6 Prof. A. Schuster on a Simple 
lie near some surface G G’ which moves forward with the group 
velocity. I have shown, in a paper communicated to the recent 
meeting of the British Association, that the shape of the 
impulse changes periodically and alternately passes through 
its original shape and one exactly equal 
but opposite in direction. If now the Fig. 3. 
impulse has passed through the prism li 
and a wave-front for a homogeneous 
wave of length A would lie in the direction 
RS, the “impulses”? will be confined at 
toa region immediately surrounding a 
plane HS, the position of which may 
be calculated by the ordinary law of re- 
fraction, substituting the group velocity 
for the wave velocity. But on HS the 
impulsive motion is not uniform, but H 
alters periodically from the original type 
to that which is equal and opposite to it. 7“ 
Hence if the emergent beam be received s 
by a lens, the disturbance at the focus 
of the lens consists of a periodic motion which is the more 
homogeneous the greater the resolving power of the prism. 
It will be noticed that this explanation of the modus ope- 
randt of a prism differs materially from that given by 
Dr. J. Larmor (‘ Aither and Matter,’ p. 248); but as we may 
imagine continuous media of such elastic properties as to 
give dispersion, the true explanation must be independent 
of the sympathetic vibrations which Dr. Larmor calls to his 
aid. To calculate the angle between RS and HS, we note 
that H BR is equal to the space passed over in air in the time 
equal to the difference between that necessary to traverse the 
thickness ¢ of the prism when the velocity is that of a 
homogeneous wave and when it is that of the group. Hence 
U being the group velocity, V the wave velocity in vacuo, 
and V’ the wave velocity in the prism, 
t t 
Vi 
7 ye ee 
and if w= V/V’ be the refractive index, 
j 
= (V’—U). 
