W. U. 8. DEPARTMENT OP AGRICULTURE, "WEATHER BUREAU. STUDIES ON THE METEOROLOGICAL EFFECTS IN THE UNITED STATES OF THE SOLAR AND TERRESTRIAL PHYSICAL PROCESSES. Reprints from the Monthly Weather Review, December, 1902, January and February, 1903. BY FRANK H. BIGELOW, M. A., L. H. D., PROFESSOR OF METEOROLOGY. PEEP ABED UNDEb THE DIRECTION OF WILLIS L. MOORE, CHIEF U. S. WEATHER BUREAU. WASHINGTON : ATHER BUREAU 1903. W. B. No. 290. U. S. DEPARTMENT OF AGRICULTURE, WEATHER BUREAU. STUDIES ON THE METEOROLOGICAL EFFECTS IN THE UNITED STATES OF THE SOLAR AND TERRESTRIAL PHYSICAL PROCESSES. Keprints from the Monthly Weather Review, December, 1902, January and February, 1903. BY FRANK H. BIGELOW, M. A., L. H. D. PROFESSOR OF METEOROLOGY. 10635 PREP ABED UNDER THE DIRECTION OF WILLIS L. MOOEE, CHIEF U. S. WEATHER BUREAU. WASHINGTON: WEATHER BUREAU 1903. (. Errata I. The semidiurnal periods in the earth's atmosphere The double and single diurnal periods The solar radiation Radiation function in the normal spectrum Remarks on the solar constant The terrestrial radiation Explanation of the formation of the two typos of diurnal periods II. Synchronous changes in the solar and terrestrial atmosphere General remarks Distribution in longitude Distribution in latitude Variations in latitude in the 11-year cycle III. The structure of cyclones and anticyclones on the 3500-foot and 10,000-foot planes for the United States. . . . Examples of selected cyclones IV. The mechanism of counter currents of different tempera- tures in cyclones and anticyclones , The Weather Bureau cloud observations The general circulation The local circulation in cyclones and anticyclones The isobars and stream lines on the sea-level piano, the 3500-foot plane, and the 10,000-foot piano The mechanism in cyclones and anticyclones Comparison with other observed configurations The interaction of three thermal currents Examples of the interaction of abnormally cold and warm strata General results stated , I. Table 1. Energy spectra at solar temperatures reduced to the distance of the earth, expressed in units of gram calories per square centimeter per minute. 2. Energy spectra at terrestrial temperatures, ex- pressed in units of gram calories per square centimeter per minute II. Table 1. Moan observed distribution in latitude during the 11-year solar cycle. Solar prominences 2. Mean observed distribution in latitude during the 11-year solar cycle. Solar spots and facultc . . . 3. Italian observations. Observed mean monthly dis- tribution of the solar prominences 4. Observed mean monthly distribution of the solar spots 5. Observed mean monthly distribution of the solar facula; IV. Table 1. Pressure and temperature gradients in English measures. Fall of pressure in inches per 100 feet 2. Summary of the data for the Cottage City water- spout, August 19, 1896 Page. iv 1 1 2 3 3 7 9 9 9 11 14 20 21 25 25 25 25 25 32 32 34 35 37 12 14 15 15 1(> 35 36 ILLUSTRATIONS. I. Fig. 1. Diurnal variations of the meteorological elements in the atmosphere at the surface of the earth 2. Diurnal variations of the meteorological, electrical, and magnetic elements in the atmosphere at some distance above the ground 3. Energy spectra at solar temperatures reduced to the distance of the earth 4. Energy spectra at terrestrial temperatures 5. Illustrating the formation of the double and single diurnal periods of the absolute humidity II. Fig. 1. Comparison of the total sun-spot area, 1854-1891, with the magnetic curves in the 26.68-day period. . . . 2. Observed variation of the relative frequency of the solar prominences in 10-degree zones 3. Mean variation in the distribution in latitude during the 11-year periods of the interval 1872-1900 . . . 4. Movement of the maximum point of relative fre- quency in latitude during an 11-year cycle of the solar prominences, spots, and faculte III. Chart 1. Sea level (January 2, 1903) 2. 3500-foot level (January 2, 1903) '. 3. 10,000-foot level (January 2, 1903) 4. Sea-level components, (January 2, 1903) 5. 3500-foot level components, (January 2, 1903) .... 6. 10,000-foot level components, (January 2, 1903) . 7. Sea level (January 7, 1903) 8. 3500-foot level (January 7, 1903) 9. 10,000-foot level (January 7, 1903) 10. Sea-level components, (January 7, 1903) 11. 3500-foot level components, (January 7, 1903) .... 12. 10,000-foot level components, (January 7, 1903) . . IV. Chart 13. Sea level (February 7, 1903) 14. 3500-foot level (January 7, 1903) 15. 10,000-foot level (February 7, 1903) 16. Sea level (February 8, 1903) 17. 3500-foot level (February 8, 1903) 18. 10,000-foot level (February 8, 1903) 19. Sea level (February 27, 1003) 20. 3500-foot level (February 27, 1903) 21. 