Mr. J. H. Cotterill on Elliptic Ribs. 25 



orders be denoted by Fj and E p 



l + 8 in«£ f cos 2 /3 1 



^- 3sin 2 /3 I l+sm 2 /3* 1 + ±il J 



_ (l + sin a /8)E 1 -cos a ffF 1 

 ~ 3sin 2 /3 



The functions E x and F T are tabulated for each degree of the 

 angle ft in Moseley's ' Engineering and Architecture/ 

 The integrals Q and R are easily found to be 



n _ 1 — cos 3 ft -p _ sin ft. cos ft + ft 

 U ~Tim^~ ; K ~ 2sin/3 '* 

 Again, 



= a I 2 M(l — cos (p')pd(f) 

 Jo 



= a*\ 2 M(l-cos(/) / )A'^ 

 and consequently, substituting the value of M, 



- = F « 3 cos ft f ' sin<£'(l -cos </>') A'<ty' + H « 3 f 2 (1 -cos<//) 2 AW<£' 



Jo Jo 





+ M o*r a (l-cos^A'^'. 

 Since j 2 A'<7</>', or I Vl— sin 2 y3cos 2 </>V<£' is equal to 



i 



^l~sin 2 /3sin 2 <£W<£', 



that is, to E u and since moreover 



J 2 (l-co8^) 2 A'^ , = 2f 2 (l-cos(/>')A^<//- psin^AWf 



= 2E 1 -P-2r 2 cos0'A^ / , 

 Jo 



