xviii. 4] INTERPRETATION OF THE QUANTUM 251 
the two systems of mechanics appear so different in their origin, 
and in the point of view adopted, they lead to practically identical 
results, and it has been shown that mathematically they are almost 
equivalent. To the physicist the wave mechanics makes a stronger 
appeal than the matrix mechanics, because it seems to provide the 
possibility of an image of the processes involved, and does not 
rely exclusively on operations carried out by means of mathemati 
cal symbols which convey no definite physical idea. 
In this connection it is of interest to recall the suggestive work 
of Carl A. Bjerknes, which has been extended and generalized 
by his son, V. Bjerknes.* In experiments exhibited at the Paris 
Electrical Exhibition of 1881 most of the well-known actions 
between currents and magnets were imitated by means of bodies 
pulsating and vibrating in water and other fluids. “ A very 
remarkable analogy became evident between the field of motion 
in a fluid and the electric or magnetic field of force : the bodies 
produced fields of motion of precisely the same geometric structure 
as static or stationary electric or magnetic fields. Moreover, they 
exert apparent actions-at-a-distance upon each other, equal to, 
but—most curiously—opposite to the actions-at-a-distance 
between the corresponding bodies in the electric or magnetic 
fields.” The analogy maybe pursued in the most minute details, 
but it is necessary to emphasize the fact that although there is 
a direct geometric analogy between the hydrodynamic field and 
the electric or magnetic field, the dynamic analogy is inverse. 
In the new wave theory of matter the material point is con 
ceived as a singularity in a wave. The chief difference between 
the work of de Broglie and that of Schrödinger is that the former 
is dealing with progressive waves, while the latter is thinking 
of stationary wave motion. 
“ With de Broglie the concept of the electron or other element 
of energy is primary, whilst that of the phase-wave is secondary, 
but with Schrödinger the position is reversed. In his theory the 
principal part is played by the so-called wave-function yi, which 
determines the phase-waves and is a solution of a linear partial 
differential equation of the second order of the type of the wave- 
equation in classical mathematical physics. The electron, or 
element of energy, becomes merely a focus of a group of phase- 
waves, and in the atom, where the focus is ill-defined, it loses its 
individuality altogether. In order to re-establish contact with 
electro-dynamics, Schrödinger finds it necessary to introduce a 
new and at first sight arbitrary hypothesis defining the density 
of electric charge in terms of the wave-function, but justified by 
the results to which it has led.” | 
* V. K. F. Bjerknes, Nature, voi. 114, p. 47 2 > I9 2 4- 
f G. A. Schott, Nature, voi. 119, p. 820, 1927.