The Two Disturbances Of The Aether

Each of the two disturbances of the aether is propagated at the speed of light.

By itself, it obeys the ordinary laws of the electromagnetic field.

These laws are expressed in the simplest form if, besides the dielectric displacement d, we consider the magnetic force H. These together determine one state of the aether or one field.

With this, I introduce 2 pairs of vectors:

1. The one d belonging to the field that is produced by the positive ions
2. The other pair d indicates the state of the aether which is called into existence by the negative ions.

I have 2 sets of equations:

1. one for d , H
2. the other for d ′ , H,

having the form which I have used in former papers[1] for the equations of the electromagnetic field, and which is founded on the assumption that the ions are perfectly permeable to the aether and that they can be displaced without dragging the aether along with them.

I shall immediately take this general case of moving particles.

Let us further suppose the charges to be distributed with finite volume-density, and let the units in which these are expressed be chosen in such a way that, in a body which exerts no electrical actions, the total amount of the positive charges has the same numerical value as that of the negative charges.

Let ϱ be the density of the positive, and ϱ ′ {\displaystyle \varrho ‘} {\displaystyle \varrho ‘} that of the negative charges, the first number being positive and the second negative.

Let v {\displaystyle {\mathfrak {v}}} {\displaystyle {\mathfrak {v}}} (or v ′ {\displaystyle {\mathfrak {v}}’} {\displaystyle {\mathfrak {v}}’}) be the velocity of an ion.

Then the equations for the state ( d , H ) (II)

In the ordinary theory of electromagnetism, the force acting on a particle, moving with velocity v {\displaystyle {\mathfrak {v}}} {\displaystyle {\mathfrak {v}}}, is

per unit charge.[3]

In the modified theory, we shall suppose that a positively electrified particle with charge e experiences a force (10)

on account of the field ( d , H ) {\displaystyle ({\mathfrak {d}},{\mathfrak {H}})} {\displaystyle ({\mathfrak {d}},{\mathfrak {H}})}, and a force k 2 = β { 4 π V 2 d ′ + [ v . H ′ ] } e (11)

on account of the field ( d ′ , H ′ ) \beta having slightly different values.

For the forces, exerted on a negatively charged particle I shall write (12)

and (13)

expressing by these formulae that e is acted on by ( d , H in the same way as e’ by ( d ′ , H ′ , and vice versa.