368 Mr. M. Ponton on certain Laws 
of bisulphuret of carbon. But the indices thus obtained are 
subject to a further correction, by the addition or subtraction of 
that portion which is due to the extrusion of the fixed lines 
attending the irrationality of the spectrum. 
The remaining portion of the variable part of the index cor- ~ 
responds to this extrusion of the fixed lines from their normal 
positions, in consequence of which their mutual distances are 
altered from what they are in the unrefracted spectrum. This 
is quite a distinct pheenomenon from dispersion, which is simply 
the greater or smaller expansion of the coloured spaces, and the 
consequent greater or smaller length of the spectrum which the 
medium presents. Besides the shortening of the wave, attribu- 
table to the increased density of the ether within the medium, 
and the further shortening which it undergoes by losing a defi- 
nite number of the particles embraced in its length, it may be 
still further modified by an alteration in the period of vibration 
of each of its component ethereal particles,—an alteration which 
will cause a corresponding small variation in the length of the 
wave, and in the position of the fixed line corresponding to it. 
These alterations, it has been shown, always take place accord- 
ing to certain determinate laws; and the total amount of the 
positive and negative extrusions is so related to the dispersive 
power, that, by means of the ratio between these two, there may 
be always found for the normal wave-lengths an exponent at which 
the extrusions are reduced to zero, this exponent being the above 
ratio multiplied by 10°8 and added to unity. By applying this 
exponent to the normals, the indices of refraction become reduced 
to ¢wo terms instead of three, as already pointed out. 
In explanation of the irrationality two views may be suggested. 
The displacement of the fixed lines is obviously due to the cir- 
cumstance that the waves corresponding to the central lines D, 
E, and F are leas refracted; while those corresponding to the 
extreme lines B, C, G, and H are more refracted than they 
would otherwise be. There is thus a transfer of motive energy 
from the extremes to the central region of the spectrum. Now 
this distribution corresponds to that of the brightness; for all 
spectra are brighter towards the centre than towards the extremes. 
The brightness being proportional to the squares of the ampli- 
tudes of the individual vibrations embraced in the wave-length, 
it follows that, at the recipient surface, the amplitudes of those 
vibrations are greater towards the centre than towards the ex- 
tremes of the spectrum. This correspondence raises a presump- 
tion of there being some connexion between these two pheeno- 
mena. ‘The medium may be supposed to produce a certain effect 
on the amplitudes of the vibrations, decreasing them by a certain 
definite amount, and increasing the rapidity of the vibration and 
