}'2 FORCES OK A r\];n 



nil a rlj resolved. By algebraic*] :i<Mition of the I 



which act in the same straight line we have 



03 <*! + P, cos a, + P cos a, + . . . along the axis of x, 

 P, sin a, + P t sin a f + P, sin or, + ... along 1 >fy. 



shall express th< bj SPcOi 7 ami the latter by 



i a. when- the synil.>l ! dfimtcs that \vr take tli- 

 of all the quantities of which the quantity l>cl'rc which it is 

 placed is the type. 



If we put P t cos a, = A' an 1 P l sin a t = 1* , and use a similar 

 notation for the other components, we have two forces rcj<. 

 the whole system, namely ^X along the axis of x ami ^! )' 

 along that of Y. It' // <lenote the resultant of these tore. 

 a the angle at which it is inclined to the axis of x, we have, 

 by Art. 17, 



tan = v ^. 



*x sr 



A UO cos a = 5 ; sm a = -^- 



11 li 



To find the conditions of equilibrium ir1,m any nit 

 offerees act on a particle in one plane. 



When the forces are in equilibrium we must have /t = 0; 

 therefore 



therefore ^A'=0; 2F=0; 



and these are the conditions among the forces that they m.-iy 

 be in equilibrium. 



Three forces act on a 



ired to ji 

 and direction of their result 



Let AB, AC, AD represent the three for- < A'. )'. '/ in 

 magnitude and direction. Complete the parallelogram BC, 



