M.r.xiw.i: Mm- 



ply (1) by - and (2) by -jr and subtract ; thus 



' >--')-. 



from which, since , ' . * -*} O t we ii 



4(^->-) 



7 



Again, multiply (1) by -?- and (i) by H~ and add; then 



4S**3H- 



From (3) and (4) by eliminating r, we deduce 







"37 



:i is the general equation to the curve when given forces 

 act in one plane. 



192. In Art. 188 we have found the equations 



' .......... "> 



<f> be the angle which the resultant force mF&s makes 

 with the tangent at the point (x t y, r); 1 



