p= 



W 



_Fdr 1 



id dx 



T 



= Ti + 



F d Tl 



id dx 



U14 Dr. J. Prescott on the 



A comparison of (147) and (148) shows that a particular 

 integral of the former equation is 



(149) 

 vu lv u< it- 



Then it follows that 



P rl-r. 



(150) 



is a solution of equation (142), and this solution satisfies 

 the condition that the torque is zero at the free end where 

 x — ; that is, 



—- ■= where A' = 0. 

 dx 



The only other condition that it is necessary to satisfy 

 is that 



r = where ® = l, 

 that is, 



T t -i r^=0 where x=L . . . (151) 



w dx 



and from this equation m is to be found. 



Let T^j\mx). (152) 



p 

 Then, since m - is small, 

 w 



f( mx + m - ) = f(mx) + m - f(mx) 



P^Ti 



10 tffo 



(153) 



It is now clear that equation (151) can be written in the 

 form 



f(ml + m^)=0 (154) 



But we found in the first paper (equation (55)) that the 

 solution of the equation 



f(ml) = 

 was given by 



m*P = 6-43 (155) 



It therefore follows that the solution of equation (154) is 



m ^ + ?) 3 =6-43; 



that is, 



m 3 / 3 ( 1 + yj ) — 6'43 approximately. 



