Part 1

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

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

MECHANICKS.

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

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

An Instrument to measure the Force of Falling Bodies.

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

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

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

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

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

The general Principle of Mechanicks established upon this Method.

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

The Resolution of Forces into those of other Directions.

All the various Kinds of Levers explain'd.

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

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

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

The Screw, with the manner of computing its Force.

A Compound Engine.

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

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

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

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

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

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

That the Line described by a Projectile is a Parabola.

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

6th—Experiments concerning Pendulums.

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

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

Experiments concerning the Expansion of Metals by Heat.

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

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

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

MAGNETICKS.

8th Day. Attractive and Directive Powers of Loadstones.

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

Magnetick Power acts thro' all Bodies but Iron.

The Attraction of different, and Repulse of corresponding Poles.

The manner of touching and untouching of Needles.

The Law of Magnetick Attraction discover'd.

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

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

Their Variation _East_ and _West_.

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

The Terrestrial Magnetism consider'd.

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

OPTICKS.

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

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

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

12th—Experiments to shew the Manner of Refraction.

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

An Instrument to measure the Refraction of Fluids.

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

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

The Dissection of the Eye.

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

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

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

A Multiplying Glass.

The Magick Lanthorn.

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

The _Camera Obscura_.

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

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

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

Experiments concerning the blending and Production of Colours by Motion.

HYDROSTATICKS.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Advertisement.

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

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

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

1 MECHANICKS.

An Explication of the First PLATE.

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

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

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

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

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

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

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

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

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

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

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

MECHANICKS. 2

An Explication of the Second PLATE.

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

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

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

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

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

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

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

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

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

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

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

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

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

MECHANICKS. 3

An Explication of the Third PLATE.

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

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

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

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

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

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

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

MECHANICKS. 4

An Explication of the Fourth PLATE.

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

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

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