329 
For X — 0, v = 1\ and for X = oo we deduce 
7> __ ^ ~f~ % 9 H~ g — ff) 
(7 + <r)(7-<7) 
( 4 ) 
where <7 is given by (6), § 9., and K denotes the dielectric constant. 
In the case where x cannot be neglected, formula (2) of the 
preceding section may be used. Let us consider a place in the 
spectrum such that 
It follows from (2), § 12., that in this case 
( 5 ) 
(v 2 — x2J ï _2)(v 2 — X 2 — l)-^4v 2 x 2 < 0; (6) 
hence 
{v 2 — l-\- x 2 ) 2 -f ;< 2 + 3 (> 2 — 7) < 0; (7) 
from this it appears that for X <C X Q we must have v <C 1. 
That the general properties of any real substance will be found 
to agree exactly with those of the mono - electronic model is an 
assumption which a 'priori seems of course very improbable. In 
subsequent articles we shall find, however, that within certain limits 
in the spectrum the dispersion of some gases seems to conform 
to the laws which can be deduced from this simplifying hypothesis. 
The behaviour of such bodies can be accounted for by taking into 
consideration the structure of the two quantities 67, (§§ 5. and 10.) 
on the first of which the dispersion chiefly depends; the second, 
<$, is practically responsible for the extent of absorption. The ex¬ 
planation afforded will be improved if we suppose that, in a given 
volume of the substance, electrons of various classes occur in very 
different proportion. 
§ 14. Professor R. W. Wood has supplied Optical Theory with 
a beautiful series of data x ) respecting the dispersion of sodium- 
vapour, at the temperature of 644° C. The refractive indices are 
given for wave-lengths ranging from 2,26. to 5,8896 (10“ 5 cm.) and 
again for wave-lengths ranging from 5,916. to 7,50 (10 -5 cm.). 
The density of the vapour is not known; this is unfortunate in con- 
q Philosophical Magazine, Ser. (6), Vol. VIII., p.293. 1904. — Phy¬ 
sical Optics. New-York 1905. p. 344. 
