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.
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.
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.
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.
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.
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.
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.
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.
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.
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.