Earth? s Nonadiabatic Atmosphere. 517 



It may be noted in passing that Cj> is usually treated as a con- 

 stant in the works of meteorologists, as by Margules in his 

 paper, Uber die Energie der Sturm e, k. k. Centr-Anst., Wien, 

 1903, where n=l and R is a constant ; or by v. Bjerknes in 

 his Dynamic Meteorology and Hydrography, Carnegie Institu- 

 tion of Washington, 1910, .Formula B, page 51, which gives 



J: _ i- nk _ i 



the value of — = I fft I a , thus making B,=R , 



and the derivation of — , inconsistent with that of p , as may 



be seen by comparing (6), (7), (8). The system of units 

 employed by v. Bjerknes makes g — 1. 



We have, therefore, adopted as the working formulas : 



(6) 



k 



P /T\fc=l 



p„~\tJ • 



nk 

 P /T\fcZI 



Po~\t o ; • 



(8) 



Po \ A J 



■ n 



(8)' 



R = R„. 



R /T \ n-1 



r;~\tJ 



(9) 



qp. = B*-. 



C„ = R * . 



It will be often convenient in making transformations to use 

 the following auxiliary formulas. The mean values for T, and 

 T are expressed by T 10 , or for Cp, and Cp by Gp 10 . 



(10) n x Q P% (^-T.) = Q P% (T a -T ) 



(11) n I -q Pli (T 1 -T i ) = qp li (T.-T i ) 



(12) PP M = B».i^i* 



dT T,-! 1 ,, l T, 1 



T" = ^F = "M log ~T~ = M~ (log T ' ~ log T ^- 



(i.) /. 



nA . rdT* T a -T n 1 T a 1 



5 ) ^= ( ^T ) -M- log l:=^r'io o g R 1 - log Ro). 



