( m ) 
the electromagnetic action exerted by a particle is found to be wholly 
determined by itS' electric moment. Therefore, in considering the 
influence of a particle on the propagation of light, we may replace 
it by a single electron, to which we may assign an arbitrarily chosen 
charge e and whose displacements x, y, z have such values that the 
products ex, ey, ez are equal to the components of the electric 
moment of the particle. This imaginary electron may be called the 
“equivalent electron”. 
If a particle were outside the magnetic field (but in the position 
it really has in the field) and if it were free from resistances and 
from the influence of the other particles, its electrons would be able 
to vibrate in a number of definite modes. We shall suppose that, 
in these circumstances, there are certain groups of “fundamental 
vibrations”, of such a kind that all the vibrations belonging to one 
and the same group have a common frequency n 0 , corresponding 
to a definite spectral line. Whenever it is necessary, we shall 
distinguish the different groups from each other by the indices 
a, by c ,..., and we shall denote by k the number of modes of 
vibration in a group. 
Let us next suppose the magnetic field to be excited, without, 
however, as yet introducing the resistances and the mutual actions 
between the particles. Then, instead of any group consisting of k 
modes of vibration with equal frequencies n 0 , we shall have k modes 
whose frequencies are unequal, all differing slightly from this original 
common value. In order to distinguish these k modes, we shall 
assign to each of them an index (x), which we shall write on the 
right-hand side and at the top of the symbols relating to the mode 
in question. 
Now, in each of these fundamental vibrations that can go on in 
the magnetic field under the circumstances just stated, the equivalent 
electron will have a motion which, according to the theory of vibrating 
systems, must be, generally speaking, a harmonic elliptic vibratioD. 
It can be further specified, if we take into account the states of 
polarization observed in the ZEEMAN-effect. From these one can 
infer that the path of the equivalent electron must be, either a 
straight line in the direction of the field, or a circle whose plane is 
at right angles to it. The index x, will be applied to those 
fundamental modes for which the first case occurs, and similarly the 
index x 2 to the second case; if we want to distinguish whether the 
circular motion of the equivalent electron is in the direction coire- 
sponding to that of the lines of force, or in the opposite one, we 
shall use the index x 2 + or x 2 _. However, in order not to encumber 
