OF THE EQUILIBRIUM OF A SYSTEM. 189 



0=fPdm, 0=fQdm, 0=fRAm;0=f{Py-Q^) 

 dm, 0=f{Pz-Rx) dm, 0=f{Ry-Qz) dm. 



In fact we have only to conceive the solid as a system of 

 an infinite number of points, united in an invariable man- 

 ner. If, then, we suppose Am to be an infinitely small 

 point or atom of the body, of which a:, y, and z are the or- 

 thogonal coordinates, and P, Q, R, the forces acting on 

 the particle in the directions of x, y, and z, the equations 

 (m) and (w) will only require the substitution of P for S 



■=r-f Q for S K— , and R for S rr-> to which they are respec- 

 tx 6y cz J r 



tively equal, and we shall have SPatwzzO, . . . , and conse- 



quentlyyPdwizrO; [for since the fluxions are always in a 



constant ratio to the evanescent increments, whenever 



SPawiziO, we may makeyPdmirO also; and in the same 



manner the substitutions in all the six equations may be 



shown to be admissible : the character of integration f 



being understood as extending to the whole solid, in all its 



dimensions. 



Scholium. If the body is only at liberty to move round 



a given point, at which the coordinates begin, the latter 



three equations are suflScient to determine the conditions 



of its equilibrium. 



