160 DR. J. BOTTOMLEY ON THE CHANGING 



From the foregoing equations we obtain 



L 1 =L+^(w+m l )^- / , (9) 



T J I 



L 2 =#(m + mJ^, + L + - + m,^. . . (10) 



If Lj be the distance of the axis of the rod from the 

 fixed beam, we have 



1^ = 1;,+-. . (II) 



If we add (4) and (5), and substitute from (6), we get 

 t J + t z =- l (D-d-2l) (12) 



Thus the sum of the tensions is constant, and is indepen- 

 dent of the weight of the ring. 



If the following condition holds, there will be no tension 

 in the upper cord, 



m, <7 + 2 A, 



Now suppose the rod disturbed from its position of rest. 

 Let X denote the distance of the axis of the rod from the 

 fixed beam, and X x the distance of the centre of the ring. 

 The tension in each cord sustaining the rod will be 



t =e( x -*-4 W> 



also 





