﻿598 The late W. Gordon Brown on the 



element will be 



for 



C>d ? 



-Sd m (E + Vq w B), 



(13) 



^-(T-U) = ^-[i^VqA) 2 



D'/K] 



1TI2 



2 



= =£- [22M-dmVq„Vq s d s )-i(Sd„) 2 /(K)] 



00-m 



-(E + Vq„,B), 



(14) 



where the summations include all values of the suffixes ra, s, 

 the differentiation of terms such as ( — cU"Vq m Vq m d m ) being 

 performed by means of (11), since (— Vq w Vq m ) is a self- 

 conjugate operator ; and that of cross-products, such as : — 



(— d m Vq m Vq s d 5 ) by means of (10), writing a= — Vq TO Vq 5 d s . 



B C 



Thus, if in the figure the unit segment is removed from 

 the position AD (at which (14) has the value — (E + Vq m B)) 

 to the parallel position BC (at which (14) has the value 

 — (l + gr\7) 0E + Vq m B), AB = Sr), then the total increase in 

 L is given by 



SL=-8rv.&L(E + Vq w B). 



It will now be convenient to suppose (as we may without 

 loss of generality) that the ??ith set consists of but one tube, 

 so that 6d m =d m and is in fact a unit vector. 



Then 



8 1 L=-arv.d w (E + Vq IM B), . . . (15) 



and in applying the axial differentiator Sry we must re- 

 member that neither cU nor q m as they occur explicitly are 

 to be considered variable. 



But to preserve the continuity of the tube we require to 

 introduce the segments AB, CD, as shown in the figure, so 



