420 
MR. J. H. .THINS ON THE DISTRIBUTION OF MOLECULAR ENEROAL 
Now it appears from the scheme of values just found that terms of the form 
can only arise in connection with the s co-ordinates, so tliat (-r) mav he 
d^\rUj r^\iUj 
replaced hy — e where 
— 1 ^ I 1 
Tl lus the gain to N^ arising from the cause (y) will be 
-dl.t ® ” J + e N„ cU 
(xL). 
We have now counted u}) all sources of change in Nj; we therefore have, as the 
equation to be satisfied by Nq, 
= JdPdt + KdPdt -h 
vt Cq dt 
§ 2-3. We have found the etpiation ( (i.), p. 415), 
(xii.). 
and 
No = :SN„ 
where the summation is such as to cover all ranges of p and u. 
We may therefore write 
where 11 is given by 
N,. = HF (7P 
II = \e (/n.(xiii.), 
and is therefore a function of h only. 
Substituting this value of Nq in equation (xii.), we have the equation 
|(HF) = J + K + .HF-Hr|f . . . 
. (^N) 
Tjet us write F = e ^ and substitute this value for F in the integrals J and K. We 
have 
A {c"’’FF'} = + 
- g - (^ + X + x') (J - 1 + X + X') _ ■[ j 
lleferring to equation (iv.) we find that 
T7 -h X x' “ h'{m (c" -p c') + 2^' -g 2'F -f- 20] -f y “F X • 
From the equation of energy (see p. 412), 
