MR. CLERK MAXWELL ON THE DYNAMICAL THEORY OE GASES. 
61 
If we assume n— 5 and put a 4 =2 cot 2 2<p and x=\/l— tan 2 p cos\J/, 
l-e=V c-os^f 1 
2 v r J 0 v 1 — surf sury 
=\/ cos 2<p F sin(p , 
where F sin ^ is the complete elliptic function of the first kind and is given in Legendre’s 
Tables. I have computed the following Table of the distance of the asymptotes, the 
distance of the apse, the value of Q, and of the quantities whose summation leads to A, 
and A 2 . 
b. 
Distance 
0 . 
sin 2 9 
sin 2 29 
<p> 
of apse. 
sin 2 2 <p 
sin 2 2ij> 
6 
0 
infinite 
infinite 
6 6 
0 
0 
5 
0 
2381 
2391 
0 31 
•00270 
•01079 
10 
0 
1658 
1684 
1 53 
•01464 
•03689 
15 
0 
1316 
1366 
4 47 
•02781 
•11048 
20 
0 
1092 
1172 
8 45 
•05601 
•21885 
25 
0 
916 
1036 
14 15 
•10325 
•38799 
30 
0 
760 
931 
21 42 
•18228 
•62942 
35 
0 
603 
845 
31 59 
•31772 
•71433 
40 
0 
420 
772 
47 20 
•55749 
1-02427 
41 
0 
374 
758 
51 32 
•62515 
•96763 
42 
0 
324 
745 
56 26 
*70197 
•85838 
43 
0 
264 
732 
62 22 
•78872 
•67868 
44 
0 
187 
719 
70 18 
•88745 
•40338 
44 
30 
132 
713 
76 1 
•94190 
•21999 
45 
0 
0 
707 
90 0 
1-00000 
•00000 
A 1 =§47rcidci sin 2 0=2*6595 (15) 
A 2 =J Toidtx sin 2 20=1*3682 (16) 
The paths described by molecules about a centre of 
force S, repelling inversely as the fifth power of the 
distance, are given in the figure. 
The molecules are supposed to be originally moving 
with equal velocities in parallel paths, and the way in 
which their deflections depend on the distance of the path 
from S is shown by the different curves in the figure. 
3rd. Integration with respect to dNj. 
We have now to integrate expressions involving various functions of r h £, and V 
with respect to all the molecules of the second sort. We may write the expression to 
