Philosophical State of the Physical Sciences. 499 



his masterly work on electricity and magnetism, which appeared 

 in 1873, has built a monument to Faraday, and unconsciously to 

 himself also, out of the strongest mathematics. For forty years 

 mathematicians and physicists had laboured to associate the laws 

 of electrostatics and electrodynamics under some more general 

 expression. An early attempt was made by Gauss in 1835 ; but 

 his process was published, for the first time, in the recent com- 

 plete edition of his works. Maxwell objects to the formula of 

 Gauss because it violates the law of the conservation of energy. 

 Weber's method was made known in 1846 ; but it has not 

 escaped the criticism of Helmholtz. It represents faithfully the 

 laws of Ampere and the facts of induction, and led Weber to an 

 absolute measurement of the electrostatic and electromagnetic 

 units. The ratio of these units, according to the formulas, is a 

 velocity; and experiment shows that this velocity is equal to the 

 velocity of light. As Weber's theory starts with the conception 

 of action at a distance, without any mediation, the effect would 

 be instantaneous, and we are at a loss to discover the physical 

 meaning which he attaches to his velocity. Gauss abandoned 

 his researches in electromagnetism because he could not satisfy 

 his mind in regard to the propagation of its influence in time. 

 Other mathematicians have worked for a solution, but have lost 

 themselves in a cloud of mathematical abstraction. The two 

 theories of light have exhausted all imaginable ways in which 

 force can be gradually transmitted without increase or loss of 

 energy. Maxwell cut the Gordian knot when he selected the 

 luminiferous aether itself as the arena on which to marshal the 

 electromagnetic forces under the symbols of his mathematics, 

 and made light a variety of electromagnetic action. His analysis 

 gave a velocity essentially the same as that of Weber, with the 

 advantage of being a physical reality and not a mere ratio. Of the 

 two volumes of Mr. Maxwell, freighted with the richest and 

 heaviest cargo, the reviewer says: — " Their author has, as it were, 

 flown at every thing ; and, with immense spread of wing and 

 power of beak, he has hunted down his victims in all quarters, 

 and from each has extracted something new and interesting for 

 the intellectual nourishment of his readers/' Clear physical 

 views must precede the application of mathematics to any sub- 

 ject. Maxwell and Thomson are liberal in their acknowledg- 

 ments to Faraday. Mr. Thomson says : — " Faraday, without 

 mathematics, divined the result of the mathematical investiga- 

 tion ; and, what has proved of infinite value to the mathema- 

 ticians themselves, he has given them an articulate language in 

 which to express their results. Indeed the whole language of 

 the magnetic field and lines of force is Faraday's. It must be 

 said for the mathematicians that they greedily accepted it, and 



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