ON A VIEW OF THE CONSTITl'TION' OF A I.l MINOl'S (I.\S SUGGESTER RY I.OREN'TZ'S TIIEORY OK RISPERSION'
J J THOMSON
The refractive index y. of a gas for light whose vibratiou frequencv is /i was shown bij Loukntz to be giveu by the Kquation
ft ~ 1 ^ ~ y Ne2 t q2 i j\
rj.1 -)- 2 3 m (u2—j/1)
where e is the charge aiul m the mass of au ion ; n the frequencv of a free vibratiou, N the nutnber of ions vibrating with tliis frequencv, / (l the velocity of light in a vacuum, and the sumniation is to be taken for all the modes of vibratiou of the molecule, i. e. for all the lines in the spectrum of the gas. For ven long waves p is approximately zero, r y-2 = A where A" is the specitic inductive capacity of the gas. If /. is the wavelength corresponding to the frequency //, then r // = /J~ ~ and equation (1) beconies
4 77 m
In the denominator of the left hand side of equation (2), A 2 Iims been put equal to 3 as A for all gazes is approximately unity.
Now from the spectrum of the gas we can determine the various values of '/■ and if we assume tliat all the molecules can give out the vibratiou whose wave-length /., we can tind Ne.e m is equal to 10' if the vibrating ion is negatively charged. Now let us apply tliis fonnula to some gas, we shall take Helium; each line in the spectrum will eonliibute to the right hand side of equation (2) so tliat if we only take into