-50 Statics. 



ry to take with contrary signs the moments of bodies that are 

 found on opposite sides. 



85. We will here make a remark, that is suggested by what 

 has been said, and which will enable us to abridge, in many 

 cases, the process of finding the centre of gravity, as well as the 

 solution of other problems. 



Since the distance of the centre of gravity is expressed by 

 the sum of the moments divided by the sum of the masses, if this 

 centre happen to be in the point, line, or plane, with respect to 

 which the moments are considered, the distance being zero, the 

 sum of the moments must also be zero. Therefore, the sum of 

 the moments with respect to any such plane as may pass through the 

 centre of gravity is zero. 



86. Hitherto we have considered bodies as so many points, 

 and we have seen how the centre of gravity of all these points 

 may be determined, whatever be their number and position. 

 Now a body of any size or figure whatever, being only an as- 

 semblage of other bodies or material parts, which may be con- 

 sidered as points, it follows that, by the method above pursued, 

 we may determine the centre of gravity of a body of any figure 

 whatever. 



Also, since the centre of gravity is simply the point through 

 which passes the resultant of all the particular efforts made by 

 the several parts of a body in virtue of their gravity, and since 

 this resultant is equal to the sum of all these particular efforts ; 

 it follows, that we may in all cases suppose the whole weight of a 

 body united at its centre of gravity, and the weight would have 

 the same effect upon this point, when thus united, that it would 

 have in its actual state of distribution through all parts of the 

 body. 



87. When, therefore, it is proposed to find the common centre 

 of gravity of several masses of whatever figure, we begin by 

 seeking the centre of gravity of each of these masses, which is 

 attended with no difficulty. Then, the weight of these masses 

 being considered as united each at its centre of gravity, we seek 

 the common centre of gravity, as if all these bodies were points 

 situated where each has its particular centre of gravity. 



