61 
1918-19.] The Origin of Anticyclones and Depressions. 
temperature and pressure (subject to the conditions mentioned above), 
and y is the “ adiabatic constant” for air** 1*41. 
From these two equations it is easy to derive others by means of which 
any of the four quantities p, p, 0, E can be expressed in terms of any two 
of the others. For convenience of reference the results are here tabulated 
without proof. 
(y-l)K _e 
p = Kp 0 = K y e « p y = e K 0y~ 1 
i (y-i)e i 1 
'-s-v 7 ‘ ^ T_1 • ■ • • • • <3) 
(y-i)B 7-1 Y -i 7 -i (y - i)e 
0 = - = e * p v =« P e ” (*) 
KCl L 
Substituting in equation 1 the first value of p from equation 3, we find 
(6) 
a well-known equation. 
Hence if B, the barometric pressure at the level H = 0 (ground level) 
is known, and if 6, like g, is given as a function of H, the pressure (and 
by inference the density and entropy) at every height is absolutely 
determined. 
Now let us assume that over some area A the air between heights x 
and y is cooled, and over another area C the air in the same layer is 
heated, the temperature being unaltered at all other heights and in the 
surrounding undisturbed area U (see fig. 1). The temperature changes 
are assumed to be such that the lapse rate is not made to exceed the 
adiabatic rate and that no condensation occurs. 
In the absence of an “ immediate inrush of air ” over C, and an 
“ immediate expulsion of air ” over A, the barometric pressure at level 
H = 0 will remain B. 
For values of H <x, J q i s unchanged. 
.*. p, p, and E are unchanged, both over A and over C. 
For values x<H <y, 0 is increased over A and diminished over C. 
