30 Mr. J. H. Cotterill on Elliptic Ribs, 



But 



j 2 sin 3 <£'A'^' = R- ( 2 cos 2 <£' sin <£'A'^', 

 where E == 1 sin fiA'dcf) 1 is an integral used before, and by parts 



and 



(4sin 2 /3-l)R-{-cos 3 /3 



(\in 3 </)'AW<// = 



4sin 2 /3 



Again, proceeding in like manner for -tjt", we have 





[-:=a 2 ( 2 M(l--cos(/>')A'd</>' 



= Jpa 4 sin 2 /3 j 'sin 2 <£'(1 - cos <£') A'd<£' 



= \pa A sin 2 £ JP - ( 2 sin 2 ^ cos QbldifJX ; 

 but by parts 



J/™' *' cos W = S5F* " Siln^f cos *' A '^ 



- si/3 - 3^ + y. 2 cosS ^' A '^ 



also 



\ 2 sin 2 ^ cos 0'A'^'=S- I 2 cofPtfA'dtf; 



•'•J. *"^W'A'#' = W/3 ; 



