Updegraff — Flexure of Telescopes. 253 



the flexure curves for the upper and lower halves of the tube 

 respectively, 



El — -J — — - wxycosd — - w;x 2 sin#, 

 dx 2 3 J 2 



„ r d 2 y 1 1 



EI-r- 2 — + o wxycosd — g ivxh'md. 



1 wcos# 1 ivs'md 



If we put a — g jjiT and 6 = ^ ^j , 



these become 



# y 



— 2 = — axy — bx\ (19) 



d?y /oa\ 



~ 2 = + aay — &« 2 . (^j 



It is evident on inspection that Eq. (19) is satisfied by the 

 relation 



y = — ■£*> ( 21 ) 



which is a particular solution, so called. 



If to this value of y be added that given by solving (19) 

 with the term bx 2 put equal to zero, the sum put equal to y 

 will, according to a well known theorem of Differential Equa- 

 tions, be the complete or general solution of (19). We 

 have now to solve the differential equation, 



