1887.] Sir W. Thomson on the Equilibrium of Gas. 
117 
curvature calculated from (13) with the value of du]dx found from 
the step-by-step process. If this preliminary construction is done 
with care, by aid of good drawing-instruments, u x calculated from 
u o by quadratures will be found to agree so closely with u Q , that v 0 
itself will be seen to be a good solution. If any difference is found 
between the two, u Y is the better : u 2 is a closer approximation than 
«q ; and so on, with no limit to the accuracy attainable. 
Mr Magnus Maclean, my official assistant in the University of 
Glasgow, has made a successful beginning of working out this pro- 
cess for the case u = 1 6 where x = oo ; and has already obtained a 
somewhat approximate solution, of which the produce useful for our 
problem is expressed in the following table 
dlu 
Numerical Solution of 4 
H- X U 
0 . 
Distance from 
centre 
= r= l/x. 
Keciprocal of 
distance from 
centre 
= cc=l jr. 
Temperature 
- u. 
Density 
= w' 2 ' 5 . 
Mass within dis- 
tance r from the 
centre 
= du/dx 
dxu 2 ' 5 x--i 
0 
8 
16-00 
1024 
■oo 
•100 
10 
14-46 
795-2 
•28 
•111 
9 
14-14 
751-6 
•38; 
•125 
8 
13-71 
695-8 
•52 
•143 
7 
13-10 
621-2 
•731 
•167 
6 
12*20 
520-0 
1-056 
•200 
5 
10-92 
394-1 
1-566 
•250 
4 
9-00 
243-0 
2-336 
•333 
3 
6-15 
93-81 
3-436 
•500 
2 
2-25 
7-595 
4-366 
•667 
]-5 
0 
0 
4-49 
The deduction from these numbers, of results expressing in terms 
of convenient units the temperature and density at any point of a 
given mass of a known kind of gas, occupying a sphere of given 
radius, must be reserved for a subsequent communication. 
laboratory in 1874, in a series of skilfully executed drawings representing a 
large variety of cases of the capillary surface of revolution, which have been 
regularly shown in my Lectures to the Natural Philosophy Class of the Uni- 
versity of Glasgow. These curves were recently published in the Proc. Roy. 
Instit. (Lecture of Jan. 29, 1886), and Nature, July 22 and 29, and Aug. 19, 
1886 ; also to appear in a volume of Lectures now in the press, to be published 
in the Nature series. 
