About 1850, Kirchhoff published his laws relating to branched or divided circuits. He also showed mathematically that according to the then prevailing electrodynamic theory, electricity would be propagated along a perfectly conducting wire with the velocity of light. Helmholtz investigated mathematically the effects of induction upon the strength of a current and deduced therefrom equations, which experiment confirmed, showing amongst other important points the retarding effect of self-induction under certain conditions of the circuit.