Updegraff — Flexure of Telescopes. 249 



^^,=-p'^ + q'y. (2) 

 Inteo;rating these equations we get 



2^3^ j5^^g,W-i+i5f^e-?W-i_^a;, (3) 



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



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



dy 

 2/ = ; and for a; = Z, -r- = 0, Z being the half length of the 



tube. 



From (3) 



|=;jA>"-->^7C.-"-J. (5) 



Putting X = Hn (5), 



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



Putting cc = in (3), 



K, + K, = 0. (7) 



From (6) and (7) 



K^ = t and 7f, = - — ? ^_ . 



Substituting these values in (3), 





