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LXVI. A Kinematical Explanation of Groups of Spectrum 

 Lines with Constant Frequency -Difference. 



To the Editors of t lie Pliilosopjldcal Magazine. 

 Gentlemen, 



IX the November number of your Journal, Prof. R. "W.Wood 

 has published an investigation on the fluorescent and 

 magnetic-rotation spectra of sodium, in the course of which 

 he has demonstrated the existence of five or more groups of 

 nearly equidistant lines in the blue-green region of those 

 spectra. During an investigation on the radiation from 

 systems of electrons I have obtained a result, which I think 

 has sufficient bearing on Prof. "Wood's discovery to be of 

 interest to the readers of his paper. 



Consider a circle of n equidistant electrons rotating with 

 uniform angular velocity o> in a controlling field of such 

 a kind as to ensure stability. The electrons can execute 

 vibrations about their mean positions in steady motion, in 

 which the displacement of the ith electron is of the tvpe 



Aexp. tl^— k J, damping being neglected. The kine- 

 matics of these vibrations is given by Maxwell, ' Saturn's 

 Rings/ Part ii. §§ 10-13. 



It may be shown that the electromagnetic forces due to the 

 vibration at a point (r, 0, <j>) are the sums of terms of the 

 type 



BA exp. i { [g + (k + sn)a>]t~(k + sn)<j>}, 



where s is an integer. At a great distance B is very small 



for large values of k + sn ; near the ring it is much larger. 



Consider a second ring [n f , co') coaxal with the first : for 



2iii 

 the zth electron of this ring we have (f> = co't + z — r . Hence 



the electromagnetic forces relative to the second ring, and 

 therefore also the disturbances in it, are of the type 



[q + (k + sn)(ft) -co')] t — (k + sn) — T > . 



Just as in the case of the first ring, these disturbances of 

 the second ring give rise to electromagnetic forces of the 

 type 



B'CBAexp. i {[g+ (k + sn)(a)--<0') + (k + sn + s r n')& , ]t 



— (k + sn + s'n'^}, 



where s' is an integer ; at a great distance from the ring B' 

 is very small for large values of k + sn + s'n'. 



