METEOROLOGY THEORY 221 
points on this diagram, and all mixtures of the two 
kinds would be represented by points on the straight 
line drawn between the two initial points. 
The practical case occurs when one point represents 
a large homogeneous mass of air, and the other a 
fixed boundary condition at the ground or water sur- 
face. The straight line then represents the mixtures 
that can occur in the vicinity of the boundary. For 
these the line shows specific humidity as a function 
of potential temperature. The relation between poten- 
tial temperature and potential refractive index could 
be shown by a similar diagram. 
Figure 12 shows some corroboration of this method 
and also how the method can be applied. This charac- 
teristic diagram has the same orientation as the 
Rossby diagram which is in routine meteorological 
use but with somewhat different coordinates. 
The ordinate is temperature and the abscissa is 
vapor pressure. A pair of curves gives the vapor pres- 
sure over fresh water and over sea water. The family 
of curves gives refractive index at radio frequencies 
and at a total pressure of 1,000 mb, or h = 0. 
On the diagram are plotted a few of a long series 
of determinations made by reading a sling psychrom- 
eter at half-minute intervals. These were recently 
obtained by the Woods Hole Oceanographic Institu- 
tion at the masthead of a ship crossing the Gulf 
Stream at a time when the air was much colder than 
the water. The water temperature was 70 F, fixing 
the boundary condition. The points lie fairly well 
on the straight line through the boundary value. They 
cover a range of 5 X 10~ in refractive index. Prob- 
ably a greater range would be indicated by a psy- 
chrometer having a more rapid response. 
It is seen that, whenever the fluctuation in refrac- 
tive index at a point in the atmosphere is due to 
turbulent mixing between a large homogeneous mass 
of air and air controlled by a fixed boundary condi- 
tion, the fluctuation may be obtained as follows: 
Measure the average temperature and humidity at this 
point and at the boundary, thus determining the rela- 
tion between refractive index and temperature. Meas- 
ure the fluctuation of temperature, from which the 
fluctuation of refractive index may be found from the 
established relation. 
It may be noted that the water temperature less 
the average air temperature gives a value for the 
temperature deficit. In the same way one may arrive 
at a humidity deficit and an M deficit (one million 
times the deficit of refractive index). Each of these 
quantities is represented on the diagram by the 
change from one end to the other of the line. It follows 
that the suggested method may be stated in terms of 
the relation that the ratio of temperature fluctuation 
VAPOR PRESSURE IN MILLIBARS 
2 Se S SPS Ti 8. 
=f SOO 
ea ee 
A a. fe 
Sic aaa 
oO Ss 
Z 7 o 64 
1 alle Siw 
z 1 2 of l/l 
eS 
Ba] Es 
Fs 12 rd 54 
| aaa AMAA LY VV 
oll col i 
9 48 
S 46 
u 44 
; a2 
A TAAL TAA 
SEP ge 
FAvivi 7a 
VPP OVe USS Acnaew 
PAVIA FAO A ACTA” A OS 
a eA A a Sl 
9 wo UW 2 8 14 8 6 Ff 18 19 20 2 2 23 24 2 
Se a ear ATE 
A 
|i} HAA 
Figure 12. Observations on February 24, 1945 at masthead of ship in Gulf Stream, wind 14 knots. Characteristic 
diagram. Vapor pressure over water is shown by lower bounding curve, over salt water by upper bounding curve. 
The family of curves gives modified index for 1,000 mb and zero height; or (n—1)106 for microwaves at 1,000 mb, zero 
height, where 7 is refractive index at h = 0. 
