412 
MR. J. H. JEANS ON THE DISTRIBUTION OF xMOLECULAR ENERGY. 
We shall assume that these co-ordinates are principal co-ordinates of the system, so 
that both the kinetic and potential energies will be the sums of squares. We may, 
in fact, write 
2V = cpq2 _p cpv + . . . + c,?v 
2T = mc2 + 2Q -h 2S 
where 
2Q = + ^^9.2 + • • • d~ ^n9n 
2S = “h -f- . • . “h clnS,“. 
We shall suppose the oscillations of the r, s co-ordinates to be so small as to be 
isochronous, and in this case the c and d coefficients will be constants. Since the r 
co-ordinates are to be very small, the “ configuration ” of a molecule may be supposed 
to be determined by its p co-ordinates. 
With a view to simplifying subsequent analysis, we shall assume that the ds also 
are constants. It will be seen that the character of our results is not materiallv 
modified by this .simplification, and the assumption is, of course, legitimate if we 
suppose the molecule, except as regards small oscillations, to behave like a rigid 
body, the atoms never moving far from certain equilibrium positions. We shall 
s\q)})Ose that the A’ibrations of the molecule result in a radiation of energy, and we 
accordingly assume a dissipation function G. This will be siq^posed to be a quad¬ 
ratic function of the 6’ co-ordinates with constant coefficients ; it will not in general 
be reducible to the sum of squares. The existence of G inqjlies an interaction 
between matter and ether. The assumption that G contains no terms in u or q is in 
strictness only legitimate if we suppose the u and q velocities to be unintluenced by 
the ether, but it is easy to see, as in § 14, that even if these velocities are acted upon 
by the ether, the neglect of these actions is of no Importance so long as they are 
sufficiently small. 
We have spoken of T and V as kinetic and potential energy, but there is ilo 
reason whv these energ-ies should not be regarded as electro-magnetic and electro- 
static energy, or indeed as energy of any other kind, provided only that it is always 
possible to deduce the equations of motion from the energy function by LagkaxgeIs 
method. But it is probaldy best to regard the system just specified as simply a 
dynamical system in the strictest .sense, this system being capable of illustrating all 
the })roperties which experiment .shows to be po.s.sessed by a molecule. 
§ 18. Corre.sponding to a collision in the ca.se of two S 2 )heres, we shall suppose that 
it is possible for an action to take place between two molecules, and this action will 
he spoken of as an “encounter.” For the present, it is not necessary to specify the 
exact nature of an encounter, but it will be supposed 
(i.) that the duration of an encounter is infinitesimal, so that an encounter 
causes no direct change in the co-ordinates of position of a molecule. 
