232 DISCHARGE OP ELECTRICITY. 



Ill the matliematk-al treatment of the pheiioiueua of the "Electro- 

 magnetic Field," it is customary and not inconvenient to regard the 

 electro-motive force as derived from two sources, or rather as consisting 

 of two parts, one i^art being calculated by the ordinary rules of electro- 

 statics from the distribution of electricity in the field, the other part 

 being the difterential coefficient of the vector potential with respect to 

 the time. From a mathematical point of view, there is a good deal to 

 be said for this division; the two forces have very distinct and sharply 

 contrasted analytical properties. Thus the electrostatic force possesses 

 the property that its line integral taken round any closed curve van- 

 ishes, while the surface integral of its normal component taken over a 

 closed surface does not in general vanish. The "vector potential 

 force," on the other hand, does not in general vanish when integrated 

 round a closed curve; the surface integral of its normal component 

 taken over any closed surface however vanishes. When however 

 our object is not so much mathematical calculation as the formation of 

 a mental picture of the processes going on in the field, this division 

 does not seem nearly so satisfactory, as the fundamental quantities 

 concerned, the electrostatic and vector potentials, are both of con- 

 siderable complexity from a physical i3oint of view. We might judge 

 that this division of the electro-motive force into two parts, the one de- 

 rivable from an electrostatic, the other from a vector, potential, is rather 

 a mathematical device than a physical reality, from the fact which I 

 pointed out in a report on electrical theories [B. A. Report^ 1886), that 

 though the electrostatic jiotential satisfies the mathematical condition 

 of being propagated with an infinite velocity, the total electro-motive 

 force in the electro-magnetic field travels with the.velocity of light, and 

 nothing physical is jiropagated at a greater velocity. 



In an experimental investigation such as that described in this paper, 

 it is not so important that our method of regarding the phenomena 

 should lead to the shortest analysis as that it should enable us to pic- 

 ture to ourselves the processes at work in the field, and to decide 

 without much calculation how to arrange the experiments so as to bring 

 any effect which may have been observed into greater prominence. 



The method which I have adoj^ted for this purpose is the one de- 

 scribed by me in the Philosophical Magazine, March, 1891, and which 

 consists in referring everything to the disposition and motion of the 

 tubes of electrostatic induction in the field. These tubes are either 

 endless, or have their ends on places where free electricity exists, every 

 unit of positive electricity (the unit being the quantity of electricity on 

 the atom of a univalent element) being connected by a unit tube to a 

 unit of negative electricity, the tube starting from the positive elec- 

 tricity and ending on the negative. At any point in the field the elec- 

 tro-motive intensity varies as the density of the tubes of electrostatic 

 induction at that point. When the electricity and the tubes in the 

 field are at rest, the tubes distribute themselves so that the electro-motive 



