534 
0°Z Ox A 0°Z dy fg 0?Z dz i _& 
dx? OT  OxdyOT Owdz OF °° Te 17 
0:Z Oz 0°Z Oy 0?Z dz Q, 
OudyOT | Oy? OT | dedzdT |T BEE C7 
0°Z Ow 0°Z dy 0?Z de Ms 
Oxdz OF’ Oydz OT dz? OT Gs TET 
: , OV Qe 
We have again written AV, for nn ete., and — for 
Lv 
oH 
——Y7,, ele. 
Dm 
0: 
If we multiply the first of the equations (6a) by = the second 
Oy 
by — =, 
TE 
ete. and add together the 2n equations, we obtain an equation 
the right hand side of which is: 
A 4 Ox Oy 
etc, the first of equations (66) by Do’ the second by an’ 
P p 
The left hand side of the resultant equation is zero. This may be 
shown as follows. Each term of the left hand side contains one of 
dz O 
Uno UM OE = iat etc. from the equations (6a). Let us consider 
Pp 
Op 
: : Ow 
the terms which contain one of these unknowns, e.g., ae In the sum- 
mation these terms are contributed (1) by the first terms of the 
equations (6a) and by no other terms of these equations, (2) by the 
complete left hand side of the first equation (66), which was multi- 
0 
plied throughout by = and by no other equation of (65). 
P 
Om 
The terms involving = therefore : 
Ie 
Ox OZ Oy OZ Oz 0°Z 
07 dc?’ or dwdy’ OT drde’ 
OZ0« OZ0y 0°Z dz 
Oa? 07" dady 07" dxdz OT" ” 
. from (6a) and 
from (60), 
0 
all terms being multiplied by ar 
B 
From the structure of equations (6a) and (65) it appears that the 
