Dr. Ketteler on the Dispersion of Light in Gases, 339 



The simultaneous increase of pressure was from 1 atmosphere 

 to 2-56. 



A similar series of experiments in which the pressure of the 

 air was gradually reduced to 0'63 atmosphere, gave exactly the 

 same numbers ; so that these are strictly applicable within the 

 wide limits of 1 and 4. 



If these limits are exceeded, of course allowing for the slight 

 modifications which then become necessary, and if we bear in 

 mind the well-known equations 



L (n 1 A — n' A ) = ™a Xa, T 



L (u'b — n B ) = m B A,b, J 



where L denotes the length of the tube, and \ A and X B two 



given wave-lengths in space destitute of dispersive power, to 



which correspond, .for an initial condition, the indices n A and n B , 



and for any given final condition the indices u'a and n' B , and 



the numbers m A and m B of bands simultaneously displaced, we 



arrive at the following law, which is as simple as it is important : 



n' A —n A 



-t= = const. 



»'b*-«B 



Supposing the final condition to be a vacuum, we have 

 ri A =n' B = l, 

 and consequently 



^^i= const (I) 



The consequences of this interesting law are the following : — 



1. If we consider the variations of an index of refraction cor- 

 responding to any given wave-leu gth A, when the density d is 

 either increased or diminished, we have, as a general case, 



n-l=F(d,X); 

 or, according to equation (I), 



n-\ = ${d).f{\). 

 If now, as the simplest assumption that can be made, we put 

 $(d)=:d } or 



n-l=df(\), (II) 



and remember that, within the limits of experimental error, 

 (n— 1) is identical with \{n*—\), the law (I) brings us back to 

 the familiar law of the constancy of the refractive power. Direct 

 experiments, which will be discussed below, have proved that the 

 above assumption is really warranted. 



2. The quotient — — = = -^ — 7 A • -^-, which for the limiting 



* n B — 1 \ B — l B l A & 



case d=0 becomes a differential coefficient of the form -jr-'^* 



Z2 



