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 ,[1] there is a certain amount of electromagnetic momentum. If we represent this, in direction and magnitude, by a vector , the couple in question will be determined by the vector product[2]
. | (1) |
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 are given[3] 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 ; it tends to turn the condenser into such a position that the plates are parallel to the Earth's motion.
In the apparatus of Trouton and Noble 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. Poincaré[4] has objected
- ↑ A vector will be denoted by a German letter, its magnitude by the corresponding Latin letter.
- ↑ See my article: Weiterbildung der Maxwell'schen Theorie. Elektronentheorie. Encyclopädie V 14, § 21, a. (This article will be quoted as M.E.)
- ↑ M. E. § 56, c.
- ↑ Poincaré, Rapports du Congrés de physique de 1900, Paris, 1, p. 22, 23