234 
MR. STOKES ON THE THEORY OF CERTAIN 
in applying the formula (4.), (5.) or (6.) to the other system of bands, the third prin- 
cipal index must be substituted for (jtJ. 
It is hardly necessary to consider the formula which would apply to the general 
case, which would be rather complicated. 
9. If a plate cut from a uniaxal crystal in a direction perpendicular to the axis be 
placed in the fluid in an inclined position, and be then gradually made to approach 
the vertical position, the breadths of the bands belonging to the two systems will 
become more and more nearly equal, and the two systems will at last coalesce. 
This statement indeed is not absolutely exact, because the whole spectrum cannot be 
viewed at once by light which passes along the axis of the crystal, on account of the 
dispersion accompanying the first refraction, but it is very nearly exact. With 
quartz it is true there would be two systems of bands seen even in the vertical posi- 
tion, on account of the peculiar optical properties of that substance ; but the breadths 
of the bands belonging to the two systems would be so nearly equal, that it would 
require a plate of about one-fifth of an inch thickness to give a difference of one in 
the number of bands seen in the whole spectrum in the case of the two systems re- 
spectively. If the plate should be thick enough to exhibit both systems, the light 
would of course have to be circularly analysed to show one system by itself. 
Section 11. — Investigation of the mtensity of the light on the complete theory of undu- 
lations, including the explanation of the apparent polarity of the hands. 
10. The explanation of the formation of the bands on the imperfect theory of 
interferences considered in the preceding section is essentially defective in this re- 
spect, that it supposes an annihilation of light when two interfering streams are in 
opposition ; whereas it is a most important principle that light is never lost hy inter- 
ference. This statement may require a little explanation, without which it might 
seem to contradict received ideas. It is usual in fact to speak of light as destroyed 
by interference. Although this is true, in the sense intended, the expression is per- 
haps not very happily chosen. Suppose a portion of light coming from a luminous 
point, and passing through a moderately small aperture, to be allowed to fall on a 
screen. We know that there w'ould be no sensible illumination on the screen except 
almost immediately in front of the aperture. Conceive now the aperture divided into 
a great number of small elements, and suppose the same quantity of light as before 
to pass through each element, the only difference being that now the vibrations in 
the portions passing through the several elements are supposed to have no relation 
to each other. The light would now be diffused over a comparatively large portion 
of the screen, so that a point P which was formerly in darkness might now be strongly 
illuminated. The disturbance at P is in both cases the aggregate of the disturbances 
due to the several elements of the aperture; but in the first case the aggregate is 
insensible on account of interference. It is only in this sense that light is destroyed 
by interference, for the total illumination on the screen is the same in the two cases ; 
