Mr. J. H. Cotterill on Elliptic Ribs. 29 



and in this case p is constant and q is zero; 



-*-->{'♦ w\"% 



d J" n , J 2 1 -'cos 2 ,8 



where, as before, 



A = \/l-sm 2 /3sin 2 </>; 



but 



,2 



/, d 2 \ A cos 2 /3 

 = — pa 



dA 

 Thus, omitting terms which contain the constants, 



F = K= —pa-T7> 



dK fcos 2 ^ d 2 A\ 



M=J Kp#=-^co S ^J i- 3 ^^ 



4 -0 



= ^ pa 2 COS 2 



But 



= ^ W/3 !^!W, 



,, cos/3sin<f> 

 sin 9' = -r — -> 



.-. M= ijo« 2 sin 2 /3sin 2 0'. 



Here, as before, ft is the inclination to the major axis of the 

 corresponding section of a circular rib from which the elliptic 

 rib can be derived by projection. 



Now 



d¥ 



:f 2 M^ P dcf ) = a cos j3 { 2 Msin<£'p#- 



Jo «*o Jo 



Substituting for M its value just given, and for pdcf>, as before, 

 aA'dfi, where A'^v'l-sm^cos 2 ^; 



d¥ 



ipa 4 cos £ sin 2 \ * sin 3 $Md$. 

 Jo 



