400 
MR. J. H. JEANS ON THE DISTRIBUTION OF MOLECULAR ENERGY. 
Since the total energy remains unaltered at every collision, we must have 
dKjdt == - dK/dt - 
it is therefore only necessary to calculate one of these differential coefficients. 
§ 4. The state of a molecule at any instant will be determined by the following 
12 variables, 
(i.) The co-ordinates in space of its centre of gravity x, y, z, and their time-rate 
of change u, v, tv. 
(ii.) Any three independent variables, e,f, g, sj^ecifying the orientation in space 
of the molecule. 
(ili.) tn-o, CTg, the rotations about three principal axes, the last of these being 
the rotation about the axis of symmetry of the molecule. 
Let accented letters refer to a second molecule ; then a collision between these two 
molecules, if possible, is completely specified by the whole 24 variables, but these 
are not all independent, and the collision will, as regards transfer of energy, be 
sufficiently specified by the independent variables 
u — u , V — v\ w — tv', 
' f f 
TTTi, aT23 7^3*3, tS" oT 2, ^3? 
and six other variables to determine the direction in sjDace of the axes of the mole¬ 
cules, and the line of centres. 
Let the variables after collision be distinguished from those before collision by 
placing a Ijar over them, then we can from the ordinary equation of impact calculate 
the value of 
c" + c"^ — (c^ -j- c'^) 
where c" = td tv^, in terms of the variables before collision. 
This expression must be a quadratic function of the velocities, and ts-g, cir'g cannot 
enter. If we write 
(u — u')^ -j- (v — + (tv — w')^ = 
O I O 0 
“ 1 “ 
it is easily seen that the expression must be of the form 
4 . - (c^ + c'^) = -f .(L), 
where a^, are functions of the six variables determining orientations in s^Dace, 
and are algebraical functions of r, in vffiich the lowest power is 