10,000-foot level (February 27, 1903) 22. Sea-level components, (February 27, 1903) 23. 3500-foot level components, (February 27, 1903) . . 24. 10,000-foot level components, (February 27, 1903). Fig. 25. The formation of local anticyclones and cyclones in the general circulation about the poles 26. The vectors of motion and their components in anticyclones and cyclones at the 1000-mile and 3000-mile levels 27. The stream lines at cumulus levels for cyclones and at cirrus levels for hurricanes 28. Scheme of the distribution of the eastward drift by the penetration of a cyclono vortex into the upper strata IU 10 13 17 20 20 20 21 21 21 22 22 22 23 23 23 26 26 26 27 27 27 28 28 28 29 29 29 31 33 33 ERRATA. Page 33, column 1, description. of fig. 26, for " miles " read "meter " in both cases. Page 33, fig. 27, column 2, transpose the legends of figs. I and II, but not the numbers, iv STUDIES ON THE METEOROLOGICAL EFFECTS OF THE SOLAR AND TERRESTRIAL PHYSICAL PROCESSES. I. THE SEMIDIURNAL PERIODS IN THE EARTH'S ATMOSPHERE. THE DOUBLE AND THE SINGLE DIURNAL PERIODS. The problem of accounting for the well known semidiurnal periods in the meteorological elements, barometric pressure, vapor tension or humidity, and electric potential, as observed at the surface of the earth, is still awaiting its complete solu- tion, but since additional information on the subject has been obtained in the past few years through the different kinds of observations in the strata at higher levels above the ground, this is sufficient reason for bringing the subject before this section 1 of the American Association for the Advancement of Science. Fig. 1 shows the average curves deduced from the surface observations, as they have been repeatedly made in all parts of the tropical and temperate zones. 2 There are two minima and two maxima, the first minimum at about 4 a. m., the second at about 4 p. m. ; the first maximum at about 10 a. m., and the second at 8 to 10 p. in. If the sun is supposed to rise and set at 6 o'clock, this indicates that the diurnal atmospheric processes lag several hours behind the hour angle of the sun, just as the seasonal processes lag about forty or fifty days behind the annual temperature changes. Since this retardation occurs chiefly through the slow radiation and convection of the atmosphere, just as the annual tempera- ture wave lags in penetrating the ground through its slow con- duction, so therefore, these retardations in the diurnal elements may become the means of calculating the coefficients of con- ductivity and convection in the air. Now it is to be noted that while the pressure, vapor tension, and electric potential give a decided double period, the diurnal actinic radiation from the sun shows only a small midday depression, and the temperature none at all, for this is a curve with a single maximum at 3 p. m. and a minimum at 4 a. m. This suggests the problem to be resolved, namely, the occurrence of single and double diurnal periods at the same time in the lower strata of the atmosphere. In past years, before it was recognized that the single period prevails throughout the atmosphere, except in its lowest layers, efforts were made to account for the surface double period in two ways : (1) by referring it to a dynamic forced wave involving the entire atmosphere, as was done by Lord Kelvin, and (2) by seeking to explore the possible connections between the observed waves and the manometric waves due to temper- ature effects in the lower strata. The first of these theories must be abandoned for weighty reasons: (1) because the double wave does not exist throughout the atmosphere, as has been stated, but is confined to the lowest strata; (2) because the double wave system breaks at the latitudes CO north and south, and reappears in the polar zones at right angles to that system, 3 with a change in the phase of 90 ; and (8) because there is no known physical principle requiring the existence 1 Road before the Physics Section, B, of the American Association for the Advancement of Science at the Washington, D. C. , meeting, Decem- ber 28, l'M'2. 2 Compare pages 120 and 121 of my paper, Eclipse Meteorology and Allied Problems, Weather Bureau Bulletin I, 1902. 