10 PROFESSOR G. H. DARWiJT ON THE MECHANICAL CONDITIONS OF 
Whatever be the arrangement of the gas, the density at the centre must have some 
value. I therefore start with a central density co, corresponding to the value y of 
so that 
.(15) 
Pi 
For the sake of brevity the suffixes 1 will be now* omitted from the various symbols, 
to be reaffixed later when they are required. 
At the centre, where x is infinite, dijjdx, d^yjdx^, &c., are all zero, and we put 
y = i- 
Let ^ = e'^/x^, and let us assume 
y = 7) -{■ V 
Now, the differential equation (14) to be satisfied is 
dx^ A 
But 
x~ 
.nhi 
-2.3A,i+^-5A,e-6.7A,i^+ ... , 
and by expanding e” we obtain 
- ^ - (A, + 1 A,2) + (A, + A,A, + ,1- A,3) 
— {A^ + A^A^ + I A^^ + ^ 
+ (^5 + ^i^4 + ^2^3 + + 2“3 • • • 
By equating coefficients in these two series, I find 
and 
/4 — A A — - 1 - 
^1 — 6 5 m.2 — 12 0 5 
A — 6 29 
0 2 24,5 3 2,000 ’ 
A — _JL_ 
^3 — 18 9 0 5 
6 1 
A _ J^^O 7 383.^. 
6 1 5 6 X 1 0« 
1,6 3 2,9 6 0 5 
&C., 
log = 9-2218487, 
log = 5-5723543, 
log Ag = 7-9208188, log Ag = 6-7235382, 
log Ag = 4-4473723, log A^ = 3-3392964 ; 
whence, by extrapolation, 
log Ay = 2-243, log ^8 = 1‘13. 
In M, Bitter’s paper, already referred to, he takes a certain function u as equal to 
1-031, when the radius is unity. Now, Bitter’s function u is equal in my notation to 
