UC-NRLF C 3 250 55E js. NO. 273. U. S. DEPARTMENT OP AGRICULTURE, "WEATHER BUREAU. STUDIES ON THE STATICS AND KINEMATICS OF THE ATMOSPHERE IN THE UNITED STATES. Reprints from the Monthly Weather Review, January to July, 1002. FRANK H. BIGELOW, M. A., L. H. D., PROFESSOR OF METEOROLOGY. PREPARED UNDER THE DIRECTION OF WILLIS L. MOORE, CHIEF 1. S. WEATHER BUREAU. WASHINGTON : WEATHER BUREAU. 1902. W. B. No. 273. 10254 U. S. DEPARTMENT OF AGRICULTURE, t|,5 "WEATHER BUREAU. , IU ' - 1 STUDIES ON THE STATICS AND KINEMATICS OF THE ATMOSPHERE IN THE UNITED STATES. Reprints from the Monthly Weather Review, January to July, 1902. PRANK H. BIGELOW, M. A., L. H. D., PROFESSOR OF METEOROLOGY. PREPARED UNDER THE DIRECTION OF WILLIS L. MOORE, CHIEF U. S. WEATHER BUREAU. WASHINGTON: WEATHER BUREAU. 1902. Page. I. A new barometric system for the United States, Canada, and the West Indies Preliminary remarks ... The adopted standard elevation for the epoch, January 1, 1900. Other corrections to the station pressures The sea level, 3,500-foot and the 10,000-foot planes of reference . The new reduction pressure tables Previous discussions of the plateau problem Bigelow's system of barometry, 1902 The sea-level temperatures The first pressure reduction to sea level 4 To find t 6 The first process The second process 5 The second pressure reduction to sea level 5 Pressures computed on the 3,500-foot and the 10,000-foot planes The first computation of .B, -B 2 The second computation of B l B t 6 II. Method of observing and discussing the motions of the atmos- phere Introductory remarks 9 Notation and coordinates 9 The axes of coordinates 10 The azimuth rotation 10 The composition and resolution of the vectors of motion 11 The resolution of forces 12 Vectors of motion in high and low areas rectangular coordi- nates 12 Vectors of motion in high and low areas cylindrical coordinates. 14 III. The observed circulation of the atmosphere in the high and low areas 17 General description of the vectors obtained by observation ... 17 Description of the circulation over high and low areas 20 Discussion of the vectors in high areas 20 Discussion of the vectors in low areas 21 The numerical values of the vectors 23 IV. Keview of Ferrol's and Oberbeck's theories of the local and general circulations 27 General comparison of Ferrel's and Oberbeck's theories 27 The supply of local centers of heat 27 Ferrel's local cyclone 28 Ferrel's solution 29 The German solution 30 Ferrel's theory of the general circulation over a hemisphere . 31 Oberbeck's solution of the general circulation 32 V. Relations between the general circulation and the cyclones and anticyclone 37 Unequal distribution of cyclones in North America and Europe- Asia 37 Criticism of the canal theory of the general circulation 37 Modification of the canal theory 39 The structure of the anticyclone 41 Structure of the cyclone 41 Special features of the circulation 43 The velocities in tornadoes 44 Tiie waterspout off Cottage City, Mass., August 19, 1896 .... 45 VI. Certain mathematical formula- useful in meteorological dis- cussions 47 The need of a standard system of formulae 47 The general equations of motion 47 (1) The polar equations of motion on the rotating earth 47 (2) The cylindrical equations of motion on the rotating earth. 48 Remarks on the several terms in the general equations of motion 48 Integration of the general equations of motion in polar coordi- nates , , 48 Expressions for the gradients of pressure Evaluation of the coefficient ' and other terms Evaluation of the gradients in polar coordinates The equation of continuity, and some derived relations The problems of the aqueous vapor contents of the atmos- phere VII. A contribution to cosmical meteorology General remarks Summary of the discussion of 1898 The magnetic observations, 1841-1899 Comparison of the variations of the solar prominences with those of the terrestrial horizontal magnetic force for the interval 1874-1900 The variations of atmospheric pressure over the entire earth . Table 1. Direction and velocity of motion in high and low areas rectangular coordinates (Tables 34 and 38) Table 2. Total velocity in highs and lows without regard to direc- tions (Table 33, Section I) Table 3. General rectangular components of motion in high and low areas ( Tables 42 and 43) Table 4. Southward and eastward components of velocities in highs and lows (Table 33, Section II); mean normal com- ponents of velocities for the United States (Table 33, Sec- tion III) Table 5. Component velocities in selected areas between high and low centers (Table 33, Section IV) Table 6. Anticyclonic and cyclonic components (Tables 44, 46, and 45, 47) Table 7. Mean anticyclonic and cyclonic components grouped in three levels (Table 52) Table 8. Normal component velocities on six selected planes .... Table 9. Rectangular and cylindrical coordinates in high areas . . Table 10. Rectangular and cylindrical coordinates in low areas . . Table 11. Mean components on the I, II, III circles Table 12. Northward and southward velocities in selected areas. Table 13. Theoretical west-east velocities Table 14. Vertical diminution of pressure Table 15, I. Components on the meridians due to the rotation of the earth II. Components on the meridians due to the relative motion of the atmosphere Table 16, I. First components on the parallels due to the rota- tion of the earth II. Second components on the parallels due to the rota- tion of the earth Table 17, I. Vertical components due to the rotation of the earth. II. Vertical components due to the relative motion of the atmosphere Table 18. Anticyclonic and cyclonic velocities at each 1,000-meter Page. 49 49 50 51 52 55 55 55 56 level Table 19. Application of the formula; for a cyclone Table 20. Dimensions and velocities in the waterspout off Cottage City, Vineyard Sound, Mass., August 19, 1896 Table 21. Comparison of several determinations of the total tem- perature change from the surface to high levels Table 22. Total variations of the horizontal magnetic force for the earth generally, arranged in 26.68-day periods Table 23. The variations of the annual mean atmospheric pres- sures in many districts of the earth, in units of 0.001 inch . . ILLUSTRATIONS. Figure 1. Comparison of the two azimuth systems Figure 2. Example of the graphic composition of wind vectors. . . Figure 3. Plan of the subareas, azimuths, and compass points, adopted in high and low areas, for the discussion of cloud observations Figure 4. Direction and velocity of motion in high and low areas of tho cirrus levels (Chart 15) , , . , iii 59 60 13 13 14 14 14 15 15 17 21 21 23 23 31 32 33 33 33 34 34 34 42 42 44 '53 57 61 11 11 12 13 IV Page. : I '\-j(i iv r>. A ill toyolonlo and cyclonic components of the cirrus level (Chart Hi) 14 Figure (i. Adjustcd mean vectors of direction and velocity of mo- tion in high ureas 18 Figure 7. Adjusted mean vectors of direction and velocity of mo- tion in low areas 1!) Figure 8. Total eastward velocities in high and low areas 20 Figure 9. Curling of the northward and southward streams about the centers of high and low areas 21 Figure 10. liadiul and tangential components in anticyclonic and cyclonic ureas 24 Figure 11. Ferrel's circulation in warm-center cyclones 2!) Figure 12. Ferrel's circulation in cold-center cyclones 29 Figure 13. Oberbeck's circulation in warm-center cyclones 30 Figure 14. Ferret's general cyclone 32 Figure 15. Oborbeck's component motions in the general cyclone. 32 Figure 16. Ferrel's component currents by the canal theory 37 Figure 17. Bigelow's component currents from the Weather Bu- reau observations 38 Figure 18. Scheme of self regulation of the circulation by the rise and fall of the gradient 40 Figure 10. Mixed system of hyperbolic and parabolic components. Figure 20. General scheme of the structure of cyclones Figure 21. Vertical section through the atmosphere Figuro 22. Illustrating the formation of the equation of continuity. Figure 23. Total temperature fall from the surface to high levels by several systems Figure 24. Relative secular variations in the sun spots, the European magnetic field, and the American meteorological system Figure 25. Variation of the sun-spot numbers and the amplitude area numbers Figure 26. Semiannual period in the horizontal force of the ter- restrial magnetic Held, arranged in six successive 11-year periods Figure 27. Semidiurnal period of the direct type Figure 28. Comparison of the solar prominence variations with those of the terrestrial horizontal magnetic force and the atmospheric pressures over the entirj earth Figure 29. Positive and negative pressure variations over the earth as a whole for successive years, on a s^ale of relative numbers . . 53 55 58 58 59 STUDIES ON THE STATICS AND KINEMATICS OF THE ATMOSPHERE IN THE UNITED STATES. 1 I._A NEW BAROMETRIC SYSTEM FOR THE UNITED STATES, CANADA, AND THE WEST INDIES. PRELIMINARY REMAKES. On January 1, 1902, at the 8 a. m. observation, seventy-fifth meridian time, a new system for the reduction of the station barometric pressures to the sea-level plane, was put in oper- ation for the United States, Canada, and the West Indies. Ihe daily weather maps iised in forecasting the intensity and the path of storms, and the other allied phenomena, are there- fore constructed upon a basis differing from any hitherto used. Students who consult the published weather maps should re- member that the series terminating with the above date is not comparable with the others following it, the difference at some stations on the Rocky Mountain Plateau for certain seasons of the year amounting to several tenths of an inch of pressure by the mercurial barometer. The problem of reducing the pressures observed at stations located on the Rocky Mountain Plateau to sea level has always been recognized as one of un- usual scientific difficulty, and it has been under discussion in the Washington Office at intervals ever since the establishment of the Government service. So far as can be judged at the present writing the success of the new system is assured, and if this favorable opinion is confirmed by continued use, it will mark the termination of thirty years' effort to solve this ques- tion in a practical form. The other plateau districts of the world, Mexico, South America, especially Argentina, south Africa, Australia, and southern Asia, will doubtless profit by the experience of the United States Weather Bureau, on con- sulting the solution adopted for the United States, Canada, and the West Indies. Prof. R. F. Stupart, Director of the Canadian Meteorologi- cal Office, has courteously cooperated by supplying the neces- sary data for the Canadian stations, since the common interests of both countries require the adoption of the same methods of barometric reductions. There is no task properly belonging to the Weather Bureau upon which more time and labor has been expended than upon this problem, and the present dis- cussion is the sixth well defined attempt to reach a satisfactory conclusion. The importance of putting the barometric pres- sures on the elevated plateau, covering one third of the terri- tory for which the official forecasts are made, on a satisfactory scientific basis, fully justifies this work, because it is of pri- mary importance not to attribute to weather conditions any pressure changes that are in reality due to the method of reduction to the plane of reference. The eastern and central portions of the United States and Canada are generally at levels less than 1,000 feet above the sea, and also the Pacific coast is at low level, so that for these districts the barometric reduction offers no difficulty. Be- tween these, throughout the Rocky Mountain region, there is a rough country where the stations are at different elevations up to 7,000 feet, where the surface temperature conditions range enormously, say from 40 F. to +60 F. on a single map in _' llppi-intcd from the Monthly Weather Review for January, 11)02. extreme cases, where the prevailing winds from the Pacific Ocean produce one type of weather on the western slopes of the mountains and another on the eastern, to say nothing of the effect of great arid districts between them, and where the configuration of the mountain valleys, in which many of the stations are located, relative to the neighboring ranges rising up to 12,000 or 14,000 feet in some cases, causes various local peculiarities in the behavior of the barometer. A description of the construction of our new station pressure normals is properly a preliminary to the solution of the plateau problem. In the years between 1871-1880, while the baro- metric network was being extended over the plateau districts, many of the elevated stations were at the Army posts where no measurement of the altitude had been made, except by the ba- rometer. We now know that several of these early elevations were seriously in error, say from 10 feet up to 200 feet, and as a change of 10 feet in altitude corresponds approximately to 0.010 inch pressure, the irregularities on the sea-level plane arising from this source alone were not inconsiderable. The gradual extension of the various surveys by the Government over the plateau, together with the railroad levels executed and revised by the different companies, have gradually built up a system of check levels at intersecting points, with accu- rate differential levels between them, so that now the absolute elevations of the several stations have been determined with much accuracy. An adjustment of these levels was made by Prof. Cleveland Abbe in 1871-72; the work was then taken up by the Geological Survey, and the latest results of these surveys are given in Gannett's Dictionary of Altitudes, edition of 1900. The Weather Bureau was supplied with the corrected altitudes before the publication of this report by the Geological Sur- vey, so that we have had the advantage of this data from an early stage in our own work. THE ADOPTED STANDARD ELEVATION FOR THE EPOCH, JANUARY 1, 1900. Besides the incorrect actual elevations which, for one reason or another, have been adopted during thirty years, there have been numerous changes in the elevation of the local offices of the service at the same station, involving many small variations in the altitude above sea level. A very careful reexamiuation of the station records of the respective stations showed that it was practically impossible to assign correct absolute eleva- tions for the several changes as referred to the sea level, but that it was possible to discover the differences by which the successive changes in height followed each other (that is, the height of the barometer in the new office above or below that in the old office), the series of variations giving a chain of steps up and down in the succession of changes. These were care- fully determined, and they were then applied to the elevation occupied by the station at the epoch January 1, 1900, so that the actual heights were thus found for the respective inter- vals during which the barometer remained in one position, and they were referred iu this way to our latest and beat elevations as given by recent surveys. Having adopted the elevation for the station at the given epoch, all the recorded actual pressures were reduced to the elevation of 1900 by small differential pressure corrections, so that the entire pressure system be- comes homogeneous for the station. During the years following 1900 a similar plan is to be fol- lowed, and all pressures will be reduced back to the standard elevation, so that the series will be maintained strictly com- parable throughout the life of the station itself. There is great advantage in this procedure, for two reasons. It was found that in the other attempts to construct pressure nor- mals the earlier computations were readjusted to the latest ele- vations at the different dates, thus obscuring the record and consuming a great amount of labor without arriving at final results. Also, the reduction tables to sea level, provided for the use of the stations, had to be renewed with every removal, which also consumed much time. On the new plan; however, each year's observations is added directly to a homogeneous station system, and the same reduction table serves without modification in consequence of any local changes. Indeed it is absolutely essential to reach such a basis of operation in meteorology as this, if there is to be made possible a scientific study of the secular variations of the weather, that is, the large problem of why and how the seasons, the climate, and the crops, differ from year to year, this being the next great prob- lem awaiting practical meteorology. Evidently all the cos- mical questions involving variations in the radiations of the sun must be compared with as definite a pressure system as this, if scientific results are to be secured from the meteoro- logical data. It may be stated in passing, that in recent years, since the Government has erected large buildings in the cities of the United States, the Weather Bureau offices have been more permanently located, and that the average series of un- broken observations is growing longer than it used to be 10 and 20 years ago. At the same time the elevations are a little higher, because the offices are usually placed in the upper rooms of the lofty federal buildings. OTHER CORRECTIONS TO THE STATION PRESSURES. Besides reducing the observed pressures to an adopted station elevation it was necessary to make several more corrections in order to obtain a homogeneous system of normals. ( 1 ) The records were thoroughly inspected for the several corrections which ought to be applied to the barometer readings, and we have now a complete list of the barometer numbers and their errors for capilarity, scales, etc. Besides eliminating a few mistakes, there were two important special corrections to be applied. During the interval 1873-1878 a correction of 0.013 inch had been added to the Signal Service standard barome- ter to reduce it to the supposed Kew standard, but a system of comparisons instituted in 1877-78 showed that this was probably an error, and I have, therefore, removed it from the new series. A policy prevailed in the office from 1888 to 1898 to the effect that small errors could properly be neglected in the barometer reductions, and in accordance with it all corrections for scale error and capillarity smaller tuan 0. 007 inch were discarded; these have now been all restored. (2) The correc- tion to standard gravity, at sea level on the forty-fifth parallel of latitude, was applied during some years and omitted during others, so that there was irregularity in this respect. The gravity correction has now been systematically added by me since the beginning of 1873. (3) The hours of simultaneous observation have been changed several times since the opening of the service, but practically the observations can be grouped in two series of selected hours, 7 a. m., 3 p. m., 11 p. m. , till June 30, 1888, and 8 a. m., 8 p. m. since that date. Referred to the mean of 24 hourly observations which is the natural stan- dard to adopt for the world, these two systems present very different types of corrections for the North American Conti- nent, and they must be reduced to some one system in order to be comparable. Accordingly auxiliary tables were prepared by which observations at a few selected hours could be re-i duced to the mean of 24 hourly observations, and the different series have been so corrected since January 1, 1873. These 24 hourly corrections will be applied in the future to all monthly and annual pressures published by the Weather Bu- reau, so that the fundamental system may remain intact in case other hours of observation should ever be adopted, differ- ing from those now in use. The application of the corrections for local elevation, scale error, capillarity, instrumental temperature, gravity, and diur- nal variation, to the barometric readings, gives a smooth homo- geneous system of values, from which the mean annual and the mean monthly station normals were derived and checked by cross addition; they are noted as IS. From these the annual and the monthly variations from the general mean were ob- tained, and they have been thoroughly discussed in the He- port of the Chief of Weather Bureau, 1900-1901, Vol. II. In order to determine our final station normals, /! t . it was further necessary to reduce all the short series to a standard fixed by the long 27-year series for a large number of stations sufficient to control the work. There are about two hundred and sixty- five stations, including the Canadians, to be dealt with, and of these about seventy-five had a long record of twenty-seven \ ears. The run of the monthly residuals increases in irregularity as the number of years of observation decreases, but \\ e lia\c so managed the discussion that a short series normal can be re- duced to the long series normal, and thus the station placid upon the standard basis. Whenever a new station is opened by the Weather Bureau a standard normal pressure can now be constructed by a brief computation, and the normal is more ac- curate than any that could be obtained by fifteen years direct observations, since these take up all the turbulent pressure fluctuations due to the general and local circulations, which it is impossble to eliminate, except by the use of the observations of many years. I may add that my experience with the baro- metric observations of the United States convinces me that they have always been of a high order of scientific excellence, and that the apparent residuals are not in fact due to acciden- tal irregularities, but possess general and even cosmical sig- nificance when they are thoroughly discussed. It has been a mistake to assume that they are not worth the most exact treatment in the reductions; on the other hand there is every reason to believe that they will become of prime importance in the solution of several solar-terrestrial problems. THE SEA LEVEL, 3,500-FOOT AND THE 10,000-FOOT PLANES OF REFERENCE. Having obtained these reliable station pressures throughout the United States and Canada, the plateau problem now conies before us for discussion, in order to reduce the pressures taken at different elevations to the adopted planes of reference, in our case to the sea-level plane, to the 3,500-foot plane and the 10,000-foot plane. All the forecasting problems have been heretofore studied solely on the sea-level plane. But it seems evident that our grasp upon the weather problem will bo greatly strengthened if we can study at least three sections through the atmosphere daily instead of the one at the bottom of it. I selected the 3,500-foot plane because this is the aver- age height of the Rocky Mountain stations, to which the least possible reduction is required; also, because it is the average altitude of the base of the cumulus cloud sheet over the eastern districts, upon which observations can be most favorably made with theodolites for gradients of pressure, temperature, and vapor tension. Besides this, it is the altitude at which the moving currents of air are sufficiently distant from the ground to take on their natural configuration when freed from the surface turbulent friction. The 10,000-foot plane was chosen because it is already in use by the MONTHLY WEATHER REVIEW to show the monthly mean isobars at a considerable altitude. Furthermore, it is just in the midst of the most rapid-moving horizontal local currents, which build up the cyclones and anti- cyclones of the middle latitudes and upon which the intensity of storms depends. We know that the isobars on these three planes differ considerably from one another, the closed curves on the lower plane tending to open out into long sweeps on the upper plane, and it is probable that an interconiparison of these varying isobars from map to map will be valuable. THE NEW REDUCTION PRESSURE TABLES. It is evidently necessary to possess reduction tables of a perfectly general and flexible kind in order to make the neces- sary reductions from the several stations to these three planes, and from one plane to the other, in either direction upward or downward. As there are no such tables in print, I have first computed logarithmic reduction tables in English meas- ures, similar to those in metric measures, described in the International Cloud Report of 1898-99, the intervals being for every 100 feet up to 10,000, and for every 10 F. from 40 to + 100. From these general tables the special station tables were made, giving the corrections to be applied to the station pressure at intervals of 0.20 inch to reduce it to the three planes, respectively. These individual tables contain a correction for the humidity term separated from the dry-air term, a correction for the plateau effect, a residual reduction for a few stations, and two temperature arguments rirst, the mean temperature of the air column, and second, the cor- responding surface temperature, which is the mean value of two successive 8 o'clock observations, the last always including that hour for which the reduction is made. In order to sim- plify matters as much as possible for the observers on the stations, the individual station tables are constructed by com- bining all these corrections and applying them at short inter- vals of the station pressure, namely, for every tenth of an inch, and for such close intervals of the temperature argument that there shall be no interpolation necessary in this direction in order to obtain the hundredth of an inch of reduced pressure. The result is contained in three tables, one for each plane, with the surface temperature and station pressure as the arguments, and the reduced pressure to the three planes, respectively, in the body of the table, instead of the correction to the observed pressure. There is thus no computation to be done at the station to reduce the observation, and the time consumed in preparing this portion of the cipher code message is very short. The special tables for the stations for use in reduction to the 3,500-foot and the 10,000-foot planes are now being made up, the first and the second forms leading up to them being completed and checked. The tables for reduction to sea level are already in operation, and, so far as known, there is no occasion to modify the reductions at any of the stations. When one considers the large amount of painstaking and careful labor required to produce such a result as this in so complex a problem, it is a pleasure to commend the faithful work of Mr. Heiskell and Miss Hawkins, who have been my assistants in this computation. We hope to be able to make a trial of the working of the pressures on the higher planes before very long. PREVIOUS DISCUSSIONS OF THE PLATEAU PROBLEM. After all these preliminary matters have been concluded we may proceed to the really difficult portions of the work. They group themselves around three points, (1) the proper relation between the observed surface temperature, t, and the mean tem- perature of the air column, It, corresponding to and substituted for the plateau at the regular intervals for which the general logarithmic reductions were computed; (2) the effect of the plateau itself upon the free air pressure; (3) the residual local effects which can not be classified with the other reductions. Those will become clearer to the reader by briefly mentioning the previous methods which have been employed in reducing the plateau pressures to the sea-level plane. (1) From 1871 to June, 1881, the old Guyot tables were used in reducing low-level stations, with the surface temperature and pressure at the time of observation as the argument. Certain annual constants wore employed in the cases of high stations. The effect was to cause the isobars to swing widely between the morning and evening hours, and generally the maps were very unsteady. (2) July, 1881, to June, 188(5, monthly constants were used for each station, as recommended by the first board on barometer reductions; a single constant answered for each mouth; these are sometimes known as the Abbe-Upton con- stants. (3) July, 1886, to June, 1887, the entirely new system of tables by Professor Ferrel was used, thus introducing several valuable principles. Thus, the mean temperature of the preced- ing twenty-four hours was used instead of that belonging to the respective hours of observation; this was reduced by a vertical temperature gradient, 0.165 per 100 feet, to the approximate mean of the column ; the pressure and temperature arguments (B, t) were both employed in entering the table ; a special cor- rection for the plateau effect was made in the form C, J 0, H, where C'= 0.00105, J is the variation of the temperature from the annual mean, and H is the altitude in units of a thousand feet. The application of the correction for the plateau effect removes the wide range in pressure which occurs on the plateau between summer and winter and reduces it to about the same value on the plateau and in the low level eastern districts. For example, if the mean annual temperature is 50, that for January 25, and for July 80, at a station 5,000 feet above the sea" level, we have 0.00105 x ( 25) x 5 = 0.131 inch for January, and 0.00105 x( + 30)x 5= +0.158 inch for July. The annual range for high stations on the plateau is about 0.400 inch, and on the low levels it is only 0.150, the difference being simply the plateau effect. Professor Ferrel's tables were not used very long. (4) July, 1887, to December, 1890, a mix- ture of Ferrel's and Hazen's tables; 1891-1901, Hazen's tables. Professor Hazen constructed a general empirical formula with the object of simplifying the form of the station table. For this purpose he assumed that Mount Washington is the type for the plateau reductions, which is in fact erroneous, since that isolated mountain acts like a free air point, except for the modified value of 0; he assumed that the sea-level pressure should always be exactly 30.00 inches, and at the same time abandoned the pressure argument entirely, with all depending upon it, and computed the correction under these conditions; he rejected the plateaii effect correction, and at the same time the change of surface temperature to the mean temperature, 0, was neglected. On applying this system to the daily map it was necessary to make certain arbitrary changes in the com- puted reductions in order to produce smooth isobars. The great simplicity in the use of this table, having only the sur- face temperature as argument, seems to have been considered sufficient ground for substituting these tables for Ferrel's, so that from 1891 till 1901, inclusive, they have been employed in making the daily weather maps, although well known to be unscientific and inaccurate. However, it should be said that although the plateau correction was omitted, the practical working of the Hazen method was such as to make the sea- level reductions conform much more closely to the Ferrel sys- tem than to the pure Laplacean system, which is correct for free air rediictions only. On this account the Ferrel and the Hazeu systems work in the same direction for wide departures of the temperature from the annual mean, and to some extent relieve the plateau exaggeration, so that we conclude that the weather maps have served fairly well for the practical purposes of forecasting. (5) 1895-1896, Professor Morrill, in connec- tion with a second board on barornetry, rediscussed the prob- lem