For a

will suppose) 30 seconds; we may thence collect the height to which it arose. projected body will both rise and fall in the same time; therefore we are to take half the time above-mentioned, or 15 seconds: then it will be 15X15X16 3600 feet, or 1200 yards, which is not far short of 1⁄2 of a mile.

But we are to observe, that, in the application of this theory, two things are taken for granted, before we arrive at any one of these conclusions. First, that the theory itself is true in practice to a mathematical exactness. That it is very nearly so, may be fairly concluded from the experiments which have been made; but nothing more can be concluded with absolute certainty. Secondly, that the motion is performed without any impediment; in other words, that it is performed in vacuo, or in a medium that gives no resistance; which is false in fact: no experiments of any considerable compass haying been made, or being possible to be made, without a great degree of interruption from the resistance of air. Upon this account, the well, whereof you are finding the depth, will not be so deep as may be imagined by several feet; nor will the stone, projected from the volcano, rise near so high as we kave already

concluded. This resistance of the air will be different at different seasons: and to find the absolute quantity of it at any time, and in any particular experiment, is a problem so difficult and complicated, as hardly to admit of an adequate solution.

In the experiments made by Mr. Hawksbee, of which we have an account in his Physico-Mechanical Experiments, p. 278, and in Sir Isaac Newton's Principia, lib. 2. prop. 40, some glass balls, filled with quicksilver, were observed to fall 220 feet in 4 seconds of time. By the theory they should have fallen 256 feet: therefore, the resistance of the air, added to some error in the performance, diminished the space by about one-seventh of the whole. Some other experiments made by Dr. Desaguliers with balls of lead (see Philos. Transact. N° 362. p. 1071), and executed with a better address than these of Mr. Hawksbee, came nearer to the theory. But let us consider that when these balls touched the ground, supposing them to have descended through a space of 256 feet, they moved only at the rate of 128 feet in a second: and what is this to the ve locity of light? which, according to the usual computation, moves above a million of times

swifter

swifter than a cannon-bullet.

Should this

fluid be the natural cause of gravity, and should the spaces described be less than the theory requires, on account of a nearer approach in the velocity of the body to the ve locity of the fluid that moves the body, such a discovery is far beyond the reach of all human experiments.

If what hath been here said, should tempt an inquisitive reader to search farther and deeper into the application of this theory of falling bodies to the motion of pendulums, the flight of bombs and other projectiles; he may find satisfaction by perusing part i. c. 6, &c. of Mr. Rowning's System of Natural Philosophy-S' Gravesande's Elements of Nat. Phil. by Desaguliers, b. i. c. 19 & 24 -Mr. Maclaurin's Account of Sir Isaac Newton's Discoveries, b. ii. c. 5. Or see

Dr. Keil's Introd. to Nat. Philos. lect. 15 and 16; than which there is nothing more exact and complete upon the subject,

ON CHAPTER IV.

Page 52, 1. 27, &c.

In order to prove by

some easy experiment, that the resistance which a body gives to any force that is ap

plied to put it in motion, is just so much as ought to proceed from the action of gravity upon it, and no more; I considered, that if the resistance in the ball of a simple penduJum should proceed wholly from its gravity; then the same force ought to move it more easily through a segment of a greater circle, than through a segment of a lesser.

Having put together an extempore apparatus, I took two balls of lead, the greater of which weighed one pound and an half, the lesser one quarter of a pound. These were suspended by lines, so that the centre of each ball, being at equal heights, was 28 inches below the points of suspension. A graduated scale being fixed parallel to the plane of their intended motion, I drew the lesser ball aside to 24 divisions from the perpendicular, and having let it fall against the greater, perceived that the stroke of it occasioned the greater ball to move over 4 divisions and from the perpendicular. Then I suspended the greater ball from a point 7 feet and 8 inches above its centre; and letting go the lesser ball from the same distance as before, found that the application of the same force did now occasion the greater ball to move over 9 divisions and very nearly, There

Therefore, in this latter trial, where the distance of the heavier ball from the point of suspension is almost quadruple of what it was before, the resistance becomes lesser than before by about one half.

The times of the vibrations of different pendulums being in the subduplicate ratio of their lengths, their velocities compared with each other will be inversely as the square roots of their lengths; that is, if the length of the greater pendulum be quadruple, and its time of vibration double, its velocity in a similar arch will be the velocity of the lesser pendulum. In this experiment, then, the resistance is lessened in the same proportion with the velocity: but the velocity is deducible only from the active force of gravity; therefore, the resistance must be owing to the same force. For if the resistance here found be such as ought to flow naturally from the gravity of the body, and no other resistance is to be discovered; must it not follow, that what has been called a vis inertia is but the same thing with the force of gravity? if not, how are they to be distinguished in this experiment?

That the resistances above-mentioned do not exactly coincide with the inverse ratio

of