252 The Mathematical Electricians of the 



measured by the electrodynamic effects of the cell with the 

 circuit closed ; and, further,* that when the circuit was closed, 

 the difference of the tensions, measured electrostatically, at any 

 two points of the outer circuit was proportional to the ohmic 

 resistance existing between them. But in spite of all that had 

 been done, it was still uncertain how " tension," or " electro- 

 scopic force," or " electromotive force " should be interpreted 

 in the language of theoretical electrostatics ; it will be 

 remembered that Ohm himself, perpetuating a confusion which 

 had originated with Volta, had identified electroscopic force 

 with density of electric charge, and had assumed that the 

 electricity in a conductor is at rest when it is distributed 

 uniformly throughout the substance of the conductor. 



The uncertainty was finally removed in 1849 by Kirchhoff,f 

 who identified Ohm's electroscopic force with the electrostatic 

 potential. That this identification is correct may be seen by 

 comparing the different expressions which have been obtained 

 for electric energy; Helmholtz's expression^ shows that the 

 energy of a unit charge at any place is proportional to the 

 value of the electrostatic potential at that place ; while Joule's 

 result shows that the energy liberated by a unit charge in 

 passing from one place in a circuit to another is proportional 

 to the difference of the electric tensions at the two places. It 

 follows that tension and potential are the same thing. 



The work of Kirchhoff was followed by several other 

 investigations which belong to the borderland between electro- 

 statics and electrodynamics. One of the first of these was the 

 study of the Leyden jar discharge. 



Early in the century Wollaston, in the course of his experi- 

 ments on the decomposition of water, had observed that when 

 the decomposition is effected by a discharge of static electricity, 

 the hydrogen and oxygen do not appear at separate electrodes ; 

 but that at each electrode there is evolved a mixture of the 



* Ann. d. Phys, Ixxviii (1849), p. 1. 



f Ib. Ixxviii (1849), p. 506 ; Kirchhoff's Get. Abhandl, p. 49 ; Phil. Mag. (3), 

 xxxvii (1850), p. 463. 



I Cf. p. 242. Cf. p. 239. 



