the gram, the second and the centigrade degrees are adopted as
units of measure, and differs for each gas. For aqueous vapour
in a gaseous state and not near the point of condensation R has the
value 47·061. For ordinary air in which x is the mass of the aqueous
vapour that is mixed with the unit mass of dry air, the above
equation becomes pv =(29·272 + 47·061x) T. This equation is
sometimes known as the equation of condition peculiar to the
gaseous state. It may also be properly called the equation of
elasticity or the elastic equation for gases, as expressing the fact
that the elastic pressure p depends upon the temperature and the
volume. The most exact equations given by Van der Waals,
Clausius, Thiesen, are not needed by us for the pressures that occur
in meteorology.
Diffusion.—In comparison with the convective actions of the winds, it may be said that it is difficult for aqueous vapour to diffuse in the air. In fact, the distribution of moisture is carried on principally by the horizontal convection due to the wind and the vertical convection due to ascending and descending currents. Diffusion proper, however, comes into play in the first moments of the process of evaporation. The coefficient of diffusion for aqueous vapour from a pure water surface into the atmosphere is 0·18 according to Stefan, or 0·1980 according to Winkelmann; that is to say, for a unit surface of 1 sq. centimetre, and a unit gradient of vapour pressure of one atmosphere per centimetre, as we proceed from the water surface into the still dry air, at the standard pressure and temperature, and quantity of moisture diffused is 0·1980 grams per second. This coefficient increases with the temperature, and is 0·2827 at 49·5° C. But the gradient of vapour pressure, and therefore rate of diffusion, diminishes very rapidly at a small distance from the free surface of the water, so that the most important condition facilitating evaporation is the action of the wind.
Viscosity.—When the atmosphere is in motion each layer is a drag upon the adjacent one that moves a little faster than it does. This drag is the so-called molecular or internal friction or viscosity. The coefficient of viscosity in gases increases with the absolute temperature, and its value is given by an equation like the following; 0·000 248 (1 + 0·0003 665t) 23, which is the formula given by Carl Barus (Ann. Phys., 1889, xxxvi.). This expression implies that for air whose temperature is the absolute zero there is no viscosity, but that at a temperature (t) of 0° C., or 273° on the absolute scale, a force of 0·000 248 grams is required in order to push or pull a layer of air 1 centimetre square past another layer distant from it by 1 centimetre at a uniform rate of 1 centimetre per second.
Friction.—The general motions of the atmosphere are opposed by the viscosity of the air as a resisting force, but this is an exceedingly feeble resistance as compared with the obstacles encountered on the earth’s surface and the inertia of the rising and falling masses of warm and cold air. The coefficient of friction used in meteorology is deduced from the observations of the winds and results essentially not from viscosity, but from the resistances of all kinds to which the motion of the atmosphere is subjected. The greater part of these resistances consists essentially in a dissipation of the energy of the moving masses by their division into smaller masses which penetrate the quiet air in all directions. The loss of energy due to this process and the conversion of kinetic into potential energy or pressure, if it must be called friction, should perhaps be called convective friction, or, more properly, convective-resistance.
The coefficient of resistance for the free air was determined by Mohn and Ferrel by the following considerations. When the winds, temperatures and barometric pressures are steady for a considerable time, as in the trade winds, monsoons and stationary Cyclones, it is the barometric gradient that overcomes the resistances, while the resulting wind is deflected to the right (in the northern hemisphere) by the influence of the centrifugal force of the diurnal rotation (ω) of the earth. The wind, therefore, makes a constant angle (α) with the direction of the gradient (G). There is also a slight centrifugal force to be considered if the winds are circulating with velocity v and radius (r) about a storm centre, but neglecting this we have approximately for the latitude
G sin α＝2ωv sin φ, G cos α＝ κv,
where (κ) is the coefficient connecting the wind-velocity (v) with the component of the gradient pressure in the direction of the wind. These relations give κ＝2ω sin φ/ tan α. The values of α and v as read off from the map of winds and isotherms at sea level give us the data for computing the coefficients for oceanic and continental surfaces respectively, expressed in the same units as those used for G and v. The extreme values of this coefficient of friction were found by Guldberg and Mohn to be 0·00002 for the free ocean and 0·00012 for the irregular surface of the land. For Norwegian land stations Mohn found φ＝61° α＝56·5° κ＝0·0000845. For the interior of North America Elias Loomis found φ＝37·5° α＝42·2° κ＝0·0000803.
