PROFESSOR STOKES ON THE CHANGE OP REFRANGIBILITY OF LIGHT. 499 
less part, a little true dispersion, just as another colourless glass would do. But this 
has plainly nothing to do with the peculiar reflexion which attracts notice in such a 
glass. 
Observations on the preceding results. 
80. There is one law relating to internal dispersion which appears to be universal, 
namely, that when the refrangibility of light is changed by dispersion it is always 
lowered. I have examined a great many media besides those which have been men- 
tioned, and I have not met with a single exception to this rule. Once or twice, in 
observing by the fourth method, there appeared at first sight to be some dispersed 
light produced when the small lens was placed beyond the extreme red. But on 
further examination I satisfied myself that this was due merely to the light scattered 
at the surfaces of the large prisms and lens, which thus acted the part of a self-lumi- 
nous body, emitting a light of sufficient intensity to affect a very sensitive medium. 
81. Consider light of given refrangibility incident on a given medium. Let some 
numerical quantity be taken for a measure of the refrangibility, suppose the refractive 
index in some standard substance. Let the refrangibilities of the incident and 
dispersed light be laid down along a straight line AX (fig. 2) taken for the axis of 
abscissae ; let AM represent the refrangibility of the incident light, and draw a curve 
of which the ordinates shall represent the intensities of the component parts of the 
truly dispersed beam. According to the law above stated, no part of the curve is 
ever found to the right of the point M ; but in other respects its form admits of great 
latitude. Sometimes the curve progresses with tolerable uniformity, sometimes it 
presents several maxima and minima, or even appears to consist of distinct portions. 
Sometimes it is well separated from M, as in fig. 2 ; sometimes it approaches so near 
to M that the most refrangible portion of the truly dispersed beam is confounded 
with the beam due to false dispersion. 
82. Let f (x) be the ordinate of the curve corresponding to the abscissa x, a the 
abscissa of the point M. Since f (jr) is equal to zero when x exceeds a, the curve 
must reach the axis at the point M at latest, unless we suppose the function capable 
of altering abruptly, as is represented in fig. 3. I do not think that such an abrupt 
alteration, properly understood, is necessarily in contradiction with the law of con- 
tinuity. For the sake of illustration, let us consider the phenomenon of total internal 
reflexion. Let P be a point in air situated at the distance ^ from an infinite plane 
separating air from glass. Conceive light having an intensity equal to unity, and 
coming from an infinitely distant point, to be incident internally on this plane at an 
angle where y is the angle of total internal reflexion. The intensity at P is 
commonly, and for most purposes correctly, considered as altering abruptly with 6, 
having, so long as d is negative, a finite value which does not vanish with 6, but 
being equal to zero when d is positive. The mode in which the law of continuity is 
in this case obeyed is worthy of notice. In the analytical expression for the vibra- 
tion, when 6 passes from negative to positive, the coordinate passes from under a 
