245 
THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
absorption in the ultra-red.^ The specific refraction however always tends to the 
limit unity as or K' increases ; so that the large dielectric constants of water and 
alcohol (at ordinary temperatures) are not so abnormal in their optical as in their 
electrical aspect. These large values are an indication that the constituents of 
the molecules are distantly and loosely connected together, which may be related to 
the powerful action of these substances as solvents ;t it has been noticed that high 
inductive capacity is usually associated with conductivity. 
33. It IS of interest to contrast these results with the ones that flow from a purely 
mechanical theory of dispersion. If the molecule consist of a dynamical system, 
simple or gyrostatic, of dimensions small compared with the wave-length, joined 
on to the mther by mechanical connexions, the uniform oscillatory dkpllcement 
of the aether will exert no differential statical force on the molecule, but the kinetic 
energy of the whole compound system will contain terms involving products of the 
In VON Helmholtz’s memoir on the electric theory of dispersion, he found satisfactory ao-reement 
between the formula with one ultra-violet absorption band and the observations for glycerin^ and he 
suggested that agreement might also be established for carbon bisulphide by assuming slight dissipation 
such as would not sensibly modify the laws of reflexion: but he apparently omitted to notice that this 
veriflcation is defective in not making the square of the index equal to the statical dielectric constant for 
the case of very long waves. To amend it, another region of absorption would have to be assumed in 
the ultra-red, far down so as not to sensibly affect the visible radiations, thus leading to the Ketteler 
type of formula, which is approximately ^ = A + + CX-2 for slightly dispersive substances : in the 
case of glycerine C would be small. When there is only one absorption band, the dispersion formula 
common to these discussions is in form the same as one derived by von Lommel (‘ Wied Ann ’ 13 p 353) 
from a mechanical theory, and compared by him with observation for a considerable number of media 
In al media whose dispersion is effectively controlled by one absorption band, that band must he far in 
the ultra-violet or else the dispersion of the visible radiation will be excessive, so that the formula must 
approximate y coincide with Cauchy’s : thus it is only substances for which approximately equal 
o u slightly greater than K, which can have any chance of coming into that class. 
It appears from the above that in this formula for dispersion in a medium dominated by one main 
band of absorption, as given in Part IL, §11, we must make the distinction, that the value of 2./n for 
which IS infinite is not the free period of a single molecule by itself, or that of the bright line in a 
gaseous spectrum, but is the period when it is vibrating in step with all the surrounding molecules 
under whose influence it lies. 
For very slow perrnds there is no dispersion in a transparent medium and the refraction depends 
w 0 y on the statical character of the medium, including its density. For higher periods of the incident 
ra la ion, e ree periods of the molecules introduce dispersion and also absorption bands; but the 
position of these bands depends not merely on the free periods, but also slightly on the density of the 
me lum, roug t e influence of the latter on its statical inductive capacity. It is not impossible that 
e free molecular periods, as well as the absorption bands, may be affected in this way. An influence 
density of the medium on the position of the lines in the spectrum has been found and investigated 
by the Baltimore spectroscopists. [Gf. FitzGerald, ‘ Astrophys. Journal,’ 1896.] 
_ t The reason here assigned is different from the one that has been given by various writers, that hio-h 
m uctive capacity of an intervening medium weakens the electric forces between the ions in the dissolved 
molecule. Here it is taken as an indication that the effective ions arc far apart in the molecules of the 
solvent, so that a dissolved molecule can come under the influence of one of these ions alone, without 
much counteracting effect from the other ion. 
