LAPSE RATES 5 
with elevation. The density, of course, 
is a function of the temperature and 
pressure, and is slightly affected by 
the moisture content. In the atmos- 
phere the pressure decrease with ele- 
vation is such that it nearly always 
overbalances the increase in density 
caused by the usually observed drop 
in temperature with elevation. If the 
temperature falls off sufficiently rap- 
idly with elevation, however, a state 
will be reached wherein the density 
of the air is constant with height. If 
the lapse rate exceeds the value 3.42 
C deg. per 100 m there must be an 
increase in density with elevation— 
obviously a very unstable condition. 
This particular case has been given 
various names, the best one probably 
being mechanical instability. gs rep- 
resents a state of mechanical insta- 
bility. This condition is never ob- 
served in the upper atmosphere, since 
it is such an unstable state. It is, 
however, frequently observed imme- 
diately overlying flat regions which 
become greatly heated during the 
summer daytime hours. 
In the case of instability with sat- 
urated air the lapse rate must be 
greater than the saturated adiabat. 
In fig. 1 the line q: represents such 
a lapse rate between 1 and 3 km. It 
should be noted that the layer above 
3 km. is not unstable for saturated 
air, since the rate of change of the 
temperature along gi above 3 km. is 
less than that along B: 
38. Neutral equilibrium. With dry 
air this state is reached when the 
lapse rate is equal to the dry adiabat. 
Under this condition the rising parti- 
cle will possess the temperature of 
the surrounding air at every stage in 
its ascent. Thus it will neither as- 
sist nor resist displacement. If the 
rising air is saturated then the con- 
dition for neutral equilibrium re- 
quires that the lapse rate equal the 
saturation adiabat. 
4. Conditional equilibrium. It was 
pointed out that the lapse rate given 
by the line gq: is stable for rising air, 
while between 1 and 8 km. it is un- 
stable for saturated air, because the 
lapse rate qi: lies between the saturat- 
ed and the dry adiabat. When this 
state obtains the layer is said to be 
in conditional equilibrium. The con- 
dition is simply that the layer is un- 
stable if saturated, but stable if un- 
saturated. This lapse rate is fre- 
quently observed in aerological sound- 
ings, and has been found to be impor- 
tant in the development of thunder- 
storms and showers. It should be 
noted that the conditional instability 
in the case of fig. 1 extends through 
the layer between 1 and 3 km., and 
no higher. Beyond 3 km. the lapse 
rate g: does not lie between the dry 
adiabat and the saturated adiabat for 
the temperatures at these elevations. 
The rate of change of temperature 
along the line @ (above 3 km.) is 
greater than along the line q:. 
A summary of the above conditions 
is presented in algebraic form be- 
low: where q represents the existing 
rate of change in temperature with 
elevation (the lapse rate) ; y the dry 
adiabatic lapse rate; the B, the satur- 
ated adiabatic lapse rate. 
Condition Type of equilibrium 
a<y Stable for dry air 
a<8 Stable for both dry and saturated air (abso- 
lute stability) 
a>vy Unstable for dry air (absolute instability) 
vy <a< 3.42° C per 100 m. Unstable for saturated air 
a>B Unstable for both dry and saturated air 
a= Neutral for dry air 
a = (6; Neutral for saturated air 
Ba<y Conditional 
a — 3.42 C deg. per 100 m. Upper limit of mechanical stability (density 
remains constant with elevation) 
a > 3.42° C per 100 m. 
All air is mechanically unstable (density in- 
creases 
with height); ‘“auto-convective 
gradient”. 
