# H. A. Lorentz. Electromagnetic phenomena in a system moving with any velocity smaller than that of light. // Proceedings Royal Acad., Amsterdam. Vol. VI., 1904

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Plate N°. 19. a = 0,05867, b = 0,2591.

 g V ft Observed. Calculated by R. Dili'. Calculated by L. Diff. Calculal R. ted by L. 0.1495 0.0104 0 0388 + 16 0.0379 +25 0.990 0.954 0.199 0.0529 0 0527 2 0 0522 + 7 0.969 0.923 0.247 0 0678 0 0075 + 3> 0.0674 + 4 0.939 0.888 0.296 0.0834 0 0842 — 8 0.0844 —10 0 902 0.849 0.3435 0.1019 0.1022 — 3 0.1026 — 7 0 862 0.811 0.391 0.1219 0.1222 — 3 0 1226 — 7 0 822 0.773 0.437 0.1429 0.1434 — 5 0 1437 — 8 0.782 0.736 0.4825 0 1060 0.1665 — 5 0.1664 — 4 0.744 0.702 0.5205 0 1916 0.1906 + io 0.1902 +14 0.709 0.671

has been made by Trouton ’) at the suggestion of Fitz Gerald, and in which it was tried to observe the existence of a sudden impulse acting on a condenser at the moment of charging or discharging; for this purpose the condenser was suspended by a torsion-balance, with its plates parallel to the Earth’s motion. For forming an estimate of the effect that may be expected, it will suffice to consider a condenser with aether as dielectricum. Now, if the apparatus is charged, there will be (\$ 1) an electromagnetic momentum

(Terms of the third and higher orders are here neglected). This momentum being produced at the moment of charging, and disappearing at that of discharging, the condenser must experience in the first case an impulse — © and in the second an impulse + ©.

However Trouton has not been able to observe these jerks.

I believe it may be shown (though his calculations have led him to a different conclusion) that the sensibility of the appai’atus was far from sufficient for the object Trouton had in view.

Representing, as before, by U the energy of the charged condenser

3) Trouton, Dublin Roy. Soc. Trans. (2) 7 (1902), p. 379 (This paper may also be found in The scientific writings of Fitz Gerald, edited by Larmor, Dublin and London 1902, p. 557).

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in the state of rest, and by U -j- XJ' the energy in the slate of motion, we have by the formulae of this paper, up to the terms of the second order,

an expression, agreeing in order of magnitude with the value used by Trouton for estimating the effect.

U'

The intensity of the sudden jerk 01* impulse will therefore be —.

Now, supposing the apparatus to be initially at rest, we may compare the deflexion «, produced by this impulse, to the deflexion a' which may be given to the torsion-balance by means of a constant couple K, acting during half the vibration time. We may also consider the case in which a swinging motion has already been set up; then the impulse, applied at the moment in which the apparatus passes through the position of equilibrium, will alter the amplitude by a certain amount and a similar effect (>” may be caused by letting the couple K act during the swing from one extreme position to the other. Let T be the period of swinging and I the distance from the condenser to the thread of the torsion-balance. Then it is easily found that

.......(39)

According to Trouton’s statements U' amounted to one or two ergs, and the smallest couple by which a sensible deflexion could be produced was estimated at 7,5 C. Gr. S.-units. If we substitute this value for K and lake into account that the velocity of the Earth’s motion is 3 X 10" c.M. per sec., we immediately see that (39) must have been a very small fraction.