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HERMANN VON HELMHOLTZ 



elements due to one another it is now possible (by a method 

 of Kirchhoff) to develop the values of electrodynamic potential 

 for currents that are continuously distributed in space, and it was 

 shown with the help of Green's law that the value of the 

 electrodynamic potential produced by all the currents present 

 in relation to the three components of current in a volume 

 element, are constant everywhere, with the exception of points 

 at which the electrical currents are infinite. 



With the help of this expression of potential we obtain the 

 equations of motion for electricity, which lead to an analogy 

 between the motions of electricity in a conductor and those 

 of a gas, and Helmholtz next investigates the nature of these 

 differential equations, and the course of the electrical dis- 

 turbances as determined by them, in regard to the value of 

 the constant introduced by him as above into the law of 

 potential, which has the value i in F. E. Neumann's law, o in 

 Clerk Maxwell's (under a given assumption), i in Weber's and 

 C. Neumann's. He finds that if k is zero or positive, the 

 differential equations with given potentials give the same 

 initial value for the motion of electricity, and that the work 

 equivalent of the electrical motion is positive ; for a negative 

 value of k it may be negative, i. e. less than in a state of rest, 

 so that the equilibrium of the electricity at rest in conducting 

 bodies for negative values of k must be unstable. Helmholtz 

 proved that if this quantity of work once becomes negative, 

 the motion, left to itself, will increase continuously, and lead 

 to infinite velocities and densities of electricity. These motions 

 and infinite progressive disturbances of electrical equilibrium, 

 however, on the unstable side can actually be produced with 

 the methods at our command for causing electrical motions 

 if k has a negative value (as indeed happens, generally 

 speaking, whenever electric disturbances are produced in a 

 homogeneous conducting sphere, by bringing an electrically 

 charged body near it, and taking it away again), and he thence 

 concluded that the assumption of a negative value for the con- 

 stant k, as made in Weber's law of induction, is inadmissible. 



Helmholtz next investigated the influence of the constant 

 k with practicable experiments, and finds that if k i or is not 

 disproportionately greater than i, the motions of the electricity 

 in experiments with earth conductors will not differ perceptibly 



