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 ressure of one current of air against another. Fig. ll, prepared for the U.S. Monthly Weather Review (Oct.
After Brillouin.
FIG. II.-Diagram illustrating Clouds due to Mixture. 1897), gives five of the cases elucidated by Brillouin. 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 q.sion 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 si ht of owing to the great horizontal and small vertical dimensions 0? 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 art 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, ]an.-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 ormula,
P., (T n:¢(cx-1)
P T.,
In our fig. 1 above given, Cottier has assumed n=I-2, but as the values have now been computed for all altitudes from the observations given by balloons and kites, and have a very eneral 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 ressure we find the modifications needed in the energy formula fgr non-adiabatic processes-and Bigelow applies the resultin formula most satisfactorily to a famous waterspout of the 19th of Auust 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 and the Wind fI'0!T1 the west. The l'€3.(.l€I' will 5613 that l Values of 1; between sugceggive levels, in each case, depending on the relative temperatures and winds, layers of cloud are formed of marked in- Alt1tl1d¢S- America. Europe. Both A. and E. All. dividuality. As none of these clouds appear in the . ', H, International Cloud Atlas or the various systems of Wmmf- 5Umm€1'- Winter- Summer- Winter- Summernotaticgi for clouds, ope is all tléie mtge gm pressed k | ' V with the im ortance o t eir stu y an the success '~ with which ligrillouin has opened up the way for future 1644 3'04 T32 304 3'59 3°O4 3°2° investigators. “ We have no longer to do with perl l4'12 453 2' 2 4'39 3'°4 4'3g 3'88 sonal and local experience, but with an analytical 124° To V72 2-08 V64 2'° I' I' 8 description of a small number of characteristics easy IO' 3 V52 1'47 V52 V41 V52 V42 P48 to comprehend and applicable at every locality 3' V39 V41 V41 V32 I'4° V3 I'3 throughout the globe." ' ' Z P41 L22 V41 V41 V41 V26 V44 From a thermodynamic point of view the most Z; V45 I” 7 V41 V52 l'4g I' 0 V52 important study is that published by Margules, Ueber 5 P52 V52 P41 V62 V4 V52 V22 die Energie der Stzirme (Vienna, 1905). This work 5' V79 V41 V67 I'7° 17% V5, I' 4 considers only the total energy and its adiabatic trans- 4' 3 1:97 I '22 'I '79 V94 1186 1'6§ P76 formations within a mass of air constituting a closed 3' 2 2 10 V85 2'0l 2'30 2'°8 V9 2'°2 system. Truly adiabatic changes inclosingd systems ' 2' I 3'52, I' 3 2'24 V67 2'8 V75 T32 do not occur within any special portion of the earth's I' O 2'3° P83 2'47 V64 2'38 V74 i 2'°6 atmosphere, neither can our entire atmosphere be considered as one such system-but Margules' results are approximately ap licable to many observed cases and complete the demonstration oi) 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 com rehensively and rigorously. . .
Tile three equations of energy on which Margules bases his work are:-
R+5(K+P)+5A=oal-aA=Q
R+6(K+P)+aI =Q
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; l=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 ap lied 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 expan-XVIII. IO.
storms (Monthlg Weather Review,
with consider ab e success.
We have thus passed in review the steady progress of mathematical physicists in their efforts to unravel the complex d namics of our atmosphere. The profound importance of this suiiject 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 modelsof 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 fin the revious sections, but one of the most important questio'ns»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 189I as physicist to the US. 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, II
November 1907-M&fCh IQOQ)