with that represented in the next Figure, as joined to the condensing
Engine it self; and acts by pulling up the Sucker above the Hole H, for
the Admission of a full Cylinder of common Air, and then crouding it down
into the Receiver; at the Bottom of this Syringe is a Valve, that hinders
what is once crouded in from returning back again, as is necessary on all
such Occasions.

_Fig. 2._ Is the usual Brass Condenser it self, with a Stop-cock E F near
it; to be interposed between the Syringe and the Receiver upon Occasion.
The Instrument, besides the Frame, is composed of a Recipient of Brass,
made of Two Hemispheres, or what is equivalent to them, closed together by
a Ring of wet Leather, to keep in the Air; and because in this Case the
dense Air within endeavours forcibly to disjoin these Hemispheres, they
are confin'd down close by a strong Piece of Iron, and Screws belonging
thereto. The Syringe already describ'd, is represented as join'd to it
after the same manner that it is when the Air is thereby intruded. This
Brass Recipient will bear Air very much denser than the foregoing Glass
one, tho' it being not transparent as the other is, cannot be so pleasant,
nor so well shew the Mutations that happen to Animals or other Bodies in
condens'd Air as the former.

_Fig. 3._ Is the Logarithmick Curve A C _c_, with its Ordinates A B, C D,
_c d_, K δ representing Absolute Numbers, and its Abscissæ, C G or D B,
I _c_ or B d and B δ, representing their Logarithms, whose famous Property
it is, that one Ordinate as A B, is to another Ordinate as C D, or _c d_
or K δ, as that unlimited Space between the Curve and Asymptote above the
one, is to that above the other; and whence is deduc'd the Proportion of
the Air's Rarity at all Altitudes whatsoever; that at 7 Miles high it is 4
times as rare; at another 7, or 14 Miles, it is 16 times as rare, and so
for ever, in a Geometrical Proportion of Rarity, compar'd with the
Arithmetical Proportion of its Altitude; tho' all this is here upon the
Hypothesis that the Distances are not so great, that the real Gravity of
the Parts be sensibly diminished. For in that Case,

_Fig. 4._ Gives the Scheme, which is made use of to discover the Air's
Rareness, even at such Distances, as imply a considerable Alteration in
that Gravity; whence it will appear, that the Density of the Air is
diminished in that Case more than 4 times for every 7 Miles of Altitude.



                   [[Plate IIII. ― I. Senex sculp.^t]]



                             PNEUMATICKS. 18

                   An Explication of the Fourth PLATE.


Figure 1. Is a compound Instrument, to shew, why in a Storm the Mercury in
the Barometer vibrates so much, by a parallel Case in an Imitation of such
a Storm. A A is a large hollow Brass Sphere, into which by the means of
the Syringe in _Fig. 2_. Air is crouded till it is 8 or 10 times as dense
as usual. H F and L K are Two Barometers, with their Basons in the Boxes
F F, K K, which Boxes communicate by a long hollow Tube I I. E E is a
Brass hollow Tube, to convey the crowded Air near the Surface of one of
the Basons of Quicksilver, which Air passes out of that into a larger
hollow Pipe G G, and so into the open Air. Upon the turning of the
Stopcock C to give vent to the condensed Air, it rushes with great Force
along the hollow Pipes E E, G G; and as it passes not far off the Surface
of the Bason of Quicksilver F F, it causes the Mercury in both the
Barometers H H, and L L, to descend and vibrate several Inches, as the
great Storm made Barometers descend and vibrate in Chambers at a distance
from it.

_Fig. 3._ Is a Transferrer; containing one common hollow Stem I (here
represented as screw'd to a square Piece of Wood, and thereby held
upright) with its Stopcock I, and its Horizontal Hollow G H with which it
communicates. Upon this Horizontal Piece two more hollow Stems are
erected, and communicate therewith. These also have Stopcocks E and F, and
to these are screw'd Two Brass Plates A B and C D, on which Two Recipients
may be fix'd, and may communicate with the rest. By this means the whole
Instrument may be apply'd to the Air Pump, and one or more of its
Recipients exhausted; and afterward any Factitious or Natural Air may be
transferr'd from one Receiver to another, as Occasion requires: Of which
Instrument Mr. _Boyle_ made great Use in his Second Continuation of
Experiments.

_Fig. 4._ Are very small or capillary Glass Tubes, of different Bores, let
down into Tinged Water, in Vacuo, to shew, that by the Attraction of the
Glass the Water will be elevated, contrary to the ordinary Law of
Hydrostaticks, and that to a considerable Height; and what is chiefly
remarkable, is, that the Altitude of the Liquid in the Tubes is the same
in Vacuo as in the open Air, and is always in an exact reciprocal
Proportion to the Diameters of their Bases.

