QUATIOHS TO THB S1MOLI EttfLTAJTT. 



parallel to the co-ordinate axes drawn through the poisjt 



iii.l l.y wining / v J r v V,-/ 



*i* **~ 5 ^ or the nsMsiss 



iierefore 



-L-J, 



Similarly 



-Jf-rl 



-2(i'(*-0-.v(j-.o) 



-A 

 , ' can be to taken as to make //. M\ and N 9 



y' t '). The three equations 



j: r-o.. i), 



IT-^l /f-0.. j), 



e equivalent to two i < qoationj ; for if we elimi- 



te :' from (1) and (2), we have 



-.i/Sl" ATL2T-0, by 

 therefore A ySA'-O. 



(3) is a necessary consequence of (!) and (2). Hence 

 tid (2) will <: a straight lino at 'it of 



resultant couple vanishes; that is, the straight line 

 the single resultant force acts. 



1'y the following method we may determine at once 

 the < for the existence of a single resultant and the 



equations to its direction. 



pose that the forces can be reduced to a single Jotes 

 : at the point (x, y', *') Let the single fines be resolred 



