i64 Dr. J. BOTTOMLEY on 



tion of c; by reference to Fig. 4, it will be seen that 

 B 



CEFG = 4-OEC = 4(0BHK - EBHC - CHK). 

 X being the abscissa of the point H, we have the following 

 relations (^ denoting the angle HCA). 



EBCH = ^.BH-^'(7r-0); 



BH 



J sir 



dX , 



sin^' 



OBHK = ^|-^v^'''-^%'''sin-^L 

 a [^ 2 2 a j ' 



X = 



\/ a' + l^han-d 



Cos<p 



b yJlr-C- 



c \J d- - b 

 CHK= cos(^sin(^. 

 From these equations we obtain by elimination 



CEFG= -^ P + 2rt/'sin ^-a/ — — 77. 



b by/ a- - b- 



_ 4^^ f ''^' + 2ci-- _ sin-\ A5E^. 



bj v/(aV-^*)(-^-<:-) V2 cSf a" - [^ 



This formula applies from 



c= to c = o. 

 a 



If we suppose the last figure to revolve round the axis 