3 International Cloud Report, chapter 9. of any semidiurnal forced wave system. The second theory is not satisfactory because it has been found impossible to estab- lish any positive synchronism in its details between the tem- perature changes and the corresponding diurnal variations of pressure due to manometric heat effects. Dr. Julius Hann for years sought to explain the phenomena along these lines, but was obliged to abandon the attempt and to accept Lord Kelvin's dynamic wave theory for want of anything better at hand. FIG. 1. Diurnal variations of the meteorological elements in the at- mosphere at the surface of the earth. Like so many other scientific problems which are difficult of solution, the trouble apparently lies in the fact that the neces- sary observations have not been made in the right place. It was supposed that the variations noted at the ground were common to the adjacent strata up to considerable heights, but since meteorologists have succeeded in getting some upper air observations, this supposition turns out to be contrary to fact, as is indicated by tig. 2. Figure 2 is based on data that are now easily accessible, and we need not quote the authorities in detail. Generally speaking, when we go upward from the surface of the ground into the atmosphere, all the double diurnal periods become single periods, and this occurs at a comparatively low elevation. Thus at the top of the Eifel Tower the double periods greatly Mid 12, 1456789 J)lll f},; u, Duirna //-?/ / s; o/' TensiQ, fW rfAf'tff/ff'/f _J}u7*nfz TWtricJGrTiporten(& tTr. JSlectric^ J'p. S34SG7S9X i'-l- i ' Jtadiccti ofthe&t^. X "N^ \/ \ llMid. FIG. 2. Diurnal variations of the meteorological, electrical, and mag- netic elements in the atmosphere at some distance above the ground. weaken or entirely disappear, and at the elevation of one or two miles, where the convectional ascents of the aqueous vapor contents of the air cease to form cumulus clouds, only the single period seems to exist. Thus the truncated actinometer curve with serrated top, fig. 1, becomes the parabolic curve, fig. 2, even at the surface when observed in very dry atmos- phere ; the barometric pressure curve and the vapor tension or the absolute humidity curves synchronize with the surface temperature curve, which itself retains the single period as high up as any diurnal variations occur, and the electric potential fall becomes a single period curve at surprisingly short dis- tances above the surface. Finally, in the temperate zones the diurnal wind components, and the magnetic deflecting vectors of the earth's magnetic field, not only agree together as vectors constituting a single system, but they also synchronize in their turning points and phases with all the other elements just mentioned. It is impracticable to go through a full descrip- tion of the local exceptions to the general conditions, but they form a most interesting study for-the meteorologist who keeps in mind their significance in connection with the great cos- iiiicnl problems in physics. Enough has been said to show that we need to fix our attention upon the cause of the trans- formation of the double period into the single period in the lowest strata of the atmosphere. 77ie solar radiation. -In my judgment there can be but one line of argument that needs to be discussed, namely, the be- havior of the aqueous vapor in the presence of the solar and the terrestrial radiations. The water content of the atmos- phere at any elevation is determined by the temperature and humidity of the air, and therefore the unit volumes contain- ing equal vapor contents stand upon isothermal surfaces which span the Tropics in great arches, stretching from the north polar zone to the south polar zone. These vapor contents rise daily from lower to higher levels during the forenoon and midday, but sink back again during, the afternoon and evening hours. The process is well understood and it is briefly as follows: The incoming solar radiation of short waves penetrates the earth's atmosphere, with depletion of the short waves by selective reflection, and of the long waves by the absorption in the aqueous vapor; the earth's surface is heated by the residue of the radiation, and it then radiates like a black body at its own temperature, which being relatively low limits the outward radiation to much longer terrestrial waves than the incoming solar rays. The heat received at the surface also evaporates the water of the surface, heats the lower strata, and raises the isotherms by convection currents as well as by radiation, till at the average elevation of 1000 to 2000 meters the vapor tends to condense or actually forms the visi- ble clouds. The outgoing radiation is also depleted by aque- ous vapor absorption, and this with greatly increased vigor at the level where the water vapor turns into liquid water in the first stage of condensation. We have, therefore, a daily rise and fall of the vapor in the lower atmosphere, and it is the behavior of this vapor blanket which must be studied carefully to account for the transformation of the double daily into the single daily periods described above. But it will be desirable to examine a little more fully the