240 
MR. J. LARMOR OX A DYNAMICAL THEORY OF 
of a solution or chemical compound, is made up, according to this formula, of the 
aggregate of those of its constituents.'" 
27. Let us consider briefly the case of a perfectly transparent substance whose 
dispersion is dominated by a single free period, say : the equation is 
,j? + 2 
that is, 
ih~ - r 
p.2 = I 4- 3 
Wh 
0 o y 
Pi - P~ / 
/('i- 
P\ - P-J 
It will be convenient to form a graph of the formula for ; when ^3 is small, 
has a positive value, which should be the statical dielectric constant of the material; 
as 'p increases, p," increases until it becomes infinite when it then 
becomes negative, but again attains a positive value after p~ — + 2)ig^ which 
corresponds to value zero. Thus there is a band of absorption, which is absolutely 
complete for some distances on both sides of the bright spectral line corresponding to 
the substance in the gaseous state, but which extends about twice as far on the 
upper side of that line as it does on the lower when ng^ is positive, as will be the case 
when p exceeds unity and the dispersion is in the normal direction. When, as in all 
ordinary media, the dispersion of the visible light is small, being for example of the 
order of one per cent, for glass, must be great compared with p, and the range of 
this single dominant ultra-violet band of absolutely complete absorption would be 
measured by an interval i^p\p) equal to i (p^ — l)/(p^ + 2) below the free period, 
and one equal to (p^ — l)/(p^ -f 2) above it, where p is the index for luminous rays. 
28. For a substance such as a gas, with numerous narrow bands of absorption, in 
the immediate neighbourhood of any one of them the value of p“ depends on that one 
alone; the breadth of the band of complete absorption thus corresponds to a total 
interval {Ipjp or — SX/X) equal to 2,ngil2p^, which should thus be proportional to 
the densitv of the gas. The distance on each side of the band to which the anomalous 
dispersion extends, which may possibly be observed as has been done by Kuxdt for 
sodium vapour, ought also to be of the order of magnitude of ngijpi- The law of 
Janssen, that the amount of the absorption in a compressed gas is roughly pro¬ 
portional to the square of the density, seems to show that in dense media most of 
the actual specific absorption is outside tliese limits of complete blackness, and is 
conditioned by the molecular encounters deranging the states of steady directed 
synchronous vibration, say by rotation of the molecule, and so necessitating absorption 
of fresh energy from the radiation in order to re-establish them. It is to be observed 
that this process would be a true absorption of radiation which would go to heating 
the gas, as contrasted with mere refusal of a perfectly transparent gas to transmit 
radiation in a region in which p" is negative.! The gradual change from an emission 
* In cases however in wliicli a formula of the Cauchy type is sufficiently exact, so that 
_ 1) / (^,2 + 2) p = A -t- B //\3 -h C /X-i -h . . . , not only is A an additive refraction-equivalent, 
but there wall also be additive dispersion-equivalents B, C, . . . . 
b The validity of the general formulte is not vitiated by this circumstance that the molecules are in 
