﻿446 Mr. G. B. Jeffeiy on the 



the vectorial equation of motion is 



Dv 4 



p vyr =/oF — grad.jo + o P grad. div. v — /it curl, curl v *. (1) 



The transformations of div. and cwrZ follow at once from the 

 definition of these operators in terms of surface and line 

 integrals respectively. 



If a j /?, 7 are orthogonal curvilinear coordinates, and if 



••■■■=m +(£)'+&■ 



while 7i 2 , h s are defined by the same operation carried out 

 upon y8, 7 respectively, so that elements o£ arc measured 

 along the normals to the coordinate surfaces at any point 

 are 



8a 8y8 S7 



then f 



curl v = M S {|j(g)- l y {Q). 



where u, v, w are the components of v along the normals to the 

 surfaces a,, ft, y= const, respectively. In (3) put v=grad.<f), 

 and we obtain 



v- w, 1 1 (A |f) * a>(4 M) + 1, G& S9 } • <*> 



By a second application of the operations implied in (2) 

 we have, denoting the direction of a component by a suffix, 



curUurlv = ;a 3 [ B |{^(f a (£)-^(e)} 



d fhhfb /u\ _ B_/™\\ 1 "1 

 97 I A, \by\lj 3«W/J J" 



* C/; the corresponding elastic equation. Love, 'Theorv of Elasticity,' 

 p. 138. 



t Love, p. 54. 



