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Rh standard units, should be given on the edge of a meteorological chart, unless the isobars shown thereon already contain this correction. On such charts it will be perceived that the barometric pressure at sea-level is by no means uniform over the earth’s surface, and daily weather charts show very great fluctuations in this respect, the lowest pressures being storm centres and the highest pressures areas of clear cool dry weather. But even the normal average charts show high pressures over the continents in the winter and low pressures over the oceans, these conditions being reversed in the summer time; moreover, Schouff (Pogg. Ann., 1832) first demonstrated that the average pressure in the neighbourhood of the equator is slightly less than under either tropic, and that there is a still more remarkable diminution of pressure from either tropic towards its pole. The exact statement of these variations of pressure with latitude was subsequently worked out very precisely by Ferrel, and forms the basis of his explanation of the general circulation of the earth’s atmosphere and its influence on the barometer. The series of monthly charts for the whole globe, compiled by Buchan and published by the Royal Society of Edinburgh in 1868, as well as Buchan’s later and more perfect charts in the meteorology of the “Challenger” Expedition, Edinburgh, 1889, and in Bartholomew’s Atlas, first revealed clearly the fact that the distinct areas of high and low pressure which are located over the continents and the oceans vary during the year in a fairly regular manner, so that the pressure is higher over the continents in the winter season and lower in the summer season, the amount of the change depending principally upon the size of the continent. A part of this annual variation in pressure is undoubtedly introduced by the methods of reduction to sea-level; indeed, if the data of the lower stations are reduced up to the level of 10,000 or 15,000 ft., we sometimes find the barometric conditions quite reversed. These annual changes are intimately connected as cause and effect with the annual changes of temperature, moisture and wind; it is quite erroneous to say that the observed charted pressures control the winds; there is a reaction going on between the wind and the barometric gradient, the resistance and rotation of the earth’s surface, such that the true relation between these factors is a complex but fundamental problem in the mechanics of the atmosphere.

The vertical distribution of pressure as deduced from observation shows a rate of diminution with increasing altitude very closely but not entirely accordant with the laws of static equilibrium, as first elaborated by Laplace in his hypsometric formula. The departures from this law of static equilibrium are sufficient to show that, if our atmosphere is really in a state of equilibrium, it must be a matter of dynamics and not of statics. The general average relation of the density of the air to the altitude and temperature, and the total pressure of the superincumbent atmosphere, are shown in the accompanying diagram (fig. 1), which is taken from a memoir on the equations of motion by Joseph Cottier, published in the U.S. Monthly Weather Review for July 1897. The diminution of pressure with altitude, as shown in this diagram for average conditions, but not for the temporary conditions that continually occur, follows a logarithmic law, and can undoubtedly be extended upwards for the normal atmosphere only to a height of 20 or 30 m., owing to our uncertainty as to the actual conditions in the upper portions of the atmosphere. This diagram is based upon the assumption that the atmosphere is in a state of convective equilibrium such that the ascending and descending masses expand and cool as they ascend, or contract and warm up as they descend, nearly but not quite in accordance with the adiabatic law of the change of temperature in pure gases.

The departure of atmospheric temperatures from the strictly adiabatic law, as shown by Cottier, is undoubtedly due largely to the heat absorbed by and radiated from moist or hazy or dusty air. In 1890, Abbe showed that a very moderate rate of radiation from the atmosphere suffices to explain the coolness of slowly descending air. The absorption by the atmosphere of radiations from the earth and sun, or the balance between warming by absorption and cooling by radiation, is the basis of the arguments of W. J. Humphreys (Astrophysics, Jan. 1909), and E. Gold (Proc. Roy. Soc., 1908, lxxxii., 45 A.), explaining the existence of the “thermal layer.”

The direct evaluation of this radiation and absorption has been attempted by many. The genuine law a(q−p) is adopted by Gold as closely representing nature, whence it follows that (1) the adiabatic rate of cooling in convection currents must cease at a height corresponding to one-half of the barometric pressure at sea-level; (2) an isothermal layer must exist at the level where the absorption of solar radiation equals that of the terrestrial and atmospheric radiation; (3) within this thermal layer convection is difficult or impossible; (4) above this region the vertical temperature gradient must depend essentially on radiation and is less than that needed for convective equilibrium; (5) below this level the atmospheric radiation exceeds the atmospheric absorption and vertical currents can only be kept up by the convection of heat or aqueous vapour from the earth’s surface to the adjacent layer of air.

