OF THE EQUILIBRIUM OF A SYSTEM. IBS 



similar equations for x and z, omitting y, and for y and z, 

 omitting x, so that 



o=...(.g-4;);o=..s(.£-.|); 



0=.».(yg-.|). («) 



Now the quantity 'SimSy^ is the rotatory pressure of all 



the forces reduced to a direction- parallel to x, with regard 

 to an axis parallel to z (256, 304). In the same manner 



the quantity SwSx ^ is the sum of the rotatory pressures 



of all the forces parallel to y, tending to turn the system 

 round the axis of z, but in a direction contrary to the 

 former : it follows therefore from the first of the equations 

 (n), that the whole rotatory pressure must vanish with 

 respect to the axis parallel to z. The second and third 

 equations indicate, in a similar manner, that the sum of 

 the rotatory pressures is nothing with respect to axes 

 parallel to y and to x : and these six equations complete the 

 conditions of equilibrium expressed in the proposition. 



308. Corollary. If any point in the 

 system, invariably connected with the whole, 

 be permanently at rest, it must be in conse- 

 quence of a force equal and opposite to the 

 result of the three forces acting in the three 

 given directions ; and the conditions of equi- 

 librium will then be reduced to the equality 

 of the rotatory pressures with respect to the 

 three orthogonal axes. 



