caused, by this general deep swift upper current of air that began as an ascending east wind above the calm equatorial air but speedily overflowed as west wind settling down to the sea-level in the temperate and polar regions as great areas of high pressure and dry clear cool weather containing air on its return passage to the equator. The upper air is thrown easily into great billows, and wherever it rises the warm equatorial wind flows in beneath it, but when it descends we have blizzards and dry clear weather. It is a covering for the lower strata of air, it flows over them in standing waves and sometimes mixes with them at the surface of contact. It receives daily accessions from below and gives out corresponding accessions to the lower strata, by a process of overturning such as has been studied theoretically by Margules and Bigelow. At the fifth conference of the International Committee on Scientific Aeronautics (Milan, October 1906) Rykatchef presented the results of kite-work during 1904 and 1905 at Pavlosk, near St Petersburg, from which we select the results for these two years given in table at foot of page 270.
Many inversions occur during January below 1000 metres. The decrease is more rapid in summer than in winter and in clear weather than in cloudy, but of course these observations did not extend above the upper level of the cumulus cloud layer. A general survey of the existing state of knowledge of the upper atmosphere is given in the Report of the British Association for 1910.
Distribution of Aqueous Vapour.—The distribution of aqueous vapour is best shown by lines of equal dew-point or vapour tension, though for some purposes lines of equal relative humidity are convenient. The dew-point lines are not usually shown on charts, partly because the lines of vapour pressure are approximately parallel to the lines of mean temperature of the air, and partly because the observations are of very unequal accuracy in different portions of the globe. In general we may consider any isotherm as agreeing with the dew-point line for dew-points a few degrees. lower than the temperature of the air. The distribution of moisture is quite irregular both in a horizontal and in a vertical direction. On charts of the world we may draw lines based on actual observations to represent equal degrees of relative humidity, or equal dew-points and vapour pressures; but as regards the distribution of moisture in a vertical direction we are, in the absence of specific observations, generally forced to assume that the vapour pressure at any altitude h follows the average law first deduced from a limited number of observations by Hann, and expressed by the logarithmic equation, , which is quite analogous to the elementary hypsometric formula, . Therefore, in general, the ratio between the pressure of the vapour and the pressure of the atmosphere at any altitude is represented by the approximate formula, . Of course these relations can only represent average or normal conditions, which may. be departed from very widely at any moment; they have, however, been found to agree remarkably with all observations which have as yet been published. The average results are given in the following table, which is abbreviated from one published by Hann, but with the addition of the work done by the U.S. Weather Bureau, as reduced by Dr Frankenfield in 1899. The vapour constituent of the atmosphere is not distributed according to the law of gaseous diffusion, but, like temperature and the ratio between oxygen and nitrogen, is controlled by other laws prescribed by the winds and currents, namely—convection.
Diminution of the Relative Vapour Pressure with Altitude.
| Authority. | 1500 ft. |
2000 ft. |
3000 ft. |
4000 ft. |
5000 ft. |
6000 ft. |
7000 ft. |
8000 ft. |
No. Obs. |
| Kites. | 0.82 | 0.78 | 0.70 | 0.61 | 0.52 | 0.49 | 0.39 | 0.44 | 1123 |
| (U.S.W.B.) | |||||||||
| Balloons. | 0.97 | 0.96 | 0.87 | 0.68 | 0.44 | 0.59 | — | — | 4 |
| (Hammon.) | |||||||||
| Balloons. | 0.89 | 0.83 | 0.80 | 0.78 | 0.67 | 0.46 | 0.44 | — | 2 |
| (Hazen.) | |||||||||
| Balloons. | 0.84 | 0.80 | 0.66 | 0.61 | 0.50 | 0.54 | 0.41 | 0.37 | 15 |
| (Hann.) | |||||||||
| Mountains | 0.83 | 0.81 | 0.80 | 0.66 | 0.61 | 0.58 | 0.55 | 0.47 | 6 |
| (Hann.) | |||||||||
| Computed | 0.85 | 0.81 | 0.72 | 0.65 | 0.58 | 0.52 | 0.47 | 0.42 | — |
| by Hann. |
Note.—The vapour pressure at any altitude is supposed to be expressed as a fraction of that observed at the ground. When the altitudes are given in ft. Hann’s formula becomes log e/e0＝h/29539.
| Alt. | km. | km. | km. | km. | km. | km. | km. | km. | km. | km. | km. | km. | km. |
| 0·5 | 1·0 | 1·5 | 2·0 | 2·5 | 3·0 | 3·5 | 4·0 | 4·5 | 5·0 | 6·0 | 7·0 | 8·0 | |
| mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm. | |
| Stüring | 0·83 | 0·68 | 0·51 | 0·41 | 0·34 | 0·26 | 0·20 | 0·17 | 0·14 | 0·11 | 0·054 | 0·028 | 0·013 |
| Hann | 0·83 | 0·70 | 0·58 | 0·48 | 0·40 | 0·34 | 0·28 | 0·23 | 0·19 | 0·16 | — | — | — |
From 78 high balloon voyages in Germany, 1887–1899, Süring deduced the average vapour pressure in millimetres as found in the first line of the table at foot of this page (see Wissenschaftliche Luftffahrten, Bd. III., and Hann, Lehrbuch, 1906, p. 169). The observations on mountains gave Hann the pressures in the second line. Süring’s figures result from the use of Assmann’s ventilated psychrometer and are therefore very reliable.
