14 AIR MASS ANALYSIS 
the chart. One can derive that p:°** 
=) (1000) 7emand) thus pw 
varies only as T1; 6 and (1000)°*** be- 
ing constants for any individual @ line 
starting at 1000 mb. Thus T is linear 
on the abscissae scale, and p°** is 
linear on the ordinate scale. Note also 
that on any given T line the vertical 
intervals between unit @ values di- 
minish upward, since @ varies as 
T/P:**, The convergence upward of 
the dry adiabats follows from the re- 
lation that p.°°“ varies as 71/6, so 
that as @ increases the slope T:/@ de- 
creases along the 1000-mb line towards 
lower values of @. 
[Wet adiabats (= equivalent-poten- 
tial or wet-bulb temperature iso- 
therms) are often added to the adiaba- 
tic chart making it a pseudo-adiabatic 
diagram on which the behavior of sat- 
urated particles can also be studied; 
but this is of no concern to the present 
discussion. Saturation specific humidity 
lines may also be added on the p°*™ 
type of chart. These have the advan- 
tage of being straight lines but are 
curved on the log p diagram. ] 
If the pressure and temperature of 
any particle of air be known, then 
one may find its potential tempera- 
ture with the aid of the adiabatic 
chart by moving the original point 
parallel to the dry ‘adiabatic lines 
until the 1000 mb line is intersected. 
The temperature at this intersection 
is the potential temperature. An 
easier way is to label the slanting 
lines (the dry adiabats) with the par- 
ticular potential temperature which 
remains constant along them. Thus 
any point on the adiabatic chart which 
is determined by a pair of values of 
p and T has one potential tempera- 
ture, which may be ascertained from 
the dry adiabats. Potential tempera- 
ture is practically always expressed 
in degrees Absolute. 
With the help of the adiabatic 
chart and definitions which have been 
given, the student should be able to 
deduce the following important gen- 
eralizations: 
1. The potential temperature along 
a dry adiabatic line is constant. 
2. A decrease in potential tem- 
perature with elevation corresponds 
to a superadiabatic lapse rate. 
8. The greater the rate of increase 
in the potential temperature with ele- 
vation, the greater the stability. 
It is essential that the reader be 
thoroughly familiar with the concept 
of potential temperature in order to 
appreciate the Rossby diagram. 
It should be mentioned here that, 
strictly speaking, the potential tem- 
perature as here defined is not the 
quantity used as the ordinate in the 
Rossby diagram, but a very nearly nu- 
merically-equivalent quantity known 
as the partial potential temperature 
with respect to dry air. The total 
pressure exerted by air is made up 
of the pressure of the dry air (i.e., 
all the gases with the exception of 
water vapor) plus the pressure 
exerted by the water vapor. The 
partial potential temperature with 
respect to dry air is then defined as 
the temperature the particle would 
have if it were reduced adiabatically 
from the pressure exerted solely by 
the dry air to a pressure of 1000 mb. 
The algebraic representation of this 
quantity will serve to clarify the 
definition. If ga represents the partial 
potential temperature with respect to 
dry air, p the total pressure of the 
air, 7 the temperature of the par- 
ticle, and e the partial pressure 
exerted by the water vapor, we have: 
1000 0.288 
o-7 (2) 
p—e 
This is, of course, similar in form to 
the formula for the potential tem- 
perature, (p—e) replacing the p in 
