dies at C exceeds that of the body at D. If the new body weighed but half as much as the others, it must be removed to d, fo as to have the distance Kd quadruple the distance K, C. Now if CD be a wire, and it be fupported under K, the three bodies, whether D or d be used, will be thereby fuftained. In taking the center of gravity at K, we confider the wire as a mathematical line without substance or weight.

If these three bodies, united to or acting upon one another proportionably to their maffes, be carried round their common center of gravity, that point will be at reft. Hence alfo in our fyftem, where the fun and all the planets move round their common center of gravity, that center is at reft in the middle of the fyftem. The fun is on account of it's vaft bulk, &c. compared with the other planets, considered in general as the center of the fyftem.

Though the center of gravity of a body, or of a fyftem of bodies, is often neither within the body itself, nor any of the combined bodies; yet it is to be confidered, with refpect to it's fupport, defcent, or motion, in any direction, as if it were fo fituated. Thus let us fuppofe A and b, fig. 24, pl. 1, to be at the distance A b from each other, and that Ab is no longer a wire but a line reprefenting their distance, we fhall then find their center of gravity at C without the bodies; and if instead of the wire CD, fig. 92, we fuppofe D joined to A and B by the wires AD, BD, the center of gravity K will be neither in thefe bodies nor the wire; fo that to fupport them you muft fuftain fome part of the wire, as G, which being made tl e center of motion, the center of gravity will be under it; or if we fupport the point H, the bodies will be at reft, because the center of gravity is over H the center of motion.

VOL. II.

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In

In the ring A BE, fig. 10, pl. 2, the center of gravity is in no part of the ring, but may be fupported by any other point, O or E. Thus the center of gravity of the ring of Saturn is within the body of the planet; and though the common center of gravity of the fun, moon, and earth, is within the body of the fun, yet the common center of gravity of the moon and earth is in neither of the bodies, but between them.

When any number of bodies move in right lincs with uniform motions, their common center of gravity moves alfo in a right line with an uniform motion; and the fum of their motions, estimated in any given direction, is precisely the fame as if all the bodies in one mafs were carried on with the direction and motion of their common center of gravity.

For the fum of the motions of the bodies eftimated in any given direction is preserved invariably the fame in their collifions, without being affected by their actions upon cach that are equal and mutual, and have contrary directions; and confequently their center of gravity is no ways affected by their collifions on any fuch actions, but perfeveres in a state of reft or uniform motion, as any one body perfeveres in it's flate till influenced by fome external circumftance.

The name fyftem does not belong properly to any unconnected affemblage of particles, but can only be applied with propriety to fuch collections of particles as are connected together by mechanical forces. The varieties in fuch connecting forces are innumerable, but we only confider here the motions of fuch fyftems whofe particles are connected by mutual and equal forces.

Equal and contrary motions communicated to any fyftem of bodies will have no effect upon their center of gravity, for they would not disturb a

body

body equal to the fum of them all placed in their center of gravity.

The center of gravity of a system of bodies will not be difturbed by their mutual attractions, as the motions thus communicated are always equal and oppofite; hence the center of gravity of our fyftem is either at reft, or moves on uniformly in a ftrait line. The latter is fuppofed by Dr. Herschel to be the cafe from the change which has been obferved in the relative fituation of fome of the fixed ftars.

Hence alfo the center of gravity of the earth is not affected by the motions on it's furface and bowels: when a cannon ball, for inftance, is thrown upwards, the projecting force re-acting on the earth caufes it to move in a contrary direction, but as the motions are equal, the center of gravity remains the fame.

The motions and actions of bodies upon each other in a space that is carried uniformly forward, are the fame as if that space was at reft; and any powers or motions that act upon all the bodies fo as to produce equal velocities in them in the fame or in parallel right lines, have no effect on their mutual actions or relative motions.

Thus the motions of bodies on board a fhip that is carried fteadily and uniformly forward, are performed in the fame manner as if the fhip were at reft. When a fleet of fhips is carried away by an uniform current, their relative motions are no way affected by the current, but approach to or recede from each other as they would if no fuch current exifted. The motion of the carth and air round it's axis has no effect on the action of bodies and agents on it's furface, only fo far as it is not rectilineal and uniform.

In general, the actions of bodies on each other depend not upon their abfolute but relative mo

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tion,

tion, which is the difference of their abfolute wher they have the fame direction, but their fum when they are moved in oppofite directions.

GENERAL OBSERVATIONS.

The stability of a body on an horizontal plane depends, as we have already obferved, on the pofition of the line of direction relative to the base of the body; the nearer this line approaches the cen- . ter of the bafe, the more firm the body ftands, and the contrary, which we experience daily in a thoufand different ways.

When a man is ftanding, the line of direction paffes directly between the feet; when he walks, most of the motion is to preferve this line in the fame pofition.

A man standing with his feet close is not near fo firm as when they are at fome distance.

A man fitting in a chair cannot rife without bringing his body forward, and moving his feet backwards, till the center of gravity be before his feet, or at least upon them, when to prevent falling forward he brings one foot forwards.

For when we are fitting on a chair our center of gravity is on the feat, and the line of direction falls behind our bafe; we therefore lean forwards to bring the line of direction towards our feet, and draw our feet backwards at the fame time, that we may carry our bafe towards the line of direction; when the center of gravity is reduced fo as to be exactly over our feet, we are able to raise ourfelves upright.

In walking up a steep hill a man brings his body forward, and preffes only on his toes or fore part of his feet, fo that the center of gravity may be

between

between his feet, and prevent his falling backwards.

And for the fame reafon, by an easy and natural motion we carry the body from right to left, and from left to right at every step.

Rope dancers alfo ufe a pole loaded with lead at it's two extremities, in order to counterballance their various movements, and always regulate the motion of the center of gravity.

In general our motions, and particularly the friction of the feet, ferve to modify confiderably the effect of our weight, and to preferve conftant ftability amidst a variety of caufes which tend to destroy it.

To confider walking more particularly in walking, the foot from which we fet off is our base at first, till by turning the ball of it round, we have thrown the center of gravity forwards beyond it, by which means we fhould throw ourselves down if we did not take up the other leg from the ground, and fet it before us fo as to catch ourselves upon it as upon a prop or fupport to prevent us from falling. This is taking one ftep; in order to take a fecond, the center of gravity must be brought directly over the prop, that is, the foot which we put before us must be made our base, from which we may fet off in taking a fecond step. We do this by turning the ball of the foot ftill farther round, fo as to push the ground that we ftand on back with our toe, and the ground by it's refiftance pushes our center of gravity forward till the line of direction is got to the place where we want to have it reduced. Hence in walking, the line of direction paffes through each foot alternately, and if we fet one foot directly before the other in every step that we take, then this line will move evenly forward; but if we ftraddle as we walk, then the line of direction does not go on evenly, but is car

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ried