SPECTRAL LINES 453 



perhaps one exception. The shift has been shown to be pro- 

 portional to N, which was assumed to be proportional to the 

 density of the vapour in the arc. Experiment shows it to be 

 proportional to the pressure of the surrounding gas. Can these 

 two be assumed proportional to one another? No experiments 

 seem to have been conducted which could decisively settle this 

 point, and in the absence of further evidence it seems legitimate 

 to assume that the proportionality holds until it should be dis- 

 proved. 



It remains now to examine whether the quantitative agree- 

 ment between theory and experiment is as good as the qualita- 

 tive. Unfortunately, the comparison is made somewhat un- 

 certain by a lack of definite knowledge of N, the number of 

 electrons per unit volume in the arc, emitting vibrations of a 

 given period. Humphreys' experiments gave, as a result of 

 measurements of a large number of iron lines ranging round 

 A. = 4.10 - " 5 cms. values of d\/\ per atmosphere varying between 

 2.10 -6 and 4.10 ~~ 7 . Using the formula 



dX Ne a X a 

 X "~ 67rmc e 



an approximate value of N can be calculated. 



Taking e/mc = 1 77. io 7 , e = 47. io~ 10 , which are the mean values 

 of the best recent determinations, values of N are obtained 

 which range between 17.10 16 and 8*5. io 16 . 



This is the approximate number of electrons per unit volume 

 which are concerned in the production of a given spectral line 

 for iron. For the other metals tried by Humphreys N is found 

 to have about the same value. Now if the arc were an ideal 

 gas at 2730 absolute temperature and a pressure of one atmo- 

 sphere, the number of molecules per cubic centimetre would be 

 4.10 18 . The conditions in the arc are too uncertain to permit of 

 the estimate of the vapour density, but at first sight it does not 

 appear that the two results are discordant inter se. The ques- 

 tion is really, however, whether the above estimate of N is a 

 reasonable one. To determine this it is interesting to compare 

 this value with the value determined by other methods. Hallo 1 

 deduced N for the case of sodium vapour in a flame from 

 measurements of the breadth of an absorption line and of the 

 magnitude of the magnetic rotation of the plane of polarisation, 

 and obtained for the constant p = 47rNe 2 /m of the dispersion 



1 Diss. Amsterdam, 1902, Arch. N/er/. (2), 10, p. 148, 1905. 