and computed a set of tables which have not been pub- lished, though they have been used for some office work, espe- cially the construction of the sea level and the 10,000-foot plane maps for the MONTHLY WKATHER HKVIKW (luring 1896-1901. The Laplacean free air reduction was computed by special tables for the pressure and the temperature arguments, the value of being found by certain adopted average vertical gradients varying for the different seasons of the year; the humidity term was made so as to modify the logarithmic argu- ment; the plateau term was entirely omitted; the tables were in the form of a logarithmic argument, which was not very convenient for rapid work. It was suggested at the same time that a system of constants, daily rather than monthly, be re- sumed for making the necessary forecasting isobars. BIGELOW'S SYSTEM OF BAROMETRY, 1902. We now come to the sixth attack upon the problem, and shall here merely enumerate the steps in the discussion, while the report itself will be found in Volume II, Annual Report, Chief of Weather Bureau, 1900-1901. In substance the prin- ciples laid down by Ferrel have been adopted, but the work has been carried far beyond the degree of perfection possible to him nearly twenty years ago, in consequence of the numer- ous observations at our disposal, whereas Professor Ferrel contented himself with only four years of observation at the plateau stations preceding the time of his studies. THE SEA-LEVEL TEMPERATURES. The object to be obtained is to separate the temperature argument from the plateau effect, and to arrive at smooth isobars in correct relations to the winds and the weather throughout the Rocky Mountain region. Having prepared the monthly station pressure normals, as described above, the corresponding station temperature and vapor tension normals were extracted from the office records. The plateau is there- fore to be considered as dotted over with GO or 70 stations where the monthly values of the elements (It, t, e) are known. Assuming an average vertical temperature gradient of 0.30 per 100 feet, the temperatures were first reduced from those given at the station elevation, to corresponding values at selected heights, 500, 1,500, 6,500 feet, through short distances; for example, all between and 1,000 feet were corrected to 500 feet, and so on. This concentrates the reductions on a few planes. Then a preliminary set of temperature gradients in latitude and longitude was computed from the temperatures on these few planes, throughout the region west of the Mis- sissippi Valley. Certain centers of reduction were taken, namely, where the one hundred and twentieth meridian crosses the fiftieth, forty-fifth, fortieth, and thirty-fifth parallels of lati- tude, and the one hundred and tenth, one hundredth, and ninetieth meridians cross the same parallels, and the tempera- tures were reduced by the two horizontal gradients to these centers, so that a series of temperatures varying with the alti- tude are now known in vertical directions, at about 18 geo- graphical points. These temperatures were plotted on a diagram whose abscissas are temperature values and whose ordinates are altitudes, one chart for each month and one for the year; average curves were drawn through the plotted tem- peratures and prolonged by best judgment to the sea level. In the majority of cases it was easy to do this, as the curvature was distinctly developed on the diagrams. In this way sea-level temperatures were found at several evenly distributed points beneath the plateau, and they were transferred to monthly charts on the sea-level plane, which were completed for the Pacific low level districts and for the central and eastern portions of the United States and Canada. A system of well graded isotherms was drawn through them for the entire country. Small ad- justments of the temperatures on the centers of reduction were required to make the temperatures of the vertical system and of the horizontal system interlock harmoniously and agree together on the sea-level plane. Furthermore, new and more accurate temperature gradients in latitude and longitude could now be obtained, and the work was therefore repeated from the beginning to the end with the improved values. The adopted temperature system is the result of two or three such approximating computations, so that it has at last sutlicient reliability to become the substantial basis for further reduc- tions. The sea-level temperatures at the se\eral stations can easily be scaled from these charts to the tenth of a degree, and such values are called t a . The use of centers of reduc- tion commends itself by the fact that the stations can l>e grouped in several ways, since the same station can be reduced to different centers, and the local inaccuracies will thus check themselves out; also by the fact that the entire amount of computation is much smaller and its accuracv can be controlled by the algebraic differences for uniform spaces. The most important result of this discussion is the develop- ment of well defined temperature inversions during the winter on the northern Rocky Mountain slope, and in the summer in the southern California districts. The former are dm to the dynamic heating of the air blowing eastward <>\er the liockv Mountain divide, and the latter to the excessive surface heat- ing of the arid region relatively to the temperature of the Pa- cific Ocean. The introduction of these inversion gradients relieves the congestion of the isothermal lines heretofore drawn in these districts. THE FIRST PRESSURE REDUCTION TO SEA LEVKI,. Finally, the relative humidities were assumed to be the same for the surface and the sea-level plane throughout the plateau, and from the values of t a just found the corresponding sea-level vapor tensions, o , were computed. We have thus obtained all the elements required for a reduction of the sur- face pressure, B, to the sea-level pressure, />' , by taking as t -4- t i' a first approximation = ~? and the ratio ;, where li is 2 j> nearly 30.00 inches for all monthly means. Using our new logarithmic tables, the monthly and annual pressure at each station in the United States and Canada was reduced to sea level, and the results were transferred to charts. Isobars were drawn through these sea-level pressures as accurately as the data permitted, though the values of 7. were quite dis- cordant in many places, and the lines somewhat in doubt. Of course the plateau correction was included in the sea-level re- duction, as stated above. TO FIND t 0. For practical working by the tables, it was first necessary to determine the relations of t and for the entire range of tem- peratures throughout the year, and this was a task of no little perplexity. It was, however, finally accomplished by two processes. It will be remembered that in the Abbe-Upton system of monthly constants and in the Hazeu empirical tables this modification of the surface temperature argument was omitted; that Ferrel used a constant vertical gradient of 0.165 per 100 feet for the year to pass from t to <>, and that Morrill modified this gradient by taking per 100 feet, 0.150 in winter, 0.200 in spring and autumn, and 0.250 in summer. My vertical temperature gradient came out about 0.195 for each month in the year, as the average for the entire plateau, but it was distinctly shown that the several portions of the plateau have very different gradients in the same mouth, and that for the same locality they change greatly from month to month. Hence it was improper to attempt to deal with the plateau as a whole by using the same temperature gradient; so that, in fact, each station must be considered not only by itself, but also in its relations to the neighboring stations. Finally, special curves have been constructed for temperatures between 40 F. and + 100 F., showing the variable differ- ence between t, the surface temperature for twenty-four hours, and the corresponding 0, or the mean air temperature of an air column substituted for the plateau itself. The can not be considered as the arithmetical mean temperature between the surface and the sea-level temperatures, because the con- necting line is a curve and is not straight, so that it is essen- tial to arrive at an integral mean temperature instead of an arithmetical mean. In a graphical construction the values of may be taken as the abscissae and the differences, t 0, as the ordiuates of a curve, which we seek to construct. The first ap- proximation is evidently equal tot = t \(t-\- <) = J (t t ), but the true value may differ from this by several degrees at many of the high stations. THE FIRST PROCESS. We proceeded to discuss this point by two distinct methods, the first covering the low temperatures from 40 to -(-30, and the second covering the temperatures from about 10 to 90, so that there shall occur a small overlapping of the two systems in the middle temperatures, and thus allow the two to be joined together. About fifty maps were selected for the winter season, when high pressures and low temperatures pre- vailed in the Rocky Mountain districts. The pressures for the plateau stations were next reduced to the 3,500-foot plane, be- cause this requires the least average run for the corrections, and hence there is little error arising from selecting the wrong temperature arguments. This configuration of isobars was drawn in red lines; then the low stations near the Pacific Ocean and those in the Mississippi Valley were reduced to sea level; also some of the stations on the mountain slope at mod- erate elevations were reduced to the 3,500-foot plane as well as to sea level. A set of isobars was drawn on the sea level in blue lines. It was now assumed that the configuration on the 3,500-foot plane is substantially correct for that elevation, and is what the forecaster really wants at sea level for practical work. It was therefore joined with the sea-level system by simply making the red and blue lines flow together and uniting them smoothly; in other words, the upper configuration was depressed to sea level by simply renumbering the isobars in inches as determined by the true sea-level lines, so that a single system of well-balanced, isobars covered the country. Next the question was, what is the value of that will be re- quired to transform the observed station pressure into the sea-level pressure thus constructed ? This was computed from the data in a reverse direction, and the differences, t 0, found ; these were collected by groups for each station on the plateau above 1,000 feet in elevation; the means were taken and plotted as ordinates on the abscissa axis of 0. The result was very instructive, and it at once separated the plateau into groups corresponding to the geographical and climatic location, and showed that all the attempts to use one value of the vertical gradient for a given time are very erroneous. It should be re- marked that the value of t thus found was much too large, because it included within itself the real plateau effect, and this ought first to have been separated ; but it gave true rela- tive variations of t with the range of temperature from 40 to +30, so that it was only necessary to discover the reduction factor to make the scale of values correct. THE SECOND PROCESS. For the warmer temperatures of the year, from + 30 to -)- 1)0, I took the mean monthly values of t and t a , surface and sea-level temperature, respectively, and found t = \ (t. t a ) and (t = | (t + t a ). These were plotted mouth by month in coordinate points through which it was easy to draw approxi- mate mean curves. It is noted that during the winter months the ordiuates average a little larger for the same values of than during the summer months, but as we are limited to con- structing a set of tables representing mean conditions, this mean line is the best that can be taken. The variation on the mean line does not often exceed 1, and this small change in the resulting argument has really but little influence upon the sea-level reductions which are required. Finally the slope of the second system of curves at the temperatures from + 10 to -f- 30 indicated the slope that should be assigned to those found by the first method, that is, they gave us the scale factor for reducing the slope first obtained. The resulting curves are published in the full report, but they can hardly be described without diagrams. Generally speaking, on the north and east of the plateau the (t 0) curves have a short ordinate from 10 to 40, and a considerable increase toward either end; on the central portions of the plateau the curves are nearly flat, the length of the ordinates being about proportional to the altitude; on the western side of the plateau the curves have ordinates which are longest in the central parts and short- est at the ends, that is to say, they are about reversed in shape from those on the eastern plateau. These differing results are largely due to the climatic effects of prevailing winds from the Pacific Ocean, which blow upon the mountain ranges and pre- cipitate their moisture on the western side; the clear skies and cold waves prevail on the eastern side; also there are seen to be certain dynamic heating effects. This subject is, however, too large to expand in this connection. THE SECOND PRESSURE REDUCTION TO SEA LEVEL. Equipped with these first approximate values of for each month as derived from the surface t, the reductions to sea level were made for the mean monthly normal station pressures, B a , as already mentioned, and the corresponding isobars were drawn. The sea-level pressures, as shown by the resulting map itself, apart from the reduced values, are really more nearly well balanced and correct than those derived from the individual reductions, because the isobars depend upon the mean result of many neighboring stations, whose mutual claims must be simultaneously satisfied in drawing the pressure lines. The pressures were, therefore, scaled from the maps, giving B m , and the differences taken between them and the original values as reduced by the computation for B a -B m . The outcome was ex- ceedingly valuable and suggestive. For some stations the differences between the map and reduced values were such as to indicate only minor irregularities of a few thousandths of an inch, and these are to be referred to imperfections in the station normals; for others the difference was nearly constant, suggesting an error in the assumed elevation, especially for the old stations at military posts where the elevation had been derived from barometer readings; for others there was a very marked annual period in the differences, which could only be due to an error in the assigned value of the mean temperature, t>, since the differences disappeared at certain points, the signs being reversed between the low and the high temperatures. To be brief, all these sources of difference were removed, the entire work was recomputed a second time, a new system of isobars was drawn, and generally the entire subject was worked over in every available way. The practical effect was a readjust- ment of some elevations, and of the values of 0, so that the final differences between the map and the reduced sea-level pressures became small, usually less than one hundredth of an inch (0.010 inch), for the long record stations. In a few cases it was found that the constant error, called A A, was due to the fact that the initial temperature from which the plateau cor- rection was computed, namely, C A H, was not accurately chosen. Usually this was taken as a mean annual tempera- ture, but for some stations, especially on the southwestern edge of the plateau, Santa Fe, Flagstaff, Modena, Independence, etc., it should have been somewhat different. The variation can not be due to elevation, because this has been carefully determined by the surveys, but it must be caused by the local influence of the great desert in connection with the adjacent lofty mountain ranges. There are other stations of low eleva- tion, lying in the eastern or in the Pacific coast districts, where no important error can arise from the reduction data, at which there is a small constant correction required to make the station harmonize with the others, as, for example, Lynchburg.Va., and Portland, Me. These stations have been known, at the Central Office, to act out of perfect harmony with their surroundings. and it is still difficult to understand the causes of these discrep- ancies. It has been found, furthermore, that the low station:- on the north Atlantic and south New England coast and also on the north Pacific coast, are not so perfectly in accord as might be expected, and this may be due to the effect of some land and sea action which is operating in these localities. On the whole the reductions as completed are very reliable when all corrections are applied, that is to about 0. 010 inch, under all possible circumstances. We note further that the differ- ences outstanding between the finally adjusted reductions to sea level from the station normal pressures and the map pres- sures derived from the balanced system of isobars, can be properly considered as corrections to the station normals which will reduce them to the homogeneous or balanced nor- mals. This is distinctly true for stations of short record, e. g. , two or three years, where the monthly variations are really considerable, so that by applying these residuals as corrections the station normals are brought to agree with the more correct system which would be derived from a long record of obser- vations. In short, since the long record stations really control the map construction, the short records can be at once im- proved by applying these small final residuals. Such residual corrections have, therefore, been added to all station normals, and the entire system is thus reduced to a long range homo- geneous system and it is called B u , normal pressure at the sta- tion, and B m , normal pressure at the sea level. These values become our standard normals for further developements and have been so used in the remainder of the work. It is also evident that whenever a new station is opened, we can easily compute a more correct station normal pressure, by starting with the values of 7? m as interpolated from the map, than could be found by less than fifteen or twenty years of observations. PRESSURES COMPUTED ON THE 3, 500-FOOT AND THE 10, 000-FOOT PLANES. We have now obtained the following quantities: At the sta- tions, B f , t, e, R. H., normal pressure, temperature, vapor ten- sion, and relative humidity; on the sea-level plane, B , t , e a ; also the ratio was computed for use in the reductions. > It is next proposed to compute -B,> <,, e v on the 3,500-foot plane, and # < 2 , e r on the 10,000-foot plane. For this purpose the temperature gradients in the free air must first be determined. There are three sources of information available, namely, the European balloon ascensions, the American kite ascensions, and the Washington gradients derived from computation on the cloud formations observed with the theodolites in 1896-97. These were all thoroughly discussed and they agree together sufficiently well to permit the assignment of average gradients from the surface to the two upper planes in the free air. The temperatures were computed on these planes for enough sta- tions to permit drawing systems of . isotherms with accuracy. As regards the 3,500-foot plane, the temperatures were found from the free air gradients for stations outside the plateau and of lower elevation than 3,500 feet; for points within the plateau the temperatures on that plane were taken from the diagrams of vertical temperatures, previously constructed; these two systems agree well together, and the isotherms are continuous. The isotherms on the 10,000-foot plane are simple curves joining the Atlantic and Pacific districts and present no trouble in crossing the plateau. There is one re- sult of interest, however, at the surface of the plateau, which I call "gradient refraction. " Within the plateau the vertical temperature gradient averages about 0. 195 per 100 feet, and in the free air for the eastern districts about 0.300 up to 10,000 feet. Now it is evident that this plane is high enough above the plateau to escape the influence of the surface con- ditions, and that it is in the midst of the rapidly drifting cur- rent of air whose direction is eastward, so that quite uniform temperature must prevail along the same parallel of latitude. Hence, it follows that by using the smaller gradient 0. 195 to the surface of the plateau, larger values than 0.300 must be employed from the surface to 10,000 feet, if the average gra- dient is to be about 0.300, such as it would be if the plateau were removed. Therefore at the surface of the plateau there is something like an abrupt change in the gradients which is similar to refraction. Finally, by means of the temperatures thus found and the relative humidities, assumed to be the same as for the surface stations, the vapor tension on the 3,500-foot plane was computed. For the 10, 000-foot plane it was assumed that the relative humidity is 50 per cent of the surface amount at all places; this may be subject to criticism, but it is near the truth and the effect on the vapor tension of even considerable changes in the relative humidity would be unimportant at the low temperatures prevailing at that altitude. THE FIRST COMPUTATION OF B I B f Instead of computing the values of /,, <> v and / s , c t , for the several stations at the outset, the work was much shortened by interpolating the values of all this data on selected points of the charts, namely, centers of reduction; that is, where the meridians 5 apart, 125, 120 65, cross the parallels 5 apart, 55, 50 C 30 On these centers of reduction the sea level B m , t o , e a were also drawn from the charts, so that the data is complete for reducing the sea-level pressures to the higher planes. There are two objects gained by this method of discussion; (1) the work of computation is short- ened very much; and also (2) the result affords an admirable check on the entire system of reductions, as will be seen by what follows. The pressures /?, and B } on the 3, 500-foot plane and the 10,000-foot plane, respectively, were computed by the logarithmic tables from the data thus obtained on the (tenters of reduction, and the corresponding systems of isobars were drawn. There now exists the same general harmony in these isobars as on the sea-level plane, and no further corrections are re- quired. It is to be especially noted that in the plateau region the reductions from sea level to the upper planes were made by the same principles as if it had b.eeu a free air column, so that all plateau questions are laid aside. THE SECOND COMPUTATION OF B Jt B } . From the B^ and B t charts the pressures belonging to all the stations were interpolated, so that the values of /',, /^, to be derived by a direct computation from the station data could be compared as a check. Meanwhile the several station reduction tables to the three planes had been completed, and as a final check the three values, B a , B v B v were computed and com- pared with the values derived from the charts, as explained in the first process. The differences between the two sets of val- ues for B a , B t , /?, were about the same on the three planes; they average about 0.010 inch, the majority being 0.000 or 0.010 inch, a few 0.020 inch, with occasional larger variations due to errors of computation readily detected, or to a local peculiarity, involving a slight readjustment of the corrections in the station tables. These checks, therefore, involved the three distinct parts of the entire discussion, since the process lias been arranged practically in a circuit so as to pass from the station B n to Ii t and B t by two separate routes, as described. Hence, ( 1 ) the processes of eliminating the plateau effect, and of computing the temperature arguments / and fl were success- ful; (2) the logarithmic tables and the numerical station tables are in agreement; (3) the charts are accurately drawn, and represent the observations with precision. As the result of this discussion we have prepared charts for the United States and Canada, giving the monthly and annual normals of pressure, temperature, and vapor tension on the sea-level plane, the 3,500-foot plane, and the 10,000-foot plane. also the relative humidity on the sea-level plane, i. e., 130 charts for these data. There are also charts of gradients of temperature in latitude, in longitude, and in altitude; and charts of pressure variations for a few selected hours referred to the mean of 24 hourly observations. Furthermore, the corresponding numerical values are entered in a summary table for all stations on the sea-level plane, about 265 in number; also for all the stations which Were in use by the Weather Bureau, either in the United States, Canada, and i the West Indies, at the beginning of the year 1900, or which ' have been opened for service since that date, making about 175 on the upper planes. It has not been found necessary to revise any of the reduc- tions to sea level since the tables were put in operation on January 1, 1902, showing that they bear the test of practical j work at the hands of many observers. The station tables for the upper planes will soon be tried, and an estimate made as to their value in increasing the accuracy of the forecast sys- tem of the Weather Bureau. We conclude with the remark that the pressure observations and computations of the United States have been at last placed upon a strictly scientific basis, and that all the corrections re- quired by theory will be systematically applied in the future, and the entire series from 1873 onwards will be kept strictly homogeneous. We shall, therefore, for the first time be ready to take up the problems of seasonal variation of the weather, the changes of the climate and crop from year to year, and also the true cosmical problems involved in the radiation effects of the sun upon the earth's atmosphere. Even if we do not ourselves succeed in resolving these questions, we shall have left this portion of the data in form for others to make reliable discussions. II. METHOD OF OBSERVING AND DISCUSSING THE MOTIONS OF THE ATMOSPHERE.' INTRODUCTORY REMARKS. It has been suggested to me that it would be advantageous to many who are interested in the progress of modern meteor- ology, if the results of the observations on clouds, which were made by the United States Weather Bureau during the years 1896-97, could be put in a more compact form than was adopted in the original report. 2 I am the more inclined to present anew some of my results because of the extensive use that has been made of the American observations generally in Dr. J. Hann's Lehrbuch der Meteorologie, 1901. In this judicious and comprehensive summary of the state of meteorology at the end of the nine- teenth century, Dr. Hann has given very generous recognition to the contributions of the United States, including the Weather Bureau and the Blue Hill Observatory, to the advancement of meteorology. But more important than this, the views therein adopted regarding the theories of the circulation of the atmos- phere in the general and the local cyclones, are fully in accord with the ideas set forth in my report on the cloud observations of 1896-97. It is apparent that meteorology is at last secur- ing a set of principles. founded on observations, which will super- sede much that has been heretofore taught in this connection. It is therefore important to explain the results of the Weather Bureau observations of 189697 as briefly and simply as possible. Taking a very general view of the present state of meteor- ology, it may be proper to classify the conditions as follows: The statistical side of the subject is being rapidly worked up, so that our knowledge of facts is relatively quite complete in cli- matology, and in the diurnal and annual periods of the various atmospheric elements, namely, pressure, temperature, vapor tension, and wind direction, in different parts of the world, so far as they prevail in the strata near the ground. But in the upper strata our knowledge of these elements is still very limited, though it has been considerably extended during the past ten years, by the cloud observations, and the balloon and kite. ascensions. On the theoretical side of static meteorology it may be said that meteorological analysis is well advanced, as far as concerns the barometric relations of pressure to the height, the temperature and vapor tension variations, and the adiabatic thermodynamics generally. The practical extension and application of these formula} to the upper strata is making fair progress, and is likely to result in very definite knowledge of the true state of the atmosphere throughout its extent. In dynamic meteorology, however, that is in the hydrodynamics of the atmosphere, affairs are in an unsatisfactory condition, and they can be reclaimed only by pursuing a sound policy regarding them. Looking over the entire field, one is sur- prised to find that but little has been done in the preliminary and the most necessary stages of this work, in order to make the dynamics of the atmosphere a practical scientific problem. It is wasting time to speculate on the mathematical analysis of the motions of the atmosphere till we know what the motions are, simply as a case of kinematics. In other words, the paths of motion of the average air currents should be systematically worked up all over the world, as the indispensable prelimi- nary to this study. Of course the obstacle in the way of doing this is the invisibility of the air itself, and the labor of making any observations on its direction and velocity of motion much 1 Reprinted from the Monthly Weather Review for February, 1902. 