MR. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
421 
A ' in (c' -|- c 2 (Q -j- -l- Q -f- < — 0. 
Hence A (>; + x + x') == — H, 
where C = 2A (Q + S + Q" + S') — x — X • 
Ill virtue of the assumptions which have been inacle, ^ is a small quantity, so that 
■we mav put 
- 1 = AC, 
and therefore A { e “ FF'} = Fe “ ^ AC- 
The same transformation holds if A is replaced by 1)/DL Hence we have (see 
equations (ix.) and (x.), p. 418). 
J = FL, K = FM, 
where L= dp dndp dV' du u-i dy" dz' .... (xv.), 
Making these substitutions, equation (xiv.) becomes 
-F - HF'if = F(L + M) + eHF + HF^ 
at 
dt 
0^ dt 
or dividing throughout by HF, 
I = lF",/-^-l7a+M)-X 
_ _ _ ^x 
dt ~ n dt " H ^ 0c Jt 
This is the characteristic ecjuation satisfied by x- 
(xvi.). 
(xvii.). 
Form of General Solution. 
§ 24. We must first examine in what way the integrals L and M involve q, r, and 
5. In L these co-ordinates are only involved through the factor A^^ which occurs in 
the integrand. 
Now Ar = 0, and Aq, As can, from the equations of impact, be expressed as linear 
functions of all the velocities concerned. The coefficients will be functions of p, p', r, r', 
but we may as usual put r, r' = 0. 
It follows that A^ is a function of q, r, and s of degree equal to that of and will 
involve q)> q>'^ these variables. If, then, ^ is of degree n in q, r, and s, 
we may regard A^^ as a function of r, and s of degree n, of which the coefficients are 
functions of the variables with respect to which integration is performed in 
evaluating L. Hence after integration we shall have L as a function of (p r, and 5 of 
degree n. 
