210 Dr. J. Preseott on the 



Consequently the differential equation for the twist t is 



d 2 r _ _ py+Piog 3 





EC 

 Let t = t 1 + p , ....... (126) 



where Tj is the solution of the equation 



K "^=-EiT T " • • • • ( 127 > 



that is, r r is the value of t for the case where w = 0, which 

 is the problem solved in Case 3 in the first paper. 

 In the present case, 



Kn { a? + 3? 1 = ~ KG 1 : + -f J r l Ti + p I • 



Now w is a small quantity and p, being due to w, is 

 therefore also small. Then neglecting the product ivp 

 we get 



By using equation (127) this last equation becomes 



£{p+5?*>'}i . . (129) 



that is, ^=-mV(p + r OTl ), .... (130) 





where 4 P 2 



EnCK' 



(131) 



r=%, (132) 



P' 



and, by equation (22) in the first paper, 



Tl = 6 { 1 "374 + 3.4.7.8""-r 

 The particular integral of (129) is 



o= —rb 



, ( mV 8mV 



— vn J 



(4.5 3.4.5.8.9 



+ 3.4.5.7.^.9.12.13 * j ' ' lo3; 