2 Report on the International Cloud Observations, May 1 1896, to July 1, 1897, by Prof. Frank H. Bigelow. Report of the Chief of the Weather Bureau, 1898-99, Vol. II. F. H. B. 2 I above the ground. It was for supplying just this need that the international cloud observations of 1896-97 were instituted, and to it they have contributed a valuable amount of data. Furthermore, there are the great physical problems con- nected with the absorption of the sun's radiant energy in the atmosphere, its separation into several kinds of energy elec- tric and magnetic energy, heat energy of the visible and invisi- ble spectrum, and so on. Also there is the question to be answered as to the amount of the solar output itself, the varia- tions from its mean value, how much and what kinds of energy are absorbed in the upper strata, and what in the lower. The circulation of the atmosphere in its details really goes back to these questions about which we know only a very little. Hence, in a word, the deficiency of modern meteorology is in the dynamics of the upper and middle strata of the atmosphere. NOTATION AND COORDINATES. It is not an exceptional fact in the history of science that in the first stages of its development meteorology should have grown up in a rather haphazard fashion, especially as it was dealing with a subject of popular interest, wherein many ob- servers were concerned in getting observations of one kind or another without much regard to their ultimate use in mathe- matical analysis. As the result of this lack of purpose the confusion became so great between the methods of observing and recording in different parts of the world that when com- parative studies were begun the difficulties arising from the want of homogeneity were seriously felt. In order to remedy this state of confusion the International Meteorological Com- mittee have been laboring for years to introduce uniformity into the methods adopted by meteorologists. Much has al- ready been accomplished, and yet there are at least two very important steps that remain to be taken. The first is to use only one system of measures, as the metric in place of the met- ric and the English ; and the second is to conduct and discuss | the observations in such a way that in their published form they shall be in perfect order to meet the requirements of the fundamental mathematical equations, either static or dynamic, as they are needed. At present meteorological observations are about evenly divided between the English and the metric systems of measures, since the former is in use in Great Britain, Canada, United States, south Africa, Australia, and India ; while the latter prevails in Europe, Asia generally, Japan, north Africa, and South America. Thus it is necessary to translate the figures from one system to the other in prepar- ing the data for the world and for cosmical problems; also two sets of reduction tables are required for all the elements, and two sets of constants in all the formulae. The more lamentable defect occurs from the fact that the observations are made without relation to their final use in mathematical discussions involving the motions of the atmosphere. Indeed almost no th- ing has been done to give us the true vector components of motion in the observations, so that they shall be in form for immediate introduction into the equations. The standard equations have been presented by different authors in many equivalent forms, and in consequence the subject has been made unnecessarily complex and difficult for students. The entire body of fundamental equations in meteorology is not very large, but the amount appears to be much greater than it really is by reason of the manifold notations and symbols which have been employed. No more valuable reform could be instituted than that of causing the same physical quantity 9 10 to be always represented by the same symbol. Thus, for ex- ample, barometric pressure />', pressure in units of force P, pressure in units of weight />, would put us in harmony with the leading works in hydrodynamics and thermodynamics; then absolute temperature T, thermometric temperature /, mean temperature of the air column l>, vapor tension e, maxi- mum vapor tension E, absolute weight of vapor //, weight of the unit volume a, specific weight /', and relative humidity R.H. For rectangular coordinates, displacements (JT, y, z) , velocities (it, r, ir) (/, accelerations (u, v, it)f, angular velocities ((u,, u> f <,); for cylindrical coordinates, radius ra, angle about axis of rotation y, for polar coordinates, radius vector r, polar distance 0, angle about axis of rotation /. I have felt the weight of these considerations in my com- parative studies so much that special pains have been taken in my report to exhibit all the fundamental equations in a standard system of notation, and also to reduce the analyses of several authors to the same standard system for the sake of ready intercomparison. Also, as it seems to be of the utmost importance that the observations taken to determine the motions of the atmosphere should be made in a form appro- priate for use in the dynamic equations without further trans- formation of the data, particular care was taken to make the cloud observations conform to these requirements. It was not possible to bring about this harmony between observations and the analytical theory without introducing some radical changes in the methods heretofore followed by meteorologists, both in the conduct of the observations and in the analytic develop- ment of the equations. Accordingly, some account of these changes, as well as of. the new results which were deduced from the cloud observations made by the United States Weather Bureau in 1896-97, will be given in the following pages. THE AXES OF COORDINATES. The first decision that must be made in establishing a funda- mental system of notation has regard to the choice of the axes of coordinates which shall be placed at the base of the entire study, since all the algebraic signs of the quantities depend- ing on the observations which are to be substituted in the equations, must be determined from the adopted positive direction of the axes. This choice depends practically upon two facts, (1) that the radius of the earth is drawn positive outwards, since r increases from the center, and (2) that the right-hand rotation is adopted generally in modern scientific researches. It is true that some of the German mathemati- cians use the left-hand rotation, but the trend is toward a universal adoption of the right-hand system. If we take as the primary radius that of the earth's axis of rotation in the Northern Hemisphere, as is most appropriate for all scientific problems except in terrestial magnetism, then in polar co- ordinates the positive angular development in polar distance, 0, is southward ; next, with the right-hand rotation about this axis extended upward, the positive development of )., the angle in longitude, is eastward. Hence, for all systems of coordi- nates, polar, cylindrical, and rectangular, the azimuth rotation is from the south through the eaxt, north, and west. Unfortunately this is in the opposite direction to the azimuth rotation adopted in astronomy, in navigation, and in popular meteorology, be- cause in these branches of science the simple practical consid- eration has been to follow the sun in its diurnal course, so that azimuth circles and compass cards are numbered around in the clockwise or left-hand rotation. For many statistical pur- poses, as where average wind directions are to be computed, it makes little difference what system of notation is used, because these data do not look beyond their own immediate purposes. But where we have to deal with a system of equa- tions it is not so. If we take the first set of equations, International Cloud Report (154), for linear velocities due to rotation, i 1 , = ' s '", -I- ' '., JOj = W X w. t -f // 1,1 , where .r, /, z are linear distances, u, i; u- are linear velocities. , . t are angular velocities, it is evidently necessary that all these should be defined most carefully. According to the statement given above, + (./-, (/) are referred to the southward axis, + '(.'/> '') are referred to the eastward axis, + (z, ir) are referred to the zenith ward axis, but everything will go wrong if < 3 is not taken to rotate posi- tively about the axis 3, from the south through the east, instead of through the west. Hence, and 9 of the International Cloud Report are, therefore, in accord with the coordinate directions of the formula? which are developed in the following portions of the same Report. THE COMPOSITION AND RESOLUTION OF THE VECTORS OF MOTION. It is sometimes necessary to construct the resultant velocity and direction of the motion of the air at a given place out of a large number of individual observations, as in forming charts 20-35, International Cloud Report, for example, and the fol- lowing practical devices were found convenient. Suppose it is desired to determine the velocity aud direction of motion in the cumulus cloud level on all sides of a low area, as in the Mississippi Valley. \Ve can best proceed as follows: Take a piece of tracing paper, and select a large number of cloud maps showing about the same configuration of the isobars, so that the centers of the cyclones are located in a given district. Then lay the paper on the cloud maps in succession, and trace the arrows showing the cloud motion wherever an observation is found on the map. Mark the center on the first map and pre- serve it so as to place it in coincidence with the other cyclonic centers. Continue to fill the paper till some such composite of arrows is obtained as is shown within the square of fig. 2. A scale map of squares, or any other adopted division of areas, is to be prepared as large as the tracing paper, and the two are placed together so that the scale diagram marks oft' the arrows of the composite map into groups, within each of which it is proposed to find the resultant. Then covint out the num- ber of arrows pointing N, NE, E, etc., in succession for eight directions, giving in our example, N=4, NE=4, E=10, etc.; take the excess in four directions, as S = 7, E = (>, SE = 7, SAV = 10; plot these results on a diagram and resolve SE= 7 into E = 5 and S = 5 ; also S\V = 10 into W = 7 and S = + 7; make the sums E= +4 and S= +19; plot these compo- nents and obtain the resultant I"=20; the angle

,) in the four quadrants by using the proper signs. When all the vectors ( V, 0 kin. The mean of areas 5 to 12= II, at the average distance 75(1 km. The mean of areas 13 to 20=111, at the average distance 1,J.">0 km. of the three circles I, II, III at certain evenly distributed dis- tances. The scale of the original diagram, Chart 9, Interna- tional Cloud Report, is on a radius of 3 centimeters; on the weather maps this is equivalent to 15 centimeters, where 1 cetimeter is equal to 100 kilometers. The adopted scale is therefore one-fifth the scale of the daily weather map, and on it 1 centimeter represents 500 kilometers or 310. 7 miles, and one millimeter is equivalent to 50 kilometers, or 31.1 miles. All the diagrams of the Report, as far as possible, are reproduced on this scale, but they are readily interpreted on the weather map, so far as linear dimensions are concerned. VECTORS OF MOTION IN HIGH AND LOW AREAS HKrTAXH'LAR COORDINATE. In order to prepare the observations for discussion all those 13 which were made iii the same sub area of n cyclone or an auti- cvcloue were collected together in each cloud stratum, and tiic resultant of all these individual vectors was computed in accordance with the method above described. The individual observations occur iu Table 9, and the mode of collecting them is illustrated in Table 29, page 363 of the Report. For con- venience, the United States was divided into six districts: 1, Alberta; 2, Lakes; 3, New England; 4, Colorado; 5, West Gulf; C, South Atlantic; so as to arrive at a conception of the prevailing local characteristics. Hence the heading of the form H 2 15, occurring in several tables, means that in subarea 15, of a high area or anticyclone whose center is iu the Lake dis- trict, the accompanying observations were made in the several cloud strata, and also at the surface where the instrumental meteorological data are given at the three daily observations. Table 32 contains the resulting vectors V,.y> for the northern and southern groups by districts, also for the four seasonal quarters of the year, together with the several mean values, all this extending to the eight cloud strata. In this table the relative velocities are given as derived from the nephoscope, that is on the 1,000-meter plane. TAIILE 1. Direction and velocity of motion in hiijh and low areas rectangular coordinates. * Compos Point Area number. i Cirrus; average height 9. 8 kilometers. High. IMVI. Ab.

' i' S 1 25 86 35.3 1 111 51.0 E 2 16 57 43. 1 4 96 40. 2 N ; ~3 49 76 31. 4 W 4 30 78 36.3 u lot r,8.8 S 5 37 66 37. 2 50 97 31.4 SE G 20 67 32. 3 33 101 44.1 E NE N 7 8 9 23 90 58.8 43 89 29 . 4 51 81 34. 3 10 109 36.3 7 90 49.0 NW 10 34 117 38.2 3 92 27.4 W 11 42 80 37. 2 23 77 45. 1 S\V 12 12 107 14.7 6 105 56.8 S 13 38 95 31.4 27 123 33. 3 SE 14 r,4 82 35. 3 70 1)11 32.3 E 15 28 \(X> 46.1 49 85 34. 3 NE 16 58 85 28.4 24 90 30. 4 N 17 27 88 36.3 NW 18 25 . 96 33. 3 2 122 39.2 W 19 51 98 29. 4 36 71 44. 1 s\v 20 63 109 30.4 94 90 41. 2 No. of Mciin; obs .... i 736 . 34. 9 451 '. 40.8 * Extracts from Tables 34 and 88. The vectors of Table 32 are plotted on Chart 13 of the Report, the northern in red and the southern in blue, first for the high areas and then for the low areas; also in the seasonal groups so that the comparative motions can be studied. It is evident that several years work are needed to produce smooth and evenly balanced mean vectors, which shall truly represent the average circulation. Espeoiullv it will be necessary for the Canadian stations to cooperate and supply the vectors wanting in the northern subareas of our three northern districts, as this part of the circulation usually extends into Canada. Furthermore, the vectors of Table 32 are collected together numerically in Tables 34 to 40, with a single change, namely, that the ve- locities observed on the 1,000-nieter plane have been multiplied by the adopted mean height of the given cloud stratum. For example, the mean height of the cirrus is taken as 9.8 kilometers, and hence the mean annual velocity l'= 3.6 of the cirrus in high area No. 1., page 368, is multiplied by 9.8, and it is entered at the beginning of Table 34 as F= 35. 3. I have taken the cirrus in each subarea of the high and low areas to show as an example in Table 1 and fig. 4. HIGH. LOW. FIG. 4. (From Chart 15.) These vectors are plotted on Chart 15 (see fig. 4), which shows the annual vectors on the several cloud levels in high and low areas. From Chart 15 and the Tables 34-40 are obtained the data for discussing the mean general circulation over the United States. The mean total velocities in high and low areas, without regard to direction, are found by taking the mean of the velocities in the areas of Tables (34-40) and they are given in Table 33, section 1, as in the following example, Table 2: TABLE 2. Total velocitifs in high* and lows without regard to directions.* Clouds. High areas. Low areas. Height, Idiom. All groups. North- ern. South- ern. All groups. North- ern. South- ern. Ci 9.8 9.8 8.1 5.9 4.5 2.5 1.5 0.9 34.9 39.1 33.5 30. 2 23.5 23.3 11.2 11.4 4.8 38.3 42.6 33.9 31.1 26.6 22.7 10.9 12.2 4.9 30.4 34.8 30.5 24.1 19.7 18.5 10.4 9.5 4.8 19 36 40.8 39.8 39.3 36.0 29.2 28.6 14.6 11.1 5.4 15 38 44.6 42.5 43.8 39.4 32.6 32.9 17.4 13.2 5.3 28.3 36.3 34.8 30.5 24.4 21.1 11.8 8.6 5.9 28 40 Ci S Ci Cu A. S A. Cu S. Cu Cu S Wind Range, per ct . From Table 34 35 39 'Extract from Table :!:!, Section I. Table 2 shows that the velocities are greater in the north- ern circuit than in the southern, and greater in the low areas than in the high areas. These values must be studied in con- nection with the barometric gradients to form a theory of the dynamic action in the atmospheric circulation. The vectors in the form velocity and azimuth, V, tiT!i. ( '.ml|.H^ |Mlillt. Area mi lull. I. High. Low. S + E + S+ E + S 1 + 2.5 +35.2 18. 3 +47. 7 E 2 +23. 5 +36. 2 - 4. 2 +40. N 3 + 76 +30 5 W 4 + 8.6 +35.5 14. 2 +57. s 5 + 15.1 +34.0 -3.8 +31.2 SE 6 + 12.6 +29.7 -8.4 +43.3 E 7 0. +58. 8 11.8 +34.3 NE g + 05 +29 4 N 9 + 5.4 +33.9 0. +49. NW 10 17. 3 +34. - 1.0 +27.4 \V 11 + 6.4 +36.6 +10. 1 +43. 9 sw 12 -4.3 +14.1 14. 7 +54. 9 s 13 -2.7 +31.3 18.1 +27.9 SE 14 + 4.9 +34.9 1.6 +32.3 E 15 8.0 +45.4 + 3.0 -1-34.2 NE 16 + 2.5 +28.3 0. +30. 4 N 17 + 13 +36 3 NW 18 - 5. 2 +33. 1 20. 8 +33. 2 W 19 - 4. 1 +29. 1 + 14.4 +41.7 SW 20 -9.9 +28.8 0. +41. 2 Means + 1.97 +33.7 5. 26 +39. 4 Normals 1 6 +36.6 - 1.6 +36.6 Meaiis +0 66 +40 1 3 75 +32.7 * Extract from Tables 42 and 43. TABLE 4. Southward and eastward components of velocities in highs and lows.* Clouds. High areas. Low areas. Means. Means. -fS N +E W +S N 5.26 - 9.24 3.00 - 4.60 2.38 - 4.00 - 0. 11 - 1.32 - 0.40 43 +E W North. East. Ci + 1.97 + 1.65 0.60 - 0.37 - 0.07 - 0.32 - 0.13 - 1.22 - 0.69 42 +33.7 +32.0 +32. 6 +27.2 +22.1 + 16.0 + 5.1 + 5.8 + 1.1 42 +39.4 + 35.9 +37.2 +31.3 +24.3 +24.3 + 11.4 + 7.8 + 1.5 43 1.6 - 3.8 - 1.8 - 2.5 - 1.2 - 2.2 - 0.1 - 1.3 - 0.5 +36.6 + 34.0 +34.9 +29.2 +23.2 +20.2 + 8.3 + 6.8 + 1.3 Ci. S Ci. Cu A. S A. Cu . . S. Cu Cu s Wind From Table . Extract from Table :, Sections II and III. The most important remark to be made regarding these ex- tracts is that the observations show an average northern com- ponent in the United States in all levels, provided it is a fact that as much air streams through the low areas as through the high areas on the average. (2) The subareas were collected into two groups, those having a southward and those having a northward component. Thus we have a southward compo- nent in high areas in 16, 8, 2, 7, 15, 6, 14, and in low areas in 18, 10, 4, 11, 19, 12, 20; but a northward component in high areas in 18, 10, 4, 11, 19, 12, 20, and in low areas in 16, 8, 2, 7, 15, 6, 14. The means from these groups give the mean TABLE 5. Component velocities in selected areas between high and low centers. * Clouds. Selected areas. Southward. H. 16, 8, 2, 7, IB, 6, 14 L. 18,10,4,11, 19,12,20 Northward. L. 16, 8, 2, 7, 15, 6, 14 H. 18,10,4,11,19,12,20 Ci + 0.66 - 2.11 + 4.95 + 2.79 + 6.24 +10.22 + 6.52 + 5.25 + 2.23 +40. 1 +36.9 +38.7 +26.5 + 23.7 +22.1 + 9.6 + 7.5 + 3.2 - 3.75 - 3.89 - 7.34 - 7.47 - 7.78 11.13 - 8.13 7.97 - 3.25 +32.7 +38.9 +32.1 +31.0 +21.9 + 17.1 + 6.5 + 5.1 + 0.2 Ci. S Ci. Cu A. S A. Cu S. Cu Cu 8 ... Wind Bange . . From Table 42 42 43 t:t * Kx tract from Table 33, Section IV. components of the distinctly southward and northward cur- rents in the different strata. They are collected in Table 33, Section FV, and are reproduced in Table 5. It is important to note that the most rapid currents, both northward and southward in the atmosphere, are in the strato- cumulus level, 2.5 kilometers or 1.6 miles above the ground, and that these currents decrease in velocity above and below that level. The eastward velocity averages about the same in the highs and lows. Hence we infer that the strato-cumulus level is the stratum where the interchanging motion is most rapid between the Tropics and the poles. VECTORS OF MOTION IN HIGH AND LOW AREAS- CYLINDRICAL CO- ORDINATES. We can now compute the true cyclonic and anticyclonic rec- tangular components by simply subtracting the normal values (heavy type, Table 3) from the individual subarea values in each cloud stratum. In this way the components ,, r, of Tables 44, 45 are found, and an example is given above, in Table 6, in the cirrus level for the high and low areas. Against subareas 6, 8, 10, 12, 14, 1C, 18, 20 there are placed the corresponding vectors (. Rectangular components. Cylindrical components. MJ 1>, a fl " 1 + 4.1 - 1.4 +25.1 - 0.4 + 9.2 6.1 + 10.2 - 1.1 + 16.7 - 2.6 + 14.2 -- 6.9 15.7 333 + 1.6 +22.2 + 2.1 - 7.2 7.5 286 + 7.0 2.7 15.7 -2.6 16.0 190 + 8.0 0.0 2.7 22.5 22.8 263 - 1.1 - 5.3 + 6.5 - 1.7 6.8 345 7.4 +8.8 + 4. 1 - 8.3 9.2 296 + 2. 9 0. 3 3. 6 3. 5 5. 225 2.5 7.5 8.3 -7.8 11.4 223 + 4.1 - 1.4 - 0.4 25.1 - 9.2 +6.1 + 1.1 +10.2 2 3 4 5 + 16.7 .- 2.6 + 4.9 14.9 +22.2 -- 1.6 - 6.6 +3.6 - 7.0 +2.7 +13.2 - 9.2 0.0 +8.0 + 14.0 18.0 6 . . 7 8 .... 9 10 11 12 13 - 1.1 - 5.3 + 3.4 -- 5.9 + 8.8 +7.4 - 8.7 +3.0 2.9 +0.3 + 5.0 0.0 + 7.5 2.5 0.0 11.4 14 15 16 17 18 19 20 LOW AREAS. Area No. Rectangular components. Cylindrical components. Mj U, * ft W * , 1 ... 16.7 +11.1 2.6 +.3.4 16.7 +11.1 + 3.4 +2.6 2 . . 3 4 12.6 +20.4 2.6 - 5.4 - 6.8 +6.7 9.6 136 10.2 - 2.3 20.4 12.6 5 - 2.2 - 5.4 - 0.1 +9.6 - 2.3 +10.2 6 7 8 9 + 1.6 +12.4 -|- 0.6 -- 9.2 9.3 .274 + 11.7 + 7.3 13.1 +18.3 22.6 127 16.5 - 8.7 0.0 - 4.3 4.3 270 + 4.6 - 2.4 + 1.6 - 6.2 6.4 285 - 1.6 12.4 + 6.1 +7.0 - 7.3 +11.7 22.5 +3.2 10 . .... 11 12 13 16.5 8.7 - 3.0 3.0 - 2.4 - 4.6 - 5.5 +3.2 14 15 .. 16 17 1H 19.2 3.4 19.6 190 + 16.0 +5.1 + 1.6 + 4.6 5.0 70 + 16.1 11.3 - 5.1 +16.0 - 2.2 +4.6 19 20 TABLE 7. Mean components grouped in three levels.* MKAN ANTK'VCI.OMC COMPONENTS. Extracts from Tables 44, 46 and 45, 47. Those which do not lie on the north-south west-east lines are transformed as follows: The coordinates u v v 1 are cor pounded into the vector (, high, Table 44, f/^14.2, i' ]= = 6.9, and we find reduced to three by taking the means of the three upper, the the three middle, and the three lower strata together, respect- ively, and these are shown on Chart li). The occompanyiug small Table 7 gives the corresponding numerical results; it is Table 52 of the cloud report. It is evident, that it would be of great advantage to meteor- ology to have similar observations continued systematically in the United States, so as eventually to obtain perfectly reliable vectors of motion throughout the atmosphere, and they should be extended to all parts of the world as rapidly as practicable. It is not very safe to draw conclusions extending to the entire atmosphere from the observations made at a few selected locali- ties, such as those in the United States or Europe, but it seems to be necessary for us to do so in the present incomplete state of meteorology. Moreover, we must use the material we now have in discussing what are the fundamental principles of dynamics that can be admitted into the theory, and accord- ingly I shall proceed to take up the observed general circula- tion and the local circulations, and compare them with the existing theories in order to arrive at such views as will probably determine the theoretics of the dynamic meteorology of the future. III. THE OBSERVED CIRCULATION OF THE ATMOSPHERE IN THE HIGH AND LOW AREAS. 1 GENERAL DESCKIPTION OF THE VECTORS OBTAINED BY OBSERVATION. In my original report on the cloud observations of 189G-97, it was necessary to present the data in such a form that other students could have the facts at first hand. As then pointed out there are several subareas in which only a few observations were located, and they are quite unevenly distributed about the central axis, so that the final vectors as computed do not have the well-balanced smoothness which it is desirable to ob- tain. The data was given in the form of tabulations and also of diagrams, since it is easier to secure from the latter a clear mental picture of the average configuration of the vectors of motion in all parts of the cyclones and anticyclones. Having done this at the outset I now proceed to draw up an average system of vectors by the process of graphic adjustment. There will still remain some uncertainty as to the finer details in cer- tain areas where the motion is more complicated, but I am quite sure that the results presented in this paper give a very correct idea of the mean motions of the atmosphere over the United States and Canada. It would require a good deal more labor in observation and computation than was involved in a ' single year's campaign to bring the work to that degree of perfection which is desired by meteorologists; this work must undoubtedly be expended in the interest of science some time in the future. Especially for the higher strata of the high and low areas do we need more observations, because the powerful eastward drift quickly obscures the comparatively small gyratory components that penetrate up to the high levels. It should be remembered that the vectors in hand were pro- cured by observing the motions of the air almost daily through- out the year, and consequently that all kinds of weather have entered our final results. If we want the characteristic circula- tion pertaining to well developed cyclonic and anticyclonic configurations, it can be'found only by selecting the vectors on certain days when these types are strongly organized, and dis- cussing them by themselves. Under the circumstances that pertained to the cloud year we were obliged to put every kind ' of observation together, without selection, and this necessarily produced many irregularities in the final scheme of vectors. I have now gone over the data again, and by studying the balance of the various parts of the system have brought out the revised scheme herewith presented. Its well-balanced symmetry speaks strongly for its average accuracy, and it will be possible to draw out of it many important conclusions of fundamental value for theoretical meteorology. We may re- mark that none of the principles enunciated in the original report have undergone modification by this present review. By comparing the vectors of figs. 6 and 7 of this paper with Tables 34-47 and Charts 15 and 10 of the Cloud Report, one may readily examine all the changes that have been adopted, and may also discover how closely these charts represent the mean system indicated by the original observations. Instead of carrying the discussion through on the mean cloud levels where the observations were made, it is more convenient to select certain planes upon which the average vectors are estab- lished for further discussion. It is necessary first to establish the normal mean annual vectors representing the eastward drift to which the observed vectors are to be referred, in order to decompose them and obtain the auticyclouic and the cyclonic vectors by themselves. These normal vectors are given in Table 4, which is an ex- tract from Table 33, III, International Cloud Report. The 1 Kcprintcil from the -Monthly Went tu-r lirvicw for March, 1!)02, F. H. B. 3 eastward velocities are also represented by fig. 8, Total eastward velocities in high and low areas, which shows that the low areas drift eastward more rapidly than the high areas at all levels above the stratus, where they have about the same velocity, and that they drift northward in the United States in the upper levels, at a somewhat higher velocity than in the low levels. It is important to bear in mind that the results of our observations pertain only to the central portions of the North American Continent, eastward of the Rocky Mountains, where the cyclonic storm tracks have on the aver- age a northeastward direction toward the Gulf of St. Lawrence. On the Rocky Mountain slope they have a movement toward the south before recurving in the Mississippi Valley. Gen- erally the eastward drift has a small northward or southward component varying in the different parts of the world, and it is not quite proper to draw general conclusions for the entire hemisphere from the motion of the atmosphere in one district. Furthermore, since the cyclonic areas have a special vortical progression of their own, it seems probable that the average velocities observed in the high areas represent the true motion of the total mass of circulating air more correctly than would the mean of the high and the low areas. The normal east- ward and northward components have, therefore, been chosen a little in excess of those given by observation for the high areas, and they are placed in Table 8. TABLE 8. Normal component velocities on svx selected planes. Height. Eastward ve- locity. Northward velocity. Height. Eastward ve- locity. Northward velocity. Meters. 10,000 m. p. s. 36 m. p. s. 2 Miles. 6.21 . & *. m. p. h. 4 7,500 34 - 2 4.66 76 4 5,000 26 - 1.5 3.11 58 3 3,000 20 1 1.86 45 2 1,000 8 - 1 0.62 17 2 Surface 4 0.5 Surface 9 - 1 Two points may be noted in passing: (1) The eastward drift seems to be stratified into a series of steps by a decided change of the eastward velocity, and it appears that some form of stratus cloud is to be found at the bottom, and some form of cumulus cloud at the top, of each distinct stratum of flowing air. This indicates that at the surface of discontinuity between moving strata, the stratus type of cloud forms by a process of cooling through mixture from adjacent layers of air at different temperatures, which is in accord with general theory. It also shows that the cumulus clouds form by vertical convection and dynamic cooling within a stratum having about the same uniform velocity of motion throughout its mass and this is also theoretically correct. (2) The components of average total motion do not show that the atmosphere drifts northward ill the higher levels and at the surface, but southward in the lower middle levels, somewhat elevated from the ground, as was claimed should be the case by Professor Ferrel in his canal theory of the general circulation of the atmosphere. I will return to this topic and consider it at length, but the fact here indicated is that the observations do not sustain that part of the general canal theory. It is becoming clearly demonstrated to students that the circulation of the air is a more complicated problem than the early meteorologists assumed, and in conse- quence it will be necessary to study in detail the stream lines over the several continents and oceans, find out their local 17 20 characteristics, and after that try to combine them in a large comprehensive scheme. DESCRIPTION OF THE CIRCULATION OVEK HIGH AND LOW AREAS. Figs. 6 and 7 represent the adjusted mean vectors of direc- tion and velocity of motion in high and low areas, as derived from the Weather Bureau observations of 1896-97. They are based upon about 6,000 theodolite observations made at Flo. 8. Total eastward velocities in high and low areas. Washington, D. C., and about 25,000 nephoscope observations made at 15 stations distributed quite uniformly over the terri- tory east of the Rocky Mountains. They give only a mean or average scheme of the circulation and are necessarily somewhat idealized, as regards the movements of the air in individual configurations, since they include all the anticyclones and cyclones of the cloud year, many of which were only imper- fectly developed, and could not have agreed with the best types that might have been selected. In order that no false impressions should remain with students concerning the actual circulation of the atmosphere, because of this construction of a well-balanced type, I compiled for the International Cloud Report a series of composite charts, Nos. 20 to 35, inclusive, which show the actual stream lines in high and low areas over the several areas of the United States, both for summer and winter. These charts are not only interesting, but they are very valuable, because they give the normal flow of the air when the anticyclonic and cyclonic centers are located in dif- ferent parts of the country. They ought to be studied care- fully by every forecaster, and the general knowledge given by the charts should be kept firmly in mind when considering the meaning of the individual daily weather maps, as they will guide the judgment to safer conclusions than would be possi- ble without them. For the student of theoretical meteorology they are indispensable, because they correct the impressions which may be given by a contemplation of the figs, (i and 7, or by reflecting upon the analytical formula). DISCUSSION OF THE VECTORS IN HIGH AREAS. The area about the center of circulation was subdivided into twenty small parts, numbered as already described in a previous paper; the upper left-hand plans of figs. 6 and 7 show them again for convenience of reference. Through the center of each of the three concentric groups a circle is drawn in dotted lines, and these are marked I, II, III, their distance from the center being 250, 750, 1,250 kilometers, respectively. The adopted heights of the planes of motion in meters and miles are written on each level, also the normal velocity vector in meters per second (in. p. s. ), and miles per hour (in. p. h. ). The scale of distances is 1 cm. = 500 kilometers, and the scale of velocities is 1 mm. = 2 meters per second; the latter can be reduced to miles per hour by multiplying with the factor 2.24. The left-hand plans contain the total vector as observed in the atmosphere; the right-hand plans give the component vector, which, combined with the normal vector, produces the observed vector, using the rule of the parallelogram of vectors. Each vector has been carefully constructed