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PHYSICAL AND THEORETICAL] Such balloon soundings have been made not only individually, but, by pre-arranged system, simultaneously in combination with the ascent of free-manned balloons above referred to; and at some places kites have been simultaneously used in order to obtain records for the lower atmosphere. The first experiments in simultaneous work were made in 1896 and 1897, when ascents were made at eight or more points in France, Germany and Russia. These experiments and the discussions to which they gave rise have emphasized the importance of increasing the sensitiveness of the self-recording apparatus, and as far as practicable the rapidity of the ventilation of the thermometers, and of providing more perfect protection against radiation from the sun or to the sky. It is believed that accurate records may be attained up to at least 30,000 metres, but as yet only 26,000 has been attained, and the records brought back are still under considerable criticism on account of instrumental defects. In general the wind that supports a kite also furnishes sufficient ventilation for the thermometer; but in the case of the sounding balloon, which as soon as its rapid rate of ascent diminishes floats along horizontally in the full sunshine, a strong artificial ventilation must be provided. Moreover, the sluggishness of the best thermometers is such that during the rapid rise the records of temperature that are being made at any moment really belong to some altitude considerably below the balloon, and a most critical interpretation of the records is required. Notwithstanding all criticisms, however, the balloon work in all localities agrees in showing the existence of a region above the 10,000-metre level, where temperatures cease to diminish rapidly, and may even become stationary.

The ultimate aim of those who are devoted to any branch of science is to penetrate beyond the phenomena observed on the surface to their ultimate causes, and to reduce the whole complex of observations and empirical rules based upon limited experiences to a simple deductive system of mechanics in which the phenomena observed shall be shown to flow naturally from the few simple laws that underlie the structure of the universe. A correct “theoria” or physical and logical argumentation deducing from primary laws all the phenomena constitutes the noblest achievement of man in science. It is by such works that Newton and Laplace distinguished themselves in astronomy. The development of the true physical and mechanical theories of atmospheric phenomena has made great progress, but is still inferior in completeness to astronomical work, owing to the great complexity of the meteorological problems. The optical and the thermal phenomena have been very satisfactorily elucidated, the electrical phenomena promise to become clear, but the phenomena of motion or aerodynamics have only been elucidated to a limited extent. We must, however, introduce the reader to some of the works that have been published on the subject, in the hope that thereby he will himself be persuaded to further study and stimulated to contribute to our knowledge.

The present state of theoretical physical and mechanical meteorology cannot be fully presented in non-technical English text. It is necessary to employ algebraic formulae, or numerical tables, or graphic diagrams, the former being certainly the least cumbersome and the most generally available. The uniform system of notation devised by Professor F. H. Bigelow, and a very complete summary of the formulae of physical meteorology expressing the results of many recent students will be found in chapters x. and xi. of his Report on the International Cloud Observations, published as vol. ii. of the annual report of the chief of the U.S. Weather Bureau for 1898–1899. The fundamental laws to which the atmosphere is subject are as follows:—

A. The Equation of Elastic Pressure.—The pressure shown and measured by the barometer is an elastic pressure acting in all directions equally at the point where it is measured. By virtue of this elastic pressure a unit volume of air will expand in all directions if not rigidly enclosed, but will cool in so doing. On the other hand, if forcibly compressed within smaller dimensions, it will become warmer. For a given temperature and pressure a unit volume of air of a prescribed chemical constitution will have a prescribed definite weight. The general relations between absolute temperature, pressure and volume are expressed by the formula

where T expresses the absolute temperature, p the elastic pressure, v the volume, and R is a constant which differs for each gas, being 29·2713 for ordinary pure dry air and 47·060 for pure aqueous vapour, if we use as Fundamental units the kilogram, metre and centigrade degree. This equation is sometimes called the law of Boyle and Charles, or of Gay-Lussac and Marriotte, and it is also known as the equation of condition for true gases, meaning thereby that it expresses the fact that the ideal gas would change its volume directly in proportion to its absolute temperature and inversely in proportion to its elastic pressure. All gases depart from this law; in proportion as they approach the vaporous condition on the one hand, which is brought about by great pressure and low temperature, or the ultra-gaseous condition on the other hand, which obtains under high temperatures and low pressures. The more accurate law of Van der Waals would complicate our problems too much. In place of the absolute temperature T we may substitute the expression 273° C. × (1 + t), where  is the coefficient of volumetric expansion of the gas for a unit degree of temperature ＝0·00367 and t is the temperature expressed on the centigrade scale.

B. Hypsometric Conditions.—The pressure of the atmosphere at any place depends primarily on the weight of the superincumbent mass of air, and therefore diminishes as we ascend to greater heights. If the air is in motion, that and other considerations come in to affect the pressure; but if the air is quiet relative to the earth’s