132 THE ROYAL SOCIETY OF CANADA 
atmosphere and the radiation from the sky in quality and intensity could 
thus be largely accounted for. These results were applied by Lord 
Kelvin! to the problem of sky radiation and this seems to have been 
the most recent contribution to the subject. Recent observations on 
sky-radiation seem to have thrown some doubt on the sufficiency of the 
simple Rayleigh law to account for facts. Seeing that the phenomenon 
of molecular scattering has given the subject an exceedingly wide scope 
of application to astrophysical problems, it has seemed desirable to 
investigate the problem in as general a manner as possible and apply 
for verification to the existing numerical data as to attenuation and 
scattering of radiation in the earth’s and in the sun’s atmosphere. 
The two main extensions of the existing theory which form the 
basis of the present investigation are as follows: 
(i) The introduction of a term in the equation representing the 
loss of intensity in a beam due to scattering which allows for absorp- 
tion without scattering, 7.e., a direct conversion of radiant energy in 
the ether into thermal molecular agitation in the gas. The introduc- 
tion of this term leads to an absorption equation of the form, 
E = he e —(ag + kg) T = Be e ACL a 
(11) 
where K, = y + B/M 
and 7 and # are constants. 
The existence and magnitude of the term + can then be inferred 
from observations on attenuation and in this way a numerical estimate 
made of the rate of partition of energy between the «ther and the 
molecular velocities in the gas. 
(ii). The second feature of the present paper is the mathematical 
consideration of effects due to self-llumination. Suppose a mass of gas 
to be exposed to illumination from an external source. As a result of 
scattering the whole mass of gas will be luminous, as in the case of the 
earth’s atmosphere. Thus each element of volume besides being sub- 
ject to the external incident illumination is also subject to the scattered 
radiation from the whole volume: this factor which constitutes 
the effect due to self-illumination adds considerably to the scattered 
intensity from the element of volume 

1 Kelvin, Baltimore Lectures (1904), p. 301. The writer is indebted to Dr. O. 
Klotz for a reference to more recent work of Exner (Sitzwngsbericht d. K. Akad. d. 
Wissen., Wien., M. N. Klasse, CX VIII, II a, 1909). A short account of Exner’s 
work is given by C. G. Abbot in his book on the Sun (Appleton and Co., 1911), p. 300. 
