Theory of Matter and on Radiation. 205 



§ 14. We shall now apply these results to decide whether 

 our system of rings can account for spectrum-lines of the 

 intensities of those found in nature. In § 6 we found that 

 f«-r a line of photometric intensity 10, e. g. the D lines of 

 sodium, the energy radiated is of the order 4 . 10 -12 erg 

 per sec. per atom ; and in § 10 we estimated that for a line 

 of photometric intensity 1, that is just observable, the radiation 

 is of the order 10 ~ u erg per sec. per atom. These estimates 

 are based on the assumption that every atom in the sodium 

 flame at every instant shares in the radiation. If we assume 

 that the radiation is due only to the ions, the radiation per sec. 

 per ion is greater in proportion. 



The ionization in a flame is difficult to estimate ; Stark * 

 calculates the ionization in the unstriated positive column of 

 a vacuum-tube to be of the order 10 -5 , and states that for a 

 flame it is smaller. This value makes the radiation for a line 1 

 at least 10 — 9 erg per sec. per ion. 



This is the least value that R can have for any vibration of 

 class +3 or upwards, if that vibration is to give an observable 

 spectrum-line. 



In order to calculate R we use the table of values of 

 R/o" 2 given in § 9. The values of a Q have been found in 



§ 11; for class k a Q is of order ^— , for small values of k and 

 moderately large values of n. 7r 



Let us apply our results to the case /c= +3. 



The value of R/<r 2 is W. 10" 14 for \=2.10- 5 cm. 

 Hence the value of R is 2 . 10 _16 . 



This is only one five-millionth part of the value required 

 for the faintest observable line. 



For greater wave-lengths the value of R is less still. 



Even if we had assumed all the atoms to be ionized the 

 value of R would have been 50 times too small. 



We conclude that a vibration of class + 3 or upwards is far 

 too weak to produce an observable spectrum-line. 



Again, consider the vibrations of class +2. 



The values of R/a 2 are for 



X = 2.10- 5 cm., 3-6. 10- 8 , 

 \ = 3'5.10- 5 cm., 1-2. JO" 9 , 

 \=6.10- 5 cm., 4-8. 10- 11 . 



The corresponding values of 7T are "9, *03, *001 respectively, 

 those of (1-6-> t )/yT are *66, 1, 1 respectively. The coi- 

 responding radiations are respectively 6 . 10 -10 , 3 . 10~ 11 , 

 1*2 . 10~ 12 erg per sec. per ion. 



* Die Elektrizitat in Gasen, p. 269. 

 Phil Mag. S. 6. Vol. 13. No. 74. Feb. 1907. Q 



