208 



Mr. G. A. Schott on the Electron 



This gives the following results 



? 





10. 



20. 



50. 



100. 



1000. 







2d- 





•00 



•31 



•15 



•09 



•03 



"=kT 46 



1-25 



•62 



•2G 



•19 



•04 



These values show that the vibrations of class for small 

 values of n are sufficiently powerful to give an observable 

 spectrum-line, even when the ionization is as small as that in 

 a vacuum-tube. For rings of 20 electrons or so, these lines 

 are about as bright as those of classes + 1, for larger rings 

 they are probably weaker, for smaller rings stronger. The 

 ratios of the intensities are not generally very large, but are 

 comparable with those of Jewell's scale. 



§ 17. We have found that of all the vibrations of our ring 

 only those of classes 0, +1, and occasionally ±2, can pro- 

 duce lines sufficiently strong to be observable, but it may 

 happen that the frequency of any one of these lines is outside 

 the limits of the spectrum. In § 13 we saw that 



Zirp 



ft) A 



where A, is the wave-length of the line. For the extreme red 

 -^<-0008, for the extreme ultraviolet 2 ^ < -0063 ; these 



A A 



are upper limits, since p cannot exceed the radius of the 

 atom, that is, 10~ 6 cm. For rings of from 10 to 20 or more 

 electrons /3 > *02 ; hence for such rings 



- +k< "04 for a line in the extreme red, 

 to 



— +&<*3 for a line in the extreme ultraviolet. 

 ft) 



Negative frequencies are possible ; they represent lines of 



the same absolute frequency. As usual let - 



o ' 



absolute value of ~ . Then we must have 



9 



represent the 



co 



for positive q : 

 for negative q : 



<-04-*, '3-£, 

 >£--04, £--3, 



for a red, ultraviolet line respectively 



