Concluding Deductions. 79 



of gravity will remain continually in the same state, as if the body 

 did not turn. 



Moreover, from this same principle and that of article 124 

 we conclude, that 



136. (2). If any body, whatever be its figure, or any assem- 

 blage of bodies, receive an impulse in any direction whatever 



as AB, which transmits itself entirely to the body ; the centre of Fig. 5&. 

 gravity G will move according to a line TS parallel to AB, in 

 the same manner, as if this force were immediately applied at 

 the centre of gravity in this direction. And if several forces 

 act at the same time upon different points of this body, the centre 

 of gravity will move as if all the forces in question were applied 

 directly at this point. 



137. If, therefore, at the instant the body receives an im- 

 pulse in the direction AB, we apply at the centre of gravity in 

 the opposite direction SG, a force equal to that which acts ac- 

 cording to AB, the centre of gravity will remain at rest. Nev- 

 ertheless it is evident that the other parts of the body would not 

 remain at rest, since these two forces, although equal, are not 

 directly opposite to each other. Now the only motion which 

 this body can have, its centre of gravity remaining at rest, is 

 evidently a motion of rotation about its centre of gravity. 



Therefore, if a body receive one or several impulses, in di- 

 rections which do not pass through the centre of gravity ; (1). This 

 centre of gravity will move as if all the forces were applied di- 

 rectly at this point, each in a direction parallel to that which it 

 actually has. (2). The parts of this body will turn about then- 

 centre of gravity, as they would do by virtue of the forces which 

 are actually applied to the body, if the centre of gravity were 

 fixed. 



138. We infer, moreover, that if the state of the centre of 

 gravity of a body undergoes a change, this can proceed only 

 from the action or resistance of new forces foreign to this body; 

 and that consequently this change is always determined by seek- 

 ing the resultant which all the forces would have, if they were 

 applied to the centre of gravity, each in a direction parallel to 

 that which it actually has. 



