Part 2

_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.