208 
THE QUANTUM [xv. i 
If we are observing in the direction of the field, electrons moving 
in a clockwise direction will have their frequency increased. 
We must now consider how the light waves are affected by 
the motion of the electrons. In the classical theory a vibrating 
electron gives rise to an electromagnetic wave of the same fre 
quency as that of the vibration. First we consider the light 
emitted parallel to the lines of force. In practice, to show this 
longitudinal effect the pole pieces of the magnet would have to 
be bored through, so that we could observe along the lines of 
magnetic force. The result may easily be seen from an examin 
ation of the model. The original light splits up into two com 
ponents which are circularly polarized, the polarization of one 
component being right-handed and the other left-handed. In 
accordance with our equation there will be a difference in fre 
quency due to the magnetic field equal to /\v, and so we get the 
longitudinal effect shown in the diagram (Fig. 26). 
In the next place let us consider the light which is emitted 
in a direction normal to the lines of force, for example, in the 
direction OX in our original figure. The vibrations parallel to 
the lines of force give rise to a plane polarized ray of the same 
frequency as the original ray. In the absence of the magnetic 
field the light which is due to the two circular motions will also 
be plane polarized, because the electron orbits are, as it were, 
seen sideways. Consequently we get plane polarized light in the 
two components, which are displaced by an equal amount corre 
sponding to the signs + and — in the formula. We see, then, 
that the simple theory predicts in the transversal effect the nor 
mal triplet. It should be mentioned that the observations of 
the Zeeman effect enable us to determine the ratio of e to m 0> 
and the first experiments gave the result that e/m 0 is of the order 
of magnitude io 7 E.M.U. per gram (1896). In 1897 Zeeman 
found a more accurate value, i-6 x 10 7 . Lohmann,* from 
observations on helium, obtained the value 1-737 X 10 7 . Weiss 
and Cotton,f from measurements on the blue line of zinc (wave 
length 4680) found 1*767 x 10 7 , and Gmelin J very nearly the 
same value, 1-771 X 10 7 . These values, which were the first 
determinations of e/m a from optical observations, agree very 
closely with the results obtained in other ways. In fact, the 
mean value found from other observations is 1-77 x 10 7 E.M.U. 
per gram. 
We may note, too, that the Zeeman effect enables us to 
determine the sign of the charge carried by the vibrating elec 
tron, and shows that the charge is negative. 
* Lohmann, Phys. Zeits., vol. 7, p. 809, 1906. 
t Weiss and Cotton, Journ. de Phys., vol. 6, p. 429, 1907. 
X Gmelin, Ann. d. Physik, vol. 28, p. 1079, 1909.