1906-7.] Partition of Heat Energy in Molecules of Gases. 197 
mination of the speed distribution of all atoms (p. 246). In connec- 
tion with this point, the calculation is carried out for diatomic molecules 
in the case in which A and B act upon each other in the direction of the 
central line, and only the atoms A strike each other. In this special case 
we can so complete the result of the H-theorem, by apparently plausible 
assumptions, that there results a fixed speed distribution. It appears that 
here also, both for A and B, Maxwell’s distribution law holds, and certainly 
that the mean kinetic energy (time, and number, mean) has the same value. 
§ 3. The calculation by which, in this special case, Boltzmann reached 
the result, does not settle whether the same result would hold in somewhat 
more general cases, e.g. for a molecule with more than two atoms or with 
another law of force. But the calculation which Boltzmann carried out in 
§ 86 for the two-planet case can be put in a somewhat more general form. 
This shows at once that, in the case of assumption II., for observance or 
non-observance of equipartition, it is very essential, on account of the 
structure of the molecule, that the free motion (between two collisions) 
admit an integral of the form 
ff • • • • ^ 3 ?i j ii > £ 2 1 £3 • • • • ~ const. , . . . (2) 
that is to say, an integral which does not depend explicitly either on the 
time, or the velocity components £ 3 , of the atom A.* The farther 
pursuit of this question leads, then, to a corresponding systematic determina- 
tion of non-equipartition cases. For the present purpose, it suffices to give 
one case. We choose one such which furnishes the immediate answer to 
Mr Peddie’s question. 
§ 4. We consider a mixture of two gases of the following nature. The 
molecules of the first gas are monatomic, and do not act upon each other 
with any force (except on collision). The molecules of the second gas are 
constituted of n atoms A, B, . . . which are bound together, and to their 
equilibrium position, by elastic forces. Here also the atoms A alone are to 
suffer blows, and these can come from the freely moving molecules of the 
first kind. 
The cartesian co-ordinates of the n -atoms, measured from the equilibrium 
position of each atom, may be denoted throughout by 
5 ^2 J * * * * > ^3w 5 
where £ 2 , ^ 3 , are the co-ordinates of the atom A. As elastically oscillating 
1 Moreover, it can then he shown that the integral does not contain the co-ordinates 
In I2) li- Bor the proof, one has to use the supposition that the forces depend only on the 
co-ordinates. 
