ABSORPTION OF LIGHT IN GASEOUS iMEDIA. 
393 
We notice from (37), writing 0 = 0 + 7 = + ai|Hn, that 
i.e., 
0 = A+tt^(— l)^X ‘‘H/No + a^H, 
*C = l3X~'^ + y, where /3 =l)^ H/N„, 
wliicli gives 
^zl^o/p = A“" + 7. 
(75) 
(76) 
Extensive observations on the determination of the coefficient of attenuation 0^ for 
different wave-lengths have beeii carried out at various stations by the work of the 
Smithsonian Astroph 3 ^sical Observatory, t The mean coefficients of atmospheric 
transmission for Washington, Mount Wilson, and Mount Whitney have recently been 
given by Abbot.| These are quoted in Table I., while for the sake of independent 
comparison, the results of MtTLLER§ for Potsdam are also added. 
In order to study the correctness of formula (76) the coefficients of transmission for 
the different stations are plotted on a base X being measured in microns ( 10“^ cm.). 
The results are shown in Diagram I., and give rise to a number of straight lines. If the 
aljsorption were due to air-molecules alone, (76) shows that we should obtain a family 
of straight lines all passing through the same point (X'''^ = —yl$). The straight lines 
actually ol)tained show that some variable factor in the atmosphere other than the 
molecules themselves is effective in attenuation, especially for stations below the level 
of Mount Wilson. This factor is generally referred to as atmospheric “ dust.” A 
slight generalization of the analysis by which (76) was olffained enables us to interpret 
tlie results shown graphically in Diagram I. 
Let N' he the nund)er of “ dust” particles per unit volume at a height x above the 
earth’s surface. The coefficient of attenuation, wliich includes tlie effects of scattering 
and al)sorption both by air molecules and b}^ “ dust,” ma}^ be written in the form 
^’.r— (/dX ■‘ + 7)^J»/^|, + Kb (x) I —dx, 
dx 1 > (, 
(77) 
where N'y is a constant representing the number of dust particles per unit volume at 
the earth’s surface, aiid K'o (x) depends on the nature of abs(^rption and scattering b}” 
the dust particles. The distribution of “ dust ” N' in the atmosphere may be regarded 
* The representation of the coefficient of atteinxation as the sum of two terms, one constant and the 
other varying inversely as tlie fourth power of the wave-length, seems to have been first recognized by 
Becker (see Kelvin, ‘Baltimore Lectures,’ p. 321, equation 33) from an analysis of Muller’s 
observations. 
t ‘ Annals of the Smithsonian Astrophj'^sical Observatory,’ vol. IL, by C. G. Abbot and F. E. Fowj.e, 
Washington, 1908. Referred to subsequently as ‘ Annals,’ vol. IL 
Abbot, C. G., “The Sun’s Energy-Spectrum and Temperature,” ‘ Astrophysical Journal,’ XXXIY., 
October, 1911. 
§ Muller, G., “ Photometrie der Gestirne,” Leipzig, 1897, p. 140. 
3 E 
VOL. GCXTT.-A. 
