Updegraff — Flexure oj Telescopes. 2i9 



%=-p'^ + ^'y- (2) 



Integrating these equations we get 



2/ = i5r,e^'V^+ir,e-<^'V^— ^x, (3) 



y = Ky' + K;e-'^ +^,x. (4) 



By inspection of the flexure curve we see that for a; = 0, 



dy 

 2/ = ; and for a; = ?, -p = 0, i being the half length of the 



tube. 

 From (3) 



|=.,ir,--,-,ir,-_J 



Putting X = Hn (5), 



iqK.e''' -iqK,e-'^' -^ = ^- (6) 



Putting a; = in (3), 



K,^- K, = 0. (7) 



From (6) and (7) 



E^ = t^ and K^ = t 



Substituting these values in (3), 



