270 Maxwell. 



It may, perhaps, seem as if the value of such an analogy 

 as this consisted merely in the prospect which it offered of 

 comparing, and thereby extending, the mathematical theories 

 of heat and electricity. But to the physicist its chief interest 

 lay rather in the idea that formulae which relate to the electric 

 field, and which had heen deduced from laws of action at a 

 distance, were shown to be identical with formulae relating to 

 the theory of heat, which had been deduced from hypotheses 

 of action between contiguous particles. 



In 1846 the year after he had taken his degree as second 

 wrangler at Cambridge Thomson investigated* the analogies 

 of electric phenomena with those of elasticity. For this purpose 

 he examined the equations of equilibrium of an incompressible 

 elastic solid which is in a state of strain ; and showed that 

 the distribution of the vector which represents the elastic 

 displacement might be assimilated to the distribution of the 

 electric force in an electrostatic system. This, however, as he 

 went on to show, is not the only analogy which may be 

 perceived with the equations of elasticity ; for the elastic 

 displacement may equally well be identified with a vector a, 

 defined in terms of the magnetic induction B by the relation 



curl a = B. 



The vector a is equivalent to the vector-potential which 

 had been used in the memoirs of Neumann, Weber, and 

 Kirchhoff, on the induction of currents ; but Thomson arrived 

 at it independently by a different process, and without being at 

 the time aware of the identification. 



The results of Thomson's memoir seemed to suggest a 

 picture of the propagation of electric or magnetic force : might 

 it not take place in somewhat the same way as changes in the 

 elastic displacement are transmitted through an elastic solid ? 

 These suggestions were not at the time pursued further 

 by their author; but they helped to inspire another young 



* Camb. and Dub. Math. Journ. ii (1847), p. 61 : Thomson's Math, and Phys. 

 Papers, i, p. 76. 