_Fig. 5._ Is the noble Improvement of the former Experiment by Mr.
_Hauksbee, Sen._ upon which the Learned Mr. _Ditton_ has written a small
Treatise. It is done by two Glass Plains, A C B, A D B, meeting in an Axis
at A B; and being about a Tenth of an Inch distant at the greatest
Aperture D C. These Plains are Erected in Spirit of Wine, and are like a
Series of Tubes of all different Diameters less than D C, which must
therefore elevate the Fluid a little at D C, and higher all the way to B,
where the Elevation ought to be Infinite; the Tops of the elevated Columns
will form an Hyperbola, E F G, with its Two Asymptotes, the Surface of the
Fluid D C B, and the Line B A. _Note_, That if the Angle at D C be
altered, the Bigness of the Hyperbola will be alter'd, while its Species
remains; but that if the Angle A B C be alter'd, the Species of the
Hyperbola will be alter'd also, though it will still be a true Hyperbola,
and that if the Glass be clean, to a surprizing Degree of Exactness.



                  [[Plate V. ― Sutton Nicholls sculp:]]



                             PNEUMATICKS. 19

                    An Explication of the Fifth PLATE.


Figure 1. Are _Otto Guerick_'s Hemispheres, with their several Screws and
Apparatus at large, set separately by themselves. They are designed to
prove that the Force of the outward Air, when the inward is extracted from
between them, is equal to the Weight of a Column of Quicksilver of about
29 Inches and a half: Of Water of about 34 Feet: And of Air to the Top of
the Atmosphere, all pressing upon the same Base with the largest Circles
of those Hemispheres.

_Fig. 2._ Is the Syringe, with its Hole; to be screw'd on to the Top of
the Receiver of the next Figure; in order to thrust Air into it, for the
Improvement of the former Experiment; or to shew that tho' common Air be
left in the Hemispheres, yet if that on their outward Surface be made
twice or thrice as dense, they will still sustain an equal, or a double
Weight respectively, before they are separated.

_Fig. 3._ Is that Instrument included in such a Receiver D B, and that
Receiver kept close to its Basis by a cross Piece and Screws, as in the
Condenser before: Together with a newly contriv'd Stiliard, to which the
upper Hemisphere is hung; with its fixed Base, and its Gage, to measure
the Degrees of Condensation of the Air, where by the Proportion of S P to
P K, the Weight 50 w. is equivalent to greater Weights, and shews how many
Pounds are required to separate the Hemispheres in all Cases. If the
Diameter be 3 Inches and a half, they will sustain about 150 Pounds; and
so in all other Proportions.

_Fig. 4._ Is the Plate which covers the upper Part of the Receiver. And
through the Hole C the Piece D E slides, which takes hold on the upper
Hemisphere.

_Fig. 5._ Shews the Gage of the same Instrument; this is like that for the
Glass Condenser before describ'd, and contains a bended Tube, whose open
End is in a small Basin of Mercury; and the other is Hermetically seal'd:
For this Mercury crowded by the condensed Air in the Receiver, will croud
the Air in the small Tube closer in Proportion to its Density, and so will
afford us the Knowledge of the Quantity thereof.

_Fig. 6._ Is a like Experiment of the Cohesion of polished Plates of
Brass, or of Marble; when the Air is excluded by a little Oil, and an
exact Application. This Cohesion may be weighed by the Stiliard, as well
as that of the Hemispheres; and is equal to the same, upon the same Base;
provided a Ring do prevent their side or sliding Motion; and provided the
Air can equally be excluded from between the Plates, as between the
Hemispheres. Which last yet is almost impossible to be done.

_Fig. 7._ Is a Number of great Weights, kept steady one over another by an
Iron Rod passing through them, and pressing upon a Bladder half blown,
plac'd below them: This Bladder, by the Elasticity of its included Air,
gradually elevates all those Weights; as soon as by the Extraction of the
other Air out of the Receiver, wherein they are all included, its
Counterpoise is gradually taken away.

_Fig. 8._ Is a Number of Jet d'Eaus, or Fountains, made by condens'd Air,
in a large Copper Vessel C D, pressing on the Surface of Water at the
Bottom of the Vessel; into which Water a hollow Brass Pipe is immers'd.
For if there be then a Stopcock at G, to open or shut the hollow Pipe at
Pleasure; and several smaller Pipes at I K, communicating therewith,
turning upon Balls or Joints, and plac'd in Order, we shall have a very
pleasant Set of these _Jet d'Eaus_, or Fountains; all whose Water will be
caught by the Bason A B, which Water may be again let into the Vessel C D,
by unscrewing the Pillar in the Center of the Bason.



                    [[Plate VI. ― I. Senex sculp.^t]]



                             PNEUMATICKS. 20

                    An Explication of the Sixth PLATE.


This Plate is in Reality but one compound Instrument or Apparatus, for
trying the Electricity of Glass, and its Luminousness, when put into
Motion, and rubb'd upon to heat it. Wherein B C is a Wheel, with its
String A B C. D E is a Sphere of Glass, whose Air has been drawn out by
the Air-Pump: This is turned round by the former Wheel-string at A. F is a
Stopcock, whereby the Air is exhausted, and may be readmitted at
Discretion.

