256 Bigelow — Radiation in the Earth's Atmosphere. 



P — P 



tion, — -i the mean pressure gradient per unit density, A the 



difference required to balance the check equation, 



* («,-*J = -^~ -*(<z\-?.*)-(Q -Q»), (4) 



/>io 



(Qi""Q ) * ne change in the heat of each cubic meter of air in 

 passing from one level to the other, (S,— S ) the entropy 

 change, (W x — W ) the work done in expanding the air, (U 1 — TJ ) 

 the internal energy, K 10 the mean radiation energy in the stra- 

 tum, A the exponent in the ratio equation (1). 



In order to separate the constituent coefficients c x , c and 

 the constituent exponents #„ a we first compute the coeffici- 

 ents by using the exponent A, in 



K 10 = C T 10 A (5) 



log K 10 =logC-i-AlogT 10 . (6) 



log C = log K 10 -A log T 10 . (7) 



An example of this result is given in Table 1, under log C. 

 In all cases the mean values T 10 are taken to correspond with 

 the mean values K 10 for the stratum. It should be stated that 

 in arranging Table 1 the values of T, P, /?, R are given for the 

 level of the elevation, as in the height column 3, but that for 

 all the derived values of n, Cj? ]0 , and so on, the values against 

 a given elevation are the means for the stratum of which this 

 elevation is the top, and the lower one the bottom of the stra- 

 tum. Since the computation of A, log C, depends upon two 

 preceding steps, there are two vacancies in the column just 

 below. One can supply these omissions by selecting shorter 

 steps in the lower levels, 0, 200, 400 meters, as has been done 

 in computing the diurnal convection. Comparing log C with 

 the observed T it is seen that A is negative for T t > T , and that 

 A and log C have opposite signs, so that the coefficient C is nega- 

 tive. The sign in log C applies only to the characteristic of 

 the logarithm, so that, for example, — 14*180 = 1*52 XlO -14 . 

 Similar computations have been made for twelve balloon ascen- 

 sions, of which ten are mentioned in Table 4 ; the mean values 

 T have been constructed for the hemisphere, in elevation from 

 the surface to 19,000 meters for every 1000 meter level, and for 

 every 10° in latitude from the equator to the north pole. 

 Hence, we have two large series of the values of log C, (1) from 

 twelve original balloon ascensions, and (2) from many mean 



tions is a constant. Similarly, the so-called specific heat is a ratio, or 

 coefficient, Cp a = dQ/dT = (Q a - Q ) -f- (T a - T ), 



constant so long as only adiabatic expansion and contraction occur, but 

 otherwise variable. The adiabatic specific heat Cp a , which exists only in text- 

 books and laboratories, ceases to be applicable on entering the field of 

 meteorology. 



