529 
1898-99.] Lord Kelvin on Sellmeiers Theory. 
temperature, and the relation between density, pressure, and 
temperature of gaseous sodium. 
[Added, April 7, 1899.] 
§ 10. Passing from the particular case of sodium, I add an appli- 
cation of Sellmeier’s formula, (1) above, to the case of a gas or 
vapour having in its constitution only a single molecular period 
k. Taking m= 0 in (1), we see that the square of the refractive 
index for values of r very large in comparison with k is 1 + m. 
And remembering that the dark line or band extends through the 
range of values for which ( v e /v s ) 2 is negative, and that ( v e /v s ) 2 
is zero at the higher border, we see from (1) that the dark band 
extends through the range from 
t = k to r — — - . (8). 
J 1+m 
§ 11. As an example suitable to illustrate the broadening of the 
dark line by increased density of the gas, I take m = ax 10 “ 4 , 
and take a some moderate numeric not greater than 10 or 20. This 
gives for the range of the dark band from 
r = k to t = k(1 - \a x 10 -4 ) (9); 
and for large values of r it makes the refractive index 1 10~ 4 , 
and therefore the refractivity, \a x 10~ 4 . If for example we take 
a = 6, the refractivity would be *0003, which is nearly the same 
as the refractivity of common air at ordinary atmospheric density. 
§ 12. Taking k = 1000, we have, for values of r not differing 
from 1000 by more than 10 or 20, 
, where x — t- 1000 . . . . (10). 
T A — ‘ 2iX 
Thus we have 
< n >-. 
In fig. 7 the curve marked y represents the values of the re- 
fractive index corresponding to values of r through a small range 
above and below k, taking a =4. The other curve represents the 
proportionate intensity of the light entering the vapour, calculated 
from these values of y by (7) above. 