and deserves consider- able confidence. The smoothly balanced configuration in each level and the gradual change which occurs in passing from one level to another show that this represents a natural and easy form of flow for the atmosphere, so that the motion will occur without sharp changes. The figures speak plainly for themselves, and only a few words are required regarding the distinguishing features. In the high areas the total flow di- minishes in strength from 10,000 meters to the surface; it has a slight curvature northward over the center in the highest level, but this concavity of the curves gradually increases till in the lower levels and at the surface the sinuous lines are con- verted into auticyclonic gyrations. The vectors north of the center are longer than those south of it from the top to the bottom. There is, however, a strong eastward drift in all levels, inward on the west side and outward on the east side, which is -never overcome. Passing now to the anticyclonic component vectors, it is noted that there is a remarkable symmetry in the configura- tion from the highest level to the lowest, taken as a whole. There are, however, two special features to be observed: (1) In the central areas, I, the flow is inward on the highest level, more from the north, however, than from the south; it is tan- gential on the middle level; and it is outward in the lowest level. This indicates a type of true vortex motion, which pre- vails at the center of anticyclones, and by it the air is drawn in at the top and discharged at the bottom of the vortex tube. (2) On the middle areas, II, the flow is nearly tangential throughout the entire series of strata, but on the outer areas, III, the vectors are pointed slightly outward from the top to the bottom, though more strongly on the east side than on the west side. There is, furthermore, the special feature that at the south or southwest side of the anticyclouic area, near the place marked A, a distinct discontinuity occurs in the vectors, bv which on the west side an inflow from the south takes place, and on the east side an outflow from the north is indicated, interpret these two facts together to mean that in the south- east quadrant there is a tendency for a heavy stream of the general circulation from the northwest to divide, so that a large portion moves to the south side of the adjacent cyclonic area and a small portion curls westward about the center of the high area. Also, on the west side of the high area a stream from the south divides, part flowing over the north of the high area and another part curling about the north side of the cen- ter of the adjacent low area. Fig. 9, Curling of the northward uid southward streams about the centers of high and low areas, 21 FIG. 9. Curling of the northward and southward streams about the centers of high and low areas. gives an idea of this process, especially in the strato-cumulus level, or at about 3,000 meters elevation. The heavy broken line represents the resulting sinuous eastward flow at that level. In the flow of fluids a wave motion, when the velocity exceeds a given amount, collapses and reappears in the form of whirls of discontinuous surfaces along the sides. Some- thing of this sort is apparently operating in this connection. We observe that in the 3, 000-meter level the anticyclonic vectors are stronger than in the levels above or below, the diminution toward the surface being greater than toward the higher levels. The superposition of the component gyration upon the eastward drift is distinct and even vigorous at 10, 000 meters, and hence it is inferred that the disturbance of the atmosphere in high areas extends to at least 6 or 8 miles, though only as a small deflection of the eastward drift in the upper strata. TABLE 9. Rectangular and cylindrical coordinates in high areas. DISCUSSION OF VECTORS IN LOW AREAS. The vectors in the low areas should in general be a little longer than those in the high areas. In nature the highs cover a larger territory than do the lows, but as the amount of air which streams through each of them is probably about the same, it would require a greater velocity in the lows to pro- duce an equal discharge through them. The vectors flow southward relatively to the center, and they are larger on the southern side than on the northern. The connection of the streams between the high and low areas is shown by the smooth flow of the two sets of vectors on their eastern and western sides, respectively. The stream lines are convex upward, and the curvature increases from the 10,000-meter level to the sur- face. In the 1, 000-meter level the gyratory movement nearly supersedes the sinuous or wave-like flow, but the vectors on the north side are not entirely reversed to the westward. TABLE 10. Rectangular and cylindrical coordinates in low areas. jj - t; r h S X i- 10, 000 meters. 7, 500 meters. 82 a o 1 s |l a ^ ji 10, 000 meters. 7, 500 meters. ll .38 |g - = ^ s a , , , , , , , , *l a u, v l M. 2 V. t tt, 1), M.J 1) 2 s| S 1 2 +29 2 6 + 2 +'24 + 2 10 s 1 10 +46 10 +10 6 +46 6 +12 T E 2 + 6 +31 - 4 - 6 + 8 +30 4 8 i. 25O E 2 12 +34 2 +12 12 +32 2 +12 250 N 3 + 6 +40 6 5 + 6 +36 6 2 km. N 3 4 +32 + 4+4 6 +26 f 6 + 8 km. W 4 + 4 +39 - 3 +5 4 +32 + 24 W 4 6 +40 6 4 + 4 +44 -10 + 4 S 5 1 j "** + 8 +28 1 + 88 +24 10 S 5 8 +44 8+8 10 +44 10 +10 SE 6 + 10 +30 + 29 + 8 +30 + 39 SE 6 12 +42 5 +14 12 +34 6 +10 E 7 + 7 +40 + 4-7 + 8 +36 + 28 E 7 10 +32 4 +10 10 +30 4 +10 NE 8 + 6 +43 + 27 + 8 +38 4 8 II. 750 NE 8 4 +24 4 +12 6 +26 -4+9 750 N " 9 + 2 +44 + 28 + 4 +40 4 6 km. N 9 6 +32 + 4+6 4 +28 + 4+6 km. NW 10 4 +40 2 6 8 +38 + 4 .-8 NW 10 3 +30 + 6+3 + 4 +26 + 4+8 W 11 4 +36 1 4 10 +30 + 4 10 W 11 + 6 +44 6+8 + 8 +42 8+8 SW 12 5 +28 07 8 +30 4 8 SW 12 + 2 +46 6+8 +46 7 +10 ^ B ^ s 13 + 8 +30 + 86 + 4 +24 + 4 10 S 13 4 +.44 -4+8 4 +42 - 4 -f 8 SE 14 + 9 +28 + 29 + 6 +28 09 SE 14 8 +40 -4+8 8. +38. -4+8 E 15 + 9 +40 + 4-9 + 10 +38 + 4 10 1 E 15 6 +36 0+6 8 +30 -4+8 NE 16 + 10 +42 4 10 + 9 +40 48 III. 1O f*("l NE 16 4 +28 4+8 8 +28 + 2 +10 III. 1,250 N 17 - 2 +44 + 2 8 + 3 +42 3 8 , i'.Ml km. N 17 4 +30 + 4 + 6 4 +30 + 4+4 km. NW 18 - 8 +40 + 4 .-8 - 6 +40 + 1-8 NW 18 4 +30 + 6+4 - 2 +28 + 6+2 W 19 8 +32 + 4-8 9 +30 + 4-9 W 19 + 6 +42 6+6 + 6 +40 6+6 SW 20 8 +32 -46 8 +28 -68 SW 20 + 4 +42 -4+6 + 4 +40 2+7. 22 TMH.K 9. Rectangular and cylindrical coordinate* in high areas Cont'd. TABI.E 10. Rectangular and cylindrical coordinate* in low arm* fmit'il. nS S, 000 meters. 3, 000 meters. ll S, 000 meters. 3,000 meters. $3 2 ~~~ 1? SJS I 11 S 11 5 || 1; s l Q u, t), u, v, , 1 u, , J 5 I n u l v l 2 U, U, , ! i y S 1 + 2 +18 + 2-8 + 4 +12 + 4-8 s 1 10 +42 10 +16 10 +40 10 +20 E 2 + 8 +22 2 8 + 8 +16 -48 I. 250 E 2 16 +22 - 4 +16 18 +16 - 4 +18 i. 250 N 3 + 4+34 4 8 2 +26 + 26 km. N 3 - 2 +16 + 2 +10 - 8 +12 + 8+6 km. W 4 8 +28 2 8 8 +16 + 4-8 W 4 + 14 +28 - 6 +14 + 16 .+28 - 8 +16 ,s 5 + 4 +16 + 4 10 + 6 +14 + 6 . .6 S 5 - 4 +36 - 4 +10 1C) +32 1(1 +12 SE 6' + 8 +20 + 4-8 + 12 +14 + 4 12 SE G 14 +32 - 5 +14 12 +26 - G +12 E 7 + 8 +28 + 28 +10 +20 10 E 7 12 +24 - 2 +12 14 +24 4 +14 NE 8 + G +32 08 + 6 +28 + 2 10 II. 750 NE 8 10 +20 + 4 +12 12 +12 + 4 +14 II. 750 N 9 + 3 +34 3 8 2 +28 + 28 km. N 9 10 +18 + 6 +10 12 +14 + 6 +12 km. NW 10 6 +30 + 1 - 7 8 +24 + 2 10 NW 10 +12 +20 - 6 +12 + 12 +18 7 +10 W 11 8 +24 + 28 8 +24 - 4 8 W 11 +12 +30 - 4 +12 + 16 +22 - 2 +16 SW 12 6 +20 08 - 6 +14 4 8 SW 12 + 4 +38 - 4 +12 + 12 +32 +18 ;S 13 + 4 +16 + 4 10 + 8 +10 + 8 10 s 13 - 4 +32 -4+6 G +28 G + 8 SE 14 + 8 +22 + 4-8 +10 +16 + 5 11 SE 14 G +30 - 4 +6 8 +26 2 +10 E 15 + 8 +30 + 4-8 + 10 +26 + 6 10 E 15 8 +22 -4+8 10 +18 - 2 +10 NE 16 + 7 +32 10 + 10 +28 2 12 III. 1,250 NE 16 - 6 +22 + 2 +7 10 +14 + 4 +10 III. 1,250 N 17 +36 10 + 2 +30 2 10 km. N 17 8 +20 + 6+8 12 +14 + 12 + 6 km. NW 18 9 +32 + 1 -11 12 +24 + 4 12 NW 18 + 6 +22 2+7 + 10 +18 -6+8 W 19 10 +24 + 2 10 10 +24 4 10 W 19 + 8 +28 -2+8 + 12 +24 4 +12 SW 20 8 +22 - 4 8 - 8 +14 4 10 SW 20 + 4 +34 -4+8 + 4 +28 -4+8 1 1,000 meters. Surface. %S ti c i h 1,000 IIIC'tCTS. Surface. gl 1! ii a s 1* p ll = ? Sj a 1 1 , D, , 1>, . * 5 I s l a U, 1), U, V, ' w, r, . t si S 1 + 4+2 + 4-6 + 3 + 3-4 s 1 6 +24 - G +1G 4 +10 -4+6 E 2 + 6 +12 + 46 + 3+7 + 33 I. 250 E 2 -8+4 - 4 + 8 - 6 -4+6 I. '27(1 N 3 - 6 +14 + 66 -4+7 + 4-3 km. N 3 + 10 + 4 ^10 + 4 + 4 .- 2 4+6 km. W 4 8+6 + 28 -5+2 + 2-5 W 4 + 10 +12 - 4 +10 + 8+8 -4+8 S 5 + 8+4 + 8-4 + 3+1 + 33 S 5 - 4 +20 - 4 +12 - 4 +10 -4+5 SE 6 +10 + 6 + 6 8 + 4+2 + 4-4 SE 6 10 +12 - 4 +10 6+6 2+6 E 7 + 8 +10 + 28 + + 8 + 4-6 E 7 10 + 6 - 2 +10 6+2 2+6 NE 8 + 6 +16 + 68 + 4 +10 + 27 II. 750 NE 8 10 + 8 + 8+6 - 4 2 -2+4 II. 760 N 9 4 +16 + 4-8 - 3 +10 + 36 km. N 9 + 10 + 4 10 + 4 + 4-2 G +4 km. NW 10 - 8 +10 + 1-9 5+8 6 NW 10 + 12 + 4 - 6 +10 + 6+2 -4+5 W 11 10 + 8 10 G + 2 + 26 W 11 + 8 +14 -6+8 + 6+8 -4+6 SW 12 8+2 - 2 10 3 + 2-5 SW 12 + 8 +20 - 4 +14 + 4 +10 2+8 S 13 + 8 + 88 + 4-1 + 4-5 S 13 - 4 +18 - 4 +10 -4+8 -4+4 SE 14 + 10 + 4 + 69 + 7+5 | 6 4 SE 14 10 +10 - 2 +10 -6+4 -4+4 E 15 + 8 +14 + 68 + 6+9 + 56 E 15 -8+8 0+8 -6+4 + 6 NE 16 + 8 +16 + 2 11 + 4 +10 + 27 III. 1, 250 NE 16 - 8 +10 + 8+4 4 2 -2+4 III. 1,250 N 17 - 4 +18 + 4 10 -4+8 4- 4 4 km. N 17 + 10 + 6 10 + 2 + 4-2 6+4 km. NW 18 10 +12 + 4 10 6+8 + 1-7 NW 18 + 10 + 8 -9+4 + 6 4 +6 W 19 10 +10 - 2 10 -7+4 07 W 19 + 8 +14 6+8 + 6+8 4+6 SW 20 10 + 4 4 10 5 1 2 5 SW 20 + 6 +14 0+8 + 3+8 2+5 "i southward. PJ = eastward. S = radial outward. 2 = tangential counter clockwise. 4- MI = southward. + i'i eastward. y= radial outwiinl. = taiiK<>!iti!i] counter dockfrtae. The cyclonic components are very symmetrically formed throughout the entire stratum of air that has been examined. They have the following characteristic, namely, that from the surface to the 10,000-meter level the vectors have an inflow toward the center, except in a few subareas marked with the letter A. It is noted that from the 10,000-meter level to the l,00p-meter level, near the place A, the vectors are almost ex- actly opposed to each other in direction, those on the east side flowing outward and those on the west side flowing inward. This divergence of direction indicates that a stream flows from the north to the south on the west of the low area, and that an independent stream flows northward on the east side of the ]pw area, something in the manner suggested on fig. 9. The separate streams from the north and from the south coalesce on the south side of the center of the low area, us they do on the north side of the high area, but the two streams have an origin milnidi- the areas of high and low pressure, respectively. Furthermore, it is noted that while in the high area the posi- tion of the point A is nearly stationary in all the strata mapped out, on the contrary it rotates nearly 00 from the east of 23 north at the surface to the north of west in the highest stratum. The stream of warm air from the south curls around toward the west as it ascends from the surface to the upper levels, making a quarter of a helical revolution in an ascending spiral. The length of the vectors is greatest in the 3, 000- meter level, 2 miles above the ground, and the vectors become gradually shorter upward and downward, diminishing more rapidly toward the surface. This agrees with the system of vectors in high areas, and shows that the influence of the cyclone extends above the 10, 000-meter level, where it still deflects considerably the eastward drift, though it is most vigorous in the 3,000-meter level. The length of the vectors increases gradually from the Ill-areas to the I-areas, and aver- ages about twice as long in the latter as in the former. In the auticyclonic components the Ill-vectors are even longer than the I-vectors, and they do not have any agreement with the simple vortex law m < = constant, where a is the radial distance from the axis of rotation, and Miles per hour. "s "s "2 *J "2 v i H 10, 000 7,500 5,000 3,000 1,000 - 8.5 8.7 _ 3.4 13.4 3.4 17.9 + 3.4 16.8 + 8.9 14.5 + 6.7 -- 8.5 + 0. + 2. + 2. + 6. + 5. 3 15. 7 2 18.8 9 18. 1 2 20. 1 9 18.1 6 12.1 + 4. 5 17. 9 0.0 19.7 + 3.1 21.0 + 3.1 23.7 + 6.7 21.3 + 5.6 12.5 CYCLONIC COMPONENTS. H 10, 000 7,500 5,000 3,000 1,000 7.8 +12.3 6.7 +20. 1 10.1 +31.3 7.8 +33.6 13.4 +32.4 - 8.9 +14.5 6. 8. - 4. 5. - 7. - 7. 5 +19.2 7 +19.9 3 +26.4 4 +30. 2 8 +20. 8 4 +12.3 3.4 +14.5 - 2.2 +14.8 - 3.4 +16.3 2.2 +20.1 6.5 +15.2 7.4 +11.0 TABLE 12. Northward and southward velocities in selected areas. Hoi oft Northward. Southward. S"t L. 16, 8, 2, 7, 15. 6. 14. H. 16, 8, 2, 7, 15, 6, 14. L. 18, 10,4, 11, 19, 12,20. stratum. M, -I), 1 10, 000 - 6. 4 +34. 5 7,500 - 8.4 +31.9 5,000 9.1 +25.2 3,000 10.3 +19.7 1,000 - 9.2 +7.9 Surface - 5.2 +2.6 + 4.4 +37.7 + 5.8 +36'. 2 + 8.1 +27'. 6 + 10.6 +22.7 + 8.4 +111 7 + 5.3 + 6l9 Compare Table 124, International Cloud Report, p. 606. Anf/cyc/o/j/c Area. f\ / * / ncta/a/ component t/2- -"z-''r>wc/,--t-u 2 oufiva'/-/ve/oc/fy: /0000m 7600 6OOO 3000 /OOO o 2 0-1-2 2 -f-2 -20 +2 \ \ ( / / ' l \ \ \ X ^^^ ! ^ N \ S \ N L ff / //) r ) Anf/cyc/on/c Area. Tangent/a/ component V2- ~^z= c/ocA-w'se rofcrf/or?. '0000m. 7SOO 5000 3000 /OOO O -S ff -^ 2 O -f-2 - **** *^> J v. ^.. -^~ ff ^^ f^. ^ ^ Cyc/ofi/'c Area . /7aof/a/ component u 2 - ~ U 2 - ''w&>^ve/oc/Yy. 750O 5000 3000 /OOO O - 2 -f-2 2O-+-2 2 -f-2 / ) v ^ : ^ ^ \ ) f **~ ^- / , / / / ^ r \ ff I 1 Cyc/on/c Area. / y /anqenf/a/ component V2- +^ 2 - ^ofocfrwfse^ rrtarffan^ /OOOOrn. 7600 SOOO 3OOO /OOO +2 -t-4 +6 +8 +/O -+/2 -t-/4 O +2 -+4 -t-ff -hd -+/(? +/2 -t-2 -+4 -+6 -hff S S s ^^ \ x ^. V. v s \ S ^ 1 \ \ s ^ \ \ r .- ^ ^* ^ ^^ -* X --- r^ *^ *s ' .s / / j 7i r- *-* * ^** Tt j / ^ Flo. 10. Radial and tangential components in anticyclonic and cyclonic areas. From Table 11. 25 6 and 7 that while there is everywhere a general eastward < of the low there is a southward current also strongest in the drift, there are certain subareas over which especially a north- j same level. The interchange of air between the pole and the ward component prevails, and others over which there is a Tropics appears, therefore, to be brought about by alternate southward component. In order to lind the maximum me- currents in middle latitudes flowing past each other on the ridional components it is expedient to select the following same levels, and not over each other at entirely different levels, areas for the northward component: Low (16, 8, 2, 7, 15, 6, as the canal theory requires. The thermal equilibrium of the 14) and High (18, 10, 11, 19, 12, 20), and for the southward air is, therefore, restored through the anticyclonic and cyclonic component High (16, 8, 2, 7, 15, 6, 14) and Low (18, 10, 4, 11, mechanism, and not by the overflowing currents from the 19, 12, 20). The values of ,, r, are taken for these areas from Tropics to the poles and underflowing currents from the poles Tables 9 and 10, and the mean of them is given in Table 12, to the Tropics, as commonly taught. This profoundly modi- Northward and southward velocities in selected areas. It can fies the canal theory of the general circulation of the atmos- be seen at once that the general canal theory is by no means phere and introduces us to a new point of view. The discus- supported by the observations. The fact seems to be that sion of the theories of the circulation of the air as explained between the high and low centers, west of the high and east by Ferrel, Oberbeck, and other meteorologists must be taken of the low, there is a northward current in all levels, strongest up next in order, and their views contrasted with the results at about the 3,000-meter level, while east of the high and west of our observations. IV.-REVIEW OF FERREL'S AND OBERBECK'S THEORIES OF THE LOCAL AND THE GENERAL CIRCULATIONS.' GENERAL COMPARISON OF FERREL 's AND OBERBECK'S THEORIES. In order to discuss the theories which have been proposed to account for the circulation of the atmosphere in cyclones and anticyclones, and in general over an hemisphere of the earth, it will be convenient to confine our attention to the j views propounded by Ferrel and Oberbeck because their treat- ment is quite complete, and also because they represent a large number of writers who agree with them more or less perfectly. There is another theory of quite a different type which can be taken up profitably after some critical remarks have been made on the validity of these earlier views. In their treatment of the general circulation of the atmosphere both Ferrel and and Oberbeck adopt the "canal theory " of the circulation, and work out their solutions along that line. Oberbeck places his origin of coordinates at the center of the rotating earth, de- velops the equations of motion, and transforms to the surface when they are employed in the evaluation of the resulting ve- locities. He also deduces the terms in the pressure due to the absolute motion of the earth, and to the relative motions of the atmosphere. Ferrel places his origin of coordinates at the siirface of the earth, transforms his equations to include a temperature term through the variations of the density, and discusses the meaning of the equations under special limita- tions, with illustrations from the observed motions of the atmosphere. It may be remarked that von Helmholtz intro- duces the temperature terms into the equations of motion, not through the density, but through the pressure, by using the equation of elasticity, p v = R T. This procedure is probably a better method of solution. There is not much difference in the results as derived from the analysis by these authors, but there is serious difficulty in making them agree with the modern observations of the motions of the atmosphere in the higher strata, as determined by the international cloud work. In their treatment of the cyclone Ferrel and Oberbeck di- verge radically from each other, though they start with the same physical principle, namely, a local overheated mass of air which in rising through its own buoyancy produces the cy- clonic circulation. Ferrel assumes a fixed cylindrical boundary about his cyclone, and considers a warm-center cyclone (circu- lation anticlockwise), surrounded by a pericyclonic ring (circu- lation clockwise), in the Northern Hemisphere, the two portions being separated by a surface where the gyratory velocity vanishes. By maintaining a cold mass of air in the center in- stead of a warm mass the circulation is reversed, and a cold- center cyclone is developed. Oberbeck does not assume any external boundary to the circulating mass of air, but in the central region, bounded by a cylindrical surface, there is a vertical component, while outside of it there is no such vertical ascent of the air. At this boundary there is a discontinuity in the vertical velocity, and at the same distance from the center the gyratory velocity about the axis is a maximum; this falls away to zero at the center and also at some indefinite distance in the outer region. It is essential to the existence of these two theories, although they differ so radically from each other, to establish the fact that such local centers of heated air in the warm-center cyclones do occur in nature, for without them these two theories entirely fail of applicability to our meteor- ology. They are both possible forms of vortex motion, but il is necessary to show that the antecedent physical conditions, prevail, before they can be accepted as explanations of the ob- served cyclonic motions. IVoni the Monthly Weather licvicw lor April, l'M'2. F. H.li. Both of these authors have experienced much difficulty in accounting for the anticyclones. Ferrel explained that the interference of two of his pericyclonic rings would heap up the air and produce an area of high pressure with a clockwise out- flow, but this theory is so far from being in conformity with the facts, that it is now, by general consent of meteorologists, considered to be of only historical value. Oberbeck sought, by simply reversing the sign of the vertical component of velocity, to invert his cyclone into an anticyclone. He met with a stumbling-block in the mathematical analysis, but was relieved of this by Pockels, who correctly evaluated the constant of integration. No attempt was made to show that the resulting stream lines conform to the motions of the air in high areas of pressure. Indeed, since the modern observations have given us more correct lines of flow, it is quite certain that the anti- cyclone can not be explained in this way. THE SUPPLY OF LOCAL CENTERS OF HEAT. It is evident, therefore, that the first practical question to decide is whether such local masses of air exist, heated in the under strata and more or less cylindrical in form, as will pro- duce either of the above forms of cyclone. Meteorologists have generally supposed that this is the case, and they have usually attributed the source of the vertical convection to the latent heat of condensation. Dr. J. Hann, in 1890, and again in his Lehrbuch der Meteorologie, has shown in great detail the inadequacy of this source of heat to produce cyclones, and he has indicated that the source of cyclonic action consists rather in horizontal convection currents. As this agrees with the view which I have already advocated, since it seems to me to be in conformity with the observations, I will therefore make a resume of my remarks on this topic in the Interna- tional Cloud Report. It will be a great gain if meteorologists can be persuaded to reject the old condensation theory, which has an apparent but really illusory plausibility, in favor of the really efficient source of dynamic action contained in the long, horizontal currents which flow between the Tropics and the polar regions in the middle strata of the atmosphere, as illus- trated in the preceding Paper III. There is, in fact, a fundamental difficulty in accounting for the local supply of heat which is assumed to set the vertical convection in operation. Ferrel himself doubted the efficiency of the latent heat of condensation, for he says in his Meteoro- logical Researches, Appendix No. 10, United States Coast and Geodetic Survey, Part II, page 201 : " The condensation of aqueous vapor, therefore, plays an important part in cyclonic disturbances, but is by no means a primary or a principle cause of cyclones." Professor Loornis asserted in Silliman's Journal, July, 1877: "Rainfall is not essential to the formation of areas of low barometer, and is not the principle cause of their formation or of their progressive motion." Indeed, a reasonable familiarity with the United States weather maps proves conclusively that there are many deep, fully-developed storms which form near the north Pacific coast and advance to the Gulf of St. Lawrence without any precipitation worth mentioning. Also, cyclones form frequently in the southern Rocky Mountain districts and advance into the lower Missis- sippi Valley without any important rainfall; from that region onward in their course the precipitation and intensity of the storm often greatly increase, since the latent heat derived from the inflowing moist air of the Gulf of Mexico undoubtedly assists the vertical convection in the center of the cyclone. If the 27 28 horizontal currents which converge upon a cyclonic center are bearers of moisture, the vertical motion caused by the dynamic action condenses the aqueous vapor; but if such currents are drv, the cyclone advances unattended by precipitation. Hence, it follows that rainfall is a secondary phenomenon, and is not sufficient of itself to produce true cyclonic gyrations. There are, on the other hand, many cases of copious pre- cipitation without any attendant low pressure. Thus, on the front of an advancing cold wave there is often a long baud of rain area stretching from the Great Lakes to the Gulf of Mexico, but without cyclonic formation, the precipitation being in fact caused by the upward lift of a warm southerly current which overflows the wedge-shaped cold wave in its southward movement. This is a dynamic uplift by overflow, instead of by vortical gyration, and it is sufficient to cause condensation and precipitation by the mechanical action of an underflowing stratum of very low temperature. Furthermore, on one side of a mountain range, as the Alps, rainfall is observed to oc- cur in the midst of the high pressure, while on the other side of the mountains the atmosphere is clear and the pressure is relatively low, thus reversing the required conditions. In the summer season, local thunderstorms are quite as likely to hap- pen in the midst of an area of high pressure as in that of low pressure, but here the vertical convection distinctly exists and arises from a superheating of the lower strata. If buoyancy of the lighter air is the principal cause of the gyration of cyclones, then we should expect to find a similar rotatory motion developed in the formation of cumulus clouds and thunderstorms in hot summer weather, when the vertical com- ponent is evidently strong. But, on the contrary, while the ascension of the heated air is clearly visible in these clouds, there is usually no evidence of gyration of the cyclonic type. It has been found by Hann's mountain observations and by the Berlin balloon ascensions that the temperature of the cen- tral portions of the cyclone is colder than the temperature in the midst of the anticyclone at the same levels. Hence, if the relative density of the air column is the source of cyclonic gyration, we perceive that this fact is in direct contradiction to the requirements of the condensation theory, which demands that the central column of the cyclone shall be warmer than its surroundings. Since the advocates of the condensation theory of cyclones usually regard the generation of the tropical hurricanes as the best example of that source of gyratory energy, it may be proper to state that the observed facts do not appear to sus- tain the theory. For (1) there is no evidence of a decided increase in the local temperature at the center of hurricanes. In this connection it is believed that the sudden rise in tem- perature in the Manila hurricane of October 20, 1882, was due to the direct radiation of the sun through the calm, eye of the storm; (2) the winds are not sufficiently changed in direction at the feeble ring of high pressure to conform to the Ferrel pericy clone; they should be turned through at least 90 more in azimuth; (3) the conditions of heated, saturated air pre- vail in the Tropics throughout the year, but the hurricanes are produced at certain seasons only, and these are the times when the counter currents of the trades are most active at their northern and southern limits. Dr. Hann rejects the rain theory, and adopts the counter current theory for huricaues: Lehrbuch der Meteorologie, pp. 5G3-566. It can be proved conclusively from observations that two counter currents flow together at the places where tornadoes are formed, where the tropical hurricanes are generated, and also where the cyclones of the middle latitudes are produced. These currents are especially active in the strata one or two miles above the ground, and this is probably the reason why they have not received due attention in constructing the theory of storms. It may be concluded that the local overheated central region does not exist in cyclones as the chief cause of their motion, and that the theories fail which depend upon it. There are, however, other serious difficulties of a mathematical nature to which attention must be directed. KEKKEL'S LOCAL CYCLONE. On page 595, and following, of the International Cloud Report, the fundamental foruiuhe and assumptions, as em- ployed by Professor Ferrel in his discussion of the local c\ clone, are summarized, and an abstract for our purposes, in the nota- tion already described in Paper II of this series, MONTHLY WEATHEU REVIEW, February, 1902, p. 81, is given in the follow- ing lines: Cylindrical equations of motion applicable to the local cir- culation in cyclones. See International Cloud Report, p. 502. 