STRING OK SMOOTH CUEVE. 



a bo the length of the cnrvc measured from some fixed 



up to P t and PQ - S* ; let JtB denote the resistance of 



on PQ, T tlie tension at /', T+&T the tension 



Suppose the element PQ to become rigid, and resolve 



ibices acting on it along the tangent and normal at P; 



0... ..... (2). 



Now co.W-l-^+ 



hence (1) gives by division by 



therefore ultimately 



therefore T= constant . (3). 



Also = p&0 ultimately, p being the radius of curvature at /*, 

 therefore, from (2), we have 



i * * 



T is constant, the string will not be in equilibrium 

 s the forces pulling at its two ends are eaual; t: 

 usually assumed as self-evid* nt in the theory of the pully. 



whole pressure on the curve will be flld* ; therefore by 

 (4), the whole pressure 



Since T is constant, fTdO =* TO + constant ; 



therefore the whole pressure - T(6 L-^,), supposing O l the 

 value of 6 at A, and 0, the value of 6 u 



