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( 809 ) Physics. — “Electromagnetic phenomena in a system moving with any velocity smaller than that of light” By Prof. H. A. Lorentz. § 1. The problem of determining the influence exerted on electric and optical phenomena by a translation, such as all systems have in virtue of the Earth’s annual motion, admits of a comparatively simple solution, so long as only those terms need be taken into account, which are proportional to the first power of the ratio between the velocity of translation to and the velocity of light c. Cases in which quantities of the second order, i.e. of the order may be perceptible, present more difficulties. The first example of this kind is Michelson’s well known interference-experiment, the negative result of which has led Fitz Gerald and myself to the conclusion tliat the dimensions of solid bodies are slightly altered by their motion through the aether. Some new experiments in which a second order effect was sought for have recently been published. Rayleigh ') and Brace ^{a}) have examined the question whether the Earth’s motion may cause a body to become doubly refracting; at first sight this might be expected, if the just mentioned change of dimensions is admitted. Both physicists have however come to a negative result. In the second place Trouton and Noble ’) have endeavoured to detect a turning couple acting on a charged condenser, whose plates make a certain angle with the direction of translation. The theory ^{5}) Rayleigh, Phil. Mag. (6) 4 (1902), p. 678. ^{2}) Brace, Phil. Mag. (6) 7 (1904), p. 317. ^{!}) Trodton and Noble, London Roy. Soc. Trans. A 205 (1903), p. 165. | ( 810 ) 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 w ^{x}), 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^{3}) .........(1)Now, if the axis of z is chosen perpendicular to the condenser plates, the velocity u> having any direction we like, and if U is the energy of the condenser, calculated in the ordinary way, the components of © 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 a is the angle between the velocity and the normal to the plates, the moment of the couplc will be; it tends to turn the condenser into such a position that the plates are parallel to (he 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 experiments of which I have spoken are not the only reason for which a new examination of the problems connected with the motion of the Earlli is desirable. Poincare^{4}) has objected ^{]}) A vector will be denoted by a German letter, its hiagnitudp by the corre spo'nding Latin letter. ^{2}) See my article: Weiterbildung der Maxwell’schen Theorie. Electronentlieorie in the Mathem. Encyclopadie V 14, § 21, a. (This ai ticle will bp quoted asM.E.) ^{s}) M. E. § 56, c. ’ ^{4}) Poincar£, Rapports du Congres de physique de 1900, Paris, 1, p. 22, 23. |