THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 329 
As explained in § 8 (E), however, the determinants V ( S rs b rs ) and V (S rs c rt ) derived 
from the above by successive differencing are much more useful and suitable for 
numerical calculation. # They may conveniently be written as follows, where the 
factor above each column or before each row is to be multiplied into all the elements 
of that column or row as written ( e.g ., the right-hand element on the second row of 
V (S„b„) is equal to -59 . {2 3 3.7.11.2.7}- 1 ) 
1 (2.7)- 1 (2 a 3 a 7) 1 (2*3.7. ll)" 1 
(221) 
^ (KJ->rs) ~ 
1 
1 
1 
-1 
1 . . 
(2.7)-' 
1 
45 
103 
-59 . . 
(2 2 3 2 7)- j 
-1 
103 
5657 
6783 . . 
(2 3 3.7.11)- 1 
1 
-59 
6783 
149749 . . 
(222) 
II 
V. 
■o 
1 
(2.7)-' 
(2 2 3 2 7)- j 
(2 3 3.7.11)- 1 
1 
1 
1 
-1 
1 . . 
(2.7)-' 
1 
2 0 5 
3 
163 
2 8 7 
3 
(2 a 3 a 7) _1 
-1 
163 
11889 
16798f . 
(2 3 3.7.11)- 1 
1 
2 S 7 
3 
16798f 
329573-2T • • 
As we are throughout concerned with ratios of determinants, the above fractional 
expressions for the elements, from which the column-factors or row-factors can for 
many purposes be omitted, are the most suitable for calculation. The following 
values of the elements in decimal notation (to six places) are of interest, however, as 
showing the relative magnitudes of the various terms :— 
(223) 
V (S rs b rs ) = 
1‘000,000 
0-071,429 ' 
-0-003,968 
0-000,541 . . 
0-071,429 
0*229,592 
0-029,195 
-0-002,280 . . 
-0-003,968 
0-029,195 
0-089,081 
0-014,565 . . 
0-000,541 
-0-002,280 
0 - 014,565 
0-043,849 . . 
(224) 
V ( 8„c rt ) = 
rooo,ooo 
0-071,429 
-0-003,968 
0-000,541 . . 
0-071,429 
0-348,639 
0-046,202 
-0-003,698 . . 
-0-003,968 
0-046,202 
0-187,216 
0-036,072 . . 
0-000,541 
-0-003,698 
0-036,072 
0-096,504 . . 
* This process of differencing renders the determinants much more convergent in appearance ( cf. . (219] 
and (220) with (223) and (224), without really altering in the least their value or the value of any of the 
partial determinants formed by the first n rows and columns. 
2 Y 2 
