238 Dr. 0. Lodge on the Electrostatic Force between 



the speed of light, Mr. Heaviside has attacked the general 

 problem in the Philosophical Magazine for April 1889. He 

 there shows that between two planes perpendicular to a wire 

 thus moving and moving with it at a distance apart equal to 

 the length of the wire, the electrostatic intensity is 



and the magnetic intensity is 



r 

 where X, the linear density, may be distributed anyhow on the 

 wire. Outside these two planes the force is zero. 



If the two intensities were to act, one on a stationary charge 

 of any number of electrostatic units, the other on a stationary 

 magnetic pole of the same number of magnetic units, the two 

 forces would be equal. If they act on a wire conveying a 

 steady current, and charged up to a certain linear density, 

 the forces will be equal when the statical measure of density is 

 equal to the magnetic measure of current, i. e. when C = i?X; 

 for then 



EX=H / uC. 



Lastly, if the two forces due to one bit of charged wire, 

 moving in its own line with the speed of light, act on 

 another similarly moving piece, the current equivalent to the 

 second wire will be v\' ; and again there will be an equality 

 between electrostatic and electrokinetic forces ; 



2X 2Xv v 



Kr r 



Not by any different X, or by any rearrangement of X, can the 

 balance be disturbed : only by a different v. If either wire 

 moves with velocity less than that of light, the electrostatic 

 force overpowers the other, but, so long as the full velocity 

 is maintained, the density on either wire may have any value 

 positive or negative without disturbing the balance ; and this 

 is natural enough, when, as here, X and C vary together ; 

 for if X be zero or negative anywhere, C is also zero and 

 negative, and the balance persists. 



Now proceed to the case of alternating pulses travelling 

 along parallel stationary wires. Their speed of travel is the 

 speed of light, and though the distribution of both density 

 and current is sinuous there is nothing in that disturbing to 

 a balance; moreover, so long as the waves are freely progres- 

 sive, X and C still accompany each other exactly, and nothing 

 but a balance will be observed in a closed circuit, however the 

 phases operating in the acting portions be altered, if the right 



