234 I NO ON SMOOTH 



1 1 :icc the equations become 



(IT 

 or -T- 



T 



and -- Fm sin <f> = 0, 



and the solution may be continued as in the last Article. 



We have supposed the force repulsive, that is, tcmlincr 

 from ; if it act towards the figure will be convex towards 

 and we shall have the results 



dT T 



-IT- mJFcos <f> = 0, -- mFsin < = 0. 



194. A string is stretched over a smooth plane curv 

 find the tension at any point and the pressure on the curve. 



First suppose the weight of the string neglect** 1. 



Let APQB be the string, A and B being the points where 



it leaves the curve. Let P, Q be adjacent points in the string ; 

 let the normals to the curve at P and Q meet at 0\ let In- 

 the angle which PO makes with some fixed straight line. :m<l 

 + 80 the angle which QO makes with the same line. The 

 nt PQ is acted on by a tension at P along the tangent 

 at P, a tension at Q along the tangent at Q, and the resi.^; 

 of the smooth curve which will be ultimately along PO. 



