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XIV. On Physical Lines of Force. Byh C. Maxwell, F.R.S., 

 Professor of Natural Philosophy in King's College, London*. 



Part IV. — The Theory of Molecular Vortices applied to the 

 Action of Magnetism on Polarized Light. 



THE connexion between the distribution of lines of magnetic 

 force and that of electric currents may be completely ex- 

 pressed by saying that the work done on a unit of imaginary 

 magnetic matter, when carried round any closed curve, is pro- 

 portional to the quantity of electricity which passes through the 

 closed curve. The mathematical form of this law may be ex- 

 pressed as in equations (9)f, which I here repeat, where a, /?, y 

 are the rectangular components of magnetic intensity, and^, q, r 

 are the rectangular components of steady electric currents, 



1 47r\dy dz) y 

 - JL (£. _ *1\ 



q -~47T\dz dx)> 



4-7T \dx dij/ 



(9) 



The same mathematical connexion is found between other sets 

 of phenomena in physical science. 



(1) If a, (3, 7 represent displacements, velocities, or forces, 

 then p } q, r will be rotatory displacements, velocities of rotation, 

 or moments of couples producing rotation, in the elementary por- 

 tions of the mass. 



(2) If a, ft, 7 represent rotatory displacements in a uniform 

 and continuous substance, then p, q, r represent the relative 

 linear displacement of a particle with respect to those in its im- 

 mediate neighbourhood. See a paper by Prof. W. Thomson 

 " On a Mechanical Representation of Electric, Magnetic, and 

 Galvanic Forces/' Camb. and Dublin Math. Journ. Jan. 1847. 



(3) If a, /3, y represent the rotatory velocities of vortices 

 whose centres are fixed, then j}, q, r represent the velocities with 

 which loose particles placed between them would be carried along. 

 See the second part of this paper (Phil. Mag. April 1861). 



It appears from all these instances that the connexion between 

 magnetism and electricity has the same mathematical form as 

 that between certain pairs of phenomena, of which one has a 

 linear and the other a rotatory character. Professor ChallisJ 



* Communicated bv the Author. 



t Phil. Mag. March 1861. 



X Phil. Mag. December I860, January and February 1861. 



