AND DEFORMATION OF A THIN KI.ASTIC SHELL. 



507 



6. To express K.,, A,, *, in the same way, we suppose a system of fixed axes at P, 

 whose directions coincide with those of the (x, y, z) axes at P before strain. The 

 coordinates referred to P of a point near P on the deformed surface are 



S = 



. 

 * 



u 80 3 , 



8*7 = + dv - 

 8 = dw u 



where 80,, 80 2 , 80 3 , are the elementary rotations of the axes (x, y, z) about themselves, 

 when the origin is changed from a, ft to a + 8a, ft -|- 8/8, viz. : 



80, = - .- f )dp = - ~ </& 



"** \ A 1 A O 



i 



(14) 



' J 



Hence, by equations (4), 



substituting for o-j, o- 2 , and neglecting small quantities of the second order, we find 





whence, 



dw u 



(15) 



3T 2 



