20 R. F. GwYTHER, Specification of the elevients of stress. 



The solutions which I have given of the corresponding 

 statical equations are 



r, I - X- a-Oj , I B-e, , I 3(6., 4- Gs) 



Jr — ■ — ■ — — -p ~ -r 



r- Zx'- f'{i—x^)d(p' r dr 



Q_c^e3 ^_ I 3'9i _^_ I 9(263- 9,) _x 99i 



8?^ ?-"( I - x'-) d<p~ r dr r' dx 



J? = ?!^ + ^ -^ " ^'Qi . I 9(29o - 9i) _ A- a9i 

 dr^ r^ dx^ r dr r^ dx 



S=l ^'Qi + -^' 39i 



?-( I - ic^) 8a-90 r^( I - .T') 9^ 



^^_ I 9'93 ^ jc 8(9; - 93) _ I 89i /g. 



r 9r9.r r(\ - o<?) dr r^ dx 



Also with the same notation 



du /-if, / o^v^ 1/ 9z£;\ 



^=— , f=-U^^rxv-{\-x-)^\, g=-[u + XV^~~\ 



dr r\ dx) r\ dcp / 



^"' -:.('-;-*--'©• 



dti d7V 



,1/1 9z/ aze* \ 



d = ~[ -, - + r—~ - w 



r\\ - X' 0(p or J 



\( dv du\ / » 



^=-(/'^ -z'-^j (39)- 



r\ or ox/ 



Having given these expressions it will not be neces- 

 sary to write P\ Q, R' in full. 



14. As before we equate 5 to na, Tto nb, S to nc, and 

 by a precisely similar analysis we find 



dr r 



nv^ - — 5-^9,-03- Wj;-— -r- 



2r dx t\i - X-) ' 



' ^ (93-9i-9,) . . . (40), 



2r{i - x:^) d(f) 



