formed, as from various accidents, have been found in a feries of ages liable to alteration.

Though gravity, and the revolution of the earth round it's axis, are ftandards of force and time, fo plainly pointed out by nature, as to have found univerfal reception among mankind, yet as the application of them requires fkill in the theory, and dexterity in the practice of mechanics, thefe measures have not been adopted as general and invariable ftandards; for men find it neceffary to weigh and to meafure, before they become philofophers; and in more improved times, philofophy is of too little confequence to alter what has been established by centuries of continual use.

OF THE MOMENTUM, FORCE, OR QUANTITY OF MOTION.

Though the force of a body in motion increases with it's velocity, yet it's force, or quantity of motion, cannot be determined by confidering the velocity alone; the mafs, or quantity of matter moved, muft alfo be taken into the account.

The force impreffed on a body, to put it into motion, is diftributed uniformly to all the parts of this body, and impreffes on each a velocity fimilar to that in the body; which can neither move with more nor lefs velocity than it's parts. The velocity is only, then, an expreffion denoting the force refident in each part: for if one body contain a quantity of ponderable matter ten times greater than another, then may the heavier be divided into ten bodies, each equal in quantity, of fuch matter, to the lighter; and whatever force be required to produce a certain velocity in the lighter body, ten of thefe forces will be, neceffary to impel the ten bodies through the fame fpace in the fame time; fo that the velocities of all the bodies fhall be equal

at

at the end of the motion: and it is the fame as to the velocity produced, whether the bodies be feparated or united; the ten forces ftill acting upon

them.

We must therefore take in the mafs, as well as the velocity, in order to judge of the force which animates a moving body; it's mafs, for the number of parts poffeffing a certain velocity, or given force; it's velocity, to know the intensity of the force refident in each of it's parts.

Thus, let the body b, weighing one pound, have fix degrees of velocity, whilft another body, a, of four pounds weight, has alfo fix degrees of velocity; the body a may be confidered as compofed of four other bodies, each equal to b, and having the fame velocity; confequently the body a has four times the momentum, or quantity of motion, of b. Multiply the mafs b, equal 1, by it's velocity, and the product is 6; but multiplying the mafs a, of four pounds, by it's velocity 6, the product is 24; expreffing the quantity of motion eftimated by multiplying the quantity of matter by the velocity, and the momentum, or force, is confidered as in a ratio compounded of the quantity of matter and the velocity.

As the quantity of motion in bodies is as the product of the mafs by the velocity, it follows, that the velocity is as the quotient of the motion divided by the mass, and their mass is as the motion divided by the velocity.

In computations relating to forces, motions, times, &c. the proportions of the quantities to each other are confidered, and not the quantities them

felves.

felves. In fuch computations therefore, when any two quantities are compared together, we may subftitute any other two quantities, which have the fame proportion to each other, as numbers, lines, &c.

1. It follows, from what has been faid on the quantity of motion, that if the velocity of a body increases whilft it's mafs remains the fame, it's force will be augmented as the velocity is increased; or if feveral bodies, of the fame mafs, move with different degrees of velocity, their force will be as the velocities with which they move.

2. If feveral bodies are poffeffed of the fame velocity, their forces will be as their maffes; i. e. they will have as much more force as they have more mafs, being poffeffed of a greater number of parts animated with the fame force.

3. That a force being given, it will produce lefs motion in a body, in proportion as that body contains a greater number of parts.

4. That the forces will be equal in two bodies, when the velocities are reciprocally as the maffes; i. e. when the velocity of that which has the leaft mafs, exceeds the velocity of that body with the greatest mafs, as much as the mafs of this exceeds that of the former.

It follows from what has been faid, that a fmall body may have as much momentum, or force, as a large one, provided their velocities are reciprocally proportional to their maffes. This is one of the reasons that, fince the invention of gunpowder, the battering rams of the ancients have been difufed: for their machines were large and ponderous, not easily moved; and when moved, acting with only a small velocity.

The effect of mechanical engines depends in a great degree upon this principle; for if a fmall weight is to ballance a great one, we must con

trive

trive to increase it's velocity juft as much as it wants of matter, and then it will ballance the large weight, if they act in contrary directions; for their momenta being equal and contrary, deftroy each other.

The battering rams of the ancients confifted of very large beams of wood, terminated by folid bodies of iron or brafs. Such a mass being fufpended as a pendulum, and driven partly by it's gravity, and partly by the impulfe of men, against the walls of a fortification, exerted a force which in fome refpects exceeded the utmost efforts of our battering cannon, though in other refpects it was probably inferior to modern ordnance.

To compare the effects of a battering ram, the metal extremity of which fuppofe equal in magnitude to a twenty-four pounder, with that of a cannon - ball of twenty-four pounds weight; in order that the two bodies may have the fame effect in cutting a wall, or making a breach in it, the weight of the ram muft exceed that of the ball in the proportion of about to the fquare of the velocity with which the battering ram could be made to impinge against a wall expreffed in feet. If this may be estimated at about 10 feet in a fecond, the proportion of the weights will be that of about 2890000 to 100, or 28900 to 1; the weight of the battering ram must therefore be equal to 346 ton. In this cafe, the battering ram and the cannon-ball moving with the velocity of 10 feet on 1700 feet refpectively in a fecond, would have the fame effect in penetrating the fubftance of an oppofed obftacle. But it is probable that the weight of the aries never amounted to fo much as is above defcribed, and confequently the effect of a cannon-ball to cut down walls, to make a breach in them, muft exceed thofe of the ancient battering ram. But the motion of thefe, or the impetus whereby

whereby they communicated a fhock to the whole building, was far greater than the utmost efforts of cannon-balls: for if the weight of the battering ram were no more that 170 times the cannon-ball, each moving with it's refpective velocity, the momenta of both would be equal: but as it is certain they were above 170 times the weight of our heaviest cannon-balls, it follows, that their impetus to shake or overturn walls, was far fuperior to that which is exerted by the modern artillery: and as the ftrength of fortifications will be generally proportioned to the means which can be used for their demolition, the military walls of the moderns have been conftructed with lefs attention to their folidity and maffy weight, than those of the ancients.

OF THE LAWS OF MOTIONS.

LAW.I. Every body perfeveres in a state of reft or of motion uniformly in a trait line, unlefs in fo far as by fome force impreffed upon them they are obliged to change that state.

This propofition was invented by Def cartes, who afferts, that a body once put in motion by the impulfe of another body, will continue always to be moved in a ftrait line, till it's motion be stopped or altered by fomething extrinsic to it. And in this refpect reft and motion are faid to be governed by the fame law; becaufe as the body continues at reft till it be moved by something extrinfic to it, fo it alfo continues in motion till it be stopped in the fame way.

This law, as it is generally understood, has been much objected to, and is, I believe, now given up by the best mathematicians and philofophers both here and abroad. They have confidered it not

only