BANDS SEEN IN THE SPECTRUM. 
229 
3. Although the explanation of the polarity of the bands depends on diffraction, it 
may be well to account for their formation on the imperfect theory of interferences, 
in which it is supposed that light consists of rays which follow the courses assigned 
to them by geometrical optics. It will thus readily appear that the number of bands 
formed with a given plate and fluid, and in a given part of the spectrum, has nothing 
to do with the form or magnitude of the aperture, whatever it be, which limits the 
pencil that ultimately falls on the retina. Moreover, it seems desirable to exhibit in 
its simplest shape the mode of calculating the number of bands seen in any given 
case, more especially as these calculations seem likely to be of importance in the 
determination of refractive indices. 
4. Before the insertion of the plate, the wave of light belonging to a particular 
colour, and to a particular point of the slit, or at least a certain portion of it limited 
by the boundaries of the fluid, after being refracted at the two surfaces of the prism, 
enters the object-glass witli an unbroken front. The front is here called unbroken, 
because the modification which the wave suffers at its edges is not contemplated. 
According to geometrical optics, the light after entering the object-glass is brought 
to a point near the principal focus, spherical aberration being neglected ; according 
to the undulatory theory, it forms a small, but slightly diffused image of the point 
from which it came. The succession of these images due to the several points of 
the slit forms the image of the slit for the colour considered, and the succession of 
coloured images forms the spectrum, the waves for the different colours covering 
almost exactly the same portion of the object-glass, but differing from one another 
in direction. 
Apart from all theory, it is certain that the image of a point or line of homo- 
geneous light seen with a small aperture is diffused. As the aperture is gradually 
widened the extent of diffusion decreases continuously, and at last becomes insen- 
sible. The perfect continuity, however, of the phenomenon shows that the true and 
complete explanation, whatever it may be, of the narrow image seen with a broad 
aperture, ought also to explain the diffused image seen with a narrow aperture. The 
undulatory theory explains perfectly both the one and the other, and even predicts 
the distribution of the illumination in the image seen with an aperture of given form, 
which is what no other theory has ever attempted. 
As an instance of the effect of diffusion in an image, may be mentioned the ob- 
served fact that the definition of a telescope is impaired by contracting the aperture. 
With a moderate aperture, however, the diffusion is so slight as not to prevent fine 
objects, such as the fixed lines of the spectrum, from being well seen. 
For the present, however, let us suppose the light entering the telescope to consist 
of rays which are brought accurately to a focus, but which nevertheless interfere. 
When the plate is inserted into the fluid the front of a wave entering the object- 
glass will no longer be unbroken, but will present as it were a fault, in consequence 
of the retardation produced by the plate. Let R be this retardation measured by 
2 H 2 
