( 8 1 i ) 



to llic (wisliiim' lliooi'v of ('l(M-li-i(' ;ni(l oplical plKMioniciia in nio\iii|L;' 

 hodios thai, in oi-dcr lo explain AIk ni'.i.sox's noualixe rcsnll, (he 

 iiitrodnclion ol' a new li vpolliesis lias Ixmmi rcNinircd, and llial llie 

 same necessity niav occnr each time new facts will he l»rou,i>iit to light. 

 Snrelv, this conrse of inventing K|)eciai hypotheses foi- each new expe- 

 rimental i-esnit is some\vhat artificial. It wonid \)o more satisfactory, 

 if it Avere possible to show, by means of certain fnndamental assnni|)tions, 

 and withont neglecting terms of one (n-der of magnitnde oi- another, 

 that ma]iy electromagnetic actions are entirely independent of the 

 motion of the system. Some years ago, I have ah-eady songlit to 

 frame a theory of this kind '). I helie\'e now to l^e able to treat 

 the snbject with a better resnlt. The only restriction as regards the 

 velocity will be that it be smaller than that of light. 



§ 3. I shall start from the fnndamental eqnations of the theory 

 of electrons '^). Let b be the dielectric displacement in the aether, 

 h the magnetic force, q the volnme-density of the chai-ge of an 

 electron, i> the velocity of a point of sncli a particle, and f the 

 electric force, i. e. the force, reckoned ])ei- unit charge, which is 

 exerted by the aether on a volnme-element of an electron. 'J'hen, 

 if we nse a fixed s\stem of coordinates, 



{^) 



1 shall now sn|)pose that the system as a whole mo\es in the 

 dire<*tion of ,/■ with a constant \elocify ti\ and I shall denote bij u 

 any \'elocily a point of an electron may lin\e in addition to this, 

 so that 



If tlu^ eipiatiojis (2) are at the same time i-efei-red to axes moxing 

 with the system, they become 



1) LoRENTZ, Ziltingsverslaü;' Al<ad. v. Wcl.. 7 (,1S91»), p. 507; Amsterdam I^roc, 

 1S'»8— •.»'.», p. 427. 

 -; iM. E., i5 2. 



