AND MODERN PHYSICS. 165 



tbe law to bo discovered by calculation. Where he has per- 

 ceived a law he has at once stated it. in terms ns unambiguous 

 as those of pure mathematics, and if the mathematician, re- 

 ceiving this as a physical truth, deduces from it other laws 

 capable of being tested by experiment, he lias merely assisted 

 the physicist in arranging his own ideas, which is confessedly 

 a necessary step in scientific induction. 



"In the following investigation, therefore, the laws estab- 

 lished by Faraday will be assumed as true, and it will be 

 shown that by following out his speculations other ami 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 generalised so as to extend to phenomena 

 of a different class, these mathematical connections may 

 suggest to physicists the means of establishing physical con- 

 nections, and thus mere Ejaculation may be turned to account 

 in ex)>eri mental science." 



Maxwell shows how to obtain a mathematical ex- 

 pression for Faraday's electro-tonic state. In hi* 

 " Electricity and Magnetism," this electro-tonic state 

 receives a new name. It is known as the Vector 

 Potential,* anil the paper under consideration contains, 



* It is difficult to explain without analysis exactly what is 

 measured by M:ixwcll*s Vector Potential. Its rate of change at any 

 point of *iacc measures tho electromotive force at that point, EO far 

 as it is due to variations of tho electric current in neighbouring con- 

 ductors ; tho magnetic induction do|rnds on tho first differential 

 cocfliciciits of tho components of tho electro-tonic state ; the electric 

 current is related to their second differential coefticients in the same 

 manner as tho density of attracting matter is related to tho potential 

 it produces. In language which is now frequently used in mathe- 

 matical physics, the electromotive fon e at a point due to magnetic 

 induction is proportiouod to the rate of change of the Vector Potential, 

 tho magnetic induction depends outho "curl" of the Vector Potential, 

 while tho electric current is measure.! by the "concentration " of the 

 Vector Potential. From a knowledge of tho Vector Potential these 

 other quantities can be obtained by processes of differentiation. 



