1910-11.] Illustration of the Modus Operandi of the Prism. 291 
paper on “ The Propagation of Groups of Waves in Dispersive Media ” 
( Proc . Roy. Soc. Lon., lxxxi., 1908). As it is only the general features of 
the wave-system after emergence that are of interest to us, it is unnecessary 
Fig. 1. 
to consider effects due to the plane boundaries of the prism not touched by 
the incident light pulse. 
§ 3. The problem in hydrodynamics analogous to that of § 2 is to 
determine the wave-system arising from the application of a point- 
pressure which moves with constant velocity over the water surface. In 
each case the disturbance can be determined by the consideration of wave- 
trains whose velocity varies with the wave-length, and we can therefore 
take the ship-waves pattern to illustrate the main features of light- 
propagation through the prism. The analogy here referred to was also 
remarked upon by Lord Rayleigh with respect to the origin of the prismatic 
colours {Phil. Mag., Oct. 1905). By means of it the expression for the 
number of waves having a certain length X arising from the action of a 
given pulse is easily obtained, provided the greatest thickness of the prism 
traversed by waves of the corresponding length in glass is known. 
The ship-waves pattern indicated by the curved lines of constant phase 
in the accompanying diagram, fig. 2, which is taken from Lord Kelvin’s 
paper on “ Deep-sea Ship-waves” {Proc. R.S.E., vol. xxv., 1904-1905), gives, 
of course, the wave-system built up after a long ajiplication of the moving 
point-pressure. When the pulse is applied for only a short time, few of the 
transverse waves have had time to form, and there is, in addition, wave- 
disturbance beyond the line of cusps OC on either side. But for the 
application of the diagram which we intend to make, the argument is the 
same whether the pulse be of long or short application, as it involves only 
the principle of stationary phase in relation to each group of diverging 
waves of definite wave-length chosen for observation. 
§ 4. In the diagram (fig. 2), AO is the line of motion of the ship, and the 
straight line OC is the line of cusps beyond which there is no disturbance. 
The curved lines OC, OD, OE, are lines of equal phase in the diverging 
wave-system. For convenience they may be regarded as three successive 
