METEOROLOGY — THEORY 213 
quantity is not M but differences in M at various 
heights. 
Wet Term. Since 
e = (RH)eé’ 
relative humidity, 
= saturation vapor pressure, 
where RH 
e 
and since e’ is a function of temperature only, it is 
possible to prepare a table giving M, as a function of 
RH and ¢. This is Table 5. 
A table for f, defined by equation (7), is also in- 
cluded, so that if e is known, M,, can be obtained by 
simply taking the product fe as indicated by equation 
(5). Table 6 gives the values of f. 
TABLE 6. f for / from —30 C (—22 F) to 40 C (104 F). 
OTe Val iF UO a tF BOQ a iF 
—30 6.390 —22.0 | — 6 5.289 +21.2 | +18 4.449 +644 
—29 6.388 —20.2 | — 5 5.250 +23.0 | +19 4.419 +66.2 
—28 6.286 —18.4 | — 4 5.210 +24.8 | +20 4.389 +68.0 
—27 6.2838 —16.6 | — 3 5.172 +26.6 | +21 4.359 +69.8 
—26 6.183 —14.8 | — 2 5.133 +28.4 | +22 4.330 +71.6 
—25 6.184 —13.0 | — 1 5.095 +30.2 | +23 4.300 +73.4 
—24 6.084 —11.2 | + 0 5.059 +32.0 | +24 4.271 +75.2 
—23 6.036 — 9.4] + 1 5.021 +33.8 | +25 4.241 +77.0 
—22 5.988 — 7.6] + 2 4.984 +35.6 | +26 4.213 +78.8 
—21 5.940 — 5.8 | + 3 4.948 +37.4 | +27 4.186 +80.6 
—20 5.894 — 40] + 4 4.913 +39.2 | +28 4.158 +82.4 
—19 5.847 — 2.2] + 5 4.878 +41.0 | +29 4.130 +84.2 
—18 5.801 — .4] + 6 4.843 +42.8 | +30 4.102 +86.0 
—17 5.755 + 1.4) + 7 4.808 +44.6 | +31 4.076 +87.8 
—16 5.710 + 3.2} + 8 4.773 +46.4 | +32 4.049 +89.6 
—15 5.666 + 5.0 | + 9 4.738 +48.2 | +33 4.022 +91.4 
—14 5.622 + 6.8 | +10 4.706 +50.0 | +34 3.997 +93.2 
—13 5.579 + 8.6 | +11 4.666 +51.8 | +35 3.970 +95.0 
—12 5.587 +10.4 | +12 4.640 +53.6 | +386 3.944 +96.8 
—11 5.494 +12.2 | +13 4.607 +55.4 | +37 3.918 +98.6 
—10 5.452 +14.0 | +14 4.576 +57.2 | +38 3.893 +100.4 
— 9 5.410 415.8 | +15 4.543 +59.0 | +39 3.868 +102.2 
— 8 5.370 +17.6 | +16 4.511 +60.8 | +40 3.844 +104.0 
— 7 5.329 +19.4 | +17 4.480 +62.6 
Error. The discussion of this first. group of tables 
is concluded with some observations on their order 
of accuracy. Theoretically any errors which arise are 
due to the expansions used in calculating Mg. At a 
height as great as 10,000 m, A¢ might be, say, 70°. 
This would give GAT = 13.3 for ¢ = 0. If the next 
term had been included the correction would have been 
only a fraction of this amount. Since at these heights 
M—1,800, we are safe in saying that the relative error 
is less than 0.5 per cent, probably much less than this 
amount. At altitudes of 1,000 m or less the approxima- 
tion introduces errors too small to be reflected in the 
fourth significant figure. 
Aside from this theoretical error, there are errors 
in the table due to rounding off in the numerical work. 
An effort was made to keep this error less than 0.1 
M units. 
Curvature Term. Table 7 gives the values of the 
linear term h/a X 10°, which must be added to obtain 
the index of refraction modified for use on a “plane 
earth” diagram. 
