PROPERTIES OP MATTER IN THE GASEOUS STATE. 
801 
numerical values they will be indicated by tlie letters L l5 L 2 , &c., as about to be 
assigned. 
Putting i for unity or any power of a or U, V, W, the coefficients by which the 
differentials of the corresponding terms in Table XX. must be multiplied, are as 
follows:— 
- pi &c 
dx* ' 
by 
l=\ 
expressed by L l3 
dptji dprji dp£i 
dx ’ dy ’ dz 
33 
P 2 
33 
L,, 
dp& dp%i . 
dy ’ dz ’ ‘ 
3 3 
lm _ 4 
1 37T 
33 
L 3’ 
dpgH dpp~i dp£K 
dx ’ dy ’ dz 
3 3 
P-3 
33 
Ln 
dp£H dpfH u 
dy ’ dz ’ 
3 3 
Pm .. 
P “ 8 
3 3 
K 
dp&i dptfi „ 
dx ’ dx ’ 
3 3 
Pm 
f- =Te 77 " 
lm 
3 3 
K 
The coefficients L 1? L 2 , &c., all occur in some one or other of the expressions for 
A, P>, C, &c. ; but when these expressions come to be added together it is found that 
L 2 is the only coefficient of s which has to be considered. This being the case, instead 
of L 2 s, the simple s will be used, so that in all subsequent expressions 
2 
-(mean range) 
O 
(41) 
The signs of the products of s and the differentials of the several terms in the table 
may, as will be seen from Art. GO, be expressed in the following manner, ignoring the 
numerical coefficients L 2 , &c. 
<r,(Q)=A,+B,+ C*+IX+ hh + Fd+G., -f- IX 
—s—(A*+B*+Ch+D. r — h,.— F,— (X— IP) 
- S j(A. t +B,-C,-D,+E,+ F,-G,-H J .) ^ i2) 
dy 
with similar expressions for oy(Q) and cr.(Q), the suffix to the letters being the same 
as the suffix to cr(Q) on the left. 
The following are the resulting values of cr(Q) which are required for this investiga¬ 
tion, terms of the order U 2 having been neglected. 
5 k 2 
