THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
241 
spectrum of definite lines to a continuous spectrum, with increasing density, would 
thus be due, not to auy want of definiteness of the free periods, but to changes in 
the orientation of the vibrating molecules arising from increased frequency of 
encounters, the corresponding rather abrupt changes in the radiation received at any 
point not being analyzable into the regular Foujeher periods. 
29. The possible characteristics of the dispersion of an ideal perfectly transparent 
medium may be very simply represented by a graph of the general formula 
~ f)/(/^^ + 2) =: %nm. In a curve whose ordinate is — l)/(p^ + 2) and 
abscissa the frequency all parts which lie outside the two horizontal dotted 
lines corresponding to ordinates + 1 and — belong to regions of complete opacity ; 
the points where the curve crosses the axis represent the free periods or bright lines. 
A mean continuous curve of dispersion may be sketched in, by a dotted line, which 
coincides with the actual curve in the parts where the dispersion is normal, and may 
be considered as gradually rising towards a band of intense absorption in the ultra¬ 
violet, which dominates the mean dispersion; near an absorption band the dispersion 
is anomalous, but if the band is 
narrow as in the case of gases, the 
anomaly is confined to very narrow 
range. The diagram here given 
represents a case of four free mole¬ 
cular periods, for the third of which 
g is negative while it is positive for 
the others. The refractive index 
that is determined by prismatic 
deviation is the real part of p, 
taken positively (§ 34 infra). A 
graph of this quantity is repre¬ 
sented by the thick broken line of 
the lower curve : thus near a free 
period ^Trjp-^ the ordinate rises to 
_ infinity when 
sinks instantly to zero, and remains zero until + 2ng„ when it becomes 
positive again. Slight general absorption would ease off the corners of this graph so 
various orientations which change from time to time owing to encounters. The effect of this is tliat 
he coefhcients whicii represent the interaction between the aggregate of the matter and the lether, in 
he element of volume, are now the steady aggregates of the coefficients r^, c.„.which belong to 
the various simultaneous orientations of the molecules. Thus the analysis remains intact provided 
Cl, C. 3 , . . . c„ represent average values, and, where necessary, a coefficient of absorption is introduced to 
represen the abstraction of energy from the waves owing to the continual changes of molecular 
orientation. Alter each such change of orientation of a molecule, the energy of its previously accumul¬ 
ated synchronous vibration is radiated away or degraded into heat. 
VOL. OXC.—A. 2 I 