1 OP 'In 185 - - - _] or transformed, by substituting u = . and multiplying by m, into rim dv dm 2 n cos n . m - + w -^ -f v (It dv Ov udv vdv It should be noted that i cos 0, retain the friction term, and make = - , thus rejecting the two small terms, at fil equation 397/> (2) becomes: dv uv . . , i)t + ~m + ' 422 o. 437 Taking " v = dv u 1 dra ^ <>< ;>m dm (H UV . '^ + ^ we obtain + kv = 0. There are two solutions of this equation, as shown on pages 598 and .599 of the Cloud Report, namely: First solution (inner). Second solution (outer). -i- - - u. k c v = + r k c m '. *-e ' 2 These can be expressed in two general laws: (1.) Parabolic law. (2.) Hyperbolic law. = = constant. w 2 V ). C = + . = constant. w ^ k c 2 um = c = constant. rro = -f- T c = constant. K These solutions are readily verified by substitution in the second equation of motion, 397/>, and the two forms give rise, respectively, to parabolic surfaces on the inside of a certain circle, and to hyperbolic surfaces on the outside of it. Their discussion is given on page 509; an electrical analogue is ex- plained on page 521, and they are further illustrated on pages 619 to 622 of the International Cloud Report. A diagram of the motion is shown in fig. 13 of the present paper. The re- sult is that there is an outer region in which there is no ver- tical component, w = 0, and an inner region in which there is a vertical component which increases with the altitude, w = cz ; see page 621, Cloud Report. These two regions are separa- ted by a circle where the tangential component velocity, v, is a maximum; the velocity of rotation falls away to the center by the parabolic law, and also for an unlimited distance outward by the hyperbolic law. The inner region has the isobars sepa- rated from each other by distances conforming to the law, d, = R* nJ ( J , where It is the radius of the circle of maximum velocity, and ZB ( the radii of the successive isobars; on the outside the distances between isobars are determined by d e = 2 It 1 log -j- 1 ' ; fig. 13 shows these relative distances and ve- H loci ties. Recalling the circulation depicted in Paper III, we are in- duced to make the following remarks: The theory common to the German school of meteorologists is founded upon the assumption of a vertical central current, like the electric current in a wire, which generates the cyclonic circulation in the inner and the outer parts. Now, there are a series of difficulties and objections to this view, when it is at- tempted to apply it to the observations of the actual motions of the atmosphere, fully as serious as those which have been urged against Professor Ferrel's theory. (1) There is 110 suf- ficient evidence that the vertical current is of definite local origin and powerful enough to influence the enormous cyclonic disturbances extending horizontally to 1,000 miles in radius. These storms are very shallow compared with their width, say 3 or 4 to 1,000 at the greatest depth. An upward central cur- rent in a small inner region of 200 to 300 miles radius, even if locally produced, could hardly cause the disturbances observed on the weather maps. The chief difficult}' has been to show that there is any sufficient cause for the existence of such a current, and the reasons already urged against that view hold FIG. 13. Oberbeck'B circulation in warm-center cyok s. here also, namely, that the disturbing isotherms are not cir- cles, but their gradients lie athwart the cyclone, generally from S\V to NE; that cyclones exist without precipitation; that rainfall does not necessarily produce cyclonic action; and that countercurrents from two specific directions, as MY and S, feed into the cyclone, which is not sustained from a supply equally distributed around a center. (2) The adoption of the inner and outer parts of the cyclone was due to the supposed neces- sity of avoiding infinitely great velocities at the center, if = - and y = -f _ , as would occur for small values of m. w km It will, of course,' be necessary to show how this can be done by some other solution. Even if that is accomplished we find still other practical difficulties in the German solution hav- ing an inner and an outer part. This requires a maximum rota- tional velocity v at the boundary m=li. But our observations give no support to this position any more than to Ferrel's theory that =0 at the boundary of the inner and the outer parts. A careful examination of our wind velocities shows that they increase steadily from the outer boundary toward the center, when a surface of discontinuity surrounding a calm center suddenly terminates the radial and tangential velocities. The common occurrence of the central calm in hurricanes is sufficient proof of this point. Furthermore, an examination of the cyclonic components ((/ 2 , r,), Table 10 and fig. 10, shows that the tangential velocity u increases from the outside toward the center without any tendency to fall off. Certainly, in fore- casting, no one expects to find the maximum velocities at 200 or 300 miles from the center. The two-part theory itself, al- though gradually reducing the velocity from a maximum at the boundary R to zero at the center, does not explain the ex- istence of the central calm. (3) While the differential equa- tion has two solutions which give some aspects plausible for this application, yet it is improbable that in such processes of 31 nature as the circulation of the air, there should be more than one law actually in operation. That the movement should sud- denly jump from one system of forces to another is quite un- likely, unless cause can be shown for it. (4) In spite of skill- ful devices by which discontinuity in the rotation velocity was overcome, it is evident that there still remains a vertical dis- continuity at the boundary, which becomes more and more pronounced with the increase in height above the surface, since w=cz. While it is hardly possible to actually observe the vertical components, yet the probabilities are that vertical motion sets in as soon as the isobars which surround the cy- clone are closed up, and that all over this area there is a rising current. It may be laid down as a principle that where closed isobars exist there is an ascending or a descending current, according to the direction of the rotation. Where the isobars wander about without closing up, it may be assumed that there is no rising or descending air. In the case of cyclones this is confirmed by the general tendency of precipitation to occur over the entire region of the closed isobars. The preponder- ance on the eastern side over the western is due to the action of the general drift in the upper strata upon the circulation. Hence, we conclude that while the Ferrel and the German vortices are each possible and may exist under certain condi- tions of boundary and distribution of heat, they do not agree with the cyclonic and anticyclonic circulation as given by the cloud observations of 1896-97. Although it is not possible to utilize the Ferrel vortex in further developments because the outer boundary is lacking, and though the German vortex, on the other hand, has apparently a closer application, yet even here it will be found difficult to avail ourselves of it without resorting to a modified method of analysis. We shall show, in part only, how this may be accomplished in the following papers, but the fact remains that the atmospheric circulation is usually too complex to be readily reduced to simple vortex motion of any kind. Hydrodyuamic theories of stream lines must, on the other hand, be employed on a larger scale in the meteorology of the future than has been done in the past. KEKREL'S THEORY OF THE GENERAL CIRCULATION OVER A HEMISPHERE. We can only briefly mention the principles which prevail in Ferrel's and in Oberbeck's solution for the circulation of the atmosphere over a hemisphere of the earth. In this case the boundaries are fixed, namely, the earth's surface, the plane of the equator, the topmost stratum of the atmosphere, and the pole of rotation. The heat distribution is such that the polar regions are cold and the Tropics warm. The primary idea adopted in the mathematical analysis is that of the so-called canal circulation, as, for example, when fluid in a long vessel with rectangular sides is artificially heated at one of its ends, so that the fluid rises at that end, falls at the other, moves in a horizontal direction from the warm end toward the cold end in the upper layers, but from the cold end to the warm end in the lower layers. In the same way the atmosphere is assumed to rise at the Tropics, move northward in the upper strata, fall in the polar zones, and flow southward along the surface of the earth. The effect of the contraction of the meridians, together with the rotation of the earth, is to introduce a complex torque effect, which causes the air to flow rapidly eastward in the temperate zones, especially in the upper strata, and westward in the tropical zones, especially in the lower strata. The gen- eral result is shown on fig. 14, for Ferrel's solution; and on fig. 15 the relative component velocities are given for Oberbeck's solution. These two methods of solution have some features in common, and also some of the results agree, and yet there is wide divergence in other respects, as will be indicated. The most conspicuous feature for us to note is that a neutral plane of velocity for the components along the meridian is ob- tained, where there is no northward or southward velocity t but above it an increasing northward, and below it an increasing southward velocity proportional to the distance from this plane. We shall have to compare this view with the results of the ob- servations as given in the data of the year 1896-97. The main featiires of Ferrel's solution of the general cyclone are con- tained in the following extracts from pages 588-590, Interna- tional Cloud Report: Polar equations of motion applicable to the general cir- culation over a hemisphere: uw v %n + v) v + - - ; where v = " 4 8in " Assumptions are made precisely analogous to those for the local cyclone, except that the temperature is expressed by the equation, t = - A t cos x 0, where, A = 8.50. A.= 1.75. A,= - 20.95. A s = - 1.00. ^ 4 =-2.66. The equations of general motion take the form, 200. 1 1 OP du ~ /T rOO ~ dt OP dv COS0 I OP dw 397a. _ cos a ( In dv = -,- kv. The second equation admits of integration between the pole and the plane of the equator for the entire rotating mass of air, with the resulting equation for the velocity v, /2 1 \ v = I -7; -. sin (I ) V 3 sin H J If -r= 0,0=54 44', and the latitude

r& above the neutral plane must be much greater than the -mrjc below that plane. The excess of energy Imvk -mvjf=E, must be used up in overcoming the motion of the atmosphere, employing the term friction to include the forces that retard circulation by internal turbulent motion, or by the action of the adjacent discontinuous surfaces of the larger streams. It is evident, however, even supposing this theory S4- "f Jfyua-tor L JKerccti 'oxocl. ^Ta&t- West . VeriicaZ. Fio. 15. Oberboek's component motions in the general cyclone. correct, that this source of retardation is by no means sufficient to overcome the great amount of energy which must be con- sumed in motion to equalize the heat energy derived from the solar radiation in the Tropics. Professor Ferrel never executed a complete integration involving all the component equations of motion, but merely discussed his several equations tinder different relative conditions, and thus drew out of them certain conceptions of the general circulation of the atmosphere which it was easy to show harmonized fairly well with many of the facts which were known to him at the time of his study, now nearly twenty years ago. It has become increasingly difficult, however, to believe that this solution is really as satisfactory as was then supposed. OBEKBKCK'S SOLUTION or THE (IKXEHAI, CIRCULATION. Oberbeck attacked the same problem by a more complete analysis, and reached conclusions which in general accord with those of Ferrel, but differ from his in important par- ticulars. He subdivided the total pressure of the atmosphere into partial pressures, and deduced a series of component velocities which could be computed by means of coefficients distributed at equidistant intervals throughout the atmos- phere. An upper boundary was assumed for the atmosphere, but the solution was conducted in such a manner that this limiting stratum, whose height is //, could be changed in rela- tion to the radius of the earth, li. The equations of motion were constructed for an origin at the center of the earth, while Ferrel's origin was on the surface, but the two systems of equations can be shown to be equivalent, so that the mathe- matical starting point is practically the same in both. Ober- beck held all the components together in one system, and hence, by not discussing them separately, could arrive at some conclusions which are really more instructive than Ferrel's. Yet it will be easily seen that these do not conform sufficiently well to the data of observation to be accepted as the complete solution of the problem. Taking the component equations and notation given on pages 591-593 of the International Cloud Report, Oberbeck 's solution for the component velocities is as follows: South: it = G 6 cos ft sin -^ (6/i 2 15/i* + 8-r 2 ). '48 2)i ,,= 7r cos <> sin 3 K East: ,, 2 _ 7^ C os 2 II) j- K (G li' 15/1 ff+ 8-7* <, = D sin (1 3 cos 2 0) ^ ( 9/r 5 + 15/iV 15//* 4 + 4-r 5 ). , = D 6 cos 2 II ^ (20/>V - 25/)^ + 8,r 4 ). Zenith: = (< (i _ 3 cos 2 H) ~ (l> )(3h W). r* 0, + 2v a 6 (4v, + > t ) cos 2 H + 35>, cos 4 #] _ ff )(3/i _ 2^.) x } - H = f A A = \TO' 10' TO io C= 0.5429 It 1 ; D = 0.00008532 R\ r = 11 -(- Rh = R + H= radius of earth + height of atmos- phere. r=n+tt = R + 1'- Rh = radius of earth + height of the stratum a hori/.oiital currents on parallels. : east, \vc.-t. H 10 20 30 40 50 60 70 80 90 o=:1.0 .00000 +.00315 + .00565 of Z>^ = .8 + .00702 + . 00701V r 5 , i.io.- t \ 1.405 + .OO.V.I2 X 10 s for // = + .00101 -| .(Xl2or, :,ooo:,i; . in ii ii in .9 .00000 + 305 + 547 + 680 + 683 + 573 + 391 + 199 + 54 .00000 .8 .00000 + 276 + 495 + 614 + 618 + 518 + 354 + 180 + 111 1111:11 III .7 .00000 + 231 .+ 415 + 515 + 518 + 435 + 297 + 157 + 41 . IHXXMI .6 .00000 + 179 + 321 + 398 + 401 + 336 + 229 + 117 + 32 . 01 KM III .5 .00000 + 125 + 225 + 279 + 281 + 235 + 161 + 82 + 22 .OOOOO .4 .00000 + 76 + 136 + 169 + 170 + 142 + 97 + 50 + 13 . IKNXX) .3 .00000 + 37 + 67 + 83 + 84 + 70 + 48 + 21 + 7 .IXNXX) .2 .00000 + 13 + 24 + 29 + 29 + 25 + 17 + 9 + 2 .00000 .1 .00000 + 2 + 4 + 4 + 5 + 4 + 3 + 1 . 1 II II II II 1 .0 .00000 .00000 .00000 .00000 .00000 .00000 .00000 .OOtXMI . ooooo .ooooo TABLE 17. I. Vertical components due to the rotation of the earth. w = vertical currents. + = ascending, = descending. IT 4 f-fi Coefficients of C ^4 . 5429 j^- | 2. 203 X = } 2. 203 x l&toi #=63700"'. 10 for #=6370. = 30, but vanishes at the poles. This is exactly contrary to Ferrel's result, which made the velocity i' a maximum at the pole, before the assumed modification by friction was applied. Oberbeck makes the westward drift a maximum at the plane of the equator, which is certainly not in conformity with the observations. He also makes the west- ward velocity increase at the equator from the surface to the upper boundary, and show no sign of a reversal from westward to eastward at a moderate elevation, as is generally believed to be the fact, judging from certain well known motions of the air observed in the Tropics. The United States Weather Bureau has been conducting a series of uephoscope observations in the West Indies for the past three years, and it is hoped that the discussion of these observations, soon to be undertaken, will give us some defi- nite information on this important point. The second term i\ modifies r i; but the two combined, ti = v t -f- i~ v sustain the conclusions just mentioned. This feature of Oberbeck 's solution is so far from conforming to the observed motions of the atmosphere that it seems to me to be inferior in value to Ferrel's for the Tropics. Ferrel's arch over the Tropics, shown in fig. 14, is probably a fact, and if this is so, then the only serious modification required in Ferrel's treat- ment is to show how the excessive eastward drift in the mid- latitiide and polar zones can be effectively checked. It is evi- dent that there must be a large amount of energy available for use in the construction of local cyclones and anticyclones, and that there is, therefore, no pressing need to refer the energy of these motions to any local supply of heat, as is done by those who extend to cyclones the theory of the latent heat of condensation from precipitation originally devised by Espy to explain cumulus clouds and thunderstorms. The compo- nents w and w t , Table 17, show that there is an ascending current in the Tropics, and a descending current in the higher latitudes. Thus, as the result of the theoretical discussion in general, the canal theory has several of its features verified, and yet there are serious discrepancies inherent in both Fer- rel's and Oberbeck's solutions. My statement has suggested by implication that there exists an important principle which has been neglected by these me- teorologists. They have each discussed the general and the local cyclones as if they were in a sense independent of one an- other, since separate sources of heat energy are assigned to each, and two characteristic laws of circulation are deduced therefrom. It is much more natural to suppose that these two systems are mutually interdependent, and that the excess of energy of the general cyclone is transformed into the driving forces of the local circulation; also, that the acquired motion of the local cyclone reacts upon and retards the excess of mo- tion of the general cyclone in the temperate zones. The sub- ject becomes, however, excessively complex, and I can only attempt to sketch in general terms in my next paper an out- line of this view, hoping some other time to be able to supple- ment it with a more suitable mathematical analysis, when the study of the observations now in hand has been advanced more nearly to completion. V. RELATIONS BETWEEN THE GENERAL CIRCULATION AND THE CYCLONES AND ANTICYCLONES. 1 UNEQUAL DISTRIBUTION OF CYCLONES IN NOKTH AMERICA AND EUROPE-ASIA. We have arrived at the following proposition as the result ' of the discussion of Ferrel's and Oberbeck's analysis of the general and local circulation, that the general cyclone and the local cyclones and anticyclones have been treated almost inde- pendently of one another, while in fact the imperfect results of the theory and the modern observations both indicate that these two classes of movement should be analyzed in close rela- tion with each other. The evidence compels us to regard both these circulations as the common effect of the readjustment of the thermal equilibrium, which is disturbed by the radiation of the sun falling on the tropic zones, and the true meteoro- logical problem is to trace out the successive stages in the process of this interaction through the resulting currents which circulate in the atmosphere. The results contained in this paper apply especially to the North American Continent, and it is hardly to be expected that the details will be found the same in all the other regions of the earth. Indeed there are several reasons for believing that this continent is the pe- culiar theater for the interchange between the heat and the cold of the Northern Hemisphere, and that the Euro-Asian Continent plays a very different role in the meteorological economy of this hemisphere. For it is well known (1) that while the American Continent is the place for the profuse gen- eration of cyclones, Europe is the region for their dissipation, and in Asia very few cyclones occur except along the ocean bor- ders; (2) that the velocity of motion of the atmosphere gener- ally is about twice as great over North America as over Europe. This points to a profound difference between the actions of the atmosphere in these two regions, but one cause of it at least is easily perceived. It has been shown that the currents which are especially concerned in forming cyclones are con- tained for the most part within 2 or 3 miles of the ground, though their accompanying effects may extend much higher. Hence, any barriers of elevated ground, as mountain ranges, which tend to deflect the flow of the lower strata, must strongly influence the formation of the cyclones themselves, if they are to be referred to the counter flow of long horizontal currents of different temperature rather than to local vertical couvective currents. The great range of the Himalaya Mountains stretching east and west is such a barrier to the flow of the tropical and polar currents in that region, and the result is that true cyclonic movements are almost excluded from the interior of Asia. On the other hand the Rocky Mountain range, stretching north and south along the western districts of North America, favors the counter flow from the Tropics and the polar regions by de- flecting the westward current of the Tropics toward the north, and the eastward drift of the higher latitudes toward the south. The same tendency is favored by the location of the high pres- sure belt in the latitude of 35, which causes a high pressure area to form over the middle Atlantic Ocean, while the Eocky Mountain range breaks through the midst of it. The result is to produce a powerful anticyclouic center of action over the Atlantic Ocean, which maintains a strong northward compo- nent from the West Indies toward the interior of the conti- nent. At the same time the American Continent causes the isobars and isotherms to loop southward, and thus in conse- quence to draw the Siberian atmosphere in a direction nearly parallel to the Rocky Mountain range. These physical condi- tions are a constant incentive to the formation of coimtercur- rents which meet on the Canadian and United States territory, with the result that 75 per cent or 80 per cent of the storms of the Northern Hemisphere are generated in these districts. It is not necessary for maintaining the temperature equilibrium of the hemisphere that the interchange of heat and cold should occur so as to have a uniform distribution over all portions of it, because if there is an excessive interchange in any place, as in North America, the general movements of the atmosphere will soon transfer the effects to all other parts. Keeping these facts in mind will facilitate an understanding of the views which will be briefly described as follows: CRITICISM OF THE CANAL THEORY OF THE GENERAL CIRCULATION. The immediate problem before us is this: To what extent is the canal theory of the general circulation over a hemisphere correct, and in what direction must it be modified to conform to the modern observations? Perrel derived the following equa- tions from a discussion of the first equation of 397a for the approximate velocities and gradients in the strata of the upper atmosphere : 0.016 ah 408a. Velocity; 409a. Gradient; G= G (2n + v) ' r 0.00001327 A t sin (1 + *) '' A, sin 20 when u G. P are the (1 + at)' P 9 ' values at the surface, and v, G, P, the 1 Koj>rintc\v, Miiivli liin-J, Vol. XXX, p. 117. a circulation as in a canal, northward above and southward below, we find that the interchanging motion is largely con- fined to the lower strata, by means of currents not flowing above one another, but on the same level. (2) Instead of the momentum M (i' o <) being determined by the difference be- tween the eastward flow at different levels of the same latitude, we prefer the statement tluit cyclonic gyrations are produced by the counter flow of independent streams, and that the rapid eastward drift is retarded by mechanical inflows, from above toward the base of the anticyclone, and from below through the stream lines of the cyclone into the eastward drift. The energy upon which cyclones and anticyclones depend for their activity is to be traced to a different source from that generally assigned to it by meteorologists. The common theory is that the cyclone is due to some form of vertical convection, caused by overheating a local region, and by the latent heat produced in precipitation. Our theory would more naturally depend upon horizontal convection, by means of which temperature gradients thousands of miles in extent produce comparatively shallow streams, which flow from the north and from the south, and sustain them for considerable intervals of time. The up- ward and the downward discharges, together with the rotary components which make the sinuous flow of the air in the upper levels, practically tie together the upper and the lower strata, retard the eastward drift in the higher strata, and accelerate the eastward motion in the lower. This effect is readily perceived in the eastward propagation of high and low pressure areas over the United States, which is the basis of our system of forecasting and renders it possible. It is by no means to be concluded that by suggesting this modification of the Ferrel theory, any intention exists of not recognizing fully the fact that it remains substantially correct in some of its features. There exists the eastward drift throughout the middle latitudes and the westward drift in lower levels of the tropical zone. But there is yet another reservation to be introduced. The heating of the tropical belt raises the isobars adjacent to the equator so that they slope toward the poles, and to such an extent that they almost ex- actly counterbalance the deflective force 2/iy cos tl, which is directed southward. It may properly be assumed from this that in the upper strata the directions of the isobars, the iso- therms, and the stream lines of the wind motion are verv nearly parallel to each other, if not coincident. The friction is evidently small, judging from theoretical conditions, and from the results of the observations, or else this could not be the case. There is another important deduction to be drawn from this discussion regarding the flow of currents from the Tropics toward the poles in the lower strata. According to the Ferrel theory, the overheating of the Tropics is relieved by the up- ward expansion and overflow, but in accordance with the pres- ent view the tropical congestion is relieved by irregular streams which flow outward from the lower levels. This being the case, the poleward gradients in the upper levels are called upon to sustain much less pressure from the deflection, and evidently the tendency to excessive eastward velocities is much diminished, just because the equatorial lift of the strata can not be so great, since the expansion upward, as stated, leaks off sidewise in the lower levels. The eastward drift does not therefore increase to excessive values for these two reasons: (1) The tropical strata are not elevated up to' the theoretical amount because of the escape of the currents poleward not very far from the surface of the ground; (2) the eastward drift is diminished by the operation of the vertical discharges be- tween the lower and the higher levels produced by the purely mechanical vortex motion in the cyclones and the anticyclones. The evidence before us is to the effect that the heating of the atmosphere is generally confined to a layer less than 5,000 meters, or 3 miles, thick. It is not intended to allude now to the annual range in temperature with the sun's change in 39 latitude, but rather to tlie shorter periods of only a few days length which contribute to the impulse of streams from the south. There are several reasons which lead to this conclu- sion: (1) The trend of the preceding argument has been to show that the readjustments of disturbed temperature equi- librium take place in the lower layers of the atmosphere by means of rather spasmodic impulses, controlled partly by the temperature energy in the tropic and the polar regions, partly by the distribution of land and ocean temperatures, and bv the relative radiation which takes place from them in the winter and summer season, respectively. (2) Half of the mass of the atmosphere is contained below the 5,000-meter level, and this is the layer within which the greater part of the aqueous vapor is also collected, since the vapor contents of the higher levels is in the form, of fine ice crystals, which drift eastward, encircling the earth, and perhaps seldom find- ing their way to the ground. The fact that the dust of the Krakatoa volcano was thus carried about the earth for two or three years shows that the upper current has a history of its own, to a considerable extent independent of the 3-inile layer nearest the earth. Now, the important part which the aqueous vapor plays in the absorption of heat is well understood, and it depends upon the very high latent heat of water, which is 606.5 calories per kilogram at C. The evaporation and condensation of water in precipitation is certainly confined to the lower stratum, and hence it is in harmony with this view to limit the effective heating of the air by the sun to the lowest 3 miles. (3) The diurnal variation of the temperature at the surface of the ground takes on a wide range. The tempera- ture is above the normal in low areas, in the summer season, and in the middle of the day; it is below the normal in high areas, especially in the case of cold waves in the winter, and in the night-time. The range at the ground generally amounts to 10 or 20 F., but diminishes upward with the height and disappears at the 5,000-foot level, or even considerably below that height. This is shown very clearly in the study of the changes in the vertical temperatures, as explored by means of balloon ascensions, where the 5,000-foot level marks the con- vergence of the lines which represent the gradients in the forenoon and afternoon. The range in the United States is iisually greater than in Europe at the ground, owing to the more pronounced nature of the cold and warm waves that move eastward over that region, but the evidence is that the diurnal lines converge at 2 or 3 miles above the ground. (4) The fact that the great eastward drift of the upper levels is underruu by a series of comparatively thin currents, which move about in every possible direction, shows that the dis- turbance of equilibrium is local and confined to a shallow skin near the ground, the most rapid currents belonging to the cumulus and strato-cumulus levels, which also implies that the upper regions of the atmosphere are much less affected than the lower. (5) The same conclusion is indicated very clearly by the seasonal change in the drift of the high areas over the northwestern portions of the United States, from the northwest in winter and from the southwest in summer, in conformity with the location of the permanent high areas in winter over the continent and in summer over the ocean. From these considerations it seems evident that the upper atmosphere is but slightly disturbed in its temperature equi- librium by the effects of the solar radiation, but the solar rays puss through it'with comparatively little absorption, while the larger percentage of the heat retained in the lower strata, is due to a change of the wave length. This conclusion is very important for two reasons: (1) It shows why the gen- eral circulation of the atmosphere prescribed by the Ferrel- Oberbeck theory does not seem to be confirmed by the ob- servations. (2) It also indicates where the energy comes from which is finally expended in the generation of cyclonic circulations and in the retardation of the eastward drift by the agency of inertia rather than by friction; for if the total amount of energy falling upon the Tropics does not expend itself in an upper poleward current, because the higher strata retain a temperature of equilibrium almost undisturbed, then this energy must give rise to a series of comparatively small currents moving poleward in the lower strata a fact which is abundantly confirmed by the observations. Also, if the friction of the upper atmosphere upon itself is very slight, then there will be but little retardation to an excessive east- ward drift, tending under a steady force to have a constant acceleration. The only other available agency which will pro- duce the same effect is the intrusion into the higher strata from the lower, or vice versa, of air moving eastward with a different velocity, which must suddenly be subject to accelera- tion. The discharge of the product passing through cyclonic circulations is perfectly fitted to perform this office. Hence, the theory here expounded consists of two parts as regards the eastward drift: (1) The upper poleward gradients are not built up to the amounts supposed by Ferrel, because of the lateral escape poleward of currents from the tropical belt; (2) The agency of friction as a retarder is replaced by the interchange of inertia derived from a compound circulation, the sources of the separate parts having different and inde- pendent causes. It has been important to thus carefully clear the ground for the theory of local cyclones, which will be ad- vanced to take the place of the type proposed by Professor Ferrel on the one hand, or of that advocated by the German school on the other hand. These two theories are not in harmony with each other, and neither of them seems to be in agreement with the observations. It is very evident that the six assumptions which have been made in order to pass from the general equations of motion, 200, to the working system employed by Ferrel, 397a, must be carefully revised before we can expect to put this branch of meteorology upon a correct working basis. In particular it is not suitable to omit the variations of temperature in longitude, because in so doing the turbulence of the lower strata and the alternate streams which are implied in this variation profoundly modify the general and the local circulation. It is also necessary to cor- rect the statement regarding the friction as the special agency of retarding accelerated flows and substitute, or rather add thereto, the inertia of currents which are rapidly changing their velocities. The conflict of turbulent countercurrents, especially at a short distance above the ground, must be rig- orously considered in studying the resultant effects. Like- wise the direct application of the law of conservation of areas passed over by the rotating radius vector can not apply imme- diately to the lower strata, though it may be much more nearly correct above the 3-mile level. MODIFICATION OF THE CANAL THEORY. In consequence of these considerations it seems necessary to modify the canal theory to such an extent as to be practi- cally equivalent to an abandonment of it. If this is done it is important to trace out a chain of circumstances which will give a more correct account of the general and the local circulation of the atmosphere. The canal theory is very