The vapour pressure in mm. in free air over Europe is best given by Süring’s formula
where the altitude is to be expressed in kilometres. From this formula we derive the “specific moisture” or the mass of vapour contained in a kilogram of moist air as given in the following table whose numbers do not appreciably differ from “the mixing ratio” or quantity of moisture associated with a kilogram of dry air. The relative humidities vary irregularly depending on convection currents, but in clear weather when descending currents prevail they have been observed in America and over Berlin as shown in the third and fourth columns of the following table:—
Observed Specific Moisture and Relative Humidity.
| Alt. | Specific Moisture |
Relative Humidity. | |
| U.S.A. | Berlin. | ||
| Km. | % | % | |
| 0.0 | 1.00 | — | 77 |
| 0.5 | — | 65 | 71 |
| 1.0 | 0.76 | 65 | 71 |
| 1.5 | 0.65 | 59 | 62 |
| 2.0 | 0.55 | 59 | 57 |
| 2.5 | 0.47 | 45 | 58 |
| 3.0 | 0.39 | — | 55 |
| 3.5 | — | — | 49 |
| 4.0 | 0.26 | — | 53 |
| 4.5 | — | — | 54 |
| 5.0 | 0.17 | — | — |
| 5.6 | 0.11 | — | — |
| 5.7 | 0.17 | — | — |
| 5.8 | 0.04 | — | — |
The total amount of vapour in the atmosphere, according to Hann’s formula, is between one-fourth and one-fifth of the amount required by Dalton’s hypothesis, as is illustrated by the following table taken from an article by Cleveland Abbe in the Smithsonian Report for 1888, p. 410:—
Total Vapour in a Vertical Column that is saturated at its base.
| Altitude. Feet. |
Relative Tension = e/e0 |
Actual Weight Gr. per Cubic Foot. |
Total Vapour in the Columns expressed as Inches of Rain. | |||||||
| 0 | 1.000 | 80° F. | 70° F. | 60° F. | 50° F. | 80° F. | 70° F. | 60° F. | 50° F. | |
| 10.95 | 7.99 | 5.76 | 4.09 | 0.0 | 0.0 | 0.0 | 0.0 | |||
| 6000 | 0.524 | 5.75 | 4.19 | 3.02 | 2.14 | 1.3 | 1.0 | 0.7 | 0.5 | |
| 12,000 | 0.275 | 3.01 | 2.20 | 1.58 | 1.12 | 2.1 | 1.5 | 1.1 | 0.8 | |
| 18,000 | 0.144 | 1.58 | 1.15 | 0.83 | 0.59 | 2.5 | 1.8 | 1.3 | 0.9 | |
| 24,000 | 0.075 | 0.82 | 0.62 | 0.43 | 0.31 | 2.7 | 2.0 | 1.4 | 1.0 | |
| 30,000 | 0.040 | 0.43 | 0.32 | 0.23 | 0.16 | 2.8 | 2.1 | 1.5 | 1.1 | |
A heavy rainfall results from the precipitation of only a small percentage of the water contained in the fresh supplies of air brought by the wind; if all moisture were abstracted from the atmosphere it could only affect the barometer throughout the equatorial regions by 2·8/13·6 inches, or about two-tenths of an inch, while at the polar regions the diminution would be much less than one-tenth. Evidently, therefore, it is idle to argue that the fall of pressure in an extensive storm is to be considered as the simple result of the condensation of the vapour into rain.
Barometric Pressure.—The horizontal distribution of barometric pressure over the earth’s surface is shown by the isobars, or lines of equal pressure at sea-level; it can also be expressed by a system of complex spherical harmonics. As the indications of the mercurial barometer must vary with the variation of apparent gravity, whereas those of the aneroid barometer do not, it has been agreed by the International Meteorological Conventions that for scientific purposes all atmospheric pressures, when expressed as barometric readings, must be reduced to one standard value of gravity, namely, its value at sea-level and at 45° of latitude. In this locality its value is such as to give in one second an acceleration of 980·8 centimetres, or 32·2 English ft. per second. The effect of the variation of apparent gravity with latitude is therefore to make the mercurial barometer read too high, between 45° and the equator, and too low, between 45 and the pole. The gravity-correction to be applied to any mercurial barometric-reading at or near sea-level, in order to get the atmospheric pressure in
