

TORSION OF (T.KTAIN KoKMs ()K sHAFTINc :; 1 7 



We II.-IM- t" f\|..md sinli _' lx-t \\.-.-n tin- limits -fc a in a st-rii--, < if nines as follows : 



-J^ a, sin + , sin +. . + o , sin 



-* - 



The coefficients a c , a ..... ..... are found in the usu;il \\.-tv 



also we have, substituting in (6), equating coefficients .>' sin " *, and writinj; 



2 



B . sinh 



, +l7ry . , 2rt+lir7 re** cos 2/9* \ 



A o<xsh - -r- B,, sinh - ' = - 1 -f - ) , 



2 2 (2 + l)ir ' co8h2/ 



whence, solving for A,, and B,,, we find 



1 1* /*i S *> 



= (2w + 1)^ < ~ ' > ' ^l^TIT+iw (cosh 2 * + OOR 2e cos 2 ^ > (7 



- 



8n 2e sn 2 



(a. + i) 



\vlicnce 



. -ilili -f sill L'I; 

 / = ' TC- 



rosll 2a 



. . 2n + iw . 2n+ 



'"' - JT- - (n - f ) sin -- 9"' 

 J'cosh 2a+cos 2e cos 2y} S ( 1)"- " ^ 



- 



. . 



coeh H - (^ - ) sin - ij- - 



sin -Jy sin 2e S( 1)" - . . (9). 