Limit of the Atmosphere.—The limiting height of the atmosphere must be at some unknown elevation above 20 m. where the temperature falls to absolute zero. But the uncertainty of the various hypotheses as to the physical properties of the upper atmosphere forbids us to entertain any positive ideas on this subject at the present time. If we define the outer limit of the atmosphere as that point at which the diffusion of gases inwards just balances the diffusion outwards, then this limit must be determined not by the hypsometric formula, but by the properties of gases at low temperatures and pressures under conditions as yet uninvestigated by physicists.

Cloudiness.—It is evident that the (q.v.) are formed from clear transparent air by the condensation of the invisible moisture therein into numerous minute particles of water, ice or snow. Notwithstanding their transparency, these individual globules and crystals, when collected in large masses, disperse the solar rays by reflection to such an extent that direct light from the sun is unable to penetrate fog or cloud, and partial darkness results. In a general survey of the atmosphere the geographical distribution of the amount of cloudy sky is important. When the solar heat falls upon the surface of the cloud it is so absorbed and reflected that, on the one hand, scarcely any penetrates to the ground beneath, while on the other hand the upper surface of the cloud becomes unduly heated. Even if this upper surface is completely evaporated, it may continually be renewed from below, and, moreover, the evaporated moisture mixing with the air renders it very much lighter specifically than it would otherwise be. Hence the upper surface of the cloud replaces the surface of the ground and of the ocean; the air in contact with it acquires a higher temperature and greater buoyancy, while the ground and air beneath it remain colder than they would be in sunshine. The average cloudiness over the globe is therefore intimately related to the density and circulation of the atmosphere; it was first charted in general terms by L. Teisserenc de Bort of Paris, about 1886. The manifold modifications of the clouds impress one with the conviction that, when properly understood and interpreted, they will reveal to us the most important features. of the processes going on in the atmosphere. If the farmer and sailor can correctly judge of the weather several hours in advance by a casual glance at the clouds, what may not the professional meteorologist hope to do by a more careful study? Acting on, this idea, in 1868 Abbe asked from all of his correspondent observers full details as to the quantity, kind and direction of motion of each layer of clouds; these were telegraphed daily for publication in the Weather Bulletin of the Cincinnati Observatory, and for use in the weather predictions made at that time. Since January 1872 similar data have been regularly telegraphed for the use of the U.S. Weather Bureau in preparing forecasts, although the special cloud maps that were compiled thrice daily have not been published, owing to the expense. These data were also published in full in the Bulletin of the International Simultaneous Meteorological Observations for the whole northern hemisphere during the years 1875–1884. Abbe’s work on the U.S. Eclipse Expedition to the West Coast of Africa in 1889–1890 was wholly devoted to the determination of the height and motions of the clouds by the use of his special form of the marine nephoscope. The use of such a nephoscope is to be strongly recommended, as it gives the navigator a means of determining the bearing of a storm centre at sea by studying the lower clouds, better than he can possibly do by the observation of the winds alone. The importance of cloud study has been especially emphasized by the International Meteorological Committee, which arranged for a complete year of systematic cloud-work by national weather bureaus and individual observatories throughout the world from May 1896 to June 1897. In this connexion H. H. Clayton of Blue Hill Observatory published a very comprehensive report on cloud forms in 1906. The complete report by Professor F. H. Bigelow on the work done by the U.S. Weather Bureau forms a part of the annual report for 1899, and constitutes a remarkable addition to our knowledge of the subject. Some preliminary account of this work was published in the American Journal of Science for December 1899.

Although all the international cloud-work of 1896–1897 has now been published in full by the individual institutions, as in the case of the International Polar Research Work of 1883, yet a comprehensive study of the results still remains to be made. Some of these have, however, been brought together in Mohn’s discussion of the observations by Nansen during the voyage of the “Fram” and also in Hann’s Lehrbuch and in Bigelow’s Report on Cloud-work. The mean altitudes of cirrus and strato-cumulus clouds resulted as follows.