190 Mr. G. A. Schott on the Electron 



In the present paper we shall study the radiation from a 

 ring o£ electrons in a controlling field, both when it is in 

 steady motion and when it is disturbed. The general case 

 of a system of rings is much more complicated ; it can be 

 studied by the same method, but for the sake of simplicity 

 it will not be considered here. 



It may be said at once that a single ring cannot be made 

 to account for spectrum series or bands. It follows that the 

 single ring cannot serve as a model of an atom ; nevertheless 

 'its study is useful because it throws much light on the con- 

 ditions which such a model must satisfy in order to account 

 for spectra. They are three in number : (1^ the electro- 

 magnetic waves emitted by the disturbed ring and received 

 by a stationary observer must be of sufficient intensity to 

 give observable lines ; (2) their frequencies must lie within 

 the limits corresponding to the spectrum ; (3) they must be 

 given by a formula, such as that of Deslandres for bands, or 

 these of Balmer, Kydberg, or Kayser and Iiunge for series, 

 and this formula must be satisfied within very narrow limits 

 for every line. 



Although the last condition is much the most difficult to 

 study, since it requires us to write down and solve more or 

 less complicated frequency equations, it is the only one of 

 the three on which to m}^ knowledge any work has been 

 done. In the present paper we shall only consider the first 

 two conditions; it will be found that they can only be satisfied 

 for a number of the waves emitted by a single ring too small 

 to account for the lines of even one series. Hence it is 

 useless in this case to study the third condition at all. In 

 this investigation we shall require a number of experimental 

 data, which are known only very roughly: for instance, the 

 intensities of strong and weak spectrum-lines, the ionization 

 in a gas giving a line spectrum, the time for which a free 

 ion exists on the average; but the margin of error is so large, 

 that a knowledge of the order of magnitude of these quantities 

 is quite sufficient for our purpose. For instance, any one of 

 these quantities may be estimated ten times too large or small 

 without affecting the conclusions of § 14. Nevertheless the 

 estimates of the energy radiated per second per ionized ring- 

 given in §§ 15, 16 agree so nearly with those of the energy 

 radiated in spectrum lines given in § 10, that the ideal ring 

 of &11 in this respect is a satisfactory model of radiating 

 svstoms, such as we find in flames or vacuum-tubes. 



§ 2. A first difficulty in a theory of this type is to explain 

 how it is that a system of electrons in orbital motion has a 

 definite structure at all. This ditficultv I have examined in 



