Theory to Dark Lines D 1? D 2 p reduced by Sodlu m- Vapour. 303 



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 suppo- 

 sitions 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 homo- 

 geneously 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 molecules. Subject 

 to these conditions we have (Sellmeier's formula) 



v,\2 wit 8 mf 



©- 



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 un- 

 disturbed ether filling the same volume; /c, /c / 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 undisturbed ether ; 

 v s the velocity of light of period t in the sodium-vapour. 



§ 3. For sodium-vapour, according to the measurements 

 of Rowland and Bell*, published in 1887 and 1888 (probably 

 the most accurate hitherto made), the periods of light corre- 

 sponding to the exceedingly fine dark lines D 1? D 2 of the 

 solar spectrum are '589618 and '589022 of a michronf. The 

 mean of these is so nearly one thousand times their difference 

 that we may take 



* Rowland, Phil. Mag. 1887, first half-year; Bell, Phil. Mag. 1888, 

 first half-year. 



t " Michron " is the name which I have given to a special unit of 

 time such that the velocity of light is one mikrom of space per michron of 

 time, the mikrom being one millionth of a metre. The best determi- 

 nations of the velocity of light in undisturbed ether give 300,000 kilometres, 

 or 3 xlO'4 mikrom?, per second. This makes the michron £x 10- 14 of a 

 second. 



Y2 



