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Physics. — ^Simplifed Theorij of Electrical and Optical Pheno- 

 mena in Moving Si/sfe>iis'\ By Prof. H. A. Lorentz. 



§ 1. Til former investigations I luivo assumed that, in all elec- 

 trical and optical phenomena, taking place in ponderable matter, we 

 have to do with small charged particles or ions, having determinate 

 positions of equilibrium in dielectrics, but free to move in conductors 

 except in so far as there is a resistance, depending on their velo- 

 cities. According to these views an electric current in a conductor 

 is to be considered as a progressive motion of the ions, and a 

 dielectric polarization in a non-conductor as a displacement of the 

 ions from their positions of equilibrium. The ions were supposed to 

 be perfectly permeable to the aether, so that they can move while 

 the aether remains at rest. I applied to the aether the ordinary 

 electromagnetic equations, and to the ions certain other equations 

 which seemed to present themselves rather naturally. In this way 

 I arrived at a system of formulae which were found sufficient to 

 account for a number of phenomena. 



In the course of the investigation some artifices served to shorten 

 the mathematical treatment. I shall now show that the theory may 

 be still further simplified if the fundamental equations are imme- 

 diately transformed i-i an appropriate manner. 



§ 2. I shall start from the same hypotheses and introduce the 

 .same notations as in my „Yersuch einer Theorie der electrischen uud 

 optischen Erscheinungen in bewegten Korpern". Thus, b and Jp will 

 represent the dielectric displacement and the magnetic force, (> the 

 density to which the ponderable matter is charged, » the velocity 

 of this matter, and €' the force acting on it per unit charge (electric 

 force). It is only in the interior of the iotis that the density (j differs 

 from 0; for simplicity's sake I shall take it to be a continuous 

 function of the coordinates, even at the surface of the ions. Finally, 

 I suppose that each clement of an ion retains its charge while it 

 moves. 



If, now, r be the velocity of light in the aether, the fundamental 

 equations will bu 



Divb = (>, (I^) 



I)iv.^=zO, (Ila) 



Ifot Sp = i 71 i> V i- i :i't> (Ilia) 



4 .1 F2 i?o« b = — .P) , (17^) 



^ = 4>7tV^b + lü.^] (Va) 



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