DISCHARGE OF ELECTRICITY. 233 



iuteusity at iiuy point is derivable from a potential function ; as soon, 

 however, as the equilibrium is disturbed, the tubes move about and get 

 displaced from their original positions, the disposition of tubes and 

 therefore the electro-motive intensity are changed, and the latter will 

 no longer be derivable from a i)otential function, and according to the 

 mat] lematicaltheory would be said to include forces diie to electrostatic 

 and electro-magnetic induction. According to our view, however, the 

 cause of the electro-motive intensity is tlie same in both cases, viz, the 

 j)resence of tubes of electrostatic induction, and the electro-motive in- 

 tensity ceases to be derived from a potential, merely because the dis- 

 tribution of these tubes is not necessarily the same when they are 

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

 ])a])er 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 47r times 

 the product of the strength of the tube, the velocity with A\hich it is 

 moving, and the sine of the angle between the direction of the tube and 

 its direction of motion. In an electric tield in which the matter is at 

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

 with the velocity '' r," 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 

 47r K times the density of these tubes taken round a closed circuit is 

 equal to the rate of diminution of the luimber of lines of magnetic in- 

 duction passing through the circuit. Thus, since the fundamental 

 laws of electro-dynamic action, viz, Faraday's law of iiuluctiou and 

 Am])cre's law of magnetic force, follow from this conception of the field 

 as i)roduced by tubes of electrostatic induction moving at right angles 

 to themselves with the velocity " v," and producing a magnetic force at 

 riglit 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 coiicei>tiou which will account for all the known 

 phenomena of the field. It furnishes, in tine, 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 

 electio-motive forces arising from in<lu('1ion, logicall\' comes in as an 

 intellectual middle-man wasting mental effort. 



We may thus regard the distinction between electrostatic and elec- 

 tro-magnetic* electro-motive forces as. one introduced for convenience of 

 analysis rather than as having any physical reality. The only differ- 

 ence which I think could from made from a i)hysical point of view would 

 be to <lefine those effects as electrostatic which are due to tubes of elec- 

 trostatic induction having free ends, and to confine the term electro- 

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

 however when the electro-motive forces are produced exclusively by the 

 motion of magnets that all the tubes are closed; whenever batteries or 

 comlensers are used, open tubes are ])resent in the field. 



