( 89 ) 
proceed to a discussion of the second question, that which regards 
the composition and properties of the light that has traversed a ° 
very thick layer of gas, the atmosphere of a celestial body, if we 
suppose the emission curve of the original source of light to be 
continuous. — 
Evidently the solution cannot be found by simply putting the 
value 
h 2 a De" 
y= == a 
me T 3 cm 
into the formulae (3) or (6a), and then, for each wave-length separately, 
substituting the resulting value of nx into an equation of the form 
SSR Tel ye cl) AA ee ee ene 
(in which z represents the distance travelled by the beam through 
the layer of gas). 
For this would lead to an entirely erroneous result, even if 
the layer of gas were perfectly homogeneous. It is true that the 
part of the attenuation, which is due to absorption, conforms to the 
law expressed by (12), proceeding in a geometrical progression when 
the path through the gas inereases in an arithmetical progression ; 
but the same does not apply to the part that is caused by scattering. 
If the source of light and the layer of gas are very extensive, we 
must take into consideration that each electron emits a certain 
quantity of scattered light owing to irradiation from all directions, 
and partly joining the directly transmitted beam. The attenuation of 
the beam must therefore proceed less quickly than it would do 
according to the law expressed by (12), which holds for the loss of 
intensity by absorption ’). 
ScHUSTER *) was the first to discuss in an ample way the combined 
influence of scattering, absorption, and emission of light in extensive 
masses of gas. Basing his conclusions on Kircanorr’s law, and making 
various suppositions as to the ratio between the coefficients of absorption 
and scattering, he examined into the circumstances that would make 
an atmosphere of a certain depth produce either dark or bright 
spectral lines. 
1) Rayteien, in deducing the formula (9), has not taken this into consideration; 
his result only applies to the attenuation which the original beam suffers by 
scattering, and does not include the scattered light itself. 
2) Scnuster, Radiation through a foggy atmosphere. Astroph. Journ. 21, p. 1, (1905). 
