# 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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least squares, the coefficients and k3 having been determined in such a way, that the values of v, calculated, for each observed £, from Kaufmann’s equations (34), agree as closely as may be with the observed values of •»;.

I have determined by the same condition, likewise using the method of least squares, the constants a and b in the formula

r

which may be deduced from my equations (36) and (37). Knowing a and b, I find /? for each measurement by means of the relation

For two plates on which Kaufmann had measured the electric and magnetic deflexions, the results are as follows, the deflexions being given in centimeters.

I have not found time for calculating the other tables in Kaufmann’s paper. As they begin, like the table for Plate 15, with a rather large negative difference between the values of tj which have been deduced from the observations and calculated by Runge, we may expect a satisfactory agreement with my formulae.

§ 14. I take this opportunity for mentioning an experiment that

Plate N°. 15. a — 0,06489, b = 0,3039.

 V 0 s 1 Observed. Calculated by R. Diff. Calculated by L. Dill’. Calculat R. ,ed by L 0.1495 0.0388 0 0404 — 16 0.0400 — 12 0.987 0.951 0.190 0.0548 0 0550 — 2 0.0552 — 4 0.964 0.918 0.2475 0 0716 0.0710 + 6 0.0715 + 1 0.930 0.881 0.296 0 0896 0.0887 + 9 0.0895 + 1 0.889 0.842 0.3135 0.1080 0.-1081 — •1 0.1090 — 10 0 847 0.803 0.391 0.1290 0.1297 — 7 0.1305 — 15 0.804 0.763 0.437 0.4524 0.1527 — 3 0.1532 - 8 0.763 0.727 0.48-25 0.1788 0.1777 + 11 0.1777 + H 0.724 0.692 0.5265 0.2033 0.2039 — 6 0.2033 0 0.688 0.660

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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).