Updegraff — Flexure of Telescopes. 



257 



J^{ u, ) = 



u. 



2'ra) 



S /u,V 



-m) 



3 



u 



^ 140 I 2 / 



3 /u, \i 



1820 



m 



• « • 



2*r(i) 



-im 



and 



3 



^ 56 \ 2 / 560 I 2 / • • • • ' 



9 /Wj\2 81 /w,\* 13851 /w,\6 

 ■^ "^281 2/ "^SGoIy/ "^ 203840 l^/ ' •■ 



Substituting this value of X in (33) and reducing we get 

 3 / 2 23 43 ^ \ 



And in the same way we get from Eq. (31), for the lower 

 half of the tube. 



3 / 2 23 



aH' 



43 



1820 



aH' 



(35) 



In the case of any telescope of ordinary construction aP is 

 a very small quantity and these series converge very rapidly. 

 Therefore the deflections J^ and J\ may be accurately and con- 

 veniently computed from Eqs. (34) and (35). Subtracting 



we get 



3 /4 



J, — j; = g alHsind I ^aP + 



43 „ 



aH^ 



910 • • 



)• 



or j^_j;=-a,2aan^(l+ 520^2^' ....)• (36) 



