J A u i ) = "H 



2 3 rd) 



Updegraff — Flexure of Telescopes. 

 3/«,\ a 



257 



" 1 ~ L40 I 2 / 1820 V 2 / * * 



i r- 



3 





"^ 56 V 2 / 560V2/ 



and 



X= gllj 



i . l^Wl 1 /^r.4- 13851 /M 



1 "+" 28 I 2 / "^ 560 V 2 / "^ 203840 \ 2 / 



28 V ' 203840 \ 2 



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



3 / 2 23 43 _ \ 



4 =g-aZ*tan0 (l + ^aZ 3 + 280 a ^ + 1820 a¥ ' ' )' ( 34 ) 



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

 half of the tube. 



23 



43 



j/ = gaZ 4 tan0 1 1 — y«i 3 + ^o al ~ W2b al ••••)• (35) 



In the case of any telescope of ordinary construction al z is 

 a very small quantity and these series converge very rapidly. 

 Therefore the deflections A 1 and A\ may be accurately and con- 

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

 we get 



3 /4 43 \ 



A 1 — J/ = g al 4 \.and UaZ 3 + 910^ * ' 'J' 



Q i O 



or ^-J/^^tan^l+^Z 6 . . . . J. (36) 