artificial, depend- ing as it does upon a simple laboratory experiment, in connec- tion with an obvious analysis of the general equations of mo- tion. If this theory is to be preserved, then we must be assured that the atmosphere does in fact traverse the circuits pre- scribed, for it has been commonly assumed to conform with the facts of observation. As has been shown, observation does not bear out the requirements of the theory, and I shall, there- fore, attempt to trace out in a descriptive way the circulation as it is developed over the North American Continent. The re- duction of this kinematic picture to the corresponding mathe- matical form of dynamics is a task of very great difficulty, as may readily be inferred. We may conceive the tropical strata to be elevated by ther- mal expansion relative to the polar regions, so that there is a certain average gradient slope and corresponding west-east 40 velocity which is in equilibrium with it in accordance with the usual ('(illations. If the canal theory of circulation is in opera- tion we have poleward gradients in the upper strata, and equatorward gradients in the lower strata. If, instead of maintaining this circulation, there is an escape of currents from the Tropics in the lower strata in a poleward direction, then the gradients of the canal theory diminish and become much more moderate in consequence of this release of ten- sion. Every such leakage current from the Tropics causes a break or fault in the gradient, and this must be attended by a corresponding deflection of the eastward current, through the operation of the deflecting force at right angles to it, due to the earth's rotation. Referring to the scheme of self-regulation of the circulation by the rise and fall of the gradients, tig. 18, FIG. 18. Scheme of self-regulation of the circulation by the rise and fall of the gradient. we may consider the average gradient in the strato-cumulus level. When in its mean position, as determined by the whole set of natural circumstances which produce it, the isobars and the wind with a given direction and velocity are all practically in coincidence. The velocity is just enough to maintain the slope of pressure as measured by the gradient. If the thermal expansion of the Tropics increases, the gradient slope is ele- vated, the eastward velocity is increased, and this acceleration will continue to advance till an excess of energy secures for itself a way of escape. This increase of velocity is probably checked as follows: From the Tropics in the lower levels, that is in the cumulus and strato-cumulus strata, a stream of air breaks away from the canal circuit, and pushes northward in some irregular course. This evidently causes a break in the gradient sur- faces, such as is indicated, for example, by the dotted lines of fig. 18, and the slope of pressure which held the eastward drift in its position gives way. The action of the deflecting force due to the earth's rotation bends the current southward as is indicated, and there is thus made the beginning of an an- ticyclonic local movement. In the lowest levels, from cumulus down to the surface, the break in the average gradients may be so pronounced as to offer but little check to a complete anticy- clonic gyration, such as appears at the surface of the earth. This deflection of direction causes a whirl and absorption of energy in the strata affected through the local interchange of inertia, and slows up the eastward drift by the vortex action which is produced with a downward component. The alter- nate rise and fall of the gradients, and the attendant anticy- clonic gyrations, mark the successive efforts at self-regulation which the atmosphere as a thermal engine imposes upon itself. These continental pulsations are shown on the weather maps as the procession of high and low pressure areas which traverse the middle latitudes. In consequence of the superior velocity of eastward motion in the strato-cumulus level, this region is the first to feel the decline in gradient strength, due to the tendency of a stream to escape from the Tropics, as from the Gulf of Mexico over the United States. It thus happens that the anticyclone is not only larger in area, lint it also generally precedes the cyclone in its formation. There are numerous instances in which the anticyclono overspreads the United States, while there is no important cyclone in connection with it, except possibly some depression or irregular action along the edges of the high area. Usually, however, incipient cy- clones increase in intensity from these small beginnings, and they may even seem to drink up and exhaust the air which is flowing in anticv clonic circulation. This is the reason why I have heretofore described the anticyclone as preceding the cyclone in efficiency, and have thus reversed the order of action as taught by Professor Ferrel in his well-known theorv. The warm stream from the south is deterred from mingling with the cold antievclonic air by the difference of its tempera- ture, and the result is that the eastern side of the anticyclone, which flows southward, and the warm escape current from the south, flowing northward, compose two counter currents. These two currents together generate the cyclone, which is a vortex with an ascending central velocity. The gyration is produced by the action of the two independent streams acting like a couple, since they each depend upon separate gradient systems for their own mechanical pressures. It is not a g\ ra- tion due to frictional impact, but rather to the steady pressure on the arms of a couple, since the streams are driven by inde- pendent gradients, and are held apart by having different temperatures in the two separate currents. The air is thus raised from the lower to the higher strata in great masses, by circulating through the configuration of the cyclone, and this, too, produces a retardation of the eastward drift by an imme- diate interchange in the inertia, since there is a quick mingling of air having different directions and velocities. Examples of this action can be seen by studying the Charts '20 to 35, in- clusive, of the International Cloud Report. Furthermore, the motions of the atmosphere result in placing strata of air ha\ ing different temperatures together, side by side, so that the sur- face isotherms are directed from the southwest to the north- east, and in consequence the northwest portions of a cyclone are cold and the southeast portions are warm. This does not conform to the requirements of either the Ferrel or the Ger- man theories, which demand a warm local center for the gen- eration of cyclones. Yet if two such masses of air lay along- side while they are of different temperatures, an interchange! of heat contents will take place locally between them, and thus the streams will interflow in such a way as to strengthen the cyclonic gyration. This will be accompanied by distinct strati- fication of the air currents in the local cyclones, such as is observed in the kite and balloon ascensions, since the air of different temperatures is drawn out into thin ribbons having large discontinuous surfaces, which are favorable to the inter- change of heat. It is frequently found that a great anticy- clonic area as it approaches the ocean, althoiigh attended by no cyclone, will yet suddenly cause a violent whirl to form on its edge by the mere action of these adjacent masses of dif- ferent temperatures. Such local storms are sometimes formed on the Atlantic coast during a single night, and they may cause vortices with hurricane velocities on the coast. The line of junction of these warm and cold currents, along the southern and southeastern parts of the low area, is the locus of the formation of the majority of the tornadoes of the United States, the counter flow setting up the gyration, which is con- verted into a genuine columnar vortex, through which the heated air of the lower strata escapes into the colder strata of the higher levels. The hurricanes of the "West Indies simi- larly form along the places of the counter flow between the Atlantic high area and the southeast trade winds when at their extreme northern limit, as in August to October. The vortex then travels westward and skirts around the periphery of the high area until it is absorbed finally in the eastward drift of the higher latitudes. Such dynamic intermingling of the general and the local circulation is, therefore, not only 41 in accordance with observations, but it is a suitable substi- tute for tlie defective canal theory of the general circulation, and also for the untenable theory of the local cyclones and anticyclones, supposed to be dependent upon the central heat produced by condensation of the aqueous vapor of precipita- tion. This view is attended, on the other hand, by the follow- ing disadvantage: That while the canal theory and the warm center cyclone theory lend themselves readily to mathematical treatment and to analytic solutions of considerable elegance, we are obliged to substitute for them an irregular system of stream lines in the lower strata, not at all readily put into mathematical forms. This turbulent circulation, with its self- adjusting government of the eastward flow, its interaction be- tween the general and the local vortices, its numerous subordi- nate phenomena, such as tornadoes, hurricanes, and cyclones, is easy to comprehend, but hard to analyze mathematically into the" exact dynamic forces of equilibrium. It is possible to construct several special typical configurations for each dis- trict of the earth, as was done for the United States in Charts 20-35, inclusive, of the International Cloud Report, and then draw the stream lines, with their velocities, in order to prepare for the computation of the dynamic forces involved. This is the true meteorological problem of the future. THE STRUCTURE OF THE ANTICYCLONE. We will now examine a little more closely the structure of the anticyclone and the cyclone as given by observations for the sake of the analytical problems presented by their configu- ration. It has been claimed by meteorologists that there is a southward component in the middle strata of the north temper- ate zone toward the high pressure belt, but a northward compo- nent in the upper strata and another northward component near the surface, as is indicated on fig. 13, Paper IV. The obser- vations of 1896-97 do not, however, give such a distribution oi the mean components, for they show that there is a very small average drift northward in all strata, increasing slightly with the height above the surface. That is to say, the atmosphere in the eastern and central United States drifts northward a very little and thus supplies part of the air that descends into the anticyclones through the upper strata. We have indicated how the leakage in the lower strata from the Tropics in part re- places the air which descends in the anticyclonic areas, and it is assumed that the small residual northward drift comple- ments the amount that is required to fill the anticyclonic areas. The downward vortex, therefore, draws in a portion of the air passing through it from the upper strata, as a conse- quence of the gyration induced through the countercurrent action, and therefore the feeble northward component of the circulation of the higher strata seeks the surface practically in the middle latitudes, before arriving at the polar zone through the mechanism of the local vortices. Hence, it fol lows that there is little cause for the formation of a genera anticyclone close to the pole itself, which Ferrel assumed to exist; the result of Kimball's discussion in the MONTHLY WEATHER REVIEW, September, 1901, goes to show that thii movement only feebly exists, and is in conformity with thi; exposition of the general circulation. Therefore, the air tha descends in a local anticyclone comes from two sources, the leakage currents from the Tropics in the lower and middl strata and the feeble northward drift in all strata, especially the higher. There is one feature of the anticyclonic vortex which may be mentioned, though it belongs more properly to an analyti treatment of that circulation. The anticyclonic component of fig. 6, Paper IIP, show that we are not dealing with a pur form of vortex. The two possible laws are typically the para bolic = constant, and the hyperbolic vat = constant. Monthly Weather Koview, April, 1902, Vol. XXX, p. 166. 'Monthly Weather Review, March, 1902, Vol. XXX, p. 117. Hyperbolic. m= constant. Parabolic. = constant. FIG. 19. Mixed system of hyperbolic and parabolic components. According to the parabolic law = constant, the circula- ion causes simply a depression in the center of the gyrating .uid; according to the hyperbolic law i:w = constant, there is a ertical component of circulation as in ordinary vortices. In he observed anticyclonic components the velocities v are about qual to each other on the I, II, III, circles, and it seems to ne that this can only happen if there is a mixture of these wo laws of motion. Thus we may divide the observed com- ionents r I: r u , i' m , into two parts by a diagonal as shown on ig. 19. The upper components represent the parabolic, and he lower the hyperbolic portions. This is physically neces- ary for the following reason. The anticyclone is formed by arge currents of air moving in more or less independent treams on its outer portions, while only curling offshoots each its central parts; this would produce the pure para- )olic components only. But, through imperfect pressure gradients there is also near the center a true downward com- ponent of circulation, and this can be supplied only by the iction of hyperbolic components, that is to say, of a simple vortex motion. Hence, the general anticlockwise movement f the anticyclone, strongest on the outer circles, has accom- panying it a true downward or vortex component which engthens the components u in the central portions. If this is correct, one sees an additional reason for holding that Fer- el's explanation of the anticyclone is impracticable, and also that the reversing of the cyclone to make an anticyclone, as proposed by Oberbeck and Pockels is not warranted. We need rery accurate observations to settle so difficult a point of pure ;heory, but I can not at present see any other satisfactory ex- planation of the gyratory components derived from the Weather Bureau observations. STRUCTURE OF THE CYCLONE. In Table 18 we give the results of cloud observations in the United States. In the following example the relations which should exist in a pure vortex are deduced for comparison with the data given under low areas in Table 18. Taking the inward radial velocity u = 1.25, at the distance 1,250 kilometers, assuming A = .000100 for # = 4(5 17', and c = .000002, also k = .000050, their introduction into the several formulse gives the values found in Table 19. An account will be given of the derivation of the formulae in Paper VI. It is seen that the rotational velocity -u is about the same as that given by the observations up to the circle whose radius is 150 km = 93 miles from the center, as seen under \\ of Table 18. The values of the radial velocity agree fairly well, if we admit that the observations may be somewhat imperfect for this component up to the region of the inner circle I, whose radius is 250 km. There the component u is much larger than expected in the upper strata, and this indicates some opposi- tion to the free development of the vortex near the core. It is presumed that this implies a struggle to intrude into the rapid eastward drift, accompanied by a broadening of the vor- tex tube through the resistance, v being smaller than it should be and u greater, making the angle of the inclination i much greater than it ought to be in pure vortex motion. As the computation of the vortex goes to the height of 10 miles, far beyond the altitude to which the ordinary cyclonic motion penetrates, this being only 3 or 4 miles in the moderate move- ments of the air, it is seen that v should theoretically attain 42 enormous velocities very near the center. The difference be- tween those and such as are actually observed may be regarded as measuring the energy expended in breaking up the cyclone in the higher levels, which can be balanced only by retarding the movements of the general cyclone. The vortical velocity w is extraordinarily small from the bottom to the top, and in a measure justifies the method of discussing the motions of the air in the cyclone as a case of horizontal movement. It is impossible theoretically, however, that such a cyclonic motion without a vertical component should exist at all. The fact is tli at a slow vertical movement is acting over the very large area covered by the cyclone, and is sufficient to carry oft' all (lie air which flows into it through a thin disk at the outside in horizontal directions toward the center. The checks m v and in w = 2 u s hold throughout the cyclone, thus proving that our data are at least approximately correct. The angle (', between the tangential direction and the current, theoret- ically becomes very small within 300 miles of the center. It TABLE 18. Anticyclonic and cyclonic velocities at each l,(WO-metf,r level. (Copy of Table 126 International Claud Report.) Cloud forms. Height in meters. High areas. Low llrcav. Velocities in Hi,' k'rnrntl cycloiu-. 1 l I 2 2 II u, , III u 2 u, I M 2 D a II , , III 2 a Ci and Ci St 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0000 3.5 4.0 3. 5 5. 3.0 6.0 1.5 6.5 0.0 7.0 0.0 7.5 0. 7. 5 0.0 7.0 -j-1.0 6.0 +3. 5 4. 5 +4. 2. 5 + 4.5 5.5 + 4.5 5.0 + 3.5 4.5 0. 4. 5 - 2.5 4.5 + 2.5 6.0 + 8.5 8.0 + 10.0 9.5 + 7.5 9.5 + 5.0 7.5 + 2.5 4.0 +2.5 3.0 +2.5 8.0 +2.0 9.0 1.5 8.0 4.0 7.5 2.5 8.0 0. 10. +2.0 12.0 +2.0 11.0 + 1.5 7.0 +1.0 0.0 6.5 +3.0 3.0 +8.0 2.5 +11.0 6.5 +13.5 -9.0 +15.0 9.0 +17.0 7. 5 +20. 3. 5 +23. 1.0 +20.0 0.0 +8.0 0.0 +6.0 1.0 + 3.5 3.0 +11.0 5. 5 +13. 5 5.0 + 15.0 2.0 +15.5 0.0 +15.5 0.0 +14.5 0.0 +13.0 0.0 +11.0 1.5 +8.0 3.5 +3.0 0.0 3.0 1.5 1.0 2.0 +1.0 2.0 +2.0 0.5 +3.0 + 1.5 +5.0 +2.5 +7.0 +2.0 +7.5 0. +5. 1.5 +4.0 2.0 +3.0 2.8 -i :i.-i. i 2.6 +35.0 2.4 +34.6 2. 2 +30. 2. +25. 1.8 +23.6 1.6 +22.6 1.3 +21.0 1.0 +14.0 0.8 +6.4 0.5 +1.3 Ci. Cu A. St A. Cu S Cu Cu and St Wind . . . Means of the velocities, u.,, D a .... Radius o 0. 3 5. 8 1 5.8 + 4.2 6.2 3 18.6 +0.5 - 7.6 5 38.0 4.4 +13.1 1 + 13.1 2.0 +11.2 3 +33. 6 0. 3 +3. 8 5 + 19.0 Product GJV, + MJ rr outward on radius. + u, zz anticlockwise about center. I. Oj = 250,000. II. a n = 750,000. III. o m zz 1, 250, 000. +, = south. + D, zz oast . TABLE 19. Application of the formula for a cyclone. (Copy of Table 127, International Cloud Report.) c , i/) -^ tt'Z. CONSTANTS Al =46 17' "k u 1.25 e = CT= 1,250,000 meters JD FOBMUL^;. 2ncos0rz.OOO - 2M =.000 a fc = .000 A c 100 002 050 W : + CZ. ?.. c. = .000002 k c 2 coti MZZ -o. "- ' 1" k -c2 oz ' -k-c z - DEBIVED DISTANCES, VELOCITIES, CHECKS, AND INCLINATIONS. mftfrt. 1250000 , ''/< .-. 777 z 1.00 OS 1250000 u 1.25 V 2.50 w .0000020 av 3125000 j otozz I \-1uz\ 2.5 cot; 2.00 i 26.6 O ,,. 0.34 1000000 621 1.56 1560000 1.0 3.125 31 3125000 3.1 3.12 17.6 0. 40 750000 466 2.78 2085000 0.8 4. 17 56 3125000 4.2 5.56 10.2 0.55 500000 311 6.25 3125000 0.5 6.25 125 3125000 6.3 12. 50 4.6 0.78 250000 155 25.00 6250000 0.25 12.50 500 3125000 12.5 50.00 1.2 2.03 200000 124 39.06 7812000 0.20 15. 61 781 3125000 15.6 78.12 0.7 3.00 150000 93 69.40 10412000 0.15 20.82 1388 3125000 20.8 138. 80 0.4 5. 37 100000 62 156. 30 15630000 0.10 31.26 3126 3125000 31.3 312. GO 0.2 13.90 50000 31 625.00 31250000 0.05 62. 50 12500 3125000 62.5 40000 25 977.00 39080000 0.04 78. 16 19540 3125000 78.2 30000 19 1736. 00 52080000 0.03 104.16 34720 3125000 104.2 20000 12 3906. 00 78120000 0.02 156.24 78120 3125000 150. 2 10000 6 15625. 00 156250000 0. 005 312. 50 . 0312500 3125000 312.5 43 was shown by the results of the observations that the move- ment at the cumulus level is much more rounded than in the lower strata, the difference being caused by the retardation of the air operating upon the surface irregularities of the ground. A congested or irregular inflow near the center will similarly increase the angle i, since the component u is increased and v diminished by it. The observations given on the weather maps do not record the conditions within 60 miles of the center with any definiteness. In hurricanes the core is about 30 miles broad and its boundary is quite sharp, which shows that the component v is highly developed, while u is small. But the hurricane also penetrates to much greater altitudes, as already mentioned. Finally, the gradient shows that there is a slow change near the outer limit, but that it increases very rapidly on approaching close to the center. THE SPECIAL FEATURES OF THE CIRCULATION. The special features of the circulation indicated on fig. 20, which may be mentioned are as follows: (1) It is evident that (3) The approach of a moving particle to the axis of the cyclone is attended by an increase of the velocity of rotation, which ac- celerates rapidly as it passes into the upper strata. There it accomplishes the work of deflecting the eastward drift, and it expends some of its energy in that way. The result of this op- position to free motion is to spread out the top of the vortex, reduce its gyratory velocity, and change the relations of i> 2 and u t . In the undisturbed gyratory motion the component c 2 be- comes very great in comparison with w 2 , and 2 is always a small quantity. An inspection of Table 18 shows, however, that in the strata, between 5,000 and 10,000 meters the radial velocity U 2 is relatively large, and the angle of the inclination instead of being nearly is from 25 to 35 on the inner circle II. This means that the original coefficient upon which 2w the dimensions of the cyclone depend, namely, c= , does not remain a constant, but increases from the boundary to- ward the axis of the gyration. Thus we obtain, .s / / / / / / s* ^r 20,000 m. S <9 7 6 lOOOkm. FIG. 20. General scheme of the structure of cyclones. this scheme avoids entirely the primary difficulties attending the Ferrel and also the German types of circulation. Each of these divided the cyclone into two parts having special prop- erties. Ferrel divided his cyclone at a vanishing rotational velocity, v = 0, which involved a circulation in opposite direc- tions on either side of it; the German type consists of two parts, separated by a discontinuous movement at the circle of the maximum velocity for v. The pure vortex, on the other hand, has only one law to deal with, and that, too, the simplest of all, in accordance with which the motion is generated. (2) Neither of the other types provides for a true calm region at the center of the cyclone, commonly observed in hurricanes as the eye of the storm. Ferrel's formula 402i shows that v increases from the circle J? = 0.707 to the very center; the formula; 450 and 471 show that the velocity v decreases grad- ually from the circle bounding the inner region toward the center, but does not vanish till reaching it. The construction here proposed indicates that since u is a function of the height z as well as of the radial distance ro, the air in streaming to- ward the center is gradiially lifted above the ground by purely dynamic action and leaves a core without gyratory circulation. CTI = .0000053= 0.6 1250000 4.0 e TTT =.0000005= 8.8 250000 This involves an expenditure of energy in the struggle attendant upon intruding into the swiftly moving upper stratum. Furthermore, as was previously pointed out, Fer- rel's theory of the slowing down of the excessive eastward velocities which would arise from the pure vortex law of the conservation of areas applied to the general cyclone, is ths, friction is largely concerned with the operation. It seemis however, that a much more efficient cause of retardation at the interaction between these two types of motion, namely, the linear and the rotary, by which the lower strata thrust themselves into the higher. The effect is to enlarge the size of the vortex tube at the top by the resistance, deflect the eastward drift into sinuous curves, slow down the eastward velocity, and thus restrain the general cyclonic movement from TAIU.K 2(1. 44 uiul ci'loritieft in the waterspout off Cottage City, Viiu'i/anl Sound. Mti-xx., Aiujunt /!>, /,"?.%'. (Copy of Table I2S International Cloud Iti-port. I Working formula! : 2 2o; = ; ro = " ; or Const.; 2zit=taw; 3 to VGJ Dimensions in meters. Velocities ill meters per second. iM'mcn -ion- in feel. Velocity in miles JMT hour. ft Z a tt V w 2ZM ~ GJU) ft Z a H V w 1280 00 4200 00 e 1278 2 518.4 3.13 6.26 0.02 12.53 4193 7 1701 7.0 11. i 0.04 1189 91 76.9 0.46 42.24 1. 10 84.49 3901 299 253 1.0 B4 I 2.5 1097 183 GO. 8 0.29 53.39 1.76 106. 79 3599 601 200 0. 6 111). 5 3.9 1006 274 44.3 0.27 73.31 3.31 146. 61 3301 899 145 0.6 164. 7.4 914 366 38.3 0.23 84.72 4.42 169. 45 2999 1201 125 0.5 189. 1). D 731 549 31.3 0.19 103. 77 6.63 207. 53 2398 1802 102 0.4 233. 11.'.) 549 731 27.1 0.16 119. 73 8.83 239. 47 1802 2308 89 0.4 268. 19.8 457 823 25.5 0.15 127.04 9.94 254. 10 1409 2701 84 0.3 284. 22.2 366 914 24.3 0.15 133. 89 11.04 267.78 1201 2999 79 0.3 300. 24.7 183 1097 22.1 0.13 146. 68 13.25 293. 36 601 3599 72 0.3 328. 29. G 146 1134 21.8 0.13 149. 13 13.70 298.' 26 479 3721 72 0.3 333. 29.7 1280 20.5 0.13 158. 44 15.46 316. 89 4200 67 0.3 354. 34.6 = 0.01208 excessive values. (4) The resultant of these component forces and velocities is to produce a circulation along the parallels of latitude which may be represented by the upper part of fig. 20. The upper clouds of the cirrus region precede the cyclone proper as forerunners of this type of circulation; the lower clouds follow in succession, till precipitation is produced at the elevation of 1,000 to 3,000 meters; in very rapid circulations the eye of the storm is fully developed; the clearing up is more abrupt on the westward than on the eastward side of the cyclone. (5) The progressive movement of storms is partly an effect of the cyclone covering an area of sufficient extent to be in different latitudes, so that variations in cos amount to something. But other circumstances are more important. By Table 33, Section IV, International Cloud Report, it is seen that the northward components for the group of areas which are covered by the currents of air from the south are greater than those from the north. That is to say, the movement in the streams from the Tropics is more rapid than that from the polar regions, and the result is to roll up the eastward side of the cyclone to the north more than the westward to the south. The cyclone tends to rotate along the front of a high area toward the north. At the same time its top is fastened by means of the circulation into the eastward drift at 4,000 meters elevation, and these two components make the storm move northeastward in the central and eastern portions of the United States. If the general cyclone has other direc- tions, as when hurricanes form in the Caribbean Sea, the same principles hold, and the storm there first moves westward, then northward and northeastward, because the general circulation is controlled in that region by the anticyclone in the southern portions of the north Atlantic Ocean. (6) It has been shown that the currents which feed the cyclone have different veloci- ties at different altitudes, being greatest from 2,000 to 5,000 me- ters above the ground. Each stratum forms a stream for itself conforming to the general law, but modifies its dimensions according to the constants pertaining to the special locality. Since these different strata have thus distinct local movements, especially considering the variable temperatures and densities of the currents from the north and south, respectively, it fol- lows that the conditions are favorable for the formation of tur- bulent minor circulations of all kinds. The movement of the air is therefore partly congested, and partly runs in free whirls, the difference of equilibrium in temperature being gradually reduced to the proper normal value for the latitude anil alti- tude by this forced intermingling of the subordinate parts of the cyclone. This process of restoring to an equilibrium the temperature of masses, bearing with them that of the region from which they came, is generally completed by the time the 5,000-meter level is reached, judging from the records of the balloon observations. In summer, when the eastward drift is relatively slow, the pure vertical convective ascension may ex- tend up to 10,000 meters. This is much more likely to happen on the eastward than on the westward side of a cyclone, be- cause the vortex components throw back the eastward move- ment upon itself, and thus make the strata more stagnant in vertical directions. It has also been found practically very difficult to make the kites fly on the east of the low center, the best ascensions being made on the southerly and westerly quadrants. (7) -The entire problem of amily/.ing the move- ments of the air in their details is so exceedingly complicated that only slow improvements in dynamic meteorology can be expected. A clearer idea of the fundamental conditions may, however, enable us to advance more rapidly than is now antic- ipated. It will be a very important gain if meteorology can free itself from some of the theories which have so long pre- vailed, but which now are seen to be quite untenable, and have seriously retarded its advancement. THE VELOCITIES IN TORNADOES. The motions in tornadoes are similar to those in cyclones, yet the tube is not only inverted in position, but the stream lines occupy only the central portions, and the lines of >,' become tangent to the plane whose height is 7/ o at certain distances from the center. The fundamental equations for the tornado are 303-308. <,' -(- ro'g holds for the tornado with vertical axis 4J positive downward, and the single bounding plane at the dis- 45 tance H above the ground. 