it is natural to afk, If the air accelerates a moving body as much as it retards it, how comes it to make any refiftance at all? yet certain it is that this fluid doth refift, and that very confiderably. To this it may be answered, that the air is always kept in fome certain ftate or conftitution by another power which rules all it's motions, and it is this power, undoubtedly, which gives the refiftance. It is not to our purpose, at present, to inquire what that power is; but we fee that the air is often in very different ftates: one day, for inftance, it's parts are violently agitated by a storm, and another, perhaps, they are comparatively at reft in a calm. In the first cafe, nobody hefitates to own, that the ftorm is occafioned by fome caufe or other which violently refifts any other power that would prevent the agitation of the air. In a calm the cafe is the fame; for it would require the fame exertion of power to excite a tempeft in a calm day, as to allay a tempeft in a stormy one. Now it is evident, that all projectiles, by their motion, agitate the atmosphere in an unnatural manner; and confequently are refifted by that power, whatever it is, which tends to reftore the equilibrium, or bring back the atmosphere to it's former state.

If no other body befides that above-mentioned acts upon projectiles, it is probable, that all refiftance to their motion would be in the duplicate proportion of their velocities; and accordingly, as long as the velocity is fmall, we find it generally is fo; but when the velocity comes to be exceedingly great, other fources of resistance arise. One of thefe is a fubtraction of part of the moving power; which, though not properly a refiftance, or oppofing another power to it, is an equivalent thereto. This fubtraction arifes from the following. caufe. The air, as we have already observed, preffes upon the hinder part of the moving body by

it's gravity, as much as it refifts the fore-part of it by the fame property: nevertheless, the velocity with which the air preffes upon any body by means of it's gravity is limited; and it is poffible that a body may change it's place with fo great velocity, that the air hath not time to rufh in upon the back-part of it, in order to affift it's progreffive motion. When this happens to be the cafe, there is, in the first place, a deficiency of the moving power equivalent to fifteen pounds on every square inch of furface; at the fame time that there is a pofitive resistance of as much more on the forepart, owing to the gravity of the atmosphere, which must be overcome before the body can move forward.

This deficiency of moving power, and increase of refiftance, do not only take place when the body moves with a very great degree of velocity, but in all motions whatever. It is not in thefe cafes perceptible, because the velocity with which the body moves, frequently bears but a very fmall proportion to the velocity with which the air preffes in behind it. Thus, fuppofing the velocity with which the air rushes into a vacuum to be 1200 feet in a fecond, if a body moves with a velocity of 30, 40, or 50 feet in a fecond, the force with which the air preffes on the back-part is but at the utmoft lefs than that which refifts on the fore-part of it, which will not be perceptible; but if, as in the cafe of bullets, the velocity of the projectile comes to have a confiderable proportion to the velocity wherewith the air rushes in behind it, then a very perceptible, and otherwife unaccountable refiftance is observed, as we have seen in the experiments already related by Mr. Robins. Thus, if the air preffes in with a velocity of 1200 feet in a fecond, if the body changes it's place with a ve locity of 600 feet in the fame time, there is a refiftVOL. III.

ance

ance of 15 pounds on the fore-part, and a preffure of only 7 on the back-part. The refiftance, therefore, not only overcomes the moving power of the air by 7 pounds, but there is a deficiency of other 7 pounds, owing to the want of half the preffure of the atmosphere on the back-part, and thus the whole lofs of the moving power is equivalent to 15 pounds; and hence the exceeding great increase of refiftance observed by Mr. Robins, beyond what it ought to be, according to the common computations. The velocity with which the air rufhes into a vacuum is therefore a defideratum in gunnery. Mr. Robins fuppofes that it is the fame with the velocity of found; and that when a bullet moves with a velocity greater than that of 1200 feet in a fecond, it leaves a perfe&t vacuum behind it. Hence he accounts for the great increase of refiftance to bullets coming with fuch velocities; but as he doth not take notice of the lofs of the air's moving power, the anomalies of all leffer velocities are inexplicable on his principles. Nay, he even tells us, that Sir Ifaac Newton's rule for computing diftances may be applied in all velocities lefs than 1100 or 1200 feet in a fecond, though this is exprefsly contradicted by his own experiments.

