OBLIQUE AXES. 



lircc difi- 1o which 



of the moments vanishes, we 1 nations 



= 0, 







IIcucc we deduce 



Unless the point (h lt &,), the p'int (h t , &,), and the point 

 (A 8 , h) lie in a straight line, it is impossible that 



we must therefore have 



2x=o, sr=o, #=o. 



Hence if the sum of the momenta of a system of forces in one. 

 plane vanish n-ith respect to three points in the plane n< 



' 



When a system of forces in MM j.lane can le reduced 

 single resultant, we have found in Art. 59 that tli 

 to the direction of the resultant is 



This may be written 



2 {!>'-*)- A" (y- 



The equation to the direction of the resultant thus in fact 

 determines the locus of the points for which the algebraical 

 sum of the moments of the forces is zero. 



Hitherto we have supposed our axes rectan^ilar. If 

 they are oblique and inclined at an an trie G>, we may 

 as in that a system of forces in one plane m 



reduced to 2-lf along the axis of a;, 2F aloni: tin axis of #, 

 and a couple the moment of which i - Ay . Tin- 



latter part will be easily obtained, since the moment of the 



