1915] ON THE WIDENING OF SPECTRUM LINES 295
This is for the hydrogen molecule. For the hydrogen atom (13) must be divided by \/2. Thus for absolute temperature T and for radiating centres whose mass is m times that of the hydrogen atom, we have
1-222 xV(278)x 10" ^\ //«*
' "
A V2
In Buisson and Fabry's corresponding formula, which appears to be derived from Schonrock, 1*427 is replaced by the appreciably different number 1-22*. The above value of X is the retardation corresponding to the limit of visi-: bility, taken to be represented by F= '025. In Schonrock's calculation the retardation Xlt corresponding to F='5, is considered. In (12), V(loge 40) would then be replaced by \/(loge 2), and instead of (14) we should have '
^ = 6-186x10^(1) ......................... (15)
But I do not understand how V= '5 could be recognized in practice with any precision.
Although it is not needed in connexion with high interference, we can of course calculate the width of a 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 of £ by (3) is given by
/3£2 = loge2, ......... ..................... (16)
and the corresponding value of \ by
v
Thus, if SX denote the half-width of the line according to the above definition,
...............(18)
A c\/3 \m
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 i's not so simple. Michelson assumed from the. beginning that the temperature with which we are concerned is that of the tube itself or not much higher. This view is amply confirmed by the beautiful experiments of Buisson and Fabryf,
* [1916. I understand from M. Fabry that the difference between our numbers has its origin in a somewhat different estimate of the minimum value of V. The French authors admit an allowance for the more difficult conditions under which high interference is observed.]
t Journ. de Ptysique, t. n. p. 442 (1912). , . .ard X as gradually increasing from zero, / is periodic, the maxima (4) occurring when JK is a multiple of X and the minima (0) when X is an odd