( 352 ) 



h ü^ 



(j ni^~ =r. k" -\- \ n V" 



2/t + l 



This formula is of some interest in connection witli an important 

 phenomenon that presents itself in the series of spectral lines. If, 

 namely, the number A is made to increase inrlefinitely, the frequency 

 )ih approaches to a determinate limit. 



It appears from (14) that in the present case, as well as in the 

 former one, each type of motion corresponds to a certain spherical 

 harmonic. Hence, all the rcasonino-s of the foregoing articles may 

 be repeated with only a slight modification. 



I shall not dwell at length on this subject; suffice it to say, that 

 in the magnetic field the vibrations of the first order have the 

 three frequencies 



He 



«1 and it]^ ± , 



2 m 



whereas the frequencies of the motions of the second order are 



II e 11 e 



7(3 , /(n dz and ii^ =t . 



~ 2 m 4 m 



In these expressions e again denotes the total charge, and m the 

 total mass. 



§ 11. The fundamental electromagnetic equations for the sur- 

 rounding ether enable us to determine the vibrations emitted by 

 the systems whose motion we have examined. The expressions for 

 the components of the dielectric displacement will contain terms 

 inversely proportional to the distance r, but also other terms varying 

 as the second and higher powers of »■—' . Now, it is clear that 

 only the terms of the first kind are to be taken into account when 

 we treat of the emission of light. If these terms are calculated for 

 the vibrations of the first and the second ordei', they are found in 



a 



the latter case to contain the factor — , « being again the radius 



of the sphere, and X the wave-length of the emitted radiations. If, 

 therefore, the displacements on the sphere itself in the J'o-vibratious 

 were of the same order of magnitude as those in the I'l-vibratious, 

 the light produced by the first would be very much feebler than that 

 which is due to the latter. All determinations of molecular dimeu- 



