III. On Faraday s Lines of Force. By J. Clerk Maxwell, B.A. Fellow of 



Trinity College, Cambridge. 



[Read Dec. 10, 1855, and Feb. U, 1856.] 



The present state of electrical science seems peculiarly unfavourable to speculation. The 

 laws of the distribution of electricity on the surface of conductors have been analytically 

 deduced from experiment; some parts of the mathematical theory of magnetism are esta- 

 blished, while in other parts the experimental data are wanting ; the theory of the con- 

 duction of galvanism and that of the mutual attraction of conductors have been reduced 

 to mathematical formulae, but have not fallen into relation with the other parts of the 

 science. No electrical theory can now be put forth, unless it shews the connexion not 

 only between electricity at rest and current electricity, but between the attractions and 

 inductive effects of electricity in both states. Such a theory must accurately satisfy those 

 laws, the mathematical form of which is known, and must afford the means of calculating the 

 effects in the limiting cases where the known formulae are inapplicable. In order therefore to 

 appreciate the requirements of the science, the student must make himself familiar with a 

 considerable body of most intricate mathematics, the mere retention of which in the memory 

 materially interferes with further progress. The first process therefore in the effectual study of 

 the science, must be one of simplification and reduction of the results of previous investiga- 

 tion to a form in which the mind can grasp them. The results of this simplification may take 

 the form of a purely mathematical formula or of a physical hypothesis. In the first case we 

 entirely lose sight of tlie phenomena to be explained; and though we may trace out the 

 consequences of given laws, we can never obtain more extended views of the connexions of 

 the subject. If, on the other hand, we adopt a physical hypothesis, we see the phenomena only 

 through a medium, and are liable to that blindness to facts and rashness in assumption which 

 a partial explanation encourages. We must therefore discover some method of investigation 

 which allows the mind at every step to lay hold of a clear physical conception, without being 

 committed to any theory founded on the physical science from which that conception is 

 borrowed, so that it is neither drawn aside from the subject in pursuit of analytical subtleties, 

 nor carried beyond the truth by a favourite hypothesis. 



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