EXPER. 14. Anno 1719, in the month of July, Dr. Defaguliers made fome experiments of this kind again, by forming hogs' bladders into fpherical orbs; which was done by means of a concave wooden sphere, which the bladders, being wetted well first, were put into. After that, being blown full of air, they were obliged to fill up the fpherical cavity that contained them; and then, when dry, were taken out. These were let fall from the lantern on the top of the cupola of the fame church, namely, from a height of 272 feet; and at the fame moment of time there was let fall a leaden globe, whose weight was about 2 pounds troy weight. And in the mean time fome perfons standing in the upper part of the church where the globes were let fall obferved the whole times of falling; and others ftanding on the ground obferved the differences of the times between the fall of the leaden weight and the fall of the bladder. The times were measured by pendulums ofcillating to half feconds. And one of those that ftood upon the ground had a machine vibrating four times in one fecond; and another had another machine accurately made with a pendulum vibrating four times in a fecond alfo. One of thofe alfo who stood at the top of the church had a like machine; and thefe inftruments were fo contrived, that their motions could be stopped or renewed at pleasure. Now the leaden globe fell in about four feconds and of time; and 201 from the addition of this time to the difference of time above fpoken of, was collected the whole time in which the bladder was falling. The times which the five bladders fpent in falling, after the leaden globe had reached the ground, were, the first time, 144", 12", 14", 17", and 167"; and the second time, 14", 144", 14", 19", and 16". Add to thefe 44", the time in which the leaden globe was falling, and the whole times in which the five bladders fell were, the first time, 19", 17", 18", 22", and 211"; and the fecond time, 18", 18", 18", 234", and 21". The times obferved at the top of the church were, the first time, 19", 174", 18", 22", and 21"; and the fecond time, 19", 18", 18", 24", and 214". But the bladders did not always fall directly down, but fometimes fluttered a little in the air, and waved to and fro as they were defcending. And by these motions the times of their falling were prolonged,

and increased by half a fecond fometimes, and fometimes by a whole fecond.. The fecond and fourth bladder fell moft directly the first time, and the firft and third the fecond time. The fifth bladder was wrinkled, and by its wrinkles was a little retarded. I found their diameters by their circumferences measured with a very fine thread wound about them twice. In the following table I have compared the experiments with the theory; making the denfity of air to be to the density of rainwater as 1 to 860, and computing the spaces which by the theory the globes ought to describe in falling.

Our theory, therefore, exhibits rightly, within a very little, all the refiftance that globes moving either in air or in water meet with; which appears to be proportional to the denfities of the fluids in globes of equal velocities and magnitudes.

In the fcholium fubjoined to the fixth fection, we shewed, by experiments of pendulums, that the refiftances of equal and equally fwift globes moving in air, water, and quickfilver, are as the denfities of the fluids. We here prove the fame more accurately by experiments of bodies falling in air and water. For pendulums at each oscillation excite a motion in the fluid always contrary to the motion of the pendulum in its return; and the refiftance arifing from this motion, as alfo the refiftance of the thread by which the pendulum is fufpended, makes the whole refiftance of a pendulum greater than the refiftance deduced from the experiments of falling bodies. For by the experiments of pendulums defcribed in that fcholium, a globe of the fame denfity as water in defcribing the length of its femi-diameter in air would lose the

3342

part of its motion. But by the theory delivered in this

feventh fection, and confirmed by experiments of falling bodies, the fame globe in defcribing the fame length would lofe

1

only a part of its motion equal to fuppofing the denfity

4586

of water to be to the denfity of air as 860 to 1. Therefore the refiftances were found greater by the experiments of pendulums (for the reafons juft mentioned) than by the experiments of falling globes; and that in the ratio of about 4 to 3. But yet fince the refiftances of pendulums ofcillating in air, water, and quickfilver, are alike increafed by like caufes, the proportion of the refiftances in thefe mediums will be rightly enough exhibited by the experiments of pendulums, as well as by the experiments of falling bodies. And from all this it may be concluded, that the refiftances of bodies, moving in any fluids whatsoever, though of the most extreme fluidity, are, cæteris paribus, as the denfities of the fluids.

