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In the system of fundamental partial differential equations which express the state of the atmosphere, there are four independent variables -time, elevation above mean sea level, latitude, and longitude and seven dependent variables-the three components of wind velocity, pressure, temperature, density, and joint mass of solid, liquid, and gaseous water per unit mass of atmosphere. The equations are the three hydrodynamical equations of motion of a fluid covering a rotating globe, the equation of continuity, the characteristic equation of state for gases, and two thermodynamical equations relating to the conveyance of heat and water, all of which are quite complicated.

Special difficulties are at once encountered in connection with the hydrodynamical equations. It may be demonstrated directly from the kinetic theory that although a gas is composed of discrete particles, its mass motions will obey the ordinary hydrodynamical equations derived explicitly on the very different assumption of continuity. The classical hydrodynamics, however, assumes the density to be a function of the pressure only, whereas in the atmosphere many other independent variables, such as temperature and humidity, affect the density; the theory of baroclinic fluids-those in which the density is a function of other variables besides the pressure has been worked out by Bjerknes, but is not very widely known. Furthermore, the resistance of the surface of the earth and the disturbances caused by the irregularities thereof give rise to a very turbulent condition of the lower atmosphere; the ordinary molecular viscosity of the air is so small that it may be neglected, but the effect of turbulence is to endow the air with a virtual or pseudo-viscosity many thousand times greater than the ordinary viscosity, and this must be taken into account.

The only forces acting on any mass of air are gravity, hydrostatic pressure, and friction; the acceleration of the mass is composed of two parts, viz., acceleration relative to the surface of the earth, which is observable, and acceleration common to this surface itself. It is the acceleration of the surface of the earth which gives rise to the so-called "deflecting force of the earth's rotation.” The relation between pressure distribution and winds as expressed in the empirical law of Buys Ballot can now be given an explanation on dynamical principles; in the absence of friction, the motion of the air is such that the pressure gradient is just balanced against the centrifugal force arising from the curvature of the path and the deflecting force arising from the earth's rotation. This motion of air under balanced forces as the most effective representation of actual conditions was introduced into meteorology in 1913; and it has been found that in general the wind at a height of about 1500 feet is in good agreement with the theoretical "gradient wind." At lower levels, friction and turbulence complicate the motion of the air; but even here it has been found possible to construct a mathematical theory that adequately accounts for the facts.

The principle of balanced forces merits serious attention in attempts to work out mathematical theories of atmospheric motions. According to Sir Napier Shaw, it is most practicable to regard the normal state of the atmosphere as a steady state of circulation in which gradient is

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balanced by a velocity disturbed by surface friction and other causes. The physical processes of the atmosphere then take place in some modification of the steady state, and not in a quiescent atmosphere—the cyclone, anticyclone, etc., are all parts of a single general world wide circulation of the atmosphere.

The most thorough and comprehensive investigation of the general problem of theoretical meteorology yet made is that of L. F. Richardson; he has co-ordinated practically every physical and dynamical process of the atmosphere in one systematic set of differential equations, and has applied the Calculus of Finite Differences to obtain an approximate analytical solution of these equations. The real value of such a study is the insight it gives into the mechanism of atmospheric processes; incidentally, however, he has applied his approximate solution to the numerical computation of the future weather over a region for which complete observations are available.

References

A sound knowledge of general descriptive meteorology, physics, and mathematics is presupposed, in addition to a more profound knowledge of at least certain portions of theoretical mechanics and of thermodynamics. Many of the facts of observation necessary to theoretical investigations will be found collected together in H. Hildebrandsson and L. Teisserenc de Bort, Les bases de la météorologie dynamique (Paris, 1898-1905, 2 vols.); the general physics of the atmosphere is treated by W. J. Humphreys, Physics of the Air (Philadelphia, 1920). The nineteenth century investigations in dynamical meteorology are mostly contained in the works of Ferrel (Prof. Papers, Signal Service, No. 8; Rept. Supt. U. S. Coast Survey, 1875, 1878, 1881; Rept. Chief Signal Officer, 1885) and the collections of translations published by Abbe (Ann. Rept. Smith. Inst., 1877; Smith. Misc. Coll., No. 843, and vol. 51, No. 4); Bigelow has carried out a comparative study of many of these (Rept. Chief of Weather Bureau,, 1898-99, vol. 2).

F. M. Exner. Dynamische Meteorologie. 2te aufl. Vienna, 1925. Edgar W. Woolard. Development of Meteorology as illustrative of the role of Mathematics in the progress of Science. Mon. Weath. Rev., 51, 645-649, 1923.

H. Jeffreys. On the dynamics of wind. Quar. Jour. Roy. Met. Soc., 48, 29-47, 1922.

V. Bjerknes. On the dynamics of the circular vortex, with applications to the atmosphere and atmospheric vortex and wave motions. Geofysiske Publikationer, vol. II, No. 4, Kristiania, 1921.

L. F. Richardson. Weather prediction by numerical process. Cambridge Press, 1922. On pp. 92 is given a bibliography of papers on the motion of the atmosphere in the turbulent layers.

J. Bjerknes. Diagnostic and prognostic application of mountain observations. Geofysiske Publikationer, vol. III, No. 6. Kristiania, 1924.

PACIFIC COAST MEETING IN JUNE

The Society will hold meetings in connection with the eightieth meeting of the American Association for the Advancement of Science from June 17 to 20 at Reed College, Portland, Oregon. On June 17 at 8 P. M., Dr. C. E. Grunsky, the retiring president of the Pacific Division will deliver an address on "The Climate of the Ice Age."

Earlier meetings of the A. A. A. S. will occur June 9th to 11th at Boulder, Colorado. Correspondence concerning the summer meetings should be addressed as follows:

For the Boulder meeting-Roscoe P. Johnson, Secretary of the Southwestern Division, 306 Goodrich Bldg., Phoenix, Ariz.

For the Portland Meeting of the American Meteorological Society, Mr. E. L. Wells, Weather Bureau, Portland, Oregon, has been appointed General Secretary, and Mr. M. B. Summers, Weather Bureau, Seattle, Wash., Associate Secretary. Mr. Summers has the program in hand, which will be published in the June BULLETIN.

Reports of the very interesting and well attended spring meeting of the Society will be published in the June BULLETIN.

ICE STORM IN CENTRAL NEW ENGLAND, APRIL 19, 1925 During the passage of an intense "low" on a track just south of New England the air temperature at the ground remained in the 30's. During the afternoon as the storm went out to sea the temperature fell slowly, yet so gradually that at moderate heights the temperature was below freezing for many hours, while in the lowlands the surface temperature did not reach freezing until after the rain from the overriding warm current above changed to snow. The result was a remarkable differentiation of highland and lowland with respect to ice. Above elevations of about 800 feet in the eastern part of Worcester to 700 in the central highland region, and perhaps 600 in the vicinity of Palmer, glaze on the trees formed to a considerable thickness. It appears that the formation must have begun early in the afternoon on the higher hills and have continued, reaching lower and lower elevations until the rain changed to snow during the night. The amount of ice up to one-half inch or more was sufficient to bend small trees down and to break of small branches in the region from Mt. Monadnock or farther north through central Massachusetts and southward at least to the vicinity of Palmer and probably to the southern border of Massachusetts. Knowledge of this distribution was gained through reports of students and others in Clark University, from news items, and from a field glass survey of the countryside near sunset on the 20th. The demarcation of the ice storm heights vs. lowlands was remarkably sharp; the hills glistening in their coating of ice on the 20th, while the lowlands were bare. In the vicinity of a lake in West Rutland, even though at an elevation of over 800 feet, there was no ice on the trees for a few tens of yards from the water.

The temperatures at Worcester at a height of 580 feet above sea level fell from 37 in the middle of the afternoon to 33 at 10 P. M. and to 29 during the night. At 10 P. M. both rain and sleet was falling, and presumably ice was forming on the trees at a height of not much over 750 feet.

During the clear night of the 20th to 21st, though the temperatures in the lowlands and hill slopes, at least to a height of 600 feet, were continually below freezing, even down to 28° F., the ice disappeared from the highlands within sight of a hill in West Worcester, no trace being visible with field glasses at 7.45 A. M. the 21st. It appears that the air at these moderate heights was above freezing during the night, and that the coldness was confined to the lower levels. The rapid rise in temperature on the morning of the 21st lends weight to this probability. Surely a half-inch layer of ice could not have evaporated in the course

of one night, especially in weather which allowed the grass on top of a hill over 600 feet high to be quite wet the morning of the 21st.

In New York, Vermont, New Hampshire, and southern Maine heavy snow fell to depths of 11 to 16 inches over wide areas, favoring a resumption of winter sports and logging.

The General Storm of April 18 to 20, 1925

The low pressure center, which followed a track generally from Colorado generally eastward between latitudes 39 and 41, showed a remarkable zonation of weather after reaching the Mississippi River. On the south the weather was hot, maximum temperatures being generally in the eighties. There was little rain. In a belt about 60 miles wide along the track there were very severe local storms, killing two and doing damage estimated at $1,500,000. To about 150 miles north of the track only moderate rainfall was reported. Temperatures were below 50° F. From 150 to 200 miles north of the track was the ice-storm belt at altitudes about 700 feet plus. The rainfall was heavy and thunderstorms numerous. From 200 to 250 miles was the belt of heaviest precipitation, rain in the west and wet snow in the east. There were some thunderstorms in the southern portion. From 250 to 300 miles heavy precipitation continued, then stopped suddenly. At 350 miles there was no precipitation. It was the northeast gale of this storm that brought about the foundering of the Japanese freighter, Raifuku Maru, and prevented the rescue of any of its crew of 38.-C. F. Brooks. FACTORS CONTRIBUTING TO EARTHQUAKES

A deficiency of rainfall and low barometric pressure were doubtless important factors in precipitating the earthquakes of January 7th and February 28th in New England, for anything which would tend to make the land lighter would increase the strain along the fault line. The quake of January 7th was preceded by three months of very dry weather with a deficiency of 8.1 inches of rainfall, and immediately followed by rain and a normal rainfall for that month. Then during February there was a deficiency again in rainfall and then the quake of the 28th, which was likewise followed by rain. Just before the quake of the 28th, the lowest barometric pressure for 2 years, 28.96 inches was recorded at Boston. This low moved in a northeasterly direction across New England and the Saguenay region, crossing the St. Lawrence fault. The weight of 8 inches of rainfall over all New England is computed to be 32,260,224,000 tons. No allowance for evaporation and runoff was made in this figure; yet even if these amounts were subtracted, the weight would still be several billion tons. A deficiency of 8 inches of rainfall, therefore, is equivalent to taking an enormous weight off New England. This, together with the extremely low barometric pressure of February 26-28, might well have been the set of circumstances which “set off” the shock of February 28th.-Excerpts from article by R. W. Sayles, Boston Herald, March 21, 1925.

ANCIENT CLIMATES

The papers presented at the symposium on ancient climates held at the December meeting of the American Association for the Advancement of Science appeared in the Scientific Monthly for May, 1925.

In his paper, Some Factors of Climatic Control, Dr. W. J. Humphreys states his belief that climatic changes were produced essentially by the earth itself. The warmer periods occurred at those times when land areas were relatively restricted and of small elevation, and oceanic circulation free and open to high latitudes. The colder periods including the ice ages were, presumably, at times when land was extensive, mountains abnormally high, and oceanic circulation restricted. If violent volcanic explosions occurred under these last mentioned conditions, the veil of volcanic dust would lover the average temperatures. This would lead to an extended snow covering which would result in still lower temperatures. They in turn would be intensified by the incident thinning of our protecting blanket of water vapor. In short, the earth can produce its own climatic changes through such potent agencies as land and water distribution, land elevation, oceanic circulation, atmospheric circulation, volcanic dust and surface covering.

The Solar-Cyclonic Hypothesis and the Glacial Period, by Dr. S. S. Visher, deals with the possible climatic significance of variations in storminess as studied by Dr. Huntington and others. The solar-cyclonic hypothesis has two phases: (1) that variations in storminess attend important changes of climate, and (2) that solar changes somehow lead to changes in storminess. If the changes in storminess observed during a sunspot cycle in the present were intensified and magnified sufficiently in the past some of the aspects of ancient climates which have hitherto been inadequately explained would have been produced. Conditions during a sunspot maximum are of the glacial type, and those of the sunspot minimum of the inter-glacial type. Changes in storminess, however, will not explain all the facts of ancient climate; changes in land elevation and distribution in the composition of the atmosphere and ocean, and in the direction of oceanic circulation are also important.

The problem of glacial periods and climate was considered in two papers, one by Dr. Ernst Antevs, Glacial Climatic Conditions; the other by Dr. A. P. Coleman, The Spacing of Ice Ages and the Climate of Early Pre-Cambrian Times. During the growth of ice sheets, according to Dr. Antevs, snowfall over the ice was great and summer temperatures low; during their disappearance summer temperature was high and progressively increasing, accompanied by strong insolation, clear sky, and insignificant precipitation. Dr. Coleman showed that the ice ages came closer together in the earlier geologic times than in the later ones, and said that this fact strongly supported the view that glaciation took place in the earliest known times. Such a record would indicate a cold rather than a warm climate at the beginning of the earth's history.

Fossils as indicators of former climatic conditions formed the basis of several discussions, as the following titles show: "The Evidence of Invertebrates on the Question of Climatic Zones during Mesozoic Time," T. W. Staunton; "Triasso-Jurassic Plant Evolution and Climate,” G. R. Wieland; "Distribution and Climatic Relations of the Tertiary Floras of the Northern Great Basin," R. W. Chaney; "Big Trees as a Climatic Measure," E. Antevs; "Upper Paleozoic Climate as Indicated by Fossil Plants," D. White.-F. V. T.

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