PROFESSOR AT KONIGSBERG 79 



In 'The Duration and Nature of the Electrical Currents 

 induced by Variations of Current' (Poggendorff's Annalen) he 

 begins by stating a mathematical law, which he had verified 

 by a long and difficult series of experiments. By means of 

 this law F. Neumann was enabled to solve the problem he 

 had previously laid aside, as to the distribution of current 

 in a copper disk rotating below the two poles of a magnet 

 carrying out the integrations without neglecting secondary 

 inductive actions, and propounding theorems that could be 

 experimentally tested. If an electric circuit contains voltaic 

 cells and a coil, and if / be the intensity of the battery 

 current, W the resistance of the circuit in absolute units, 

 / the time, and P the self-induction of the coil which depends 

 only upon geometrical relations, then a stationary magnet will 

 be deflected by the inducted current alone through an angle 

 directly proportional to P and /, and inversely proportioned 

 to W\ but if the battery current alone acts on the magnet 

 for the very brief time /, a deflection proportional to the 

 products of 7 and t will result ; hence it follows directly 

 that the battery current in the time represented by the quotient 

 of P and W produces the same effect as the whole of the 

 induced current. Dove had already pointed out that the 

 intensity of the counter-current induced on closing the circuit 

 is always less than that of the inducing current, while the 

 weaker current requires more time to produce the same effect 

 than the stronger, whence it follows that the minimum duration 

 of the counter-current at closure is the quotient P/W. Now, 

 since this minimum can be augmented at will, by reducing the 

 resistance W of the circuit, and increasing the self-induction P 

 of the coil by increasing its mass, it is experimentally possible 

 (and this is the cardinal point of the theorem) to make the 

 time required by the current to reach the same value at all 

 parts of the circuit very small by comparison with the above- 

 mentioned interval, and conditions can be brought about under 

 which the rate of transmission of the electric current in the 

 circuit is imperceptibly small as compared with the fractions 

 of time, in which the intensity of the current is not perceptibly 

 altered. This, however, gives the necessary conditions for 

 the application of Ohm's Law, i. e. the equalizing of current- 

 strength throughout the circuit ; for the alterations in intensity 



