416 
MR. J. H. JEAXS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
that the r co-ordinates are supposed to be very small, it is clear that it will be 
sufficient to imagine that is a function of 
(i.) /;, on account of the way in which this coefficient enters in equation (ii.), 
(ii.) the coefficients occurring in f{p) (these have, however, alread}^ been 
assumed to be invariable), 
(iii.) the p co-ordinates of molecules of class a. 
Thus, for our purpose, is a function of li and p only. 
Fixing our attention on any one of these molecules of class a, the probability that 
the centre of a molecule of class /3 may be found within the limits dx" cly" dz" 
measured relatively to the first molecule will be 
Pjy dV dll' dx" dy" dz", 
where fit' is the potential of a molecule of class 8 at this point. Now n'can be made 
up of two parts, the part due to the jmesence of the single molecule of the first 
class, and Ho the part due to all the other molecules combined. 
It is clear that will only depend on the two molecules of the encounter, and is 
therefore a function of p' v x," y" and z". 
The total number of encounters of the type we are now considering, namely those 
within limits 
dp dP dll dp' dV dll' dx" dy" dz" .(ill.), 
will be 
¥'f dp>' dV dv' dx" dy" dz", 
where the summation extends to all the molecules of class a. 
This number may be written as 
f/p' dV dll' 2 dx" dy" dz". 
Now it is obvious that the mean value of taken over all the elements of 
volume Included in the summation, will be where ‘4'' is the mean intermolecular 
potential of a molecule of class /3, and is therefore a function of h and p/ only. 
Thus, since the summation extends to N,, elements of volume, 
y ^-2;,n, y yp ^ yp, yy^ y. 
This gives us for the total number of encounters of the type we are considering, 
y^^ y-p y^ yy yp> yp yp> yy> yp. 
or, if we write 
the number is 
7? = h{m{c- -f c'-) -f 2'¥ -f 2^E' -f 2 ^ 1 ) . 
e-” ¥¥'//' dp dT dll dp' dV dll' dx" dy" dz" 
(v.). 
