﻿Widening of Spectrum Lines. 279 



spectrum line according to any conventional definition. 

 Mathematically speaking, the width is infinite ; but if we 

 disregard the outer parts where the intensity is less than 

 one-half the maximum, the limiting value or! f by (3) is 

 given bv 



/3f = log e 2, (16) 



and the corresponding value of X by 



A.-A_f = v /(log e 2) 



A C Cy/0 



(17) 



Thus, if SX denote the half-width of the line according to 

 the above definition, 



T denoting absolute temperature and m the mass of the 

 particles in terms of that of the hydrogen atom, in 

 agreement with Schonrock. 



In the application to particular cases the question at once 

 arises as to what we are to understand by T and m. In 

 dealing with a flame it is natural to take the temperature of 

 the flame as ordinarily understood, but when we pass to 

 the rare vapour of a vacuum-tube electrically excited the 

 matter is not so simple. Michelson assumed from the 

 beginning that the temperature with which we are con- 

 cerned is that of the tube itself or not much higher. This 

 view is amply confirmed by the beautiful experiments of 

 Buisson and Fabry*, who observed the limit of inter- 

 ference when tubes containing helium, neon, and krypton 

 were cooled in liquid air. Under these conditions bands 

 which had already disappeared at room temperature again 

 became distinct, and the ratios of maximum retardations 

 in the two cases (1*66, 1*60, 1-58) were not much less than 

 the theoretical 1*73 calculated on the supposition that the 

 temperature of the gas is that of the tube. The highest 

 value of X/A, in their notation N, hitherto observed is 

 950,000, obtained from krypton in liquid air. With all 

 three gases the agreement at room temperature between 

 the observed and calculated values of N is extremely good, 

 but as already remarked their theoretical numbers are a 

 little lower than mine (14). We may say not onlv that 

 the observed effects are accounted for almost completely 

 by Doppler's principle and the theory of gases, but that 



* Joum. de Physique, t. ii. p. 442 (1912). 