Though, for thefe reafons, it is evident how great difficulties muft occur in attempting to calculate the refiftance of the air to military projectiles, we have not even yet difcovered all the fources of refiftance to thefe bodies, when moving with immenfe velocities. Another power by which they are oppofed (and which at laft becomes greater than any of thofe hitherto mentioned), is the air's elafticity. This, however, will not begin to fhew itself in the way of refiftance, till the velocity of the moving body becomes confiderably greater than that by which the air preffes into a vacuum. Having, therefore, firft afcertained this velocity, which

It

which we fhall fuppofe to be 1200 feet in a fecond, it is plain, that if a body moves with a velocity of 1800 feet in a fecond, it must comprefs the air before it; because the fluid hath neither time to expand itself, in order to fill the vacuum left behind the moving body, nor to rush in by it's gravity. This compreffion it will refift by it's elaftic power, which thus becomes a new fource of refiftance, increafing, without any limit, in proportion to the velocity of the moving body. If now we fuppofe the moving body to fet out with a velocity of 2400 feet in a fecond, it is plain that there is not only a vacuum left behind the body, but the air before it is compreffed into half it's natural space. The lofs of motion in the projectile, therefore, is now very confiderable. firft lofes fifteen pounds on every fquare inch of furface, on account of the deficiency of the moving power of the air behind it; then it lofes fifteen pounds more, on account of the refiftance of the air before it; again it lofes fifteen pounds; on account of the elafticity of the compreffed air; and, laflly, another fifteen pounds on account of the vacuum behind, which takes off the weight of the atmosphere, that would have been equivalent to one-half of the elafticity of the air before it. The whole refiftance, therefore, upon every fquare inch of furface moving with this velocity is fixty pounds, befides that which arifes from the power tending to preferve the general ftate of the atmofphere, and which increafes in the duplicate proportion of the velocity, as already mentioned. If the body is fuppofed to move with a velocity of 4800 feet in a fecond, the refiftance from the air's elafticity will then be quadrupled, or amount to fixty pounds on the fquare inch of furface; which, added to the other caufes, produces a refiftance of 105 pounds

O 2

pounds upon the fquare inch; and thus would the refiftance from the elafticity of the air go on continually increafing, till at laft the motion of the projectile would be as effectually stopped as if it was fired against a wall. This obftacle, therefore, we are to confider as really infuperable by any art whatever, and therefore it is not advifeable to use larger charges of powder than what will project the fhot with a velocity of 1200 feet in a fecond. In this velocity the elafticity of the air will not make great resistance, if indeed it do make any at all; for though Mr. Robins hath conjectured, that air rushes into a vacuum with the velocity of found, or between 1100 and 1200 feet in a second, yet we have no decifive proof of the truth of this fuppofition. At this velocity indeed, according to Mr. Robins, a very fudden increase of resistance takes place; but this is denied by Mr. Glenie, who fupposes that the refiftance proceeds gradually and indeed it seems to be pretty obvious, that the refiftance cannot very fuddenly increase, if the velocity is only increased in a fmall degree. Yet it is certain, that the fwifteft motions with which cannon-balls can be projected are very foon reduced to this ftandard; for Mr. Robins acquaints us, that "a twenty-four pound fhot, when discharged with a velocity of 2000 feet in a fecond, will be reduced to that of 1200 feet in a fecond, in a flight of little more than 500 yards."

CONCERNING PENDULUMS.

A pendulum is a heavy body hanging to a small cord or wire, which is moveable upon a center. It is that well known inftrument fo useful in meafuring time, and afcertaining with accuracy it's nicer divifions.

A body thus fufpended being put in motion,

describes