286 CARNEGIE INSTITUTION OF WASHINGTON. 



This result, like Maxwell's theorem, is correct to quantities of the first 



v 

 order in -. Reference is made to results obtained by Budde, Lorentz, and 



v 

 others, which are implicit, to quantities of the first order in — , in Maxwell's 



theorem, the approximate character of which is due to its being based on a 

 principle of relativity assuming equality of electromotive intensity and mag- 

 netic induction to fixed and moving observers. 



The permeability n differs from unity so slightly for all insulators that it 

 is impossible at present to distinguish experimentally between P and Pi. 

 By embedding a large number of small steel spheres in wax, however, M. 

 Wilson and H. A. Wilson (Roy. Soc. Proc. A, 89, 1914, p. 99) formed a com- 

 posite dielectric whose mean permeability, for large volumes, was much 

 greater than unity. On the assumption that this procedure is justifiable, 

 the results of experiments which they made on the electric effect of moving 

 the composite substance in a magnetic field support the above equation for P. 

 M. and H. A. Wilson concluded that their results therefore supported the 

 (Einstein-Minkowski) principle of relativity. As shown above, however, the 

 result is entirely independent of this special theory, and follows from Maxwell's 

 theorem based on a much older, though less exact, relativity principle. 



[An abstract of the paper as presented at the American Physical Society 

 meeting in April 1922 will be found in Phys. Rev., vol. 20, 114 (July 1922)'.] 



Electric fields due to the motion of constant electromagnetic systems. S. J. Barnett. 



Maxwell's equation for the electromotive intensity and a theorem derived 

 from it in §600 of his Treatise are applied to the investigation of a number of 

 simple but fundamental fields due to the motion of constant electromagnetic 

 systems. According to Maxwell's theorem, the motion produces an electric 



field whose polar part is derivable from the potential <p = -(Av), where A is 



the vector potential of the system, v its velocity, and c the velocity of light. 



If a denotes the electric density produced by the motion at any part of the 



system where the current density is i, and if Q denotes the total electric 



moment produced, while M denotes the magnetic moment of the system, it 



(iv) 1 



follows immediately from Maxwell's theorem that o=^~ and Q = - [vM]. 



c c 



V 



The three equations are correct to the first order in — . The second result 



c 



was obtained from Clausius's theory in 1880 by E. Budde; the correspond- 



v 

 ing result with the correction for the second order term in — was obtained 



C 



by Lorentz in 1895, and by Silberstein from Minkowski's equations in 1914. 

 The third was recently given for a special case, but with the wrong sign, by 

 Swann. For a constant (originally) unelectrified system, if B denotes the 



dA 

 magnetic induction, and E the electromotive intensity, — - = — (vv)A, and 



at 



E = -(w)A — Sj(Av)=-[Bv\. A number of special cases are considered. 



c c c 



I. Two parallel wires with currents ±7, v being parallel to I. Here 



dA 1 Iv 



— = and E= — V(Av). The motion produces charges ^q= *-£ per unit 



length along the wires. 



