formed in the Prismatic Spectrum. 85 



*£=£• } 



2e' x \ c 





Here, if — < — , (which is the case, the image being form- 

 ed in the focus, so that in fact we might assume a = 0,) it 

 follows that when b and y have the same sign, this expression 

 will be negative ; that is, for the ray which has b and y on the 

 same side, or is nearest the axis after passing the focus, the 

 route will be the shortest. The difference will be very small, 

 and will vary slightly for the different rays of the spectrum. 



(14.) This difference of retardation in the several rays of 

 each primary pencil, combined with the obvious principle 

 laid down by Mr. F. Talbot, appears to me to supply an ex- 

 planation of the phenomena. 



The whole effect in these experiments is made up of two 

 parts, the original retardation, and that superinduced by the 

 plate. If the previously least retarded ray be intercepted, 

 we take the difference, if the most retarded, the sum of the 

 two effects. 



When we apply the plate, the whole resulting retardation 

 may fall within the limits, (before mentioned, § 6.) or not, ac- 

 cording to the magnitude of the two retardations, and accord- 

 ing as we take their sum or difference. If it be beyond the 

 limits for one portion of the pencil, it may be within them 

 for another. 



In general, in the original form of the experiment, that is, 

 for plates of ordinary thickness, the difference falls within the 

 limits, though the sum is beyond them, for all portions of the 

 pencil. But with a very thin plate, the sum may also be 

 within the limits for those parts of the pencil whose difference 

 of retardation is small: Or, in other words, with plates of a 

 certain thickness, the retardation is too great to give bands 

 with any portion of the pencils, when the plate is applied to 

 the previously most retarded side : but it will give bands 

 with some portion when applied to the previously least re- 

 tarded side. 



On the other hand, if an extremely thin plate be applied to 

 the most retarded side, it will still give bands with one portion 

 of the pencils, as well as when applied to the least retarded 

 side with other portions. 



Oxford, July 5, 1840. 



