216 Dr. J. Prescott on th 



and supported at the ends with just the necessary forces and 

 couples to keep the depth of the end sections upright. 



This is a combination of Cases 4 and 7 in the first paper 

 with the condition that the ratio of W to P is small. 



In this case, taking the origin at one end, 



G = i(P + W^-i^a ? 2 



W 

 = iQ^-.J-y.« 2 , ...... (157) 



Q being written for (P-J-W). 

 Therefore 



d 2 r _ QKv 2 f 1 W;r i 2 



it 1 " wl 



dtf~ ""4E«CKL ~QTJ T 



^- I r approximately, (158) 



where 4 Q 



ni 



4EhCK 



159) 



2W 



If we also write r for the small quantity -7yr > then 



Now let T = T! + />, 



f mV 

 Tl==a l*~47S + 4.5.*.9 



and therefore ^tj 



fl +^V = mVT. .... (160) 



where f m 4 <2? 5 m 8 £c 9 ") / 1/>0 > 



j- • ( lb ^) 



_ 2 +»/W 1 = 0. . . . . (163) 

 Then (160) becomes, after making use of (163), 



72 



^ + m 4 ^p = m 4 r l rr 1 , .... (164) 



the product of the pair of small quantities r and p being 

 neglected. 



A particular integral of (164) in series is 



7>l 4 ?* ft f _, ??2 4 ^ 4 ?7iV 



r o . b L 4.9 4.8.y. 



m i2 x i2 



13 



4.8.9.12.13.T7+-} * ^ 165 > 

 If we use this value of p in (161) we get a solution which 