Taste 7. M,forh from 10 m (382.8 ft) to 2,000 m (6,562 ft). 
h(m) M, h(ft) | h(m) M, _ A(t) h(m) M, h(t) 
10 16 32.8 | 280 44.0 918.6 625 98.1 2,051.0 
20 3.1 65.6 | 290 45.5 951.4 650 102.1 2,133.0 
30 4.7 98.4 | 300 47.1 984.3 675 106.0 2,215.0 
40 6.3 131.2 | 310 48.7 1,017.0 700 109.9 2,297.0 
50 7.9 164.0 | 320 50.2 1,050.0 725 113.8 2,379.0 
60 9.4 196.9 | 330 51.8 1,083.0 750.117.8 2,461.0 
70 11.0 229.7 | 340 53.4 1,115.0 775 121.7 2,543.0 
80 12.6 262.5 | 350 55.0 1,148.0 800 125.6 .2,625.0 
90 14.1 295.3 | 360 56.5 1,181.0 825 129.5 2,707.0 
100 15.7 328.1 | 370 58.1 1,214.0 850 133.5 2,789.0 
110 17.3 360.9 | 380 59.7 1,247.0 875 137.4 2,871.0 
120 18.8 393.7 | 390 61.2 1,280.0 900 141.3 2,953.0 
130 20.4 426.5 | 400 62.8 1,312.0 925 145.2 3,035.0 
140 22.0 459.3 | 410 64.4 1,345.0 950 149.2 3,117.0 
150 23.6 492.1 | 420 65.9 1,378.0 975 153.1 3,199.0 
160 25.1 524.9 | 430 67.5 1,411.0 | 1,000 157.0 3,280.0 
170 26.7 557.7 | 440 69.1 1,444.0 | 1,100 172.7 3,609.0 
180 28.3 590.6 | 450 70.7 1,476.0 | 1,200 188.4 3,937.0 
190 29.8 623.4 | 460 72.2 1,509.0 | 1,300 204.1 4,265.0 
200 31.4 656.2 | 470 73.8 1,542.0 | 1,400 219.8 4,593.0 
210 33.0 689.0 | 480 75.4 1,575.0 | 1,500 235.5 4,921.0 
220 34.5 721.8 | 490 76.9 1,608.0 | 1,600 251.2 5,249.0 
230 36.1 754.6 | 500 78.5 1,640.0 | 1,700 266.9 5,577.0 
240 37.7 787.4 | 525 82.4 1,722.0 | 1,800 282.6 5,906.0 
250 39.3 820.2 | 550 86.4 1,804.0 | 1,900 298.3 6,234.0 
260 40.8 853.0 | 575 90.3 1,886.0 | 2,000 314.0 6,562.0 
270 42.4 885.8 | 600 94.2 1,969.0 
TaseEs 8 To 11 — Mixine Ratio AND 
TEMPERATURE GIVEN 
In terms of atmospheric pressure and water vapor 
pressure, the mixing ratio w is given by 
623¢e 
y= ¢ (18) 
p—e 
Since w involves the pressure p, the scheme used in 
the first group of tables must be modified. Using 
equation (13), equation (2) assumes the form 
M =F (P,w) 1. Opp (14) 
0 
where 
A w BD 
(0,0) = mo + oe (eT): (15) 
Table 8 gives Ff for the range of usable values of 
temperature and mixing ratio. Since F is sensitive 
to variations in both 7 and w, the tabulation is made 
for all integral values of both 7 and w to avoid labori- 
ous interpolation. 
Following the procedure used in the discussion of 
dry term on page 208 ,the pressure p is calculated 
from equation (8). These results are given in Table 
9. In view of the insensitivity of p to 7’, the average 
temperature, it is unnecessary to tabulate p for all 
values of 7’; it is sufficient to tabulate p at 5-degree 
intervals of 7. 
The term Ch has been calculated in connection with 
the first group of tables and is given in Table 7. 
TABLES 10 AND 11 For Usr at Low AntrirupEs 
An objectionable feature of the method given in 
the preceding section is that it involves taking the 
product, pF’, which makes an application of the tables 
