78 Statics. 



being free, as decomposed into two others, one of which is that which 

 the body actually has after the change, the second must be such, that 

 if each of the several bodies had had no other than this, they would 

 have remained in equilibrium. 



This proposition must be admitted, since, if the second mo- 

 tions be not such that an equilibrium would result from them in 

 the system, the first component motions cannot be those that 

 the bodies are considered as having after the change, for these 

 would necessarily be altered by such a supposition. 



134. Let us suppose now that several bodies, either free or 

 connected together in any manner whatever, come to receive 

 certain impulses which they cannot entirely obey on account of 

 a reciprocal restraint, the centre of gravity will move as if all 

 the bodies were free. 



Indeed, whatever be the motion which each part of the 

 system has, we may always conceive that which is impres- 

 sed upon it as composed of two parts, namely, that which it 



40. actually takes, and a second. But in virtue of these second 



133 motions, the system must be in equilibrium; if we suppose 

 therefore, these second motions decomposed each into three 

 others, parallel to three rectangular co-ordinates, the sum of the 

 forces which would result from this decomposition, parallel to 



J29 each of the three co-ordinates must be zero. Now the course 

 which the centre of gravity tends to describe in virtue of each 

 of these forces, is equal to the sum of the forces parallel respec- 

 tively to each of the co-ordinates, divided by the sum of the 



120. bodies. Consequently the course which it tends to describe in 

 virtue of the changes arising in the system from the reciprocal 

 action of the parts is zero ; accordingly the centre of gravity 

 does not partake of these changes, that is, it moves as if each of 

 the several parts of the system obeyed freely, and without loss, 

 the force by which it is urged. Therefore, the state of the centre 

 of gravity of a body, or system of bodies, does not change by the recip- 

 rocal action of the parts of this body or system. 



135. Hence we infer ; (1). That if a body or system of bodies 

 turn about its centre of gravity in any manner whatever, this centre 



