326 Prof. J. J. Thomson on the Discharge of Electricity 



however, the cause of the electromotive intensity is the 

 same in both cases, viz. the presence of tnbes of electro- 

 static induction, and the electromotive intensity ceases to be 

 derived from a potential, merely because the distribution of 

 these tubes is not necessarily the same when they are moving 

 about as when they are in equilibrium. It is shown, in the 

 paper already referred to, that these tubes when in motion 

 produce a magnetic force at right angles, both to their own 

 direction and to that in which they are moving, the magnitude 

 of the force being 47T times the product of the strength of the 

 tube, the velocity with which it is moving, and the sine of the 

 angle between the direction of the tube and its direction 

 of motion. In an electric field in which the matter is at 

 rest, these tubes when in motion move at right angles to 

 themselves with the velocity " i?," that at which electro- 

 dynamic disturbances are propagated through the medium. 

 We can easily show that, K being the specific inductive 

 capacity of the medium, the line-integral of 4tt/K times the 

 density of these tubes taken round a closed circuit is equal to 

 the rate of diminution of the number of lines of magnetic 

 induction passing through the circuit. Thus, since the funda- 

 mental laws of electrodynamic action, viz. Faraday's law of in- 

 duction and Ampere's law of magnetic force, follow from this 

 conception of the field as produced by tubes of electrostatic 

 induction moving at right angles to themselves with the 

 velocity "v" and producing a magnetic force at right angles 

 both to their own direction and to that in which they are 

 moving, and proportional to the product of the strength of 

 the tube and its velocity, it is a conception which will 

 account for all the known phenomena of the field. It fur- 

 nishes in fine a geometrical instead of an analytical theory of 

 the field. It will also be seen that from this point of view 

 the magnetic force, when introduced to calculate the electro- 

 motive forces arising from induction, logically comes in as an 

 intellectual middle-man wasting mental effort. 



We may thus regard the distinction between electrostatic 

 and electromagnetic electromotive forces as one introduced 

 for convenience of analysis rather than as having any physical 

 reality. The only difference which I think could be made 

 from a physical point of view would be to define those effects 

 as electrostatic which are due to tubes of electrostatic induc- 

 tion having free ends, and to confine the term electromagnetic 

 to the effects produced by closed endless tubes. It is only, 

 however, when the electromotive forces are produced ex- 

 clusively by the motion of magnets that all the tubes are 

 closed ; whenever batteries or condensers are used, open tubes 

 are present in the field. 



