METEOROLOGY — THEORY 219 
by a well-known expansion, for the natural logarithm. 
The first term in the series (24) gives exactly equation 
(23). Hence, the approximation (22) amounts to 
dropping the higher-order terms in equation (24). 
The ratio of the second term to the first is only 
%[(T,—T,)/(2,+17,)]? or about two parts in 
10,000 for the first 2,000 m of the standard atmos- 
phere. This comes out to give an error of about 0.006 
mb in the pressure at this height. This is certainly 
negligible. 
For a nonlinear atmosphere the question of the 
error in equation (22) is chiefly a question of the 
accuracy in determining 7’, since any such atmosphere 
can be broken up into a number of layers in each of 
which 7’ is linear in h. 
CoNSTANTS OF THE INDEX OF REFRACTION 
ForMULA 
The formula for the ordinary index of refraction, 
n, which has been used in calculating these tables, is 
Ap_D 
(n — 1) 10° = +e (25) 
pe 
where A = 79, D = 11, B = 3.8 X 105. (26) 
The formula given in reference 11, in the unite 
adopted here, is the same as (25) but with 
A = 78.7, D = 11.2, B = 3.77 X 10°. (27) 
The formula used by Bell Telephone Laboratories 
(Monograph B-870, 1935) is also (25) but with 
A = 79:1, D = 10.9, B = 3.81 X 10°. (28) 
The third significant figure in all these constant: 
is questionable. Moreover, the absolute value of n 
(or M) is not important but only the slopes of M 
curves. For this purpose it is sufficient if the right 
form of equation and approximately correct, values of 
the constants are chosen. Hence, in these tables, equa- 
tions (25) and (26) were adopted 
DIURNAL VARIATION OF THE 
GRADIENT OF MODIFIED M INDEXe 
The vertical gradient of modified refractive index 
depends on the vapor pressure and temperature 
gradients according to the formula 
dM _ 79 ee = O14?) ED 
ey E CRE 
9600¢ aT 1 
0.1 = 
& ea «)e dz ls 
79 dp 
T dz 
"By Raymond Wexler, Camp Evans Signal Laboratory. 
*Symbols have same meaning as in preceding section, 
except that h is replaced by s. 
Coefficients of vapor pressure and temperature gradi- 
ents are about 4.5 and 1.5 respectively. The third term 
gives a positive increase of 4 M units per 100 ft. In 
this paper’** the diurnal variation of the vertical M 
gradient will be inferred from the diurnal variation 
of temperature and humidity gradients. 
Temperature Lapse Rates over Land 
On clear nights with light winds temperature in- 
versions form in the lower atmosphere. The follow- 
ing characteristics of these inversions are to be noted. 
1. The inversion begins as a shallow layer near the 
ground before sunset, rises sharply after sunset and 
then more gradually to a maximum height at about 
sunrise. : 
2. The temperature difference between two fixed 
levels in the first 100 ft of the ground is maximum 
shortly before sunset and oscillates about a slightly 
lower value the remainder of the night. (See Figure 
10.) 
Observations at Leafield, England, and Potsdam, 
Germany, corroborate this. This phenomenon is prob- 
ably due to the more favorable humidity gradient in 
the early evening and to the heat of condensation re- 
leased by dew formation in the later night hours. 
Superadiabatic lapse rates characterize the lower 
atmosphere during clear days. The lapse rates in- 
crease sharply from sunrise to 3 or 4 hours after, 
gradually reach a maximum at about noon, and de- 
crease sharply after the time.of the maximum tem- 
perature. 
Temperature Lapse Rates over the Sea 
The air over the sea has a greater diurnal range 
than the sea itself. Over the Sunda Sea this range 
has been observed to increase from 0.5 C at the sur- 
SUNSET 
~/ 12.4-1.2 M 
eo gees 
TIME (GMT) 
4 
ale 
~— 
TEMPERATURE DIFFERENCE 
IN DEGREES F 
Figure 10. Mean temperature variation on clear June 
days at Leafield, England. 
face to 1.5 C at 500 m. The night lapse rates over the 
ocean are therefore more unstable than the day lapse 
rates. Observations of the Meteor expedition in equa- 
torial regions revealed a mean inversion of 0.2 C in 
the first 9 m during the early afternoon, whereas in 
the early morning a mean lapse of 0.6 C was observed. 
Vertical Vapor Pressure Gradients 
At locations where a continuous supply of moisture 
