F. W. Very— On the Solar Constant. 207 



taken of the change of volume energy from layer to layer' 

 computed with the values of T, c and a by the ingenious 

 method developed by Professor JBigelow in his article in this 

 Journal for March, 1913, * values of about 1*460 are obtained, 

 which are in agreement with the volume energy derived from 

 the pressure. Consequently, the thermal energy which gives 

 the air pressure is maintained by the internal radiation between 

 the air molecules, and this is the real meaning of the consistent 

 numbers given by the computation. 



The air radiation (internal) is obtained from the absolute 

 temperature T, by the equation, 



J a - cT% 



where the coefficient c and the exponent a are given by thermo- 

 dynamic computations. In the article now under discussion, 

 Professor Bigelow has arbitrarily modified this equation by 

 substituting for a the value 4 demanded by Stefan's law for an 

 ideal black body, but leaving the constant c and the temperature 

 T unchanged. This amounts to assuming that the air radiates 

 like a black body, and on summing the change of volume 

 energy from layer to layer computed by this new formula, a 

 result is obtained a little less than three times as great as 

 before, this being the ratio of black-body radiation to air 

 radiation, as I have already shown. When this sum is 

 compared with the sum of the ratios of volume energy 

 corresponding to pressure change divided by the mean density, 

 they are found to agree. Professor Bigelow appears to attach 

 great significance to this relation, but it is not entirely clear 

 what this significance is. It is of course impossible that the air 

 should radiate precisely like a black body, for it would also 

 absorb radiation like a black body in that case and would be 

 wholly opaque to outside radiation. Nevertheless, within the 

 narrow range of its own limited radiations, the air does behave 

 like a black body. Dr. Paschen has shown that the summits 

 of the bands in a holograph of the spectrum of a radiating gas, 

 where the gas layer is of sufficient depth to exert its maximum 

 radiating power, coincide with points on the continuous curve of 

 black radiation at the same temperature. f Thus the radiation of 

 the air to space, wherever it is free to radiate, must agree in this 

 respect with black radiation. But the air can not radiate freely 

 to space from its lower layers, because the selective absorption 

 by the higher layers is a complete barrier to the selective 



* "On the Coefficients and Exponent of the Eadiation Equation, K 10 = cT, a , 

 in the Earth's Atmosphere. " By Frank H. Bigelow ; (4), vol. xxxv, pp. 

 254-266. 



f'Ueber die Emission der Gase ", von F. Paschen ; Aunalen der Physik 

 und Chemie, N. F., vol. li, pp. 1-39, 1894. 



