Hence it follows, that if a system of bodies, placed at rest, be permitted to obey their mutual attractions, although the bodies will thereby be severally moved, yet their common centre of gravity must remain quiescent. (175.) When one of two bodies is moving in a straight line, the other being at rest, their common centre of gravity must move in a parallel straight line. Let A and B, _fig. 69._, be the centres of gravity of the bodies, and let A move from A to _a_, B remaining at rest. Draw the lines A B and _a_ B. In every position which the body B assumes during its motion, the centre of gravity C divides the line joining them into parts A C, B C, which are in the proportion of the mass B to the mass A. Now, suppose any number of lines drawn from B to the line A _a_; a parallel C _c_ to A _a_ through C divides all these lines in the same proportion; and therefore, while the body A moves from A to _a_, the common centre of gravity moves from C to _c_. If both the bodies A and B moved uniformly in straight lines, the centre of gravity would have a motion compounded (74) of the two motions with which it would be affected, if each moved while the other remained at rest. In the same manner, if there were three bodies, each moving uniformly in a straight line, their common centre of gravity would have a motion compounded of that motion which it would have if one remained at rest while the other two moved, and that which the motion of the first would give it if the last two remained at rest; and in the same manner it may be proved, that when any number of bodies move each in a straight line, their common centre of gravity will have a motion compounded of the motions which it receives from the bodies severally. It may happen that the several motions which the centre of gravity receives from the bodies of the system will neutralise each other; and this does, in fact, take place for such motions as are the consequences of the mutual action of the bodies upon one another. (176.) If a system of bodies be not under the immediate influence of any forces, and their mutual attraction be conceived to be suspended, they must severally be either at rest or in uniform rectilinear motion in virtue of their inertia. Hence, their common centre of gravity must also be either at rest or in uniform rectilinear motion. Now, if we suppose their mutual attractions to take effect, the state of their common centre of gravity will not be changed, but the bodies will severally receive motions compounded of their previous uniform rectilinear motions and those which result from their mutual attractions. The combined effects will cause each body to revolve in an orbit round the common centre of gravity, or will precipitate it towards that point. But still that point will maintain its former state undisturbed.