254 Bigelow — Radiation in the Earth? s Atmosphere. 



Art. XX. — On the Coefficients and Exponent of the Radia- 

 tion Equation, E 10 = cT 10 & , in the Earth) s Atmosphere; 

 by Frank H. Bigelow. 



In my paper on this subject, in this Journal for December, 

 1912, the values of the exponent A, in the equation, 



o \ ■*■ a' 



were computed from the observed temperatures T^T,,, on the 

 top and bottom of a given stratum, through the radiation 

 K^K,,. The values of A depend upon the ratio T./T,,, and 

 wherever the temperature changes but slightly in passing 

 through a stratum, for example 1000 meters thick, as occurs 

 in the isothermal region, these are often very large. When T, 

 is a little less than T , A is large and positive; when T t is a 

 little larger than T , A is large and negative. The immediate 

 problem is, therefore, to determine the coefficient and expo- 

 nent in 



K 10 = cT 10 % (2) 



corresponding with the radiation equation. The ratio equa- 

 tion was formed on the supposition that for two levels c 1 = <? , 

 and a l = a — A, as for instance, 



K, cT*i /T\ A 



K -c T ao -VToi (3) 



In the free air this is not usually the fact, so that the special 

 case cannot be accepted as general, and the values of c x and c , 

 or a z and a , are not equal to each other. We proceed as 

 follows (Table 1, page 255) : 



In order that the terms of the problem may be more fully 

 understood, the several steps are reproduced from the computa- 

 tions on the balloon ascension of May 5, 1909, at Linden burg, 

 Germany, in latitude 52°, and by applying the working 

 formulas in succession to the observed temperatures at the 

 several levels from 116 to 17,000 meters, we compute the fol- 

 lowing terms : n the ratio of the adiabatic to the observed tem- 

 perature-fall in the several strata, P the pressure in kilograms 

 per square meter, p the density of the air per cubic meter, R 

 the variable gas coefficient in the Boyle-Gay Lussac Law, 

 P = p PT,* Cp 10 the mean non-adiabatic specific heat in the 

 stratum, ^{q?—q*) the change in the kinetic energy of circula- 



* The usual gas equation is assumed to be applicable, although heat trans- 

 ference to neighboring air masses and air circulation can not be prevented 

 in the free air. Consequently, the non-adiabatic gas coefficient, E J0 , must 

 vary, while R a obtained from laboratory experiments under adiabatic condi- 



