ON THE SPECTRUM OF HYDROGEN. 
379 
given by the expression I = I 0 e _/a ' 2 , where I is the intensity at a difference of wave¬ 
length x from the maximum, where the intensity is I U5 and k is a constant depending 
on the mass and the temperature of the radiating particles. Rayleigh ( loc. cit.) has 
shown that if the “ half-width ” of the line <U be defined as the value of x when 
I/I 0 — 0-5, then SX/.X = 3-57 X 10~ 7 v /(d/ m ), where 6 is the absolute temperature of the 
gas and m the mass of the radiating particles in terms of the Hydrogen atom as unity. 
Measurements of the width of a line are usually carried out by determining the limiting 
order of interference at which fringes can still be seen with such instruments as the 
Michelson or Fabry and Perot interferometer, in which the difference of path between 
successive interfering beams can be progressively increased. 
The theory of this method has been fully discussed by Rayleigh (loc. cit.) and by 
Schonrock (loc. cit.). If N is the limiting order of interference at which the fringes can 
still be seen it is shown that N = K v /(w/@), where K is a constant for which Rayleigh 
gives the value 1-427 X 10 6 , whilst Schonrock adopts the appreciably smaller value 
1-22 X 10 6 . The exact value of this constant depends on an estimate of the limiting 
visibility of fringes which can just be seen, and its value can be checked by observations 
on lines of the rare gases, following Buisson and Fabry (loc. cit.), where the mass of the 
radiating particles can be assumed. It is doubtful, however, ivhether a high degree of 
accuracy can be attained by this method, since the point at which the fringes cease 
to be visible is necessarily difficult to determine, and might well be affected by the 
intrinsic intensity of the light, by the wave-length in visual observations, and by other 
circumstances. 
We have therefore endeavoured to avoid the personal errors which are inherent in 
these methods by adopting a different procedure, in which the determination of the 
half-widths does not depend on any estimate of visibility in the ordinary sense of the 
word, but is calculated from the positions of certain definite points on a photographic 
plate, which can be measured with a micrometer to an accuracy which is limited only 
by the ordinary instrumental and personal errors which arise in the measurement of 
spectrum lines. 
It is of course a first essential that the resolving power of the spectroscope should be 
sufficiently great, but if this condition be satisfied the method is applicable, with slight 
modification, to any form of spectroscope. In the present investigation we have used 
an echelon diffraction grating, consisting of 35 plates of glass each 15 mm. thick, which 
had a resolving power adequate for the lines in question. 
The procedure simply consists in taking photographs of a line under investigation, 
firstly with the grating in the double-order position and then in the single-order position, 
with exactly the same times of exposure and without altering the conditions of excitation 
of the discharge tube. In practice we bracket photographs in the single-order position 
between photographs in the double-order position, this precaution being taken to pro¬ 
vide for the possibility of a gradual change in the luminosity of the discharge tube, and 
the photographs are taken on adjacent portions of the same plate. The photographs 
3 g 2 
