203 



Starting from the formulae of the theory of relativity we easily 

 see that also the dualism between the electric and magnetic quantities 

 is restricted to R^. 



In Rn the electric field is determined by n components, the magnetic 



w(n— 1) 

 one by — - — numbers. 



The space-coordinates in the {n -\- l)-dimensional "world" will be 



denoted by ,v^ .... .i'„ and t will be replaced by .v^ = id. The electric 



and magnetic forces can be deduced from an (n -\- l)-fold potential 



(corresponding to the four-fold retarded potential in R^) : ff„, (f\, . . . (f,,- 



nin — 1) 

 The components of its rotation : 



dcph drpje fh and k z=z 1, . . . n\ 



give the magnetic field and the n components of the rotation : 



the electric field. 



§ 3. Integrals of the equation of vibration in R„. 



(Generalization of the retarded potentials). 

 The integrals of the equation : 



1 dV/ 



have thé following properties in R, : If at the time t = we have 

 everywhere ./ — and — = except in a small domain /, then 



we have at an arbitrary later moment t (if only t is taken large 



dtp 

 enough) still everywhere (f = 0, — =0, except in a thin layer 



between two surfaces (fig. A), which in the limit, when y becomes 

 small enough, become spherical surfaces with the centre at y. 



In R^ we have something else : here we have except a disturbance 

 of equilibrium between two concentric lines round y still an asymp- 

 totically diminishing disturbance of equilibrium in the whole exten- 

 sion (III) enclosed by the inner line. 



In this respect all R2n-\-iS behave like /?,, all R2n^ like R, (see 

 appendix III). 



But among the /^2„+i's R^ is characterized by a particularity 



14* 



