Part 3

_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.