63 
1918-19.] The Origin of Anticyclones and Depressions. 
for values of H between x and y , and p is increased over A and diminished 
over C. 
Thus anticyclonic conditions are produced in the district A at all 
levels above H = x and cyclonic conditions over C, as indicated in fig. 1. 
These pressure changes at any given level are caused by a general 
elevation of the air over A due to expansion in the heated portion, and 
by a general lowering of the air over C due to contraction in the cooled 
portion. That such expansion and contraction actually occurs follows at 
once from equation (1). For the value of p at H = & is unaltered, while 
at all greater heights p is increased over A; hence the mean value of 
~ diminished ^ or the range x — y, and this demands that the actual 
value must be diminished in some part at least of the range, and certainly, 
in the region just above H = x; and g is a function of H only; therefore p 
must be diminished, i.e. expansion has occurred. 
This upward movement of the air over A (and downward movement 
over C) distorts the isobaric surfaces, but as the total movement is not 
great the tendency for the air to flow out of A and into C is not sufficient 
to produce rapid movement, and I shall show later that an opposite effect 
arises which may (and generally does) more than counterbalance this 
tendency. 
At levels above H — y in the region over A the pressure is increased, 
and the temperature unaltered ; hence from equations 3 and 5 the density 
is greater and the entropy less than before. 
In the region of expansion lying just above H = cc the pressure is 
increased and the density diminished, hence the entropy is increased 
(equation 5). 
By similar reasoning it may be shown that over C there is an increase 
of density and a diminution of entropy in the region just above H = x, and 
a decrease of density and increase of entropy at all levels above H — y. 
All these effects are indicated in fig. 1. 
So far, the changes considered have been those occurring at definite 
levels; it is interesting to compare with these the changes in definite 
portions of air. Our postulate that there has been as yet no intrusion or 
expulsion of air from the areas considered (i.e. no horizontal compression 
or expansion), combined with the condition that the lapse rate does not 
exceed the adiabatic lapse rate, enables us to recognise a definite portion 
of air by the condition that its pressure — due to the weight of superin- 
cumbent air — is constant (this statement neglects the effect of the small 
variation of g with height, see above). 
