Updegraff — Flexure of Telescopes. 258 



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

 respectively, 



^1-—^ — — ^ ^^'^ycos/? — - loxhmd, 



-£// j-2 = + 3 wxyco^d — 2 v)xHmd. 



_. 1 i^cos^ 1 tr8in<? 



If we put « = 3 xTj and = 5 f/ > these become 



— = — axy — bx\ (19) 



g = +aa.y-5cc^ (20) 



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

 relation 



2/ = —^, (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^ put equal to zero, the sum put equal to y 

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

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

 have now to solve the differential equation, 