peculiarities of the solar and the terrestrial radiations before going on to our conclusions. Let J = the radiation from any single spectral line of a black body. <7 m = the maximum radiation occurring in the spectrum of a black body. J a = the total radiation throughout the whole spectrum from a unit surface of a black body. /i = the wave length corresponding with /. / m = the maximum wave length corresponding with .7" m . Tj = the absolute temperature of the emitting body. Tj = the absolute temperature of the absorbing body. A = the solar constant or the value of J" o at the distance of the earth from the sun. R = the Tadius of the sun in kilometers. d = the distance of the earth from the sun in kilometers. Then we obtain by the Wien-Paschen formulas in units of gram calories per on 2 per second, per minute, and per day, respectively, the following equations: Radiation function in the normal xprctrum. I. Radiation from a single spectral line in gram calories per cm 1 . 9.292 x 10 s Gr. Cal. Logarithms. 0.96811 5.74626 8.90462 4.16002 3.79780 a iflfiiQ 20 / 2TM\ cm 2 , second. #uo " 2 ) 1.277xlO- 12 c 2 4 1.277 x 1Q- 12 (14455) 4 1 ~ 6 6 = 9.292 x 10 s per sec. = 5.575 x IO 5 per min. = 8.028 x IO 8 per day. c, = 5 x 2891 = 14455 cW= 14455 x 0.43429= 6277.4 II. Total radiation of a black body. 1 O77 sx 1 H 12 / 7'< T 4 \ ' ' i-vciv oof = 7.6G2 x 10- U (T, 4 r/) " per miu. = 1.1033 x IO- 1 (T, 4 TJ) " per day. 9.8843420 13.0427020 The solar constant A = .T x IF x 273 = O.OSDIMH! x 7535 * Since ji (sun) = 10333 x 27.fi = 285185, it follows that 273 x 27.0 = 7535, is the absolute temperature of the photo- sphere. It- was found that the rate of change of temperature from the photosphere vertically outward seems to be rather small, -,. = 0.013 per 1000 meters, that is, about 300 from the the photosphere to the top of the inner corona, and this would indicate that we do not have in the sun's upper atmosphere such extremes of temperature to deal with as Ekholm's formula requires. But if we assign so high a temperature as 7535 to the photosphere, the depletion by scattering as shown by the diagrams of fig. 3 must be much greater than usually assigned, as is evident by comparing the curves, and we must also infer that the solar constant is really large in order to correspond to this temperature, namely, about 4.0 gram calories per square centimeter per minute at the outer limits of the earth's atmosphere. In the earth's atmosphere selective scattering takes place on the molecules of the constituents of the air, especially in the lower strata, and absorption occurs throughout the shell occupied by the aqueous vapor, but also chiefly in the lower strata. It is again difficult to assign the relative parts due to scattering and absorption, respectively. Prof. F. W. Very contends that the aqueous vapor of the higher strata first attacks the incoming radiation and depletes it very consider- ably and thus raises the temperatures of the high strata. Our international cloud observations, and the direct temperature readings in balloon ascensions seem to sustain this view. But Ekholm argues from the heat content of the atmosphere, as- suming the solar constant of 3.0 calories, as follows: Solar constant = 3.0 calories per minute . 40 per cent absorbed = 0.40 x 3.0 Inward. (1). The air receives one-fourth of this and holds it. 432 1440 (2). Conduction to be neglected .... (3). Convection to be neglected .... Outward. (4). From vaporization of aqueous va- 3.00 1. 20 : 0. 30 0.00 0. 00 por 1G4 1440 = 0. 11 (5). Radiation from earth = 50 per cent, where the surface receives ,-. i of 3.00 = 1.00 ' = 0. 07 1440 Total received per minute 694 = 0. 48 1440 This corresponds to a mean temperature of the air 8.6 C., while the observed mean temperature is 17.0 C., or too low by 25.6 C. Ekholm says: " It follows that the supposed great ab- sorption of heat by the atmosphere does not take place. But we must admit that the atmosphere absorbs directly only a small fraction of the insolation, and that it is chiefly warmed indirectly from the earth's surface." In a word, the aqueous bands absorb some little heat, while the air is nearly diather- manous to the rest of the energy spectrum. I shall, however, venture to raise the following inquiry. Ekholm seems to have assigned certain percentages for absorption, which of course are in the nature of a conjecture so long as the solar tempera- ture remains in doubt, and a part of the discrepancy between the mean temperature of the earth's atmosphere as observed and as deduced from the solar constant, may be explained in that way. But, furthermore, he seems to compute the total energy received 011 the basis of a twenty-four hour radiation, and