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diff --git a/44019-0.txt b/44019-0.txt index e9769ab..cd825e2 100644 --- a/44019-0.txt +++ b/44019-0.txt @@ -1,37 +1,4 @@ -The Project Gutenberg EBook of A Course of Mechanical, Magnetical, -Optical, Hydrostatical and Pneumati, by Francis Hauksbee (the Younger) - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org/license - - -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) - -Commentator: William Whiston - -Release Date: October 23, 2013 [EBook #44019] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - - - - -Produced by Enrico Segre and the Distributed Proofreading -team at DP-test Italia, http://dp-test.dm.unipi.it - - - - +*** START OF THE PROJECT GUTENBERG EBOOK 44019 *** A COURSE @@ -1993,364 +1960,4 @@ account recurrences across the text: End of the Project Gutenberg EBook of A Course of Mechanical, Magnetical, Optical, Hydrostatical and Pneumati, by Francis Hauksbee (the Younger) -*** END OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - -***** This file should be named 44019-0.txt or 44019-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/4/0/1/44019/ - -Produced by Enrico Segre and the Distributed Proofreading -team at DP-test Italia, http://dp-test.dm.unipi.it - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org/license - - -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) - -Commentator: William Whiston - -Release Date: October 23, 2013 [EBook #44019] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - - - - -Produced by Enrico Segre and the Distributed Proofreading -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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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{~PRIME~}, 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{~PRIME~} 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{~PRIME~}; which Proportion of Sines being the same in all other Angles, we -hence learn that Proportion accurately and universally. - - - - - [[Plate IIII. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 Œ - - - - - [[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 29œ 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 29œ 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 29œ 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 {~GREEK SMALL LETTER DELTA~} representing Absolute Numbers, and its Abscissæ, C G or D B, -I _c_ or B d and B {~GREEK SMALL LETTER DELTA~}, 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 {~GREEK SMALL LETTER DELTA~}, 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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_ {~RIGHTWARDS ARROW~} The Ebullition of Liquors - _in Vacuo_ - - * Mechanicks, Explication of the 2nd Plate: - * Figure. 1. Is the deceitful Balance; which yet is _in Equilibrio_ - {~RIGHTWARDS ARROW~} Figure 1. Is the deceitful Balance; which yet is _in Æquilibrio_ - * _Fig. 3_ {~RIGHTWARDS ARROW~} Fig. 3. - * [Fig. 10]: perpendiculary {~RIGHTWARDS ARROW~} perpendicularly - * [between Fig. 9 and 10]: N. _B._ {~RIGHTWARDS ARROW~} _N. B._ - * [Fig. 10]: and in this Leaver {~RIGHTWARDS ARROW~} and in this Lever - - * Mechanicks, Expl. 5th Plate, Fig. 3: - * us it is less restrained. {~RIGHTWARDS ARROW~} as it is less restrained. - - * Opticks, Expl. 1st Plate, Fig. 3: - * Looking-glass {~RIGHTWARDS ARROW~} Looking-Glass - - * Opticks, Expl. 2nd Plate: - * _Fig. 8._ Shows {~RIGHTWARDS ARROW~} _Fig. 8._ Shews - * [Fig. 10]: on the like Acccount. {~RIGHTWARDS ARROW~} on the like Account. - - * Hydrostaticks, Expl. 1st Plate: - * [Fig. 5]: specifick Gravity of Water {~RIGHTWARDS ARROW~} Specifick Gravity of Water - - * Hydrostaticks, Table of Specifick Gravities: - * Spirit of Nirre {~RIGHTWARDS ARROW~} Spirit of Nitre - - * Pneumaticks, Expl. 2nd Plate: - * [Fig. 1]: 'tis by this Thteefold {~RIGHTWARDS ARROW~} 'tis by this Threefold - * [Fig. 2]: small Part of ccmmon Air {~RIGHTWARDS ARROW~} small Part of common Air - - * Pneumaticks, Expl. 5th Plate: - * [Fig. 6]: as between the Hemispheres {~RIGHTWARDS ARROW~} as between the - Hemispheres. - - * Pneumaticks, Expl. 6th Plate: - * [Fig. 6]: througn Muslin {~RIGHTWARDS ARROW~} through Muslin - - - - - -End of the Project Gutenberg EBook of A Course of Mechanical, Magnetical, -Optical, Hydrostatical and Pneumati, by Francis Hauksbee (the Younger) - -*** END OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - -***** This file should be named 44019-8.txt or 44019-8.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/4/0/1/44019/ - -Produced by Enrico Segre and the Distributed Proofreading -team at DP-test Italia, http://dp-test.dm.unipi.it - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org/license - - -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) - -Commentator: William Whiston - -Release Date: October 23, 2013 [EBook #44019] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - - - - -Produced by Enrico Segre and the Distributed Proofreading -team at DP-test Italia, http://dp-test.dm.unipi.it - - - - - - -</pre> - - +<div>*** START OF THE PROJECT GUTENBERG EBOOK 44019 ***</div> <h1> <span class="pageno target" title="I" id="page-I"></span> @@ -3432,386 +3390,6 @@ into account recurrences across the text:</p> </div> - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of A Course of Mechanical, Magnetical, -Optical, Hydrostatical and Pneumati, by Francis Hauksbee (the Younger) - -*** END OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - -***** This file should be named 44019-h.htm or 44019-h.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/4/0/1/44019/ - -Produced by Enrico Segre and the Distributed Proofreading -team at DP-test Italia, http://dp-test.dm.unipi.it - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org/license - - -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) - -Commentator: William Whiston - -Release Date: October 23, 2013 [EBook #44019] - -Language: English - -Character set encoding: ASCII - -*** START OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - - - - -Produced by Enrico Segre and the Distributed Proofreading -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 Phaenomena 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. - -_Galilaeo_'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 Phaenomena 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 Phaenomena 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 Phaenomena 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 Phaenomena 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 Phaenomena 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 Cohaesion 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. {~HORIZONTAL BAR~} Sutton Nicholls sculp:]] - - - - - 1 - MECHANICKS. - - An Explication of the First PLATE. - - -Figure. 1. This belongs to _Galilaeo'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 AEquilibrio_. - -_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 AEquilibrio_. - -_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. {~HORIZONTAL BAR~} Sutton Nicholls sculp:]] - - - - - MECHANICKS. 2 - - An Explication of the Second PLATE. - - -Figure 1. Is the deceitful Balance; which yet is _in AEquilibrio_ 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 _AEquilibrio_ 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. {~HORIZONTAL BAR~} 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 -AEquilibrio_. 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 AEquilibrio_: 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 Phaenomena 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 deg. 30{~PRIME~}, 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 deg. 30{~PRIME~} 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 deg. 30{~PRIME~}; which Proportion of Sines being the same in all other Angles, we -hence learn that Proportion accurately and universally. - - - - - [[Plate IIII. {~HORIZONTAL BAR~} 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 deg., is formed in -an erect Position at _a b_, for the View of the Spectator. - - - - - [[Plate V. {~HORIZONTAL BAR~} 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 _Phaenomena_ 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 AEquilibrio 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 AEquilibrium -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 Gemmae 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 1/4 - - - - - [[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 291/2 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 291/2 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 291/2 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 {~GREEK SMALL LETTER DELTA~} representing Absolute Numbers, and its Abscissae, C G or D B, -I _c_ or B d and B {~GREEK SMALL LETTER DELTA~}, 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 {~GREEK SMALL LETTER DELTA~}, 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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. {~HORIZONTAL BAR~} 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 Galilaeo, 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_ {~RIGHTWARDS ARROW~} The Ebullition of Liquors - _in Vacuo_ - - * Mechanicks, Explication of the 2nd Plate: - * Figure. 1. Is the deceitful Balance; which yet is _in Equilibrio_ - {~RIGHTWARDS ARROW~} Figure 1. Is the deceitful Balance; which yet is _in AEquilibrio_ - * _Fig. 3_ {~RIGHTWARDS ARROW~} Fig. 3. - * [Fig. 10]: perpendiculary {~RIGHTWARDS ARROW~} perpendicularly - * [between Fig. 9 and 10]: N. _B._ {~RIGHTWARDS ARROW~} _N. B._ - * [Fig. 10]: and in this Leaver {~RIGHTWARDS ARROW~} and in this Lever - - * Mechanicks, Expl. 5th Plate, Fig. 3: - * us it is less restrained. {~RIGHTWARDS ARROW~} as it is less restrained. - - * Opticks, Expl. 1st Plate, Fig. 3: - * Looking-glass {~RIGHTWARDS ARROW~} Looking-Glass - - * Opticks, Expl. 2nd Plate: - * _Fig. 8._ Shows {~RIGHTWARDS ARROW~} _Fig. 8._ Shews - * [Fig. 10]: on the like Acccount. {~RIGHTWARDS ARROW~} on the like Account. - - * Hydrostaticks, Expl. 1st Plate: - * [Fig. 5]: specifick Gravity of Water {~RIGHTWARDS ARROW~} Specifick Gravity of Water - - * Hydrostaticks, Table of Specifick Gravities: - * Spirit of Nirre {~RIGHTWARDS ARROW~} Spirit of Nitre - - * Pneumaticks, Expl. 2nd Plate: - * [Fig. 1]: 'tis by this Thteefold {~RIGHTWARDS ARROW~} 'tis by this Threefold - * [Fig. 2]: small Part of ccmmon Air {~RIGHTWARDS ARROW~} small Part of common Air - - * Pneumaticks, Expl. 5th Plate: - * [Fig. 6]: as between the Hemispheres {~RIGHTWARDS ARROW~} as between the - Hemispheres. - - * Pneumaticks, Expl. 6th Plate: - * [Fig. 6]: througn Muslin {~RIGHTWARDS ARROW~} through Muslin - - - - - -End of the Project Gutenberg EBook of A Course of Mechanical, Magnetical, -Optical, Hydrostatical and Pneumati, by Francis Hauksbee (the Younger) - -*** END OF THIS PROJECT GUTENBERG EBOOK A COURSE OF MECHANICAL *** - -***** This file should be named 44019.txt or 44019.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/4/0/1/44019/ - -Produced by Enrico Segre and the Distributed Proofreading -team at DP-test Italia, http://dp-test.dm.unipi.it - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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