1RAL FORCE. 



fore, by (1), 



and therefore, by (2), 



It' the force be such that its direction always passes through 

 a fixed point, the whole string will lie in a plain- j 

 through its ends and through the fixed point, for t li- 

 no reason why it should li- <n one side ratlin- than the 

 other of this plane. Let r be the distance of the point 

 (x, y, z) of the curve from the fixed point, p the perpendicular 

 from the fixed point on the tangent at (x, y, z] ; then (3) and 

 (4) may be written 



dT 



/TT 



^_ wP. (r\ 



P~ 



1 dT r fir 1 cfc 



Hence . = -=__ 



jf cfe ppds p ds 



therefore log T = constant 



or Tp = C. 



Also, from (5), T= - JmFdr. 



si 



Therefore - = - fmFdr. 



Put <f>(r) for -fmFdr-, then 



j / \ (/ 



and from this differential equation the relation between r and 

 6 must be found. 



The equation Tp=C may also be obtained simply thus: 

 suppose a finite portion of the string to become rigid; this 



