126 



STATICS. 



[211. 



Ox, Oy, Oz (Fig. 70). Let x, y, z be the co-ordinates of P and 

 X, Y, Z the components of F parallel to the axes. 



To transfer these components to O as common origin, we 

 proceed similarly as in Art. 142. Thus to transfer, say X, we 

 introduce at P', the foot of the perpendicular let fall from P on 

 the plane zx, two equal and opposite forces X, X; and we do 

 the same thing at O. Then the single force X at P is replaced 

 by the force X at O in combination with the two couples formed 

 by X at P, -X at P', and X at P' , -X at O. The vector of 

 the former couple is parallel to Oz, its moment is yX\ the 

 negative sign being used because for a person looking on the 

 plane of the couple from the positive side of the axis Oz the 



IP 



-X P' X 



Fig. 70. 



couple rotates clockwise. The vector of the latter couple is 

 parallel to Oy, and its moment is zX. 



The transfer of Y to the origin O requires the introduction of 

 two couples, zY having its vector parallel to Ox, and xY 

 having its vector parallel to Oz. 



Finally, transferring Z to O, we have to introduce the couples 

 xZ witlfla vector parallel to Oy, andyZ with a vector parallel 

 to Ox. \ 



Thus each force F is replaced by three forces X, Y, Z along 

 the axes of io-ordinates and applied at O, in combination with 

 three couples whose vectors are yZzY parallel to Ox, zXxZ 

 parallel to Oy, x YyX parallel to Oz. 



