404 
MR. J. II. JEAXS ON THE DISTRIBUTION OF MOLECULAR ENERCY. 
the state of the gas will only change very .slowly, so that the state specified by 
equation (xiii.) may be appropriately described as the " approximately steady” state. 
When H vanishes in comparison with K, the equation giving this state takes the 
simpler form 
= .(xiv.) 
The conditions which have been found to be necessary in order that this state 
may exist, are that e, ^ should be small, and that K should be so small that 
is very great. Thus the steady state will be possible for all temperatures below 
a certain temperature, namely, the temperature at which /S^/K begins to be com¬ 
parable V'ith €. Below this temperature H vanishes in comparison with K, and the 
rate of dissipation of energy is a small quantity (T the second order. 
It follows that if exj)eriments are conducted at temperatures so low as to be 
below this critical temperature, no value of y can possibly be observed except 
At higher temperatures, there is no definite ratio between IT and K which tends 
to establish itself In fact, if experiments are conducted with a view to determining y, 
the value observed will depend on the past history of the gas and the duration 
of the experiment, so that y may have any value between If and if. 
Thus it appears that if, under the conditions we are now considering, a consistent 
value is obtained for y from experiments on the gas in question, this value can be no 
other than 1|, and the temperature at which the experiments are conducted must 
1)e what has been referred to as a low temperature. It must be particularly noticed, 
that this tenqoerature is only low relatively to the other temperatures considered : no 
knowledge as to its absolute value is possible so long as e and rja remain unknown 
([uantities. If, how'ever, for the moment, we assume that the present molecules are 
a fair representation of the molecules of an actual gas, and that the dissijoation of 
energy caused by our assumed frictional reactions supplies a true analogy to radia¬ 
tion of energy in nature, then we can form some estimate as to what a “ low ” 
temperature must mean. It is a temperature at which H, and therefore the 
radiation, is inappreciable ; that is to say, it is a temperature at which the gas is 
non-incandescent. 
The Dist rihution of Energy in the approximately Steady State. 
\ 9. To sum iq), it appears that if we are v illlng to admit that our present dynami¬ 
cal system supplies a sufficiently good analogue to a real gas, then the introduction 
of a dissipation function will supply an explanation of the difficulties mentioned in 
the introduction, at any rate for the case of a non-luniinous gas. Part II. of this 
paper consists of an effort to show that our present system is a fair analogy, if not 
