Page:Electromagnetic phenomena.djvu/2

 of electrons, unless it be modified by some new hypothesis, would undoubtedly require the existence of such a couple. In order to see this, it will suffice to consider a condenser with aether as dielectricum. It may be shown that in every electrostatic system, moving with a velocity $$\mathfrak{w}$$, there is a certain amount of electromagnetic momentum. If we represent this, in direction and magnitude, by a vector $$\mathfrak{G}$$, the couple in question will be determined by the vector product

Now, if the axis of z is chosen perpendicular to the condenser plates, the velocity w having any direction we like, and if U is the energy of the condenser, calculated on the ordinary way, the components of $$\mathfrak{G}$$ are given by the following formulae, which are exact up to the first order:

Substituting these values in (1), we get for the components of the couple, up to terms of the second order,

These expressions show that the axis of the couple lies in the plane of the plates, perpendicular to the translation. If α is the angle between the velocity and the normal to the plates, the moment of the couple will be $$\frac{U}{c^{2}}w^{2}\sin\ 2\alpha$$; it tends to turn the condenser into such a position that the plates are parallel to the Earth's motion.

In the apparatus of and  the condenser was fixed to the beam of a torsion-balance, sufficiently delicate to be deflected by a couple of the above order of magnitude. No effect could however be observed.

§ 2. The experiment of which I have spoken are not the only reason for which a new examination of the problems connected with the motion of the Earth is desirable. has objected