14 FORCES ON A PAKTI 



r offerees art on a 



I uired t jn.iyiritude and of th< ir 



P., P r ...be the forrrs; let 7 , ft, % ! tin- u 

 whii-h tlic direction of Pj makes with three rertan^ular ax 



axes 



thrmi:h the proposed point; let a t , ft, y t be the angles 

 whieh the direction of P g makes with the same axes; and 

 so on. 



Then, by Art. 2."), the components of P, in the directions of 

 the axes 



P.coso,, P, cos ft, P.COS7,, (or X t , F,, .Z 19 suppose). 



Resolve each of the other forces in the same way. and reduce 

 the system to three forces, by adding those which act in the 

 same straight line, Art. 15; we thus have 



P, cos a, -f P 8 cos a, + . . . or SPcos a, or 1 

 P,cosft-f P a cos/9 8 + ... or SPcosft or S )'. 

 P, cos 7j +P S cos 7 3 + . . . or P cos 7, or ! 

 acting in the directions of the axes of x, ?/. and z respect: 



If we call the resultant E, and the angles which its direc- 

 tion makes with the axes a, b, c t we have, by Art. 24, 



and cos a = ^ , cos b = ^- , cos c 



27. To fnd tlie condit ions of eqn il'tlr < 

 of forces act on a particle. 



When the forces are in equilibrium, we must have 72 = 0; 

 therefore 



therefore IT-Oj 



and these are the conditions among the forces that they may 

 be in equilibrium. 