to have made no allowance for the fact that the earth re- ceives only twelve hours of sunshine. The solar constant per minute when applied to the residual temperature of the atmos- phere should have this fact included, but I am not able to de- cide from Ekholm's paper whether this was done in fixing upon his percentages. I infer, in any event, that the common pro- cedure of extrapolating to the value of the solar constant on the outer atmosphere by using the spectrum throughout its entire length assigns too much weight to the short waves, which certainly suffer severely from scattering, and that on the other hand the few long undepleted waves 1.5/j. to 1.7/z which are neither absorbed nor scattered, form the proper basis for deducing the true solar constant. Judging from these data it is probably not far from 4.0 calories, and the temperature of the photosphere must be about 7500. The terrestrial radiation. If the energy line plotted on curve T = 288 of fig. 4 represents the observed earth's transmission through the air as described by Very (see Bulletin G, page 124), it seems to be in conflict with the view that the earth radiates like a black body of low temperature. The strong absorption from / = 4 /i to 8 r t is evidently due to aqueous vapor, but the much greater absorption area from ). = 12 r t to 40 /x is apparently not to be attributed to the same cause. It seems to me much more probable that the earth does not radiate these long waves like a black body, but is really deficient in them and emits freely only the waves from / = 4,u to 12, a. On the other hand Ekholm 7 has drawn the curve from ll// to 20/j. in quite a different manner, by extrapolating from Lang- ley's corrected observations on the moon's radiation, so as to follow the normal energy curve much more closely. Since no observations exist to determine this point it may still be left open to doubt whether the waves are emitted or not. If they are really emitted, then the air must have other ab- sorbing constituents that have not yet been attributed to it to satisfy Very's curve. We may now study briefly the effect of the earth's long- wave radiation upon the meteorological elements, and explain the occurrence of the double periods at the surface and single periods at the cumulus cloud levels. If the scattering effect throws back into space a considerable percentage of the in- coming radiation so that it does not reach the earth at all, on the other hand the absorption by the aqueous vapor of the terrestrial long waves tends to efficiently conserve the earth's temperatures which are high relatively to that of the inter- planetary space, and at the same time it generates a series of interesting physical processes which can be described with at least approximate correctness. A field of research of unusual importance and interest is here presented to the meteorolo- gist. The discussion of the temperature and vapor pressure observations which have been taken in the United States, during the past thirty years, is now going on at the Weather Bureau, and we hope to be able to make some further contribu- tions to this subject by extending to the further study of the cloud formations those therinodynamic processes which were applied in a few cases in the International Cloud Report. We adopt the hypothesis that aside from a moderate ab- sorption of solar radiation by the aqueous vapor in the atmos- phere, the waves pass through it unimpeded, except by scat- tering, which turns back a considerable percentage into space. The energy of the portion reaching the earth's surface is ex- pended in raising its surface temperature. This increases from early morning till midday, with a lag of about two hours due to the slowness of propagation of the physical effects into 7 Ueber Emission und Absorption der Warrae und deren Bedeutung f iir die Temperatur der Erdoberflache. Nils Ekholm, Mot. Zeit., November, 1902. the atmosphere, and then declines in the reverse order till midnight. The earth radiates in the forenoon something like a black body of gradually increasing temperature, the longest waves being possibly excluded, though their energy has not yet been mapped out beyond I = 12//.. The aqueous vapor de- pletes the outgoing radiation strongly in the waves 4/t to 8/i and probably from 12,u to 20//. It is especially to be noted that when water vapor turns to liquid water in cloud conden- sation the power of aqueous absorption is increased a hundred fold, and thus the generation of clouds forms at the same time an absorbing screen at the cumulus level which practically confines the radiation emanating from the land and the ocean to the strata within a mile or two above the earth's surface. Carbon dioxide