242 MR. STOKES ON THE THEORY OF CERTAIN BANDS SEEN IN THE SPECTRUM. 
Now in passing from one band to its consecutive, f changes by 2 t, and | by e, if e be 
the linear breadth of a band ; and for this small change of | we may suppose the 
changes of f and | proportional, or but — Hence the best aperture for a 
given thickness is that for which 
If ^=0 and Ti=h, this equation becomes 
The difference of distances of a point in the plane xy whose coordinates are 0 
from the centres of the portions of the object-glass which are covered by the inter- 
fering streams, is nearly 
or^(4g+A-{-/r); 
and if I be the change of | when this difference changes by X, 
7 . 7 SAf 
— -Y' 
Hence, when the thickness of the plate is equal to the best thickness, e=S, or the 
interval between the bands seen in the spectrum is equal to the interval between the 
bands formed by the interference of two streams of light, of the colour considered, 
coming from a luminous line seen in focus, and entering the object-glass through 
two very narrow slits parallel to the axis of y, and situated in the middle of the two 
interfering streams respectively. This affords a ready mode of remembering and 
calculating the best thickness of plate for a given aperture, or the best aperture for a 
given thickness of plate. 
17. According to the preceding explanation, no bands would be formed in Sir David 
Brewster’s experiment when the plate was held on the side of the spectrum on 
which the red was seen. Mr. Airy has endeavoured to explain the existence of bands 
under such circumstances*. Mr. Airy appears to speak doubtfully of his explanation, 
and in fact to offer it as little more than a conjecture to account for an observed 
phenomenon. In the experiments of Mr. Talbot and Mr. Airy, bands appear to have 
been seen when the retarding plate was held at the red side of the spectrum ; whereas 
Sir David Brewster has stated that he has repeatedly looked for the bands under 
these circumstances and has never been able to find the least trace of them ; and he 
considers the bands seen by Mr. Talbot and Mr. Airy in this case to be of the 
nature of Newton’s rings. While so much uncertainty exists as to the experimental 
circumstances under which the bands are seen when the retarding plate is held at the 
red side of the spectrum, if indeed they are seen at all, it does not seem to be de- 
sirable to enter into speculations as to the cause of their existence. 
* Philosophical Transactions for 1841, Part I. p. 6. 
