Maxwell. 271 



Cambridge man to take up the matter a few years later. 

 James Clerk Maxwell, by whom the problem was eventually 

 solved, was born in 1831, the son of a landed proprietor in 

 Dumfriesshire. He was educated at Edinburgh, and at Trinity 

 College, Cambridge, of which society he became in 1855 a 

 Fellow; and not long after his election to Fellowship, he 

 communicated to the Cambridge Philosophical Society the first 

 of his endeavours* to form a mechanical conception of the 

 electro-magnetic field. 



Maxwell had been reading Faraday's Experimental He- 

 searches', and, gifted as he was with a physical imagination 

 akin to Faraday's, he had been profoundly impressed by the 

 theory of lines of force. At the same time, he was a trained 

 mathematician ; and the distinguishing feature of almost all 

 his researches was the union of the imaginative and the 

 analytical faculties to produce results partaking of both 

 natures. This first memoir may be regarded as an attempt to 

 connect the ideas of Faraday with the mathematical analogies 

 which had been devised by Thomson. 



Maxwell considered first the illustration of Faraday's lines 

 of force which is afforded by the lines of flow of a liquid. The 

 lines of force represent the direction of a vector; and the 

 magnitude of this vector is everywhere inversely proportional 

 to the cross-section of a narrow tube formed by such lines. 

 This relation between magnitude and direction is possessed by 

 any circuital vector ; and in particular by the vector which 

 represents the velocity at any point in a fluid, if the fluid be 

 incompressible. It is therefore possible to represent the 

 magnetic induction B, which is the vector represented by 

 Faraday's lines of magnetic force, as the velocity of an incom- 

 pressible fluid. Such an analogy had been indicated some 

 years previously by Faraday himself,f who had suggested that 

 along the lines of magnetic force there may be a " dynamic 

 condition," analogous to that of the electric current, and 



* Trans. Camb. Phil. Soc. x, p. 27; Maxwell's Scientific Papers, i, p. 155. 

 t Exp. Res., 3269 (1852). 



