ON FARADAY'S LINES OF FORCE. 189 



mental data for the direct proof of the unknown state, have not, I think, been 

 made the subject of mathematical investigation. Perhaps it may be thought 

 that the quantitative determinations of the various phenomena are not suffi- 

 ciently rigorous to be made the basis of a mathematical theory ; Faraday, 

 however, has not contented himself with simply stating the numerical results of 

 his experiments and leaving the law to be discovered by calculation. Where 

 he has perceived a law he has at once stated it, in terms as. unambiguous as 

 those of pure mathematics ; and if the mathematician, receiving this as a physical 

 truth, deduces from it other laws capable of being tested by experiment, he 

 has merely assisted the physicist in arranging his own ideas, which is con- 

 fessedly a necessary step in scientific induction. 



In the following investigation, therefore, the laws established by Faraday 

 will be assumed as true, and it will be shewn that by following out his 

 speculations other and more general laws can be deduced, from them. If it 

 should then appear that these laws, originally devised to include one set of 

 phenomena, may be generalized so as to extend to phenomena of a different 

 class, these mathematical connexions may suggest to physicists the means of 

 establishing physical connexions ; and thus mere speculation may be turned to 

 account in experimental science. 



On Quantity and Intensity as Properties of Electric Currents. 



It is found that certain effects of an electric current are equal at what- 

 ever part of the circuit they are estimated. The quantities of water or of 

 any other electrolyte decomposed at two different sections of the same circuit, 

 are always found to be equal or equivalent, however different the material and 

 form of the circuit may be at the two sections. The magnetic effect of a 

 conducting wire is also found to be independent of the form or material of 

 the wire in the same circuit. There is therefore an electrical effect which is 

 equal at every section of the circuit. If we conceive of the conductor as the 

 channel along which a fluid is constrained to move, then the quantity of fluid 

 transmitted by each section will be the same, and we may define the quantity 

 of an electric current to be the quantity of electricity which passes across a 

 complete section of the current in unit of time. We may for the present 

 measure quantity of electricity by the quantity of water which it would decom- 

 pose in unit of time. 





