500 PROFESSOR STOKES ON THE CHANGE OF REFRANGIBILITY OF LIGHT. 
circular function into an exponential with a negative index, containing in its deno- 
minator X, the length of a wave of light. As 6 increases through zero, the expression 
for the vibration alters continuously ; but if si be large compared with X it decreases 
with extreme rapidity when 6 becomes positive. On account of the excessive small- 
ness of X, it is sufficient for most purposes to consider the intensity as a function of 
d which vanishes abruptly; and indeed it would be hardly correct to consider it 
otherwise. For the use of the term intensity implies that we are considering light as 
usual, whereas those phenomena which require us to take into account the disturb- 
ance in the second medium which exists when the angle of incidence exceeds that 
of total internal reflexion, lead us to consider the nature as well as the magnitude of 
that disturbance, which no longer consists of a series of plane waves constituting 
light as usual. It is in some similar sense that I mean to say that we may suppose 
the function f {x), which expresses the intensity of the truly dispersed light, to alter 
abruptly, without thereby implying any violation in the law of continuity. In 
observing by the fourth method, the portion of the spectrum operated on, though it 
may be small, is necessarily finite, and in some cases no separation could be made 
out between the beams of truly and falsely dispersed light. Hence I cannot under- 
take to say from observation, whether the variation of f (x) be always continuous, 
though sometimes very rapid, or be in some cases actually abrupt. I think, however, 
that observation rather favours the former supposition, a supposition which, inde- 
pendently of observation, seems by far the more likely. 
83. Although the law mentioned in Art. 80 is the only one which I have been 
able to discover, relating to the connexion between the intensity and the refrangi- 
bility of the component parts of the dispersed beam, which appears to be always 
obeyed, and which admits of mathematical expression, there are some other circum- 
stances usually attending the phenomenon which deserve notice. 
When dispersion commences almost abruptly on arriving at a certain point of the 
spectrum, the dispersed beam is very frequently almost homogeneous at first, and of 
the same refrangibility as the active light. If the dispersed beam, when first per- 
ceived, be decidedly heterogeneous, its refrangibility extends almost, if not quite, to 
that of the active light, so that it is difficult, if not impossible, to separate the beams 
of truly and falsely dispersed light. On the other hand, when dispersion comes on 
gradually, it is generally found that the refrangibility of even the most refrangible 
part of the dispersed beam does not come up to that of the active light. 
Thus in the cases of the red dispersion exhibited by a solution of leaf-green, and 
of the orange dispersions exhibited by solutions obtained from archil and from the 
Mercurialis perennis, the dispersed light was at first nearly homogeneous, and of the 
same refrangibility as the active light. In the case of the green dispersions shown 
by a solution obtained from archil, and by canary glass, the dispersed light was 
heterogeneous from the first; but still, when it first commenced, a portion of it had 
nearly the same refrangibility as the active light. In a solution of sulphate of quinine 
