﻿712 



Prof. S. K. Milner on 



Let the adjacent edges of the section which contain the 

 origin be infinitesimal lengths OY = y u OZ = z l (fig. 2) of 

 the y and 2-lines through the origin respectively, and let 

 YY', ZZ' be the ^-lines through Y and Z. The area of the 



Fig. 2. 



section at the origin is y x z\. The cross-section at an infi- 

 nitesimal distance along the <r-line of 00' ■=-x l will be a 

 quadrilateral whose sides are 



OTWjfc+^lj, 0^'=^ + .,^, 



and which will be altered in size, shape, and orientation from 

 the original rectangle. If Y x and Z x are the projections of 

 Y and Z by lines parallel to 00', and we draw Y'A, Z'B 

 perpendicular to O'Yj and O'Z^ we can readily see that 





~dv X y 



By 



L 



Y X YA 



yi 



1 Y X A _ 



~" 2/i ' x i 



" y 1 ~dx ' 



and 



similarly 





~bu xz 



z 1 ~dx ' 





On 



substituting these 



in (8 a) 



that equation becomes 





ox ox 



yi«i S* 



Xm) = ° 





or 



l( 





H 2 ..v,*,) = 







VE 2 + 



o. . . . 



(9 a) 