Gravity.—The weight of the atmosphere depends primarily upon the action of gravity, which gives a downward pressure to every particle. Owing to the elastic compressibility of the air, this downward pressure is converted at once into an elastic pressure in all directions. The force of gravity varies with the latitude and the altitude, and in any exact work its variations must be taken into account. Its value is well represented by the formula due to Helmert, g＝980·6 (1 − 0·0026 cos 2φ) × (1 − fh), where φ represents the latitude of the station and h the altitude. The coefficient f is small and has a different value according as the station is raised above the earth’s surface by a continent, as, for instance, on a mountain top, or by the ocean, as on a ship sailing over the sea, or in the free air, as in a balloon. Its different values are sufficiently well known for meteorological needs, and are utilized most discreetly in the elaborate discussion of the hypsometric formula published by Angot in 1899 in the memoirs of the Central Meteorological Bureau of France.
Temperature at Sea-Level.—The temperature of the air at the surfaces of the earth and ocean and throughout the atmosphere is the fundamental element of dynamic meteorology. It is best exhibited by means of isotherms or lines of equal temperature drawn on charts of the globe for a series of level surfaces at or above sea-level. It can also be expressed analytically by spherical harmonic functions, as was first done by Schoch. The normal distribution of atmospheric temperature for each month of the year over the whole globe was first given by Buchan in his charts of 1868 and of 1888 (see also the U.S. Weather Bureau “Bulletin A,” of 1893, and Buchan’s edition of Bartholomew’s Physical Atlas, London, 1899). The temperatures, as thus charted, have been corrected so as to represent a. uniform special set of years and the conditions at sea-level, in order to constitute a homogeneous system. The actual temperature near the ground at any altitude on a continent or island may be obtained from these charts by subtracting 0·5°C. for each 100 metres of elevation of the ground above sea-level, or 1° F. for 350 ft. This reduction, however, applies specifically to temperatures observed near the surface of the ground, and cannot be used with any confidence to determine the temperature of points in the free air at any distance above the land or ocean. On all such charts the reader will notice the high temperatures near the ground in the interior of each of the continents in the summer season and the low temperatures in the winter season. In February the average temperatures in the northern hemisphere are not lowest near the North Pole, but in the interiors of Siberia and North America; in the southern hemisphere they are at the same time highest in Australia, and Africa and South America. In August the average temperatures are unexpectedly high in the interior of Asia and North America, but low in Australia and Africa.
Temperature at Upper Levels.—The vertical distribution of temperature and moisture in the free air must be studied in detail in order to understand both the general and the special systems of circulation that characterize the earth’s atmosphere. Many observations on mountains and in balloons were made during the 19th century in order to ascertain the facts with regard to the decrease of temperature as we ascend in the atmosphere; but it is now recognized that these observations were largely affected by local influences due to the insufficient ventilation of the thermometers and the nearness of the ground and the balloon. Strenuous efforts are being directed to the elimination of these disturbing elements, and to the continuous recording of the temperature of the free air by means of delicate thermographs carried up to great heights by small free “sounding balloons,” and to lesser heights by means of kites. Many international balloon ascents have been made since 1890, and a large amount of information has been secured.
The development of kite-work in the United States began in October 1893, at the World’s Columbian Congress at Chicago, when Professor M. W. Harrington ordered Professor C. F. Marvin of the Weather Bureau to take up the development of the Hargrave or box kite for meteorological work. At that time W. A. Eddy of Bayonne, New Jersey, was applying his “Malay” kite to raising and displaying heavy objects, and in August 1894 (at the suggestion of Professor Cleveland Abbe) he visited the private observatory of A. L. Rotch at Blue Hill and demonstrated the value of his Malay kite for aerial research. The first work done at this observatory with crude apparatus was rapidly improved upon, while at the same time Professor Marvin at Washington was developing the Hargrave kite and auxiliary apparatus, which he brought up to the point of maximum efficiency and trustworthiness. When he reported his apparatus as ready to be used by the Weather Bureau on a large scale, Professor Willis L. Moore, as the successor of Professor Harrington, ordered its actual use at seventeen kite stations in July 1898. This, was the first attempt to prepare isotherms for a special hour over a large area at some high level, such as 1 m., in the free air. Daily meteorological charts were prepared for the region covered by these observations; but it became necessary to discontinue them, and nothing more was done by the Weather Bureau in this line of work until the inauguration of kite work at Mount Weather in 1906. Meanwhile a special method for the reduction and study of such observations was devised by Bjerknes and Sandstrom, and was published in the Trans. American Philosophical Society (Philadelphia, 1906). The general average results as to temperature gradients were compiled by Dr H. C. Frankenfield and published in
the United States Weather Bureau “Bulletin F.” from these