330 Mr. G. F. C. Searle on the Steady Motion 



When any system of electric charges moves with uniform 

 velocity through the sether, the electromagnetic field, when 

 referred to axes moving forwards with the charges, can be 

 completely defined by means of a quantity M*, as was first 

 shown by Prof. J. J. Thomson*. The electric force E and the 

 magnetic force H are simple functions of ^. But besides E 

 and H there is another vector of great importance, viz. the 

 mechanical force P experienced by a unit charge moving with 

 the rest of the system. The value of P I have shown {§ 10 j- 

 to be given by the vector equation 



F = E + /iVuH (1) 



The equations of the field are {§4} 



curlF = 0, (2) 



H = KVuE (3) 



1 ... u 2 



If v= — === is the velocity of light, and if a. stand for 1 5 , 



VK/j, J v 2 ' 



then when the motion takes place parallel to the axis of a; 



we have { § 4} 



d* F _ d¥ d>Y 



ax ay az 



El= _f H,= _l** B,=-l« . (5) 



dx J a dij s adz ' v ' 



H,=0 H 2 =^^ H.— 5?** . ((!) 



a dz a dy v ' 



From these equations, since E has no divergence, 

 d 2 V d 2 V d 2 V n 



a M + W + ^ =Q (7) 



Here, and throughout the paper, the axes are supposed to 

 move forward with the same velocity as the electrical chai^ges. 



Prof. W. B. Morton has considered the motion of an 

 ellipsoid in a paper read before the Physical Society on 

 27th March, 1896 \. He obtains the two following results, 

 viz. : (1) that the distribution of electricity is the same as if 

 the ellipsoid is at rest, and (2) the value of M> when the 

 ellipsoid moves along one of its axes. 



Prof. Morton obtains his result by the assumption first 



* Phil. Mag. July 1889. 



+ Proc. Phys. Soc. No. 71, August 1896, p. 180 ; Phil. Mag. xli. p. 488. 



