STRING OW SMOOTH CURVE. l! 7 



from (6) 



. (8), 



p 



where p is the radius of curvature of the curve ir 



o the curve is supposed to be a known curve, * and p 

 may be supposed knov ns of B\ thus (7) and (8) will 



enable \\~ /'and R in terms of 0. Or we may express 



in term* ctangular co-ordinates of the ; 



r if we denote these co-ordinates by x and y, we have 



*'- 



thus (7) may be written 

 therefore, if m be constant, 



re C is some constant ; the value of this constant will be 

 known if the tension of the string be known at some | 

 point, for example at A or at B. 



Also from (8) 



i 



tin 

 ,) and -f- will l>c known in terms of x and y since the 



is known. 



above investigations we stated that the resistance 

 of the curve on the element PQ acts ultimately a 

 normal at P; and in tWinin^: i. -it ions of cquilihriuni 



of th.- t lonuMit of the string we supposed the resistance t 

 strict nial at J v that no 



error introduced. resistance at P is along 



ormal at P t and at Q it is along the normal at Q, hence 