These things being thus established, we may now determine what part of its motion any globe projected in any fluid whatfoever would nearly lose in a given time. Let D be the diameter of the globe, and V its velocity at the beginning of its motion, and T the time in which a globe with the velocity V can defcribe in vacuo a space that is to the space D as the denfity of the globe to the denfity of the fluid; and the globe projected in that fluid will, in any other time t, lofe the part

the part

TV
T + t

tV T+t which will be to that defcribed in the fame time in vacuo with the uniform velocity V, as the logarithm of the number T + t

remaining; and will defcribe a space,

T

multiplied by the number 2,302585093 is to the number

by cor. 7, prop. 35. In flow motions the refiftance may be a little lefs, because the figure of a globe is more adapted to motion than the figure of a cylinder defcribed with the fame diameter. In fwift motions the refiftance may be a little greater, because the elasticity and compreffion of the fluid do not increase in the duplicate ratio of the velocity. But these little niceties I take no notice of.

And though air, water, quickfilver, and the like fluids, by the divifion of their parts in infinitum, fhould be fubtilized, and become mediums infinitely fluid, nevertheless, the refiftance they would make to projected globes would be the fame. For the refiftance confidered in the preceding propofitions arifes from the inactivity of the matter; and the inactivity of matter is effential to bodies, and always proportional to the quantity of matter. By the divifion of the parts of the fluid the refiftance arifing from the tenacity and friction of the parts may be indeed diminished; but the quantity of matter will not be at all diminished by this divifion; and if the quantity of matter be the fame, its force of inactivity will be the fame; and therefore the resistance here spoken of will be the fame, as being always proportional to that force. To diminish this resistance, the quantity of matter in the spaces through which the bodies move muft be diminifhed; and therefore the celestial spaces, through which the globes of the planets and comets are perpetually paffing towards all parts, with the utmost freedom, and without the leaft fenfible diminution of their motion, must be utterly void of any corporeal fluid, excepting, perhaps, fome extremely rare vapours and the rays of light.

Projectiles excite a motion in fluids as they pafs through them; and this motion arises from the excefs of the preffure of the fluid at the fore-parts of the projectile above the preffure of the fame at the hinder parts; and cannot be lefs in mediums infinitely fluid than it is in air, water, and quickfilver, in proportion to the denfity of matter in each. Now this excess of preffure does, in proportion to its quantity, not only excite a motion in the fluid, but also acts upon the projectile fo as to retard its motion; and therefore the refiftance in every fluid is as the motion excited by the projectile in the fluid; and cannot be lefs in the most fubtile æther in proportion to the denfity of that æther, than it is in air, water, and quickfilver, in proportion to the denfities of those fluids.

SECTION VIII.

Of motion propagated through fluids.

PROPOSITION XLI. THEOREM XXXII.

A preffure is not propagated through a fluid in rectilinear directions, unless where the particles of the fluid lie in a right line. (Pl. 8, Fig. 1.)

If the particles a, b, c, d, e, lie in a right line, the preffure may be indeed directly propagated from a to e; but then the particle e will urge the obliquely pofited particles f and g obliquely, and thofe particles f and g will not fuftain this presfure, unless they be fupported by the particles h and k lying beyond them; but the particles that fupport them are also preffed by them; and those particles cannot fuftain that preffure, without being fupported by, and preffing upon, those particles that lie ftill farther, as I and m, and fo on in infinitum. Therefore the preffure, as soon as it is propagated to particles that lie out of right lines, begins to deflect towards one hand and the other, and will be propagated obliquely in infinitum; and after it has begun to be propagated obliquely, if it reaches more diftant particles lying out of the right line, it will deflect again on each hand; and this it will do as often as it lights on particles that do not lie exactly in a right line. Q.E.D.

COR. If any part of a preffure, propagated through a fluid from a given point, be intercepted by any obstacle, the remaining part, which is not intercepted, will deflect into the spaces behind the obftacle. This may be demonftrated also after the following manner. Let a preffure be propagated from the point A (Pl. 8, Fig. 2) towards any part, and, if it be poffible, in rectilinear directions; and the obftacle NBCK being perforated in BC, let all the preffure be intercepted but the coniform part APQ passing through the circular hole BC. Let the cone APQ be divided into fruftums by the tranfverfe planes de, fg, hi. Then while the cone ABC, propagating the preffure, urges the conic fruftum degf beyond it on the fuperficies de, and this fruftum urges the next fruftum fgih on the fuperficies fg, and that fruftum urges a third fruftum, and so in infinitum; it is manifeft (by the third law) that the