Middle of the Nineteenth Century. 253 



gases, as if the current had passed through the water in both 

 directions. After this F. Savary* had noticed that the 

 discharge of a Ley den jar magnetizes needles in alternating 

 layers, and had conjectured that " the electric motion during 

 the discharge consists of a series of oscillations." A similar 

 remark was made in connexion with a similar observation by 

 Joseph Henry (ft. 1799, d. 1878), of Washington, in 1842.f 

 " The phenomena," he wrote, " require us to admit the existence 

 of a principal discharge in one direction, and then several reflex 

 actions backward and forward, each more feeble than the 

 preceding, until equilibrium is restored." Helmholtz had 

 repeated the same suggestion in his essay on the conservation 

 of energy : and in 1853 W. Thomson J verified it, by 

 investigating the mathematical theory of the discharge, as 

 follows : 



Let C denote the capacity of the jar, i.e., the measure of the 

 charge when there is unit difference of potential between "the 

 coatings ; let R denote the ohmic resistance of the discharging 

 circuit, and L its coefficient of self-induction. Then if at 

 any instant t the charge of the condenser be Q, and the 

 current in the wire be i, we have i = dQ/dt ; while Ohm's law, 

 modified by taking self-induction into account, gives the 

 equation 



Eliminating i, we have 



an equation which shows that when IFC < 4Z, the subsidence 

 of Q to zero is effected by oscillations of period 



27T 



(1- * 

 \LC 4Z 



* Annales de Chiniie, xxxiv (1827), p. 5. 

 tProc. Am. Phil. Soc. ii (1842), p. 193. 



J Phil. Mag. (4) v (1853), p. 400 ; Kelvin's Math, and Phys. Papers i, 

 p. 540. 



