LIFE AND WORK OF LORD KELVIN THOMPSON. 755 



that he was master in whatever he touched. Early in 1853 he had 

 communicated to the Glasgow Philosophical Society a paper " On 

 transient electric currents," '^ in which he investigated mathematically 

 the discharge of a Leyden jar through circuits possessing self-induc- 

 tion as well as resistance. Faraday and Reiss had observed that in 

 certain cases the gases produced by the discharge of sparks through 

 water consisted of mixed oxygen and hydrogen, and Helmholtz had 

 conjectured that in such cases the spark was oscillatory. Thomson 

 determined to test mathematically what was the motion of electricity 

 at any instant after making contact in a circuit under given condi- 

 tions. He founded his solution on the equation of energy, ingeniously 

 building up the differential equation and then finding the integral. 

 The result was very remarkable. He discovered that a critical rela- 

 tion occurred if the capacity in the circuit was equal to four times the 

 coefficient of self-induction divided b}^ the square of the resistance. If 

 the capacity was less than this the discharge was oscillatory, passing 

 through a series of alternate maxima and minima before dying out. 

 If the capacity was greater than this the discharge was nonoscillatory, 

 the charge djdng out without reversing. This beautiful bit of math- 

 ematical analysis, which passed almost unnoticed at the time, laid the 

 foundation of the theory of electric oscillations subsequently studied 

 by Oberbeck, Schiller, Hertz, and Lodge, and forms the basis of wire- 

 less telegraphy. Fedderssen in 1859 succeeded in photographing 

 these oscillatory sparks, and sent photographs to Thomson, who with 

 great delight gave an account of them to the Glasgow Philosophical 

 Society. 



At the Edinburgh meeting of the British Association in 1854 

 Thomson read a paper " On mechanical antecedents of motion, heat, 

 and light." Starting with some now familiar, but then novel, gen- 

 eralities about energy, potential and kinetic, and about the idea of 

 stores of energy, the author touched on the source of the sun's heat 

 and the energy of the solar system, and then reverted to his favorite 

 argument from Fourier, according to which, if traced backward, there 

 must have been a beginning to which there was no antecedent. This 

 was a nonmathematical exposition of work which, as his notebooks 

 show, had been going on from 1850 in a very stiff mathematical form 

 in which Fourier's equations for the flow of heat in solids were ap- 

 plied to a number of outlying problems involving kindred mathe- 

 matics, including the diffusion of fluids and the diffusion or trans- 

 mission of electric signals through long cables. The Proceedings of 

 the Royal Society for 1854 contain the investigation of cables under 

 the title " On the theory of the electric telegraph." Faraday had 



«Proc. Glasgow Philos. Soc, January, 1853; Phil. Mag., June, 1853; and 

 Mathematical and Physical Papers, Vol. I, p. 534. 