4' = o w * s ^ e equation for the cyclone with the vertical axis positive upward. A multitude of minor relations and comparisons can be drawn from the two sets of equations 303-308 and 488-490. If the lower parts of fig. 20 be looked at as if the horizontal axis were the vertical, we have a picture of the half of a tornado tube. The diagram is not good because not drawn to scale, but the idea is easily understood. Hence, one law serves for all types of local storms, cyclones, hurricanes, and tornadoes, which thus theo- retically differ from each other only in their dimensions and in the details by which they are formed. Cyclones are gener- ated chiefly by horizontal convection currents; hurricanes have a stronger vertical convection current and also horizontal convection currents ; tornadoes arise chiefly from vertical con- vection, assisted by some horizontal currents which counter flow in the cumulus level. It may be remarked that the stream lines indicated by Fer- rel, page 300, Recent Advances, are conjectural only, and do not conform to the theory of stream lines in a vertical vortex tube, nor to observation, which shows that the air is quiet close up to the boundary of the tornado tube. THE WATERSPOUT OFF COTTAGE CITY, MASS., AUGUST 19, 1896. The result of the computation on this interesting waterspout is added, and it shows the dimensions and velocities in metric and English measures which were derived from the observed distances and the formulae. The most important feature is the value of the vertical velocity of 35 miles per hour at the sea level. See Table 20. VI. CERTAIN MATHEMATICAL FORMULAE USEFUL IN METEOROLOGICAL DISCUSSIONS.' THE NEED OF A STANDARD SYSTEM OF FOEML'L*. There are a large number of mathematical papers that have been written by meteorologists ill the exposition of various theories, which must be thoroughly considered by students whp seek to go beyond a descriptive statement of the problems into a close examination of the principles upon which the solutions rest. The question arose at an early stage in my study of comparative meteorology as to the form in which such mathematical discussions would be presented to the public. To traverse the entire range of treatises and explain them in detail was clearly impracticable; to adopt an abstract mathematical synopsis, such as is found in Carr's or Laska's synopsis of pure mathematics, was to put too great a strain upon readers who are not specialists in mathematical meteor- ology. Finally it seemed to me to be a fair compromise to take the following course: (1) reduce the important papers, to one common standard notation, and (2) make an analysis of the result in a sufficiently expanded form to enable a good reader to follow the series of equations without difficulty. The only step required to transform the contents of the mathe- matical compendium as given in chapters 10 and 11 of the International Cloud Keport into a complete treatise on ana- lytic meteorology is to supply such transition precepts as are usually placed between the formulre to aid the thought. It is, however, a distinct advantage for a working use of the for- mula, to one who has once become familiar with such prob- lems, to dispense with these explanatory sentences, which only take up space. A ready reference to the standard equa- tions under each subject is quickly appreciated by any one who uses these formulae in a practical way, just as one would use a mathematical table in computing. It is my purpose to complete such a collection of formulie, in addition to the tables contained in my report on Eclipse Meteorology and Allied Problems, Weather Bureau Bulletin I, 1902, by appro- priate tables covering the subjects, spherical harmonics, ther- modynamics, and the kinetic theory of gases, because these are indispensable in meteorological studies. I have taken the opportunity in this connection to present several original sets of formula), which have an advantage in their applications to meteorological problems, and it is my purpose to call atten- tion to some of them in this paper. THE GENERAL EQUATIONS OF MOTION. The methods of deriving the general equations of motion on the rotating earth, as presented in Ferrel's paper, "The mo- tions of fluids and solids on the earth's surface," or in the standard treatises of hydrodynamics, are so complicated as to discourage all who are not expert mathematicians from an ex- amination of the solution. The fact that Ferrel did not evaluate the total differential of inertia - (^^"l, introduced at an error into the equations contained in his "Mechanics and general motions of the atmosphere," United States Coast Survey lleport, 1875, Appendix 20; this was eliminated in his " Recent advances in meteorology," Annual lleport of the Chief Signal Officer, 1885, Appendix 71. There are no doubt many ways of solving this problem, but the following is original, as expanded from Table 75, International Cloud Report, and it leaves little to be desired in respect of simplicity and completeness. (1) THE POLAR EQUATIONS OF MOTION ON THE ROTATING EARTH. Using the notation already adopted in Paper II of this 1 Keprinted from the Monthly Weather Review for June, 1902. series, 2 we write the primary equations of acceleration of motion referred to axes which have their origin at the center of a nonrotating earth, as follows: The accelerations due to motion and to external forces are, 155. I OP dV du i = "jT Vot i + w 3 , tu s ) are changed as follows, denoting these terms on the rotating earth with primes: 177. u' = u v' = v -f n r sin w' = w 178. v + n r sin u r i i v + n r sin The differentials 179. d (n r sin 0) du r tan This is due to the fact that the rotation of the earth adds the velocity n r sin = n w to the eastward linear velocity, because m is the perpendicular distance from the axis of rotation. du' dv' dw' -JT-> jr> ~JT~ evaluate into, dt dt dt du' du dt '~ dt dv' dv dt dt dw' dw dt dt since M = !^? and w= by formulae 153, page 497, of the In- dt dt ternational Cloud Report. Substituting these values in the equations of motion for the rotating earth, which are the same as those of 155 with the letters all primed, and taking the equivalents of dx, dy, dz in polar cordinates from 153, we have: dt = -=T + u n cos -f w n sin dt 180. IdP "prdO 1 _ d-F ' P 1^9P Or du . (v + nrnhi/i) = dt _ (v + nrmn0 ) T -^ - + u U : r dv (v + n r sin 0) (v+nr Bind) r tan + un cos + w n sin 0, dw (v-\-nrsmO) The external forces derived from the potential Fare: dV dV 1T=_ ~ dx ~' ' ~ dy ~ dz 2 See Monthly Weather Eevlew for February, 1902, Vol. XXX, p. 81. 47 48 Performing the algebraic work, these equations reduce to 181. dP ,11' ilv = , + p r sin (Id). (It 1 ill' I' 2 COt l> -f- /HI' r 2/i cos . v r s MI- cot -\- vw r 2 cos (I sin U cos , w* -f a + "2n 2/i sin ti v rri' sin 2 0. The successive terms are the inertia, the centrifugal forces, the deflecting force, and the forces which change the figure of the earth from a sphere into an ellipsoid of revolution. (2) THE CYLINDRICAL EQUATIONS OF MOTION ON THE ROTATING EAKTH. If the axis of rotation of the earth is taken as the axis of rotation in cylindrical coordinates, the tangential velocity _ y _|_ n w; but if the axis of rotation is any radius of the earth extended above the surface, the tangential velocity be- comes = o -f- n w cos 0. Hence we have, in cylindrical coor- dinates, 182. u' =M v ' = v + n ra cos U w\ = w w , = , = n cos V w The differentials , , at at - at evaluate into, 183. du' "rfT du dt dv' du . d (n m cos 0) do . = -f- ..._^..= + u n cos dt dt dt dt dw ' dw dt "dt since u = , by formula; 152, and cos is a constant. Sub- stituting these values in the equations of motion for the rota- ting earth, which are the same as those of 155, with the letters all primed, and taking the equivalents of dx, dy, dz, in cylin- drical coordinates from 152, we have: 184. 1 dP du 1 dP dv f v\ = -r. + u n cos 6 + M ( n cos -| I 1 OP dw ~dt' The external forces derived from the potential Fare: dV dV dV =0, =0, _ a. dx dy dz Performing the algebraic work, these equations reduce to 185. du v'' = -JT 2n cos . v at zzj du (2n cos + i/j) v I dP dv uv ,. + 2n cos 0. u . + 1 HI' 7 <5r = " + (2n cos + v,) dt dw = ~dt vhere the term + ra n* cos* is neglected in the first equn- ,ion and v = the relative angular velocity. 1 ro The successive terms are the inertia, the deflecting force, ind the centrifugal forces, REMARKS ON THE SEVERAL TERMS IX THE GENERAL EQUATIONS (IF MOTION. It is customary to add to the terms developed in a friction- ess medium, a term expressing the retardation of acceleration due to friction, either in Ferrel's form + k (u, v, ), which is oroportional to the velocity and expresses a sliding friction, or in Oberbeck's form dy dt 1 dP dw . u' Now multiply these equations respectively by op - = udu + i-Ov + wdw + gdz. The integral of this is, /(>/' = i ( J + u 2 + w 2 ) + yz + const. = u. dx ' dx G _ OP _ dV = ? . y " d ii '' d' = 0.760 meter. II. We have by 50, page 490, for the standard weight of the atmosphere, 507. p = h = m AB in terms of the units of force P. 514. /' = Ap = ff m JB in terms of the units of weight p. The gradient force changes with the temperature. Let /' = the gradient force for T = 273 C. and B n = 0.760 meter. /' = the gradient force for T and B. O1O. ri IT n i 9 V T W *o - , , laP I dp IV. To evaluate and : p dx f> dx 516. We have P = gj> m B n ; and hence, 517. lf9P 1 dB I From the formulae on page 489, 47/. 101' I 'I /: ' A'in nun 520. 521. 522. 523. 13.5958 760 9.806 ~ 0.00129305 x 273 x 11 1 111 1 1 1 x II > = 0.0025833 ~ G s cot (> = (2 i;' -)- f) r, by equation 194. Hence. B cot n and similarly, ,= - 387.102 J ~ (2 V + r) ./, = + 387.102 J [ -~ (2 ,;' + ,-) r + "' - r /]. Since v' is a function of <>, that is, r' = /* rsintt, these terms can be computed by simple tables, such as those in Tables 104, 105, 106, of the International Cloud Report, where some of the terms are evaluated. By expressing the variation of 387.102 x -jp in a table with B and T as the arguments, the several products can be quickly computed. Examples : I. For B = 700 mm. and T= 260 C., _ T 2.6923; For = 30 north polar distance, 2' = 464.5 meters per second; For v = 40 meters per second, (2i/ + c) v = 20,180. Hence,G t 5 = 387.102 -^ co * " (-_V r) r = 5.71 millimeters per 111 111 meters. II. This latter has been computed from the tables as follows: 378.102 = 1,042.2; '', cot . 2u = 0.005052, by Table 104; cot II . v . v= 0.000435, by Table 106. The sum of these is COt (2v' + v)n = 0.005487. Hence n the product, G x = 1,042.2 x 0.005487 = 5.71 millimeters per 111 111 meters. Similarly, the gradients G f and G t can be computed. For these values of B and T, we find in other examples, = 40 = 50 _ .O = 60 , 7 = 51 We are at last in a position to examine the system of gradi- ents in the United States on the 10,000-foot plane and on the 3,500-foot plane. For we have obtained by the nephoscope aud theodolite observations as given in the Cloud Iteport a large number of corresponding values of n aud r, which enter these equations. The values of B and T on these planes have been carefully determined for each month, and also the gra- dients by which such values can be determined at any time. This will enable us to discuss the effect of friction at these planes, by means of the residuals which occur between the values of (f as found by these formulfe and those read off from the charts of isobars contained in the Barometry Report of 1900-1901. Furthermore, our Weather Bureau stations will soon be provided with suitable tables for computing pressures on the 3,500-foot and the 10,000-foot planes, and this will give daily configurations of isobars on these two levels. If, in addition, we had measures of the velocity of the clouds, q (u, v, w), above each station by means of nephoscopic observations, it would enable vis to make complete dynamic computations of the forces acting in cyclones and anticyclones, as is seen by an inspection of the formulie. Since the tabular computations are constructed for average conditions, it is of the utmost importance that check ohxcn'a- li. If the air is incompressible, then there will stream into a cylinder, whose radius is smaller by dm, the amount 2* (m dm) zu/i, and at the same time there will escape upward between these two cylinders the amount 2n-nj dm Hence 524. 1-m z Uf> + 2- (m dm) z v./i = 1-dm sup = Ixmdm w/>. Integrating along the entire radius from to m, we have, r ra 2-/< I zudw = 2-/ I mdm w. Jo Jo Therefore, zum t m'*w, and the equation of continuity 2 becomes 487. 23 = mw. This applies to pure vortex motion, and it finds some ex- amples in the atmosphere, such as in tornadoes, in many hurri- ;anes, and in some highly developed cyclones. It may be remarked that in treating of the general circula- tion of the atmosphere, the application of the pure vortex law = constant, has failed to give correct results, for example in the writings of Ferrel, von Helmholtz, Oberbeck, Sprung, and others. This leads to the theory of contracting rings on the earth with progressive motion towards the poles, or ex- panding rings with progression towards the equator. While the law of the sum of the momenta - mv = must prevail, the rings are in nature broken up into such complex stream lines as to render integration by the simple vortex law too rough and ready a method. We must, therefore, study the theory of typical stream lines, before attempting any general inte- gration for the entire circulation. The following derived relations are convenient: 2. Since 22= raw, we have w = __ GJ 2z = ' m, if ID = cz. 3. For sand u both constant, we have rszu = const. = <,'>. Hence, * = - C nst - = - f C i -\ -\, and by differentiation, uts \ <;/2 J nr const. dz= + r/2 = _2 2 . Therefore, CT dz dta , dz n drs - = 2 ; also, ra _ 23-,. . ra dt at 4. These give the form for the current function , and the velocity potential ro =s o m 2 z= 2r/ = muz= o = constant, m ' V u by 307, and by 308, introducing the value V* = %gz. This vortex law when modified by deflection and friction becomes, ' 492. Case I. Case II. i c k c 2 A * z = const. cz = const. 8. The inclination of the stream line to the isobars is, 491. Case I. cot i = + k-c' Case II. /i C0ll= + T*. k 9. The equation of continuity (163) is satisfied by the values in 490. 493. Case I. du u div f)w w Oz Case II. du u dw c c m + Oz = ~ 2 ~~ 2 + c = 10. The equation for gradient has a term to express the un- evaluated variation due to temperature effects, f(t x ), and it becomes, for the radial component, 494. _!> 1 OP ,, ^'* ~ /, Ox = 2 ra f & c + / c'ot i + g cot 2 11. The total velocity is i 1 . sm 2 i ' sm 12. The variation of pressure can be expressed by These formulsc are all collected in Table 121, page G02, of my International Cloud Report. This system of formula applies directly only to the pure vortex motions that satisfy the assumed current function and velocity potential. The components u, v, iv, are so simply interrelated that it is usually possible to make enough ob- servations of some sort from which to derive all the other vortex relations. Applications of them were made in the In- ternational Cloud lleport to two cases; (1) The waterspout observed off Cottage City, Marthas Vineyard, Mass., August 19, 1896, on page (i.'t:i; upon this important formation, a fuller report will be published. (2) The average velocities in a cy- clone from the data in Table 12(5, as given on page 629 of the International Cloud Report. The outcome of these computa- tion*! is to show that the natural stream lines of the atmosphere conform on the average to these formulae. There are, however, wide divergences of such a type as to indicate that the pure vortex motion is seriously modified by several conflicting forces, and that the true problems for the meteorologist consist in discovering the nature and amount of these deviations of tlio currents of the atmosphere from the simple laws. This is in fact a task of great difficulty, but it has now become evident what should be the course of scientific development for meteor- ology. There is little use in a further discussion of the gen- eral theorems at the present time, but there is great need of procuring the right kind of observations for use in such prob- lems. The Weather Bureau has accordingly been engaged in such a reconstruction of its data as will contribute to the solu- tion of these problems for the United States. We have already published a large number of nephoscope velocities for the eastern half of the country; the velocities of the upper cur- rents for the West Indies have been determined for about three years, July 1899-July 1902, and their computation will be com- menced at once; similar nephoscope observations will be un- dertaken for the Rocky Mountain and Pacific districts, begin- ning about July 1902. Our barometric observations have been thoroughly reduced for the years 1873 to the present time, and the tables necessary for reductions to the three reference planes are in hand for the construction of daily maps at three levels, containing the system of isobars corresponding with them. It will be necessary to revise the temperature and vapor tension observations and reduce them to homogeneous systems before our data will be complete for the application of the theoretical equations to the observational data. It is desirable to put an end to general mathematical speculation in meteorology, and to substitute for it definite comparisons between observations and computations together with dependent solutions for the outstanding unknown quantities. THE PROBLEMS OP THE AQUEOUS VAPOR CONTENTS OF THE ATMOSPHERE. I shall allow myself only a few remarks regarding the methods which were used in my report for the discussion of the various complicated problems that concern the aqueous vapor contents of the atmosphere, because the details are too complex for a brief summary like this, and also because the work was given in such an extended form as to enable students to follow it without difficulty. There are, however, a few leading ideas to which attention may be especially directed, as they serve for an introduction to the subject in general. There is collected in the International Cloud Report, Table 64, "Fundamental constants," a series of elementary constants in the English and metric systems, with the logarithms of the constants, and also a set of elementary formulfe which are most useful in meteorological studies. They cover nearly all the simple relations which constantly recur in manifold forms in the treatises and papers on meteorological subjects, and by transformation and combination a multitude of different rela- tions can be readily obtained. Tables 63, 64, and 65 supply the basis for much descriptive matter commonly found in treatises, in so compact and accurate a form as to quite super- sede the lengthy statements with which the same laws are usually presented, and this is a great convenience for the student and computer. Those who will take the trouble to become familiar with these tables will find much saving of 53 time in general work, and also they will be guarded from such errors of thought and statement as are likely to occur from not having these formula: in mind, or accessible for con- venient reference. Iii treating the vapor problems I have referred all the for- g mulao to the ratio -w, vapor tension divided by barometric pres- sure, as the most convenient and accurate argument for com- bination with another argument, as the height h, the tempera- ture T, or the pressure B. The Table 07 summarizes the for- mulic for the hypsometric reductions, and they are more fully explained in the forthcoming Barometry Report. The general e n idea is that having found the ratio ," at the base of a column, **0 the application of Hann's law for the diminution of the vapor pressure with the height gives the most accurate average law for computing the integral of the vapor tension throughout the entire column. A small secondary term can be added whenever our knowledge of the facts justifies such an increased degree of accuracy, though it is usually of little importance, especially for a series of observations where mean results are required. In the development of the a, /?, f, ft stages of the adiabatic thermodynamic formulae, the ratio jr is made the primary ar- gument by the series of transformations given in Table 72. These formulae are reduced to numerical tables, 94-102, and their accuracy is tested by comparing directly with the Hertzian logarithmic formulae, as given in the examples of Table 108. Their use involves a series of solutions by trials, which though laborious, yet lead to perfectly rigorous results, and after a little practise it becomes quite easy to obtain the true trial values without much difficulty. The graphical diagrams of Hertz give only approximate values, because they throw out the vapor tension term in the critical places and thus render in- accurate the very problems they were designed to discuss. Special applications were made to finding the gradients of pressure, temperature, and vapor tension in the , ft, f, K stages, and the results are found in Tables 147 for metric measures, and in Tables 153 for English measures. Finally the same tables were employed to discuss the impor- tant problem of the difference- between an adiabatic atmos- phere and the one given by the upper strata observations, whereby a new method was illustrated, with results in Table 162. The value of this computation depends, of course, upon the data 1>, T, e, adopted for the upper atmosphere, as meas- ured by the balloon and kite ascensions. It was especially necessary to have the temperatures at high levels, and for this purpose I collected such material as was available up to the end of the year 189G, when I began this compilation, and for that purpose employed the 102 balloon ascensions enumerated in Table 155, embracing all those then available for the United States, England, France, Germany, and Russia. I expressed myself cautiously regarding the result, page 750, holding the computation as preliminary to a fuller one which would be- come possible when accurate observations had been accumu- lated for the upper air temperatures, and I have therefore had an interest in examining the Berlin report of the German bal- loon ascensions.* In the first volume of this work are contained the data for each ascension, and in the Meteorologische Zeit- schrift, October, 1901, page 449, H. Hergesell gives a summary of the resulting free air temperatures. I have extracted the observed temperatures from this report, interpolated them to each round 1,000-meter level, and computed the total tempera- ture fall from the surface to the respective strata, with the result given in Table 21 and fig. 23. If the ascensions are divided into three sets, A, those reaching heights between the A. B. c D. E. F. G. II. /. 18080 60 4 68 3 71.1 115 o* 15000 59 1 6G 68 1011 0* 14000 00 9 62 5 04. 7 97.0* 13000 60 1 63 5 61.0 88. 12000 61 60.3 57.0 79.0* 1 1000 62 8 52 7 52.6 70.0* 10000 60 6 18 5 60 62 48.1 61. Of 9000 ix d 57.0 44.6 56.8 51 56 43. 4 54. 5-( 8000 47 4 51 34 9 48 7 47 48 38. 5 47. 9} 7000 38.4 44.8 31.7 39.8 38 41 -33.8 39. 6-f 6000 32 37 5 26 9 34 6 30 34 28.1 32.9 6000 20 8 25 5 32.3 23 1 27.0 25 26 22.8 26.04 4000 15.0 19. 6 28. 19.0 20.7 18 21 17.9 19.9 3000 12.9 14 3 19 5 13.0 15.4 13 16 13.1 14.51 2000 . 7.9 8.5 15.8 9.6 9.9 9 8 7.8 9.0- 1000 3 2 3.7 8.3 3.8 5.0 4 _ 4 3.9 4.3- 0000 . 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ' Wissi'iisrlial'llirhr Luftfahrten. Berlin, 18'Ji). AsKiiinim iinil I>ITSOH. 3 surface and 5,000 meters, 7?, those between the surface and 10,000 meters, and C, those between the surface and 10,000 TABLE 21. Comparison of several determinations of the total temperature change from the surface to high levels. A =49 ascensions not above 5,000 meters in manned balloons. ./? = 12 trips upward and 5 downward, not above 10,000 meters, in manned balloons. C"=9 ascensions of unmanned balloons above 10,000 meters. />= Bigelow's compiled data. Tables 156, I. IT., International Cloud Report.. E= Bcrson's mean results, Meteorologische Zeitschrift, Oct. 1901, p. 449. ,F=Teisserenc de Bort's mean results, Meteorologische Zeitschrift, Oct. 1901, p. 449. G = HergeseH's mean results. Meteorologische Zeitschrift. Oct. 1901 p. 449. Jf= Higelow's mean results, Tables 157, I. II., International Cloud Report. 7=The mean of E, F, G up to 10,000 meters, and a gradient of 9 per 1,000 meters from 11,000 to 16,000 meters. * Hergesell's assumed gradient 9 per 1, 000 meters, t Mean of E, F, G. ffft mfftem j jn> c \ \ \ \ 14000 73000 72OOO i7ooo roooo 90OO 8OOO 7OOO 6000 6000 400O 3OOO 2000 7C0O O \ \ I i \ t \ N lh V \ v \ ( \ V ^ \ \. \\ \ \ ^ \ \ \ \ \ \ ^ \ \ B \ ^ \ $ \1 4 \ \ ^ \ \ \ ^ \ \ ^ \ \ \ \ Temp H0 700 ffO 60 70 ffO' SO" 4O 30' 2O 7O' faii,C A, and B. Berlin observations with manned balloons. C. fli-rliiL oliM-rvations with unmanni'il balloons. />. Ili^elow's summary from all countries. //. Bigelow'a adopted mean result.. 7. Itcrlin adopted mean result. KK;. 'J3. Total temperature fall from the surface to high levels several systems, 54 meters, we have the following remarkable data. Class A con- tains 49 ascensions of manned balloons, and gives a tempera- ture fall of 20.8 at the 5,000-meter level; class 11 contains 12 upward and 5 downward trips of manned balloons and gives a fall of 25.5 at the 5,000-meter level,. or 5 more than cluss . I ; class G contains 12 ascensions of unmanned balloons, with a fall of 32.3 at 5,000 meters, or 11.5 more than in class A, and 57 at 9,000 meters, or 9 more than in class B. This class shows also a fall of 60.6 at 10,000 meters and G0.4 at 16,000 meters. These widely different temperature falls by classes A, B, G may possibly be explained by those who are familiar with the circumstances, but the fact deserves attention; also the other fact that there is no temperature fall between 10,000 and 16,000 meters as observed in the Berlin unmanned balloon ascensions. In column D is given the result of my own com- pilation found by taking the mean of all the figures as they stand in Tables 156, I, II; and on fig. 21 the line D is seen to fall between A and H and to cross G at the height of 12,000 meters. In his review of the Berlin ascensions H. Hergesell gave the Berson results as shown as in column E, the Teisserenc de Bort results as in column F, and his own results as in column G. He also stated the conclusion that above 10,000 meters the adia- batic rate of temperature fall in free air prevails, and this may be considered as 9.0 per 1,000 meters, as suggested by him. Column / is the mean value of E, F, G, up to 10,000 meters, and from that level to 16,000 the fall is calculated at 9.0 per | 1,000 meters, these values being plotted on fig. 21. Finally, by taking the means of the data given in Tables 157, I, II, which was derived from Charts 78, 79, as constructed to de- termine the gradients for each month in the year, we have the data of column H, also plotted on fig. 21. It is seen that my adopted result, H, lies midway between A and B, and is a fair average of all the ascensions taken in the unmanned balloons, while the adopted Berlin result, /, is 45 lower at 16,000 meters, giving at that level a temperature of 115 approxi- mately. There is a further consideration of importance to be noted in this connection. E. Rogovsky in his paper on the "Temperature and composition of the atmospheres of planets and the sun," Astrophysics, November, 1901, discusses the temperature of the interplanetary medium (according to Pouillet 142 C., Froelich 131 to 127), and assumes it to be 142 C. A fair supposition regarding the efficient depth of the atmosphere makes it 04,000 meters or about 40 miles, and hence we have the following data: llfiulii cii ;it iih'.-pln 1 1 Blgelow. IVrlin. Ti'iiiprratiirr. Neoenarj HKi'lirlll-. Tempermtara. Nrrr>s:iry gradient*. MMorv, 14,000 16,000 Sitrl'iice C. 142 55 15 a a ua C 1.8 ii. 11 100 4.4 --7.2 15 If the temperature falls from 15 at the surface to ~>~> at 16,000 meters with a gradient of about 4.4 per 1,000 meters, then to reach 142 at 64,000 meters the gradient should on the average be 1.8. It will be seen }>\ mv Charts 78 and 79, International Cloud Report, that I adopted an in- creasingly slower temperature fall with the height in the strata above 10,000 meters, in accordance with this general view. If the Berlin theory is assumed that a fall of 9.0 per 1,000 meters prevails above the 10,000-foot level, then it must some- where rapidly decrease to a very small gradient in order not to diminish the exterpolated temperatures far below that value assigned by certain astrophysicists to the celestial medium at the earth's distance from the sun. In fact the gradient becomes one-tenth of the adiabatic rate, which was actually assumed. If the temperature 260 C. is that of the interplanetary medium, as supposed by other writers, these inferences must be modified accordingly. From these two cousiderations,(l) that my temperature syst em includes the data of the highest balloon ascensions, and (2) that my gradients are in harmony with the requirements of astrophysics,' I shall let my computations on the heat differ- ence between the adiabatic and the actual atmosphere stand as they were given in my report. The accurate measurement of the temperatures in the highest strata is a very difficult process, and all efforts to secure reliable results deserve the hearty support of meteorological physicists. There are several problems whose solution depends upon the possession of such data in a satisfactory form. VII. A CONTRIBUTION TO COSMICAL METEOROLOGY. 1 GENERAL REMARKS. I have already published the results of certain computations and discussions on the subject of the direct connections between the variations of the solar output of energy, and the correspond- ing synchronisms in the meteorological elements of the earth's atmosphere. These are in particular, Solar and Terrestrial Magnetism, Weather Bureau Bulletin No. 21, 1898, and Eclipse Meteorology and Allied Problems, Weather Bureau Bulletin I, 1902, which include the substance of other minor papers related to this subject. The purpose of these studies has been, (1) to establish the fact that a synchronous connection does exist between the solar and the terrestrial forces, and (2) to derive the operation of these periodic movements so as to ulti- mately lead meteorology to a scientific understanding of the terrestrial seasonal climatic changes, and to a true basis for forecasts of weather conditions, at least one year in advance. The difficulty of reaching a correct solution of this problem is well understood by those who have worked upon it, to reside in the unsteadiness of the solar output itself, and the numer- ous subordinate transformations of the energy, through the radiation, the general and local cyclonic circulations, till it culminates in a season having certain characteristics. The material for the study consists in the variations of the pressures, temperatures, and vapor tensions at many stations in different portions of the earth, in the fluctuations of the terrestrial mag- netic field, in the changes of the spectrum energy of the solar and the aqueous vapor curves, and in the variations of the sun spots, the prominences, and the solar faculre. The magnitude of the task involved in handling this material is such as to limit the attempt to deal with it to a few institutions having these subjects specially in charge. Among them the United States Weather Bureau has been able to make some contribu- tions from time to time. SUMMARY OF THE DISCUSSION OF 1898. On pages 121-130, Bulletin No. 21, is given a brief account of an extensive discussion of the data then at hand, and the result was such as to show that there is a marked synchronism i between the solar and terrestrial variations of energy. Fig. | 24 serves to recall this fact and it shows that in the sun-spot period, 1878-1893, there was a true synchronism in the varia- tion of the sun-spot areas, the European magnetic force, which is the resultant of the two components measured on a horizon- tal plane, and the American meteorological system. The latter includes a variation of temperature at 25 stations in the north- western portions of the United States, the pressure at 10 stations, the variable mean movements of the storms in latitude and longitude, and the movement of the tracks of the cold | waves in latitude. Each of the two latter elements was derived from an exhaustive compilation of the coordinate positions of the cyclonic centers for the interval of fifteen years ending with 1893. It led me to the following summary: The increase of solar magnetic intensity is synchronous with a diminu- tion of temperature but with an increase of pressure, and this function i persists throughout every phase of the research. In spite of some irregularity, there is a distinct conformity in the gen- eral sweep of these curves, and also in the tendency to describe crests d iii-ing the same years. Indeed, the occurrence of four subordinate crests in the 11-year period suggests strongly that a 2 j-year period is superposed upon the long sweep of that periodic curve. Apparently this minor period is the basis of these seasonal variations of the weather condi- tions of the United States more than anything else, so that in long-range forecasting this period must be very carefully considered. It was for the purpose of carrying this subject one step 1 Reprinted from the Monthly Weather Keview for July, 1902. further forward that the discussion of the data summarized in this present paper was undertaken. There has been consider- able delay in completing the work on account of many other important duties. It is evident that the terrestrial magnetic field affords the data which is most available for studying the fundamental periods in this solar-terrestrial synchronism. An exact quan- titative computation for the several elements involves a very large amount of labor, and therefore it is important as an alternative to derive the periods by methods which shall give re- liable proportional variations of the elements. The ideal treat- ment is to compute the total deflecting force of the magnetic field, by using the means of 24-hourly observations of the horizontal force, the declination, and the vertical force, taking out their daily component variations in rectangular coordinates (dx, dy, dz,) and combining them into polar coordinates s, , /?. of /Sun Spots. 