488 ON PHYSICAL LINES OF FORCE. 



force on a moving conductor, and is found by calculation to correspond with 

 that determined by experiment. 



We have now shewn in what way electro-magnetic phenomena may be 

 imitated by an imaginary system of molecular vortices. Those who have been 

 already inclined to adopt an hypothesis of -this kind, will find here the con- 

 ditions which must be fulfilled in order to give it mathematical coherence, and 

 a comparison, so far satisfactory, between its necessary results and known facts. 

 Those who look in a different direction for the explanation of the facts, may 

 be able to compare this theory with that of the existence of currents flowing 

 freely through bodies, and with that which supposes electricity to act at a 

 distance with a force depending on its velocity, and therefore not subject to 

 the law of conservation of energy. 



The facts of electro-magnetism are so complicated and various, that the 

 explanation of any number of them by several different hypotheses must be 

 interesting, not only to physicists, but to all who desire to understand how 

 much evidence the explanation of phenomena lends to the credibility of a theory, 

 or how far we ought to regard a coincidence in the mathematical expression of 

 two sets of phenomena as an indication that these phenomena are of the same 

 kind. We know that partial coincidences of this kind have been discovered ; 

 and the fact that they are only partial is proved by the divergence of the 

 laws of the two sets of phenomena in other respects. We may chance to find, 

 in the higher parts of physics, instances of more complete coincidence, which 

 may require much investigation to detect their ultimate divergence. 



NOTE. 



Since the firsc part of this paper was written, I have seen in Crelle's Journal for 1859, 

 a paper by Prof. Helmholtz on Fluid Motion, in which he has pointed out that the lines 

 of fluid motion are arranged according to the same laws as the lines of magnetic force, the 

 path of an electric current corresponding to a line of axes of those particles of the fluid 

 which are in a state of rotation. This is an additional instance of a physical analogy, the 

 investigation of which may illustrate both electro-magnetism and hydrodynamics. 



