﻿276 Mr. R. F. Grwyther on an Analytical Discrimination 



For example, in the case of the components of a vector 

 u, v; iv, the changes will be : 



in u, —(D y w-\-co z v, 

 in v, —cd z u + w x w, 

 in w, —co x v-\-oc>yU. 



These changes will now be represented by partial dif- 

 ferential-operators L\, 2 , Xl 3 arranged to produce the 

 coefficients of co x , w v , co z in the quantities considered 

 respectively. 

 . Thus, for vectors generally, 



o 3 a 



This covers direction-cosines (Z, m, n), and may be made 

 the basis of most operators. For example, we may deduce 



for stresses generally : 



ni = 2S (^-li) +(R - Q) l- u 9 V T ^ 



The differential coefficients A A A resolve as corn- 

 er o t V o^ 

 ponents of a vector, but, for simplicity, we must introduce a 

 different notation. 



Write d x for B/B«, c? 2 for 3%, tf 3 for d/3*, and df„ for 

 d 2 fdx 2 , d 12 for B 2 /d<^, d 22 for B 2 /3/ 7 and so on ; then 

 for first differential coefficients 