3,000 2000 JflOO MeanAateric Elements o 90 SO 70 +JO o -JO mencan TraxA movement in Storm TracA- movement in 47 48 .00 4.OO 4.20 4.4O a. so 3.00 S.SO 3*90 S.9O 3.70 feteorological System ZN FIG. 24. The next simpler method is to omit the vertical component, as one is tempted to do in consequence of the unreliable action of the Lloyd's balance, and turn the horizontal components, dx, dy, into polar coordinates IT, ft, on the horizontal plane. 56 Since it has been proved l>y computation that the east-west component, dy, derived from variations of the declination, practically disappears, as it should do by theory, we may adopt the variations of the horizontal component, dx, along the magnetic meridians, as the best single component for com- putation. This is all the more satisfactory because the bililar horizontal magnet is the most efficient instrument in use in the magnetic observatories, and is generally free from ob- jectionable features in its operations. I have, therefore, in this discussion, adopted the variations of the horizontal force, as shown by the 24-hourly means, on the ground that they are proportional to the total variations of the magnetic field and quite free from instrumental errors. THE MAGNETIC OBSERVATIONS 1841-1899. Accordingly, the magnetic horizontal force for the interval 1841-1899 has been submitted to a discussion, the result of which is summarized in this section. The synchronous action of the solar energy, as exhibited in the variation of the sun spots, the terrestrial aurora, the magnetic field, and several other phenomena, has been frequently developed, so that the general fact is admitted by all students, but it is now im- portant to trace out this sympathetic movement in these cos- mical forces more in detail, especially as they relate to the annual and seasonal variations in the earth's atmosphere. In the Proceedings of the Koyal Society, volume 63, Mr. William Ellis, F. R. S., has exhibited this synchronism between Wolf's sun-spot numbers and the declination and horizontal force at the Greenwich Observatory for the interval 1841-1896. (Com- pare Bulletin I, 1902, page 105.) In his diagram not only do the curves present the same large sweeps, but also the minor variations appear simultaneously in the three curves. It is for the purpose of developing yet more distinctly these minor fluctuations that the compilation of the following magnetic observations was executed. Instead of confining the study to a single observatory, it lias been extended so as to practically include the entire earth, at least sufficiently to demonstrate that the variations are com- mon to the whole terrestrial magnetic field. Thus, for dif- ferent years we studied the records at the following stations: 1841-44. Toronto, St. Helena, Hobarton." 1845. Greenwich, Toronto, Singapore, St. Helena, Cape of Good Hope, Hobarton. 1846^7. Toronto, St. Helena, Hobarton. 1848. Toronto, Greenwich, Hobarton. 1849-1870. Whatever was available, as Greenwich, Toronto, Madras, Batavia, Pavlosk, some of the data being unsatisfactory. 1871-77. Greenwich, Pavlosk. 1878-1885. Greenwich, Pavlosk, Vienna, Prague, Tiflis. 1886-1887. Los Angeles, Toronto, Greenwich, Paris, Pola, Prague, Pavlosk, Tiflis, Zi-ka-wei, Batavia. 1888. Greenwich, Prague, Pavlosk. 1889-90. Greenwich, Washington, Pavlosk. 1891. Greenwich, Prague, Pavlosk. 1892-99. Paris, Pola, Pavlosk. By thus changing the stations it becomes impossible that the peculiar action of any set of instruments, should such ex- ist, can impose a bias upon the final result. It seems to me that it makes no difference what three stations are chosen to represent the cosmical variation of the magnetic field, as indi- cated by the horizontal force which is proportional to the total force. Three stations are desirable in order to eliminate the local impulses of the field, and if they had been available I should have used the same three stations throughout, all re- duced to the C. G. S. system of units, for the sake of having rigorous quantitative results. The data of this paper limit it to showing relative synchronisms, but these are quite sufficient for our purposes in the present stage of meteorology. 1 Now called Hobart Town, or Hobart, Tasmania. The horizontal force, as given by the means of twenty-four successive hourly ordiiiates, or by a smaller number of selected hours in some cases, was considered, and the <1 /In- iini-HHil haruonUAfonx was computed either numerically or graphically. (Compare the methods of Bulletins Nos. 2 'and 21.) In some of the years the normal force was found by drawing a mean line through the monthly trace of the curve, as plotted from the daily means; in other years the daily vari- ation was computed from the numerical data contained in the published reports. In all years from 1841-99 the horizontal trace was graphically transferred to curves and distributed in the period of 26.68 days, whose epoch is June 13.72, 1887; the exact adopted period was 26.67928 days, as given in the Jan- uary Epheineris. (See Bulletin No. 21, page 120.) Therefore throughout this interval the several curves, generally three in number, are plotted on the sheets, so that the irregularities as well as the agreements are open to inspection. On exam- ining this long series of curves in succession, it is evident that a decided change occurs in the amplitudes of the variable curve with regard to the normal base line which was superposed upon each of them. In some years the curves are flat and quiet, so that the ordinates are small, and the curves are free from violent or spasmodic impulses. In other years, on the contrary, the curves sway about roughly and are much dis- turbed, great irregularities being superposed upon them. My procedure was to measure, at least proportionally, the area which is inclosed between the variable curve and the average base line and to integrate these areas in the 26.68-day period, the 11-year period, and throughout the interval 1841-99. This was accomplished by measuring these ordinates from day to day, taking the mean of those stations selected for the given day, usually three in number, and transferring these mean ordinates with their plus and minus signs to the Ephemeris Tables. For by taking the ordinates from day to day, that is to say, at frequent intervals along the curve, their si/;// /.- proportional to the area ///>// liehnvn /In- liuinn/iiii/ curve f. '.tr. 7n 21 ; 184 160 2 516 2,301 1,600 1,900 l,6i*I 2,239 2, 7XS 2,470 2,389 2,604 2,197 2,293 -2,5 -701 +300 269 +608 4*8 318 81 4-21.-, 407 333 ll-YEAU PERIOD, 1852-1862. 26-davpe- , 4.. 5.. 6.. 7.. 8.. 9.. 10.. 11.. 12.. 13.. 11.. 248 11.. 258 189 153 128 133 107 154 137 1.12 129 1854. 1855. 1856. 1857. 1858. 1859. 118 175 138 13N 179 132 ' 170 168 110 100 12.; 169 189 118 108 133 161 n- 117 91 125 127 79 104 72 86 124 126 146 107 81 90 141 112 100 131 106 93 151 IH IM 147 142 I 151 I 128 95 111 163 I6B 124 a 124 168 105 117 125 188 90 125 114 192 143 213 231 2X2 281 162 186 239 241 150 262 324 190 139 177 225 103 150 134 271 191 221 199 379 20.1 10s I'.W 330 174 151 174 224 269 273 161 168 272 2*0 168 1861. 1862. Means. 281 168 208 207 131 202 170 212 267 115 1x7 148 289 . 240 ttl 182 199 IM 111 171 194 208 169 253 281 166 187 170 183 172 176 1% 173 147 161 155 171 180 179 166 192 179 Sum* Differences. 2,315 +118 2,015 -300 1,558 -457 1,594 1,W7 +36 '+343 2, 096 +159 2,926 +830 3,016 +90 2,763 3,061 2,749 -253 !-f298 312 2,430 291 11-YEAR PERIOD,1863-1873. 26-day peri<*i. 1863. 1864. 1865. 1866. 1867. 1868. 1869. 1870. 1871. 1872. 1873. Means. 1... 163 120 89 IH 85 80 183 166 120 149 137 130 9 1 In 99 121 195 80 117 82 20! 196 232 181 150 3. 1.7.1 117 94 96 80 159 91 1X4 165 167 118 130 4 12- 102 85 105 93 129 143 201 161 210 144 136 ft. 116 103 7x os 115 1H9 217 272 175 126 141 6. lit 121 147 84 73 111 UO 21 Ki 222 202 139 143 7. 99 in.-, 148 12.1 ;i4 111 17:; 151 227 130 B. 122 151 150 140 07 :) 129 144 196 101 141 !i. IH 138 113 135 09 !XI 1.19 230 160 215 125 142 10. 131 188 89 150 118 159 150 290 141 193 107 151 11. 115 176 120 124 58 178 H 118 111 225 130 151 12. 123 146 122 66 65 128 181 268 163 22- 142 143 13. 66 H H 98 71 101 189 2.11 1'Ki 144 120 118 14 '.I.", 171 98 :- 281 186 199 177 Mint- . . 1,608 1,699 1,5.58 1,643 1,099 1,673 2,123 3,012 2,157 2,702 1,665 1,983 Differ- ences . 1,141 491 141 +85 544 +574 +450 +889 855 +605 1,097 616 11-YEAR 1'KIIIOD, 1874-1884. 26-day pe- riod. 1874. 1875. 1876. 1877. 1878. 1879. 1880. 1881. 1-2. 1883. 1884. Means, l 120 239 199 202 152 188 108 159 115 112 184 182 115 97 108 212 125 132 114 128 97 82 7.1 139 100 105 91 79 114 146 109 83 93 57 85 73 79 92 105 110 120 112 X2 95 64 10- 107 14X 113 118 90 92 98 138 70 172 146 151 141 1.12 I'.ll 168 135 108 141 110 187 170 180 160 97 127 120 102 187 161 177 156 204 159 182 194 172 134 194 135 171 215 173 160 2.10 221 278 170 219 302 2.11 171 139 145 187 1.17 264 149 238 219 160 224 165 144 421 215 264 256 295 183 344 281 486 290 141 230 241 283 223 210 192 224 197 356 IM 229 287 186 235 223 1% 233 251 203 2% 184 255 242 218 264 267 244 174 181 158 179 163 172 175 174 168 186 174 206 182 157 2 3 5 7 8 9 10 11 12 13 14 Sinn- Differences 2,091 + 426 1,587 504 1,266 1,425 2,165 321 +159 +740 2,257 2,636 4-92 +379 i 2,880 +244 3,809 +-929 3,052 3,311 -717 +259 2,449 437 TABLE No. 22. Continued. 11-YEAR PERIOD, 1885-1895. 26-day pe- riod. 1885. 1886. 1887. 1888. 1889. 1890. 1891. 1892. 1893. 1894. 1895. Means. 1 265 223 194 197 324 183 273 141 177 247 171 201 221 257 136 224 276 225 198 156 174 207 263 272 242 209 127 161 162 136 172 163 130 172 178 190 208 179 149 197 194 177 160 222 218 223 161 140 149 157 171 184 205 139 127 128 153 143 147 131 130 137 138 189 184 225 251 136 101 116 126 102 94 102 115 123 115 131 lilt 140 117 111) 158 174 164 182 287 139 140 157 178 302 162 191 214 178 261 286 298 409 278 301 330 245 211 174 255 179 231 IM 279 200 220 207 209 223 230 302 212 229 312 191 247 143 389 205 254 210 189 147 250 295 269 128 295 176 135 182 156 IM 191 200 156 181 232 191 170 247 256 164 216 181 204 197 210 211 170 185 193 198 214 206 209 179 188 2... 3 4 5 6 7 g 9... 10 11 12 13 14 !,074 237 2,709 2,391 2,533 365 318 U-142 2,092 441 1,656 -436 2,626 4-970 3,608 +982 3,061 547 3,135 2,728 +74 -407 2,745 447 Differences !-,; 18W. 26-day period. Sums Differences 1896. 152 220 177 254 273 194 2M 185 209 229 227 248 261 2,834 +106 1897. 165 188 203 195 203 144 100 115 124 113 178 218 2,285 549 1898. 152 179 260 178 153 190 121 128 208 169 190 148 166 127 172 151 249 190 157 166 134 109 103 132 145 109 102 2,369 4-84 1,920 449 Means. 161 180 214 203 197 186 191 142 155 161 172 155 177 173 2,467 Average for the whole interval, 1841-1899. 166 176 176 1-0 178 162 165 158 164 176 175 172 168 172 below this limit, and I did not wish to distort the average annual numbers with these great abnormalities. The revised Wolf's table of the sun-spot numbers, by Prof. A. Wolfer, Meteorologische Zeitschrift, May 1902, page 197, 3 has been used to give the curve of the sun-spot variations, it being unimportant for this discussion whether the observed or smoothed numbers are employed. The result of this computation, "Variation of the sun-spot numbers and the amplitude area numbers," is shown in fig. 25, the figures of Table 22 being transferred thereto. The annual sums were plotted so as to give the horizontal force curve, and the mean sums for the successive 11-year periods were plotted for the mean curve. This curve brings out three variations with extraordinary clearness : (1) The 35-year period, with maxima in 1855 and 1890, a minimum at about 1868, an- other probable minimum at about 1833, and one more at about 1903. After this exhibit there can be little doubt of the exist- ence of this long period variation, discussed by Lockyer and others, and it is certain that a continuation of this method of computation will eventually fix the characteristics of this period with exactness. The fall from maximum to minimum seems to occupy thirteen years, and the rise from minimum to maximum requires a longer time, probably twenty-two years. (2) The 11- year period is seen to be in exact synchronism throughout the interval 1841-1899 with the sun spots and the horizontal force taking the curve as a whole, but there are superposed upon it a series of abrupt minor variations, which, as stated above, it is chiefly desirable to obtain for comparison with our meteoro- s This table had been originally communicated to the Monthly Weather Review and the proof sheets sent to Professor Wolfer for re- vision, so that as published in the Monthly Weather Review, April, 1902, page 175, the figures have the full authority of Professor Wolfer, and it is believed no typographical error exists therein. ED. 58 /Sun Spots. IVb^/br's Revision Horizontal maffnetic Force . Amplitude area-numbers Fia. 25. Variation of the sun-spot numbers and the amplitude area numbers. 59 logical data. (3) These subordinate crests of energy indicate that in the rise and fall of the 11-year period there is a series of spasmodic impulses, generally one in ascending the curve and two in descending, which, added to the maximum crest itself, makes four minor crests to be superposed upon the mean 11-year curve, as mentioned in the opening paragraphs, and shown in fig. 24. In the ascending branch the successive annual changes are not equal to the mean value, and this FIG. 20. Semiannual period iu tlio horizontal force of the terrestrial magnetic Held, arranged for six successive 11-year periods. \ y \ FIG. 11. branch must evidently be considered as produced by a second- ary system of crests, even though the 11-year line is not deeply indented. The discussion of this 2|-year period will be re- sumed in a later section of this paper. If the mean values of the fourteen periods as collected in the 11-year periods and indicated in Table 22 be plotted suc- cessively, the result is as shown in fig. 26. We find that there is a distinct semiannual period in the horizontal force areas, with maxima at March 22 and September 22, and minima at June 22 and December 22, thus indicating that it depends upon the orbital relations of the earth to the sun. But, furthermore, it is noted that the same 35-year period is indi- cated within this semiannual period, since there is a distinct minimum in the period 1874-1884, and maxima in the 1852-1862 and 1896-1900 periods, as measured by their amplitudes. Also, there is, apparently, a tendency for the spring maximum to surpass the autumn maximum, whenever they are strongest within the 35-year period. We have here indicated a field of research of importance in mechanical astronomy, since it im- plies that another force besides simple Newtonion gravitation is binding the sun and the earth together. It becomes an interesting problem to discover whether these magnetic forces are capable of fulfilling the outstanding theoretical require- ments involved in the orbital perturbations of the earth and the other planets. It becomes, also, a further argument, in addition to those presented in my bulletins, Solar and Terres- trial Magnetism, and Eclipse Meteorology and Allied Prob- lems, to show that the sun is a great magnetised sphere, in whose external field the earth is immersed. On fig. 27 I have copied Chart No. 19, page 106, of Bulletin No. 21, which shows the curve of the frequency of the direct type in the 26.68-day period. Its crests regularly precede those in the semiannual orbital period by a small interval, and there must be a physical reason for this divergence, such as explained in my other papers. COMPARISON OF THE VARIATIONS OF THE SOLAR PROMINENCES WITH THOSE OF THE TERRESTRIAL HORIZONTAL MAGNETIC FORCE FOR THE INTERVAL 1874-1900. It is well understood that the variations of the sun-spot fre- quency constitute only one of the manifestations of the changes in the output of the solar energy; the frequency of the hydro- gen prominences, or of the faculse, and of the extensions of the solar corona are other forms of the display of this variable force. Indeed, there is reason to believe that the sun spots are a somewhat sluggish type of the variable impulses, although the first to be studied, on account of the ease with which the spots are observed. Since scientific processes of observation have improved of late years, it has become possible to measure the frequency of the prominences and of the faculse with pre- cision, so that a continuous record is now being made of these types of solar energy. The prominences have been observed by Tacchini since 1873 and the facujie by Hale and others for several years, so that it is now possible to add to the sun-spot record that of each of these two phenomena. The promi- nences are distributed all over the surface of the sun, and the relative frequency has been determined in 10-degree zones be- tween latitudes 90 annually since 1873, so that we possess a prominence curve of relative frequency extending through more than two 11-year cycles. Through the courtesy of Sir Norman Lockyer, of the Solar Physics Observatory, South Kensington, London, I have had an opportunity to see some advance copies of different sets of curves of a very valuable character prepared by him for a paper published by the Royal Society, in which this subject is discussed, It is gratifying to note that his work confirms my curves of 1898 and is in agree- ment with those presented in this paper. I reproduce the Lockyer-Tacchini prominence curve, which represents the mean frequency in all latitudes for the years 1874-1900. It is found at the head of fig. 28. It shows a large curvature synchronous with the sun-spot frequency in the 11-year cycle, and also a series of minor crests of a characteristic nature. Underneath 00 this curve is placed the series of minor variations which were found in the horizontal magnetic force, as shown in fig. 25, after the 11-year cycle curve has been eliminated. The re- FIG. 28. Comparison of the solar prominence variations with those of the terrestrial horizontal magnetic force and the atmospheric pressures over the entire earth. markable synchronism between these curves can not escape recognition, except after the year 1894, when an extra minor crest is developed in the horizontal force. If these two curves are compared with the 15-year systems exhibited on fig. 24, it is evident that my paper of 1898 had detected the same synchron- ism, not only throughout the curve of sun-spot frequency, but also throughout the whole European magnetic field and the entire American meteorological system. THK VARIATIONS OF ATMOSPHERIC PRESSURE OVER THE ENTIRE EARTH. In the course of my studies into this set of phenomena, in- cluding the solar and terrestrial magnetic fields and the meteorological elements, it became evident that in cosmical problems we should be compelled to deal with the variations of small quantities in meteorology, such as a few hundredths of an inch of pressure and a few degrees of temperature. It was, therefore, necessary to carefully exclude all possible sources of error due to the imperfect methods of observation and reduction, in order that variations arising from such causes might not be falsely attributed to cosmical forces. The result of such a discussion of the barometric pressures for the United States will be found in Report of the Chief of the United States Weather Bureau for 1901, Volume II. A similar rediscussion of the temperature and the vapor tension will be executed as soon as practicable. It is important that comparable rigorously homogeneous systems should be pre- pared by other weather services which possess continuous long series of records of the meteorological elements. Pending the preparation of such revised systems, I have collected to- gether a considerable number of sets or series of barometric pressures, taken in different parts of the earth, and have re- duced them to a homogeneous basis, as well as I could, from a study of the published data. There are still annoying discon- tinuities at many stations, due to changes in the elevations of the barometers. It is also probable that the instrumental errors and the methods of reduction employed still need to be thoroughly examined. Table 23, "The variations of the annual atmospheric pressure in many districts of the earth," serves to indicate, at least ap- proximately, the relations of the annual barometric pressure variations to the changes in the solar output. It contains a summary of the results in the several countries where long se- ries of barometric observations exist. It is arranged in an order which will bring out a remarkable feature of the pres- sure variations, as will be briefly indicated. The table gives the mean data for comparatively large districts; it is divided into groups and the mean pressures for these groups are trans- ferred to fig. 28, which has been already mentioned. The fol- lowing catalogue shows the stations that were employed in the discussion : Northeast China. Zi-ka-wei, Pekin, Vladivostok. Japan. Tokio, Nagasaki, Hieroshima, Osaka, Kioto. North India. Leh, Murree, Simla. Central India. Darjeeling, Lahore, Lucknow, Calcutta. South India. Pachmari, Bangalore, Nagpur, Bombay, Madras. Batavia and Mauritius. North New South Wales. Albury, Bathurst, Deniliquin. South New South Wales. Goulburn, Newcastle, Sidney. Kintberley. Kimberley, Bloeinfontein. Inland Cape Colony. Grahamtown, Lovedale, Aliwal North. Coast Cape Colony. Cape Town, Port Elizabeth, East London, Mossel Bay. North Rusxta. Archangel, St. Petersburg. East Russia. Moscow, Kathariuenburg. ftussia and Southwestern Siberia. Odessa, Tiflis, Baku. Central Siberia. Tomsk, Barnaul, Irkutsk. France. Paris. Spain. Madrid, Lisbon, San Fernando, Coimbra. South Europe. Pola, Budapest, Kalocsa, O'Gyalla, Vienna. United States. Pacific coast States, 20 stations; northern 61 TABLE No. 23. The variations of the annual mean atmospheric pressures in many districts of the earth, in units of 0.001 inch. Stations. 873. 874. 875. 87ft 877. 878. 1879. 880. 881. SS2. 883. 884. StCi. 886. 887. 888. SS'.I. 890. 891. S92. 893. 894. s'.i.-,. 8%. 1897. 1898. 1899. - 8 - 8 + 8 + 4 + 4 + 6 - 8 in 8 3 2 -32 -38 -35 -16 - 1 - 2 8 + 8 + 8 - 2 - 1 7 4 + 5 +14 +30 +16 +39 + 8 + 8 -24 + 8 -4:1 -28 21 -32 21) + 3 -12 + 7 2(1 2 6 + 8 +12 + 10 +12 + 4 7 +35 +31 +43 + 7 +20 +55 +40 +50 2 '.' + 8- + 5 +35 (W :;2 I;T +49 -28 +16 -12 8 -12 8 - 9 +11 + 2 + 5 -10 3 20 -12 16 +32 M2 IS + 16 6 + 4 + 3 +11 -13 -35 -24 + 1 + 5 + 4 + 3 75 -16 24 +40 -19 Jl e :>.-> -20 -31 28 -25 -51 49 -67 f)S 44 + 4 U +10 -20 -12 9 6 14 -20 +16 9 -39 -a? -38 -25 16 - 3 -15 20 12 12 -32 9 -12 12 -28 -17 4 -24 - 9 +10 + 7 + 10 +17 + 1 + 8 +16 12 83 + 4 - 3 + 8 +24 -21 4 -13 2 +17 + 4 -71 -67 - 8 16 41 +20 + 16 1-32 +23 +19 8 6 + 13 +21 +25 + 8 4 12 8 4 + 8 +11 + 3 + 7 +16 +22 + 9 +46 +31 +39 f!6 +25 +18 +20 +16 - 4 + 8 4 + 4 -32 + 16 5 1 4 13 + 2 -15 8 -14 8 12 -20 -16 f24 +W -13 9 - 9 II +16 + 3 - 3 -18 11 +10 +17 + 4 HO +24 -32 +16 -12 1 + 8 :,:, +32 +32 + 7 4 j + 7 + 1 +20 +13 + 6 +20 + 4 +12 +24 + 8 - u; 4 5 16 7 2 -12 5 !l 14 5 -26 -15 +43 +32 +20 + 8 +26 20 +32 + 12 +21 416 is 11 +15 +15 +31 +18 +18 +16 + 4 +10 1-12 + 4 1 a +11 -24 -12 + 1 4 + 5 + 1 4 + 5 2r, f 9 +55 12 +20 +16 +35 + 4 + 39 +26 -27 - 7 5 + 2 6 1 - 8 7 +16 + 8 1-24 + 8 + 3 1C, 211 -20 + 7 +12 i:; 28 +11 8 +17 + 7 + 4 211 + 4 t- 8 1 +12 82 12 -11 -15 5 + 8 -20 12 -33 -31 15 +16 + 6 i-20 n - 5 + 7 - 8 + 8 + 5 +15 +11 +13 +38 +11 +11 +20 +55 +24 +16 +28 +31 -43 20 -16 26 2 + 5 jj 6 1:1 4 +16 +20 +18 - 4 8 3 3 + 2 - 8 12 2 2 1 +12 29 14 +18 -85 -47 + 8 32 -27 +39 28 +20 + 10 + 1 - 6 1 + 1 5 1 2 2 - 8 12 + 2 + 4 -12 + 7 + 8 + 19 U +12 r 3 +42 f44 +43 +34 + 4 -18 + 7 - 8 -55 -16 -24 -26 8 12 + 1 16 +11 + 4 +24 + 8 + 4 + 5 -20 8 14 +24 +13 '.I + 8 12 +17 +12 +26 +30 +28 + V +27 + 2 12 +79 +51 + 8 +43 +45 +12 +20 -12 + 7 15 +16 +22 + 8 + 6 11 12 + 2 + 8 +12 111 - 8 21 9 11 3 1 + 2 - 1 7 4 23 5 15 14 +47 1-20 +28 -39 + 14 H6 -16 + 16 + 5 + 16 +14 +20 +12 +11 1 +12 +12 +20 +28 +24 + 4 + 8 211 111 + 17 t24 II +15 +54 27 +41 14 + 3 + 5 - 2 +20 +36 -20 I) +24 + 12 +35 425 - 7 5 + 7 + 1 +15 + 6 + 3 8 4 - 6 - 4 8 + 6 +24 9 -12 -16 4 - 6 -23 -15 -15 -11 24 -17 - 8 +36 -12 +43 +15 -32 -39 -16 -29 + 6 + 8 + 2 211 + 4 - 8 + 6 + 5 + 8 + 8 + 8 + 4 1- 8 -14 1- 6 - 6 4 +10 + 1 -36 -47 -42 - 3 11 -13 9 -47 Hi -16 +16 -16 +20 4 +12 + 9 + 9 18 12 -32 21 -16 19 16 +24 +24 +24 +12 + 16 in 8 HI + 4 -22 - 3 - 9 3 ii 5 + 2 2 - 2 -16 - 8 + 12 -20 - 8 Hi +20 +28 +21 + 8 5 11 12 +12 +17 + 9 + 6 +16 + 8 -12 8 13 + 3 + 2 -13 - 1 + 7 - 3 + 2 + 3 - 3 + 3 + 1 +24 -12 -24 +20 + 2 -43 -47 M 44 + 8 HI 12 10 + 6 .8 7 + 2 4 - 8 6 + 12 +18 + 5 + 5 2ii + 14 +10 + 7 - 2 + 3 +12 g +15 +10 +59 ::i; +12 8 +25 +51 +35 +16 +34 - 4 + 5 + 8 + 6 + 9 +10 + 1 ? +24 t-16 + 7 - 7 + 8 + 7 + 5 + 1 + a 4 -11 + 6 - 3 4-63 89 -1- 4 + 24 +33 +20 +24 + 16 +20 + 7 + 12 + 6 +11 + 8 + 2 + 7 12 - 8 1 -16 15 -12 13 11 21 -13 17 9 2 + 2 3 +20 +16 +24 4 + 14 +32 +12 -fc!5 1 +12 + 1 11 - 3 - 3 - 1 - 1 -12 - 8 +14 - 3 +12 + 12 -'2 + 4 + 19 +18 +14 43 -24 20 +24 16 'IT a + 16 + 4 + 1 4 3 + 2 +11 + 4 + 2 - 4 - 3 : IT 7 VI + 4 - 6 + 9 - 2 + 4 -24 -20 +28 - 3 +39 +20 +12 +24 + 3 +55 -12 -20 -12 + s +24 +12 + 4 US +22 Paris -12 +12 +15 -15 1 -10 1 - 2 - 4 16 -10 +28 +19 +34 +31 ,2:1 12 +20 +16 + 8 + 4 + 9 + 9 + 8 +20 +14 West Gulf States North Yt hui tir States -12 -12 + 8 + 8 8 8 Plateau, 33 stations; southern Plateau, 19 stations; Lake re- gion, 31 stations; west Gulf States, 41 stations; North Atlan- tic States; 26 stations; South Atlantic States, 32 stations; total number of United States stations, 202. North Argentina. Villa Formosa, Corrientes, Salta, Tucuman, Santiago, Goya, Hernandarias. Central Argentina. Cordoba, San Juan, Parana, Rosario, Carcarana, Estancia San Juan, Buenos Ayres, Chacra de Ma- tanzas, Bahin, Blanca, Colonia Chabut. In all cases the mean annual pressures were extracted from the observatory reports; these were reduced to the same elevation of the barometer, usually that for 1899, and all known corrections were applied. The mean for the homogeneous series was com- puted and then the variation of each year from this mean, the result being always changed, if necessary, into units of 0.001 ; inch in the English system. These annual variations were plotted as curves on sheets for the several countries, so that the several districts could be studied for their characteristic types. The stations were finally grouped as indicated in the the catalogue, and the larger district means, including about all the region having the same type of curve, were transferred to fig 28. It was very interesting to study these local curves, and to note that the same pressure variations in fact prevail over very large districts of the earth, though varying from one region to another. The variations were also transferred to charts of the earth, one for each year, and it was found that while there is an irregularity from year to year, it was possible to discover some very suggestive features. I regret that these charts can not be reproduced in this connection. Some years show that in North America and South America the annual pressure prevails in excess, or that the variation is positive, as 1874, 1875, 1883, 1890, 1892, 1897. Others show that the en- tire Northern Hemisphere is in defect as a whole, as 1876, 1878, 1879, 1885, 1887, 1893. Others show the Northern Hemi- ispliere to be in excess, as 1883, 1896, 1897. Other years are more irregular. I have the impression that there is a west- ward movement of the defect in pressure, or of the negative residuals; and that there are similar groups separated by in- tervals of seven or eight years. This subject will require an exhaustive study by meteorologists in the future," and much valuable information will be extracted from it. If the -positive values of the pressure variations be added together for each year, and also the negative values by them- selves, the result may be indicated as it is plotted in the curves of fig. 29. The upper curve is for the positive and the lower for the negative summation, but these curves show, since they rise and fall together, that these values do not cancel each other. The curves match fairly well with the prominence curve, and I take it to mean that some external force is at work to raise and lower the total atmospheric pressure by a small amount from year to year. It is probable that a more rigorous discussion would eliminate certain distortions of this curve, and show that it synchronizes very closely with the curve of the variations of solar energy. If this proves to be so, it raises some exceedingly interesting questions in cosmical me- teorology. FIG. 29. Positive and negative pressure variations over the earth as a whole for successive years, on a scale of relative numbers. It is interesting to compare the results of this series of an nual variations, 1873-1899, with those of the series, 1874-1884, studied by H. H. Hildebrandsson,* the latter, however, extend- ing the details to the monthly values. The data of the Barome- *Quelques recherches sur les centres d'action de 1'atmosphere, par H. H. Hildebrandsson, Stockholm, 1897. 62 try Report make it possible to do tliis readily for the United States with little additional labor. Returning to tig. 28, if we compare the successive pressure groups with the prominence curve, it will be seen that India imd southeastern Asia are in very close synchronous agreement. 'I'll is synchronism extends also to New South Wales, the Indian Ocean, and even to south Africa. In Siberia and Russia the synchronism begins to break a little and seems to be trans- ferred somewhat toward the right, although this may be due in part to defective data. In Europe and in the I'nited States, while the same curve is developed as to the number of the maxima and minima, the synchronism becomes more irregular. In South America, on the other hand, the synchronism is re- sumed very distinctly, but the fin/in inn! tin- I-'.naliTn //< nii.