THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
783 
determined solely by these forces, which are far more intense than any forces due 
to mere translation through the medium; and then, when radiation occurs as the 
result of some violent disturbance, or of dissociation of the molecule, it will have 
subsided before any sensible change of size due to slowly-acting hydrodynamical 
causes could have occurred. As was pointed out by Maxwell, the definiteness of 
the spectral lines requires that at least some hundreds of vibrations of a molecule 
must be thrown off before they are sensibly damped; and on this view there is ample 
margin for such a number. 
On these ideas the velocity of translation of a molecule in a gas would not be 
connected with the natural hydrodynamical velocity of a simple vortex-atom, but 
would rather be determined by the circumstances of collisions, as in the ordinary 
kinetic theoiy of gases. The configuration of a molecule, which determines its electric 
periods, would also be independent of the movements of translation and rotation, 
which constitute heat and are the concern of the kinetic theory of gases. 
Introduction of the Dissipation Function. 
88 . The original structure of x4nalytical Dynamics, as completed by the wmrk of 
Lagrange, Poisson, Hamilton, and Jacobi, was unable to take a general view of 
frictional forces; one of the most important extensions which it has since received, 
from a general physical standpoint, has been the introduction of the Dissipation 
Function by Lord Rayleigh. He has shown"^ that in all cases in which the frictional 
stress between any two particles of the medium is proportional to their relative 
velocity, when the motion is restricted to be such as maintains geometrical similarity 
in the system— i.e. in all cases in which, and being the two particles, 
the components of the frictional stress between them are 
Px (-^1 ~ x^, py (yi r/o), p: (Z] Zo), 
where jx. are any functions of the co-ordinates—the virtual work of the frictional 
forces in any geometrically possible displacement may be derived from the variation 
of a single function J?. The virtual work for the two particles just specified is in 
fact 
P^ (.Ti - x.^) S (x^ - X 2 ) + py (vi - S (yi - 2 / 3 ) + P: - %) S (^1 - «2); 
and for the whole system it wall be found by addition of such expressions as this. 
Now if we form the variation, with respect to the velocities alone, of the expression 
df? = i t{px, (xi - Xg)^ -f IX,j {y^ - y.,f fi- IX, {z, - 
* ‘Proc. Loncl. Math. Soc.,’ 1873; ‘Theory of Sound,’ I., 1877, § 81. [An analytical function of 
this kind occurs however incidentally in the ‘ Mecanique Analytique,’ Section viii., § 2.] 
