290 Proceedings of the Royal Society of Edinburgh. [Sess. 
XV. — Illustration of the Modus Operandi of the Prism. By George 
Green, D.Sc., Assistant to the Professor of Natural Philosophy in 
the University of Glasgow. Communicated by Professor A. 
Gray, F.R.S. 
(MS. received December 1, 1910. Read January 9, 1911.) 
§ 1. It was proved by Gouy * and Lord Rayleigh j* that interference may 
be observed by the aid of the spectroscope even if the incident light were 
entirely irregular, consisting, for instance, of an irregular succession of 
impulses. This means that the “ regularity ” of the emergent light arising 
from an impulse is due to the spectroscope itself, and the extent to which 
interference may be observed is limited only by the resolving power of the 
instrument used. The greater the resolving power, the more homogeneous 
is the light in any part of the spectrum. The question regarding the 
modus operandi of the prism has been further dealt with by Professor 
Schuster in his paper “ On Interference Phenomena ” {Phil. Mag., vol. 
xxxvii., 1894) and, later, in his explanation of Talbot’s bands by con- 
sideration of group- velocities {Phil. Mag., vol. vii., 1904). In a paper by 
J. S. Ames, entitled “ An Elementary Discussion of the Action of a Prism 
on White Light ” {Astrophysical Journal, vol. xxii., 1905), a view similar to 
that of Professor Schuster is adopted. The theory given in these papers is 
now regarded as complete, but it is difficult to form from it a definite general 
impression regarding the wave-system produced by a prism from a given 
impulse; and as this may be useful, the object of this short note is to 
illustrate the action of the prism by associating with it a definite wave- 
pattern. 
§ 2. Consider the case of an incident light pulse in a plane perpendicular 
to the paper, whose trace is ac (fig. 1), when first it meets the side of the 
prism at a. The pulse travels along the face of the prism from a to b with 
uniform velocity, and the problem is to determine the wave-system which 
it originates, and to follow the configuration of each group of waves 
characterised by a given wave-length after emergence. The wave-system 
within the prism can be determined directly by means of Fourier’s theorem, 
provided the wave-velocity of all the wave-trains, into which the original 
disturbance can be analysed, is known ; or more conveniently perhaps by 
the principle of stationary phase as applied by Dr T. H. Havelock in his 
* Journal de Physique (2), v., 1886. t Phil. Mag., vol. xxvii. p. 463, 1889. 
