136 THE ROYAL SOCIETY OF CANADA 
pressure and temperature, H the height of the homogeneous atmos- 
phere and N, the number of molecules per unit volume at 0°C. and 760 
mm. pressure. Y represents a constant term expressing absorption 
without scattering. If the observed values of C, are plotted against 
1/4 for the different stations at various levels we should obtain a family 
of straight lines all passing through the same point. 
The absorption coefficients for Mt. Whitney (4420 metres), Mt. 
Wilson (1780 metres) and Washington (10 metres)! are analysed in this 
way. To these are added the results for Potsdam? (100 metres). The 
results give rise to a series of straight lines shown in Plate I. The 
results for sea-level stations require special interpretation owing to the 
effect of atmospheric “dust.” The broken lines obtained for the sea- 
level observations require us to consider separately wave-lengths 
greater than -610 /# (called long-wave radiation) and wave lengths less 
than this value (called short-wave radiation). 
(i) Long-wave radiation (X > -610 y). 
The factor referred to as amospheric “dust” is both able to scatter 
and absorb without scattering radiation travelling through air contain- 
ing it. The intersection of the lines of Plate I for long-wave radiation 
in the same point on the axis 1/A‘* leads to the general result 8/7 
= B’/y” independently of any law of distribution of “dust:” 
the accented quantities refer to the part played by this factor on the 
attenuation. This result can be stated in the form: the ratio of energy 
scattered to energy absorbed is constant and independent of the nature 
of the scattering particle whether “dust” or molecule. 
(ii) Short-wave radiation (x < -610 /). 
In this case we suppose that “dust” absorbs all wave-lengths 
without scattering so that the scattering which exists is due entirely 
to air-molecules. In order to test this result we measure the slope of 
the straight lines of Plate I and caleulate B, the barometic pressures at 
the stations of observation being supposed known. By making use of 
the known optical constants of air we may calculate N, the number of 
molecules per cubic centimetre of a gas at O°C. and 760 mm. pressure. 
The results obtained from the values of B for the different stations are 
as follows: 



? A sumary of the most recent reductions of the Smithsonian Astrophysical 
Observatory is given by C. G. Abbot, Astrophysical Journal, XXXIV, October, 1911, 
p. 197: 
? The Potsdam observations are given by Müller, ‘“ Photometire der Gestivue,” 
Leipsig, 1897, p. 140. 
3 The close agreement of theory and observation in the calculation of co-efficients 
of attenuation on selected clear days was first pointed out by Schuster, Nature, July 
22nd, 1909. 
