[ 368 ] 



XLVII. A Contribution to Electrodynamics. 

 By Bernhard Riemann*. 



I BEG to communicate to the Royal Society an observation 

 which brings into close connexion the theory of electricity 

 and of magnetism with that of light and of radiant heat. I have 

 found that the electrodynamic actions of galvanic currents may 

 be explained by assuming that the action of one electrical mass 

 on the rest is not instantaneous, but is propagated to them with 

 a constant velocity which, within the limits of errors of observa- 

 tion, is equal to that of light. On this assumption, the differen- 

 tial equation for the propagation of the electrical force is the same 

 as that for the propagation of light and of radiant heat. 



Let S and S' be two conductors traversed by constant voltaic 

 currents but not moved towards each other ; let e be an electrical 

 particle in the conductor S, which at the time t is in the point 

 \qc } y, z) ; e f an electrical particle of S', which at the time t is in 

 the point (x 1 , y\ z ! ). As regards the motion of the electrical 

 particles, which in each particle of the conductor is opposite in 

 the negative to what it is in the positive, I assume it at each mo- 

 ment to be so distributed that the sums 



2tf{x,y,z), ^f(x',y',J) 



extended over all the particles of the conductor may be neg- 

 lected as compared with the same sums if they are distributed 

 only over the positively electrical, or only over the negatively 

 electrical particles, as long as the function f and its differential 

 quotients are constant. 



This supposition can be fulfilled in various ways. Let us 

 assume, for instance, that the conductors are crystalline in their 

 smallest particles, so that the same relative distribution of the 

 electricity is periodically repeated at definite distances which are 

 infinitely small compared with the dimensions of the conductors ; 

 then, if {3 be the length of one such period, those sums are infi- 

 nitely small, like c/3 n , if /and their derivatives to the (n — 1 )th 



£ 



degree are continuous, and infinitely small like e~ P if they are all 

 continuous. 



Experimental Law of Electrodynamic Actions. 



If the specific intensities expressed in mechanical measurement 

 are u } v, w at the time t in the point (w } y, z), parallel to the three 



* Translated from Poggendorff's Annalen, No. 6, 1867. This paper was 

 laid before the Royal Society of Sciences at Gottingen on the 10th of Fe- 

 bruary 1858, by the author (whose premature death was such a loss to 

 science), but appears, from a remark added to the title by the then Secretary, 

 to have been subsequently withdrawn. 



