374 Intelligence and Miscellaneous Articles. 



From these equations we may deduce the following principle : — 

 The branching or distribution of a variable current takes place in 

 such a manner that for any time its electrodynamic energy is a 

 minimum for the same magnitude of the total current. As this 

 energy may also be represented as a magnetic one, which has its 

 basis in the magnetization of the conductor and of the medium 

 surrounding it, the principle may also be so expressed. The dis- 

 tribution of the current takes place in such a manner that for the 

 same magnitude of the total current its magnetic energy is a 

 minimum. 



In a straight conductor of circular section, which is exposed 

 to no lateral actions, electrical currents can only be symme- 

 trically arranged about the axis. In whatever manner the 

 density of the current may vary from the axis towards the surface, 

 the external magnetic action of the conductor is the same as if the 

 entire current was concentrated in the axis. The minimum of 

 magnetic energy is determined, therefore, by the fact that this 

 energy has the smallest value in the space occupied by the con- 

 ductors. This smallest value, and indeed the value zero, is attained 

 when the entire current is condensed in an infinitely thin layer on 

 the surface of the cylindrical conductor, for such a current-tube 

 has no magnetic force on the space enclosed by it. 



If the section of the conductor is not circular there is also a dis- 

 tribution of the current on the surface which makes the magnetic 

 action at any point in the interior equal to zero, and corresponds 

 to the minimum of magnetic work. This distribution is conform- 

 able with that which an electric charge acquires when it is on the 

 conductor in a condition of equilibrium. Just as the resultant of 

 the electrical forces of such a charge is zero at any point of the con- 

 ductor, this is also the case with the resultant of the various cur- 

 rent-filaments lying in the surface, if the density of the current 

 along the periphery varies in the same manner as the density of 

 the statical electrical charge. If, for instance, the section of the 

 conductor is bounded by an ellipse, the densities in the various 

 points of the ellipse will be as the perpendiculars which fall from 

 the centre on the tangents to these points. 



In his last published . experiments H. Hertz has given very 

 striking proofs that electrical vibrations of very high frequency 

 can only move along the surface of the conductor. It also follows 

 from his observations on such movements in band-shaped conductors, 

 that the density of the current at the edges of the band is far 

 greater than that in the middle of the broader side. 



It may here be observed that the principle of distribution pro- 

 pounded not only serves for estimating the deportment of vibra- 

 tions, but may also be applied to rapid electrical impulses, such as 

 lightning-flashes, or constants of very short duration. 



The velocity with which electrical waves travel in a conductor 

 depends on the product of two factors — the coefficient of self- 

 induction, and the capacity, both referred to unit length of the 

 conductor. With the distribution of the current-density on the 

 surface of a conductor, described above, the magnetic energy, and 





