ON PHYSICAL LINES OF FORCE. 471 



or dividing by V= F,+ F, + &c., 



If we make P = ir- 



ZTT 



then equation (33) will be identical with the first of equations (9), which give 

 the relation between the quantity of an electric current and the intensity of 

 the lines of force surrounding it. 



It appears therefore that, according to our hypothesis, an electric current 

 is represented by the transference of the moveable particles interposed between 

 the neighbouring vortices. We may conceive that these particles are very small 

 compared with the size of a vortex, and that the mass of all the particles 

 together is inappreciable compared with that of the vortices, and that a great 

 many vortices, with their surrounding particles, are contained in a single complete 

 molecule of the medium. The particles must be conceived to roll without sliding 

 between the vortices which they separate, and not to touch each other, so that, 

 as long as they remain within the same complete molecule, there is no loss of 

 energy by resistance. When, however, there is a general transference of par- 

 ticles in one direction, they must pass from one molecule to another, and in 

 doing so, may experience resistance, so as to waste electrical energy and generate 

 heat. 



Now let us suppose the vortices arranged in a medium in any arbitrary 

 manner. The quantities -, - -- , &c. will then in general have values, so that 



there will at first be electrical currents in the medium. These will be opposed 

 by the electrical resistance of the medium ; so that, unless they are kept up 

 by a continuous supply of force, they will quickly disappear, and we shall then 



have -? -7- = 0, &c. ; that is, adx + ftdy + ydz will be a complete differential 



(see equations (15) and (16)); so that our hypothesis accounts for the distri- 

 bution of the lines of force. 



In Plate VIII. p. 488, fig. 1, let the vertical circle EE represent an 

 electric current flowing from copper C to zinc Z through the conductor EE', 

 as shewn by the arrows. 