In _Fig. 1._ K L M is an Arch with Threads of Cruel or Yarn upon it, as
they hang about the Glass D E, (here represented by a smaller Circle
within the Arch) before it is turned round or heated by rubbing.

_Fig. 2._ G H I is the same with the former; only the Threads are here
represented as they hang at the Beginning of the turning round of the
Globe, before it be heated by Friction; being plainly bent one way, by a
Wind arising from that Convolution.

_Fig. 3._ N P O is the same; only with the Threads pointing towards the
Sphere, or its Center, when the Arch is in an upright Posture, and some of
the Threads hang partly downwards, and this upon the Spheres being heated
sufficiently.

_Fig. 4._ Q S R is the same, with its Threads pointing the same way,
though in a downward Posture, when some of the Threads thereby are forc'd
to stand erect.

_Fig. 5._ T U is a Circular Arch, in an horizontal Position, when the
Threads point towards the same Center, in the same horizontal Plain.

_Fig. 6._ Is another Sphere, communicating with the Air, and to be apply'd
to the same Wheel in the Room of D E, where-into is inserted an Axis with
a Circle affixed to it; at the Edges of which Circle the Threads are
placed. These upon the Friction and Heat of the Glass extend themselves
outward, and point from the Center to the Circumference, contrary to the
former. In both Cases the Threads, when under the Influence of the
Electricity, will be moved by the Finger, even without Contact, nay by the
Finger and Breath, even through the Glass it self; so subtle are these
_Effluvia_. The Light is made when the Air is exhausted, and diminishes as
you readmit it. It spreads and branches it self inwardly like Lightning,
when about half that Air is readmitted. The Colour of that Light is always
Purple. It spreads at some Distance, and makes the Edges of a Cravat look
a little like the milky Way, by the great Number of Sparkles it emits:
Which may also be felt by the Flesh, with a crackling Noise that
accompanies them. If you also sufficiently rub and heat a large Tube of
Glass, either solid or hollow, it becomes strongly Electrical, even
through Glass it self; tho' not so much through Muslin. Other Heat than
that by Friction signifies nothing. It will attract and repel Leaf Gold,
and the like small and light Bodies, after a strange manner, by turns;
when once they have been fully repell'd they cannot be made to touch them,
till they have been reflected from some other Body. If they lye between
two Pieces of Wood, laid pretty near, the Electricity fails of its Effect.
With other Circumstances very surprizing and unaccountable.


                                 _FINIS._



                           Transcription note:


The original punctuation and ortography of the book have been faithfully
preserved; words which are spelled variantly, or inconsistently
capitalized (e.g., _Axel_ vs. _Axle_, _crowded_ vs. _crouded_, _blue, red_
vs. _Blue, Red_, etc.) have been left as such.

Likewise, the (mis)spelling of names like Galilæo, Azout, Hugen, Guerick,
has been retained.

The following typographical mistakes have been corrected, taking into
account recurrences across the text:

  * Page III, 25th day:
       * The Ebullition of Liquors in _Vacuo_ → The Ebullition of Liquors
         _in Vacuo_

  * Mechanicks, Explication of the 2nd Plate:
       * Figure. 1. Is the deceitful Balance; which yet is _in Equilibrio_
              → Figure 1. Is the deceitful Balance; which yet is _in Æquilibrio_
       * _Fig. 3_ → Fig. 3.
       * [Fig. 10]: perpendiculary → perpendicularly
       * [between Fig. 9 and 10]: N. _B._ → _N. B._
       * [Fig. 10]: and in this Leaver → and in this Lever

  * Mechanicks, Expl. 5th Plate, Fig. 3:
       * us it is less restrained. → as it is less restrained.

  * Opticks, Expl. 1st Plate, Fig. 3:
       * Looking-glass → Looking-Glass

  * Opticks, Expl. 2nd Plate:
       * _Fig. 8._ Shows → _Fig. 8._ Shews
       * [Fig. 10]: on the like Acccount. → on the like Account.

  * Hydrostaticks, Expl. 1st Plate:
       * [Fig. 5]: specifick Gravity of Water → Specifick Gravity of Water

  * Hydrostaticks, Table of Specifick Gravities:
       * Spirit of Nirre → Spirit of Nitre

  * Pneumaticks, Expl. 2nd Plate:
       * [Fig. 1]: 'tis by this Thteefold → 'tis by this Threefold
       * [Fig. 2]: small Part of ccmmon Air → small Part of common Air

  * Pneumaticks, Expl. 5th Plate:
       * [Fig. 6]: as between the Hemispheres → as between the
         Hemispheres.

  * Pneumaticks, Expl. 6th Plate:
       * [Fig. 6]: througn Muslin → through Muslin





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