4 AIR MASS ANALYSIS 
continues to rise, its temperature 
falls, so that the total quantity of wa- 
ter vapor possible within the volume 
of rising air becomes less and less. 
Therefore the rate of cooling of the 
saturated mass becomes greater and 
greater, until at high levels, where 
the moisture content of the rising air 
is almost negligible, its “rate of adi- 
abatie cooling is practically the same 
as that for dry air. 
We are now prepared to deal with 
the types of equilibrium as outlined 
above. 
1. Stable. The rate of cooling for 
an unsaturated particle of air rising 
through the surrounding atmosphere 
is given by the broken line y in fig. 
1. This is a straight line since the 
rate is 1 C deg. per 100 m. Lines 
drawn parallel to would represent 
other dry adiabats at different tem- 
peratures. If we assume the ob- 
served vertical temperature distribu- 
tion (the lapse rate) above 1000 m to 
be represented by the line qi, it is at 
once clear that a particle of air taken 
from any position on the line g: and 
brought up or down will immediately 
find itself of a different temperature 
and hence different density from its 
surroundings. It will consequentiy 
tend to return to its original position. 
For example let us take a particle at 
1000 m. where the temperature is 20° 
C. If we bring this particle up to 
2000 m., it will follow the line y and 
at 2000 m. will assume the tempera- 
ture 10° C. The surrounding air at 
2000 m., however, has the tempera- 
ture 14° C., or 4 deg. warmer than 
the rising particle. Under this con- 
dition the particle must return to its 
former position, coming to rest at 
1000 m, where its temperature is the 
same as the surrounding air. In a 
similar fashion it is easily shown that 
downward motion of individual parti- 
cles originally lying along the line 
ai are hindered, the tendency being 
always to make the particle return 
to its original position. It is clear 
then that the line g: represents a 
stable lapse rate. In other words if 
the lapse rate is less than the dry 
adiabat the layer is stable for un- 
saturated air. 
The rate of adiabatic cooling for a 
rising saturated particle of air is 
represented in fig. 1 by the line B 
Note that 8 is a curved line, since 
the rate of cooling is dependent upon 
the heat of condensation as well as 
upon the expansion. Also note that 
the curve @ tends to straighten, 
gradually approaching the slope of y 
at upper levels, where the moisture 
content becomes smaller and smaller. 
If we now assume a lapse rate of gq 
from 1 to 3 km. it is clear that a ris- 
ing particle of saturated air will fol- 
low the line 8, and will at every stage 
in its ascent be colder than its sur- 
roundings. Thus it will tend to re- 
main at its original position and the 
layer between 1 and 38 km. will, by 
definition, be termed stable with re- 
spect to saturated air. A lapse rate 
less than the saturated adiabat may 
be termed absolutely stable since it is 
stable whether the rising air be dry 
or saturated. 
2. Unstable. Let us assume that 
the lapse rate between 1 and 2 km. 
has the form g; as in fig. 1. A parti- 
cle of air displaced upward from any 
position on the line g3 would follow 
parallel to the dry adiabat y and ob- 
viously would be warmer than the 
surrounding air, level for level. There- 
fore it would continue to rise. The 
layer possessing the lapse rate q3 is 
then unstable with respect to dry air, 
and since the saturated adiabatic 
lapse rate is always less than the dry, 
it is clear that this condition is even 
more unstable for saturated air. The 
line g3 has been constructed to rep- 
resent a special case of instability in 
which the density remains constant 
