f.fi PAKAI I! I. FORCES. 



ation of the resultant will not move. For this r< 

 point is called the cc >- / forces. 



The moment of a force with respect to a pi;- 

 product of the force into the perpendicular distance of itfl i>mt 

 of application from the plan- . 



In C..DS.-. in. -nee of this definition, the equations for d 

 mining the position of the centre of panBel forces shew that 

 the sum of the moments of any number of parallel forces with 

 respect to any plane is equal to the moment of their resultant. 



68. If the parallel forces all act in the same direction the 

 expression 2P cannot vanish ; hence the values of the co- 

 ordinates of the centre of parallel forces found in Art. ()<> < Mimnt 

 become infinite or indeterminate, and we are certain that tin- 

 centre exists. But if some of the forces are positive and some 

 negative, SP may vanish, and the results of Art. 6G become, 

 nugatory. In this case, since the sum of the positive for* 

 equal to the sum of the negative, forces, the resultant of the 

 former will be equal to the resultant of the latter. ]lcn<v the 

 resultant of the whole system of forces is a couple, unless tin- 

 resultant of the positive forces should happen to lit- in the 

 same straight line as the resultant of the negative foi 



\Ve shall give another method of reducing a system of 

 parallel forces. 



69. To find the resultant of a system of parallel forces 

 acting upon a rtjid body. 



Let P,, P,,... denote the forces. Take the axis of z 

 parallel to the forces. Let the plane of (#, y) meet the 

 tion of P, at Af^ and suppose x lt y^ the co-ordinates of 

 this point. 



Draw ^f X l perpendicular to the axis of x meeting it at 2Vj. 

 At the origin U, and also at N lt apply two forces each e<pial 

 and parallel to P, and in opposite din-cti"ns. Ilc-nx- the force 

 P l at Af, is equivalent to the following system, 



(1) P.atfl; 



(2) a couple formed of P, at 3^ and P at A : 



(3) a couple formed of P l at N l and P l at 0: 



