86 
THERMODYNAMIC METEOROLOGY 
COMPARISON OF Ri„ WITH R\ 
Height z 
116 
500 
1000 
1500 
2000 
2500 
3000 
4000 
5000 
Rio 
287.28 
286.87 
285.34 
283.14 
280.50 
278.21 
275.59 
272.06 
R'i o 
282.91 
287.35 
285.65 
281.68 
277.95 
275.46 
274.09 
268.89 
R' 10 is generally smaller than R 10 in these observations. 
Pi -Po . 
The term 
Pio 
is taken directly from Table 17, and 
Wi — Wo is easily computed. Then Ui—U 0 follows from (335). 
In computing the radiation, K i0 = ^~Z. V °> the values of 
v are the reciprocal of the density p in Table 14. Had p been 
computed by formula (175), which takes R constant, instead of 
by (176), with R variable, it is seen at once how erroneous 
would have been the derived radiations, because the values of 
K w depend upon the small differences (z>i — v 0 ) in succession. 
These radiations are mean values for the strata concerned. It 
is important to study the relation of the radiation to the tem 
perature, and to compare the exponents of formula (340) with 
the exponent of a full radiation in the Stephan Law, which is 4. 
This subject is complex in the earth’s atmosphere as will be in 
dicated. The problem is as follows: The values of K in re 
lation to T by (340) are in the form of ratios, whereas in the 
Stephan Law (344) they stand related through a coefficient. 
If the constituent of the ratio is in the form (343), it is quite 
certain that the coefficients (C . c) are not equal, nor are the expo 
nents (.A . a). We proceed to develop the relations between 
C and c, A and a. The equation (343) gives three terms, K w , 
A, T 10 , from which to compute C, and it is necessary to indicate 
what are the relative values of log C and A. With the data of 
Table 19 in the first section of Table 20, compute A log T 10 
and subtract this from log Ki 0 to obtain log C. The negative 
sign before the logarithm affects only the characteristic. Thus, 
logarithm — 11.944 gives the number 8.79 X 10 _u . In this