20(> Mr. G. A. Schott on the Electron 



We conclude that with an ionization 10~ 5 our system 

 might gjve an extremely faint line in the ultraviolet, but 

 could hardly give one in the visible spectrum. On the other 

 hand, if all the atoms were ionized it could give a strong line 

 in any part of the spectrum. 



It is noteworthy that for these vibrations of classes +2 and 

 upwards the brightest lines occur in the ultraviolet, where the 

 value of R/o- 2 is greatest. This is because the initial radiation 

 R is here of most importance. 



§ 15. From what has been said, it follows that observable 

 spectrum-lines can only be produced by vibrations of classes 

 0, + 1, and under certain circumstances by those of classes + 2. 

 We shall now consider the relative intensities of these lines. 



. For classes 0, + 1 the damping is large ; hence the radiation 

 is approximately E /T (§13). 



For E we may take the maximum kinetic energy. For 



it ino o 

 ^~ ±1> ±2 this is equal to ^-^-cr 2 , where 



and 



v „ f or Jf, 



{q + q')(n + 1) sin (kir/n) 



for — k. 



and 



{q + q')(n + 1) snl ( W'O 



The radiation becomes ^- o- 2 , which for a spectrum- 

 line reduces to n 



7r 2 C 2 w/3 2 



-—^ — k 2 o 2 = P<r 2 . 10~ 8 erg per sec. per ion (§ 14). 



For a moderately large value of n this becomes 



-, A _q f <?' kirjn y* . 



W . s — ; — -, - — 7-7 — r~\ 1 ero- per sec. per ion ior k, 

 Lq + g sin (kir/n) J c L r 



-m-Q f g kir/n "i 2 . . 



10 . < — - — , — — 77 — n > erg r>er sec. per ion ior — k. 

 { g-\-g sin [kirjn) J 6 



These are of the order (10 -9 ) of the radiation for an observable 

 line with the ionization (10 -5 ) calculated by Stark for a 

 vacuum-tube. Their relative intensities depend mainly on 

 the corresponding free frequencies g, q ' . 



§ 16. We have hitherto neglected to take into account the 

 slight disturbance due to the fact that the initial velocity and 

 radius of our ring are not exactly those necessary for the 

 steady motion of a ring of n equidistant electrons. The 

 differences are the same for each electron of the ring, 



