

n U acted on by tin two Oftdl and by 



' 



tension into 



the IH rp. ii.lu uhir from the fixed point on the tangent most 

 name value at the two ends of the fii m of 



<. Thai Tp - constant 



The results of the Uat Article give us the form of a 

 y any central force ; these results may 

 also be obtained directly hi UM following mani 



Let be the centra of force, P a point in the curve, Q an 



]>oint ; r, 6 the polar co-ordinates of P; let be the 

 length ot vc measured from some fixed point up to P t 



and PQ &. Draw PL the tangi M . and PN, QN nor- 



mals at P and Q respectively, then PN is ultimately the radius 



Let Tdeno; nsion at P t T+5 / 



n at (?, /'i/i&r the force acting on the element PQ, which 

 will ultimately be in the direction OP produced. 



PNQ-+, and ^ be the angle between PL and OP 

 produced. Resolve the forces acting on the element along PL 



and P.Y; thru 



N \v sin ^r - ultimately, and cos ^ = 1 



