through Exhausted Tubes without Electrodes. 325 



round a closed curve, the surface-integral of its normal com- 

 ponent 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 satis- 

 factory, as the fundamental quantities concerned, the electro- 

 static and vector potentials, are both of considerable com- 

 plexity from a physical point of view. We might judge that 

 this division of the electromotive force into two parts, the one 

 derivable from an electrostatic, the other from a vector, poten- 

 tial, 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 

 potential satisfies the mathematical condition of being pro- 

 pagated with an infinite velocity, the total electromotive force 

 in the electromagnetic field travels with the velocity of light, 

 and nothing physical is propagated 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 picture 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 adopted for this purpose is the 

 one described by me in the Philosophical Magazine, March 

 189 J, 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 electricity and ending on the negative. At 

 any point in the field the electromotive 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 electromotive 

 intensity at any 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 electromotive 

 intensity are changed, and the latter will no longer be deriv- 

 able from a potential function, and according to the mathe- 

 matical theory would be said to include forces due to electro- 

 static and electromagnetic induction. According to our view. 



