408 
ME. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
(x.) and (xi.) were treated. At low temperatures the ratios F E all tend to zero, and 
the equations may he replaced by 
cmjdt = pv/K 
p\/K [Sq^E, + S^i.E^ 4" ~ ^iFi = 0, 
and d'Kjdt = pv'^K (Sc^E^ + cK].(xxi.). 
A steady state would he possible, if we could simultaneously satisfy all equations 
of the type, 
+ hiK = 0 , 
together with , Sc^sE^ -}- cK =0.(xxii.), 
by values of K, Ej, E^, &c., which were different from zero. 
Let us use S to denote summation with resj^ect to degrees of freedom. Then since 
we know the solution of equations (xix., p. 406) we can, by substitution, arrive at a 
system of relations between the coefficients. 
Making allowance for the alteration in notation {cf. equations xx., p. 407) these 
relations can be written in the form 
Suis + -f 36^ = 0, 
and Sc^ “h -{- 3e = 0. 
If we attribute an amount of energy X to every degree of freedom, we have 
2oi,E, + hiK = X (Soils + 3^i) = —XS^ij 
and Sc^Es + eK = X (Sc^ + 3e) = — XSc',. 
Tims tlie equations (xxii.) are very approximately satisfied, in virtue of the 
smallness of the and c' coefficients. The solution we have found will therefore 
give a state which is approximately steady. 
§ 13 Thus at a sufficiently low temperature the energy of the gas which we have been 
considering Avill distribute itself in such a manner that an equal amount of energy 
will correspond to each degree of freedom Avhich is not retarded by friction. The 
amount of enei’gy corresponding to a degree of freedom Avhich is retarded by friction 
Avill he vanishingly small. The amount of such energy is given by the equations, 
F, = p'/'A {lq„E. + b\K} 
(xxiii.). 
If the degrees of freedom included in the E’s are n in number, and those counted in 
the F’s are m in number, it is obvious that the ratio of the specific heats must he 
taken to be 
7=1 + 
2 
n + 3 
(;xxA.), 
