temperature, a mixture accompanied by condensation always descends when the surface of separation is unstable; moreover, the adiabatic compression rapidly evaporates the mixture.
In the last three chapters of his memoir, Brillouin applies these principles and other details to almost every observed variety of mixtures due to the pressure of one current of air against another. Fig. 11, prepared for the U.S. Monthly Weather Review (Oct. 1897), gives five of the cases elucidated by Brillouin.
|
| After Brillouin. |
Fig. 11.—Diagram illustrating Clouds due to Mixture. |
In each of these the left-hand side of the diagram is the polar side, the air being cold above and the wind from the east, while the right-hand side is the equatorial side, the air being warm above and the wind from the west. The reader will see that in each case, depending on the relative temperatures and winds, layers of cloud are formed of marked individuality. As none of these clouds appear in the International Cloud Atlas or the various systems of notation for clouds, one is all the more impressed with the importance of their study and the success with which Brillouin has opened up the way for future investigators. “We have no longer to do with personal and local experience, but with an analytical description of a small number of characteristics easy to comprehend and applicable at every locality throughout the globe.”
From a thermodynamic point of view the most important study is that published by Margules, Ueber die Energie der Stürme (Vienna, 1905). This work considers only the total energy and its adiabatic transformations within a mass of air constituting a closed system. Truly adiabatic changes in closed systems do not occur within any special portion of the earth’s atmosphere, neither can our entire atmosphere be considered as one such system—but Margules’ results are approximately applicable to many observed cases and complete the demonstration of the general truth that we must not confine our studies to the simpler cases treated by Espy, Reye, Sohncke, Peslin, Ferrel, Mohn. All imaginable combinations of conditions exist in our atmosphere, and a method must be found to treat the whole subject comprehensively and rigorously.
The three equations of energy on which Margules bases his work are:—
where R＝energy lost by friction or converted into heat; K＝kinetic energy due to velocity of moving masses; P＝potential energy due to location and gravity and pressure heat; A＝work done by internal forces when air is expanding or contracting; I＝internal energy due to the existing pressure and temperature; Q＝quantity of heat or thermal energy added or lost during any operation and which is zero during adiabatic processes only.
These equations are applied to cases in which masses of air of different temperatures and, moisture’s are superposed and then left free to assume stable equilibrium. It results in every case that there is no free energy developed. Any condensation of moisture by expansion is counterbalanced by redistribution of potential energy and by the work done in the interchange of locations. The idea that barometric pressure gradients make the storm-winds is seen to be erroneous and the primary importance of gravity gradients is brought to light. “The source of a storm is to be sought only in the potential energy of position and. in the velocity of ascent and descent, although these are generally lost sight of owing to the great horizontal and small vertical dimensions of the storm areas The horizontal distribution of pressure seems to be a forced transformation within the storm areas at the boundary surface of the earth, by reason of which a small part of the mass of air acquires a greater velocity than it could by ascending in the coldest or sinking in the warmest part of the storm areas. But here we come to problems that cannot be solved by considering the energy only.”
This latter quotation emphasizes the necessity of returning to the equations of motion. The thermodynamics and hydrodynamics of the atmosphere must be studied in intimate connexion—they can no longer be studied separately. Apparently we may expect this next step to be taken in the above-mentioned work promised by V. Bjerknes, but meanwhile Professor F. H. Bigelow has successfully attacked some features of the problem in his “Studies on the Thermodynamics of the Atmosphere” (Monthly Weather Review, Jan.–Dec. 1906). In ch. iii. of his studies (Monthly Weather Review, March 1906) Bigelow establishes a thermodynamic formula applicable to non-adiabatic processes by introducing a factor n so that the pressure (P) and absolute temperature (T) are connected by the formula
In our fig. 1 above given, Cottier has assumed n＝1·2, but as the values have now been computed for all altitudes from the observations given by balloons and kites, and have a very general importance and interest, we copy them from Bigelow’s Table 16 as below:—
The existence of such large values of n shows the great extent to which non-adiabatic processes enter into atmospheric physics. Heat is being radiated, absorbed, transferred and transformed on all occasions and at all altitudes. Knowing thus the thermodynamic structure of areas of high and low pressure we find the modifications needed in the energy formula for non-adiabatic processes—and Bigelow applies the resulting formula most satisfactorily to a famous waterspout of the 19th of August 1896 over Nantucket Sound, for which many photographs and measurements are available. The thermodynamic study of this waterspout being thus accomplished, it was followed by a combined thermohydrodynamic study of all storms (Monthly Weather Review, November, 1907–March 1909) with considerable success.
| Altitudes. | Values of n between successive levels. | All. | |||||
| America. | Europe. | Both A. and E. | |||||
| Winter. | Summer. | Winter. | Summer. | Winter. | Summer. | ||
| kil. | |||||||
| 16–14 | 3·04 | 2·82 | 3·04 | 3·59 | 3·04 | 3·20 | 3·12 |
| 14–12 | 4·39 | 2·82 | 4·39 | 3·04 | 4·39 | 2·93 | 3·66 |
| 12–10 | 2·08 | 1·72 | 2·08 | 1·64 | 2·08 | 1·68 | 1·88 |
| 10– 9 | 1·52 | 1·47 | 1·52 | 1·41 | 1·52 | 1·44 | 1·48 |
| 9– 8 | 1·39 | 1·41 | 1·41 | 1·32 | 1·40 | 1·36 | 1·38 |
| 8– 7 | 1·41 | 1·52 | 1·41 | 1·41 | 1·41 | 1·46 | 1·44 |
| 7– 6 | 1·45 | 1·67 | 1·41 | 1·52 | 1·43 | 1·60 | 1·52 |
| 5– 4 | 1·79 | 1·41 | 1·67 | 1·70 | 1·73 | 1·56 | 1·64 |
| 4– 3 | 1·97 | 1·32 | 1·79 | 1·94 | 1·88 | 1·63 | 1·76 |
| 3– 2 | 2·10 | 1·65 | 2·01 | 2·30 | 2·06 | 1·98 | 2·02 |
| 2– 1 | 3·52 | 1·83 | 2·24 | 1·67 | 2·88 | 1·75 | 2·32 |
| 1– 0 | 2·30 | 1·83 | 2·47 | 1·64 | 2·38 | 1·74 | 2·06 |
We have thus passed in review the steady progress of mathematical physicists in their efforts to unravel the complex dynamics of our atmosphere. The profound importance of this subject to governmental weather bureaus, and through them to the whole civilized world, stimulates diligent effort to overcome the inherent difficulties of the problems. An elaborate system of study and laboratory experimentation leading up to research in meteorology has been devised by Cleveland Abbe, culminating in experiments on models of the atmosphere as a whole by which to elucidate both the local and the general circulations on globes whose orography and distribution of land and water is as irregular as that of the earth.
The Formation of Rain.—Not only has dynamic meteorology made the progress delineated in the previous sections, but one of the most important questions in molecular physics is in process of being cleared up. The study of atmospheric nuclei and condensation and the, formation of clouds in their relation to daily meteorological, work began with the appointment of Dr Carl Barus in 1891 as physicist to the U.S. Weather Bureau, and his work has been laboriously continued and extended in his laboratory at Providence, Rhode Island. The formation of rain, from a physical point of view,
