TORSION OF CERTAIN FORMS OF 81I.UTIXG. 327 



With rep i nl in the accuracy obtained, I may say that, where I was able to verit'v. 

 I found the values of the stresses correct to five, and sometimes to six, significant 

 I inures. In the values of the torsion moment the first five figures generally agreed, 

 so that, on the whole, the results may Ix- considered correct to the number of figures 

 given. 



The first series for S B and the second series for S A are very slowly convergent 

 indeed. The method adopted in dealing with them was the following : 



The series 



was broken up into two series 



^ - 

 2n 4- 



I ., ,. -~ v 'i \ * tauli 



~,, 7,- ; < ! + 1 )- + Ilia 1 M r o TT* (2n + 1)* + 16* 



The latter series converges rapidly, and was easily calculated. The former was 

 calculated to an even number of terms, and the remainder obtained by means of the 

 Euler-Maclaurin sum-formula, thus : 



( 1) i i 



7 *'(4/; + I? + 16* ; ^(Ic -1^+ 16.x 1 - 

 Now 



~ ] U * C ~ * H * + 2! ~& ' ' ~& da? 

 where I',, = L, B^ = - 3 1 -, &C. 



Let me write 



p- = (4.E+ I) J TT-+ 16a 2 , 



_, I* _!_ 



Then 



I w x ux = - * = - ^ i 



whence 



*-' _ ( , 6 \_ EI sin 20 (47r) J^ ain40 



**j- ^-" Vy "~ , " A * " ^ . 



2 p" 4se p* 



Put a?=co, ^ = 0, p = oo , 



WT = C, 



tlieref'ore, 



-C _JL _L ML H '" 2g /Z_\ ^. Z. S J? 4 ^ 



"" 2p* "" ' 2 " p j I / ' ,4 ". v .y 



