On Momentum in the Electric Field. 351 
As Schuster has especially emphasized, the question here 
is really one of the greup-velocity. Approximately homo- 
geneous light consists of a train of waves in which the 
amplitude and wave-length slowly vary. <A local peculiarity 
of amplitude or wave-length travels in a dispersive medium 
with the group and not with the wave-velocity ; and the rela- 
tive retardation with which we are concerned is the relative 
retardation of the groups. From this point of view it is 
obvious that, what is to be made to vanish is not (1) in which 
# is the ratio of wave-velocities V,/V, but that derived from 
it by replacing w by U,/U, or by V,/U, where U is the 
group-velocity in the dispersive medium. In vacuum the 
distinction between U, and V, disappears, but in the dis- 
persive medium 
el 2p a reais (3) 
k being the reciprocal of the wave-length in the medeum. 
If we denote as usual the wave-length in vacuo by }, 
Ver, Drips: (bi 205 Vi 
al Gume Edt iba ou: (7) 
Accordingly 
Ne dk a aiey du 
—_ = = J =p—rv. Mae 
Wea a(nV).> diy 8 ax (8) 
Substituting this for ~ in (1), we see that the position of 
the most distinct band is given by 
R+(u-1—-rF yD=0, Bika tre, (0) 
in agreement with (5). 
XXXIV. On Momentum in the Electric Field. By J. J. 
Toomson, M.A., PRS, Cavendish Professor of Physics, 
Cambridge T. 
HAVE for some years made considerable use of the 
principle proved in ‘ Recent Researches,’ p. 9, that 
momentum as well as energy is distributed throughout the 
electromagnetic field, and that changes in the momenta of 
magnets, of circuits conveying electrical currents, and other 
material systems in that field are accompanied by equal and 
opposite changes in the momentum of the field itself. Thus 
* “Theory of Sound,’ § 191, 1877. 
t+ Communicated by the Author. 
