CENTRE OF GRAVITY. 239 



Fig. 35. 



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 sev- 

 erally. 



It may happen that the several motions which the centre of gravity receives 

 from the bodies of the system will neutralize 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. 



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 recti- 

 linear 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 toward that point. But still that point will main- 

 tain its former state undisturbed. 



This constitutes one of the general laws of mechanical science, and is of 

 great importance in physical astronomy. It is known by the title "the con- 

 servation of the motion of the centre of gravity." 



The solar system is an instance of the class of phenomena to which we 

 have just referred. All the motions of the bodies which compose it can be 

 traced to certain uniform rectilinear motions, received from some former im- 

 pulse, or from a force whose action has been suspended, and those motions 

 which necessarily result from the principle of gravitation. But we shall not 

 here insist further on this subject, which more properly belongs to another 

 department of the science. 



If a solid body suffer an impact in the direction of a line passing through its 

 centre of gravity, all the particles of the body will he driven forward with the 

 same velocity in lines parallel to the direction of the impact, and the whole 

 force of the motion will be equal to that of the impact. The impelling force 

 being equally distributed among all the parts, the velocity will be found by 

 dividing the numerical value of that force by the number expressing the mass. 



If any number of impacts be given simultaneously to different points of a 

 body, a certain complex motion will generally ensue. The mass will have a 

 relative motion round the centre of gravity as if it were fixed, while that point 

 will move forward uniformly in a straight line, carrying the body with it. The 



