We find 

 fi>0 



11 = 



Theory of Matter and on Radiation, 199 



n 2 (k - + B 2 + 2AB sin a + j3 2 C 2 ) 27r 2 Ce 2 /*(/*+!) (2wp\^ 

 6 l X 2 12/4+1 \ \ J ' 



where the sign + refers to h ^Ltlve' 



x = 

 R= 



w 2 (/3 2 B 2 + C 2 ) 47r 2 C^/27r J o\ 2 



P 



T 2 Ce 2 /27riQy 



3X 2 \ X / 



In this case the terms involving A 2 , AB are of the next 

 higher order. 



A 2 27rA 2 

 Throughout the investigation terms of the orders -=-, -r — 

 ° A P- V 



have been neglected. Hence — . . . must all be small. 



r m 



The distance between consecutive electrons of the ring is 

 : — - ; except in very violent disturbances A... can hardly be 



»A 



-call it <7- 



greater than a small fraction of this ; that is 



-7rp 



can hardly be greater than a small fraction. 



The table gives values of R/o- 2 for three wave-lengths calcu- 

 lated with the numerical values of § 3. 





Class., k = 



0. 



±1- 



±2. 



+3. 



1 







CIO" 5 cm. 



•00.58 



•00029 



4-8 . 10- 11 



2-5 . 10- 1S 



64. 10" 26 



<7~ 



for X = 



3-5. 10~ 5 „ 



•0051 



•0025 



1-2. 10- 9 



1-9. lO" 16 



1-2 . 10" 23 







2. 10- 5 „ j 



•046 



024 



3-6. lO" 8 



1-7.10— 14 



3 8. lO" 21 



' § 10. It is very frequently assumed that every disturbance 

 of a system of electrons shows itself by a line in the spectrum 

 of the system. We shall now show that for a single per- 

 manent ring of electrons this is not the case, because many of 

 the vibrations emitted are far too weak to affect the photo- 

 graphic plate appreciably. 



We must first form an estimate of the least amount of 

 energy which will enable a vibration just to produce an 

 impression on the plate. Bearing in mind that the photo- 

 metric intensity of a spectrum-line is indicated by a scale- 

 number, from 1 to 10, we see that we must find out how the 

 energy of a weak line 1 compares with that of a strong line 10, 



