496 



Mr. A. B. Basset on the Finite 



pendent coordinates which, together with i/r, (j>, . . . determine 

 the whole configuration of the system in §§ J,..--., it was 

 suggested that, in hydrodynamical and kindred applications, 

 there was a difficulty in proving that BT/dx, BT/^%', . . . 

 were all zero. 



But the difficulty, if indeed it should exist, is easily removed. 

 For since the actual motion at any instant could be generated 

 from rest by impulses of types corresponding to -ty , </>,.. . only, 

 we have throughout the motion 



BT/dx = 0, c)W = 0,...; 

 and by the Lagrangiau equations for ^, %',.•• i since all the 

 generalized forces are of types corresponding to ty, </>, . . . , 

 we get 



whence 



dfdx 



^=0 

 3x ' 



d BT 



dfb% 



Bx' 



0,... 



L. Note on the Finite Bending of Thin Shells. 

 By A. B. Basset, M.A., F.R.S* 



1. 1 ITHEX a thin shell of any form is bent in any manner, 

 ▼ ▼ the most convenient way of obtaining the equations of 

 equilibrium is to consider the stresses which act on a small 

 element of the shell bounded by four lines of curvature on the 

 deformed middle surface. If A I) B be a small curvilinear 



Fig. 1. 



rectangle bounded by the four lines of curvature OA, 

 AD, t> B, and B 0, the stresses across the section A D (as 

 pointed out in my previous papers f) consist of the following 



* Commuuicated by the Author. 



t Proc. Lond. Math. Soc. vol. xxi. pp. 33 and 53; Phil. Trans. 1890, 

 p. 433. 



