20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



temperatures and found a much more rapid increase with rising 

 temperature than that indicated by Trabert. 



From (3) we shall deduce some general laws for the radiation 

 from gaseous layers. From such a layer the radiation will naturally 

 come in from all sides, R being different for different angles of 

 incidence. We may therefore write (3) in the form: 



J=l^E^(i-e- a \-y R ) (5) 



where y is always a positive quantity. Now we have : 

 dJ yX 



That is, we have the very evident result that the radiation of 

 a gaseous layer increases with its thickness (or density). For very 

 thick layers the increase is zero and the radiation constant. 

 By a second differentiation we get : 



d 2 J ^ x 



The second derivative is always negative, which shows that the 

 curve giving the relation between radiation and thickness is always 

 concave toward the R-axis. 



We may now go a step further and imagine that on the top of 

 the first layer is a new layer, which radiates in a certain way different 

 from that of the first layer. A part of the radiation from the second 

 layer will pass the first layer without being absorbed. That part we 

 denote by H. Another fraction of the radiation will be absorbed, and 

 it will be absorbed exactly at the wave lengths where the first layer 

 is itself radiating. The sum of the radiations from the two layers 

 can therefore be expressed by a generalization of (5) 



J=H + 'xk[E x -(E x -E\)e- a x-vR] (6) 



where E\ is the radiation from the second layer at the wave length 

 A. If this layer has the same or a lower temperature than the first 

 one, we evidently have : 



E\±E X 

 In that case the laws given above in regard to the derivatives of 

 / evidently hold, and we find here also that the less the thickness of 

 the layer is, so much more rapid is the increase of radiating power 

 with increase in thickness. This is true for a combination of several 

 layers under the condition that the temperature is constant or is a 

 decreasing function of the distance from the surface to which the 



