1898-99.] Lord Kelvin on Sellmeier’s Theory. 
523 
Application of Sellmeier’s Dynamical Theory to the Dark 
Lines D x , D 2 produced by Sodium- Vapour. By Lord 
Kelvin, G.C.V.O . , P. R.S.E. 
(Read February 6, 1899.) 
§ 1. For a perfectly definite mechanical representation of 
Sellmeier’s theory, imagine for each molecule of sodium-vapour a 
spherical hollow in ether, lined with a thin rigid spherical shell, of 
mass equal to the mass of homogeneous ether which would fill the 
hollow. This rigid lining of the hollow we shall call the sheath 
of the molecule, or briefly the sheath. Within this put two rigid 
spherical shells, one inside the other, each movable and each 
repelled from the sheath with forces, or distribution of force, such 
that the centre of each is attracted towards the centre of the hollow 
with a force varying directly as the distance. These suppositions 
merely put two of Sellmeier’s single-atom vibrators into one 
sheath. 
§ 2. Imagine now a vast number of these diatomic molecules, 
equal and similar in every respect, to be distributed homogeneously 
through all the ether which we have to consider as containing 
sodium-vapour. In the first place, let the density of the vapour 
be so small that the distance between nearest centres is great in 
comparison with the diameter of each molecule. And in the first 
place also, let us consider light whose wave-length is very large in 
comparison with the distance from centre to centre of nearest mole- 
cules. Subject to these conditions we have (Sellmeier’s formula) 
where m, m / denote the ratios of the sums of the masses of one 
and the other of the movable shells of the diatomic molecules in 
any large volume of ether, to the mass of undisturbed ether filling 
the same volume ; k, k / the periods of vibration of one and the other 
of the two movable shells of one molecule, on the supposition that 
the sheath is held fixed ; v e the velocity of light in pure undis- 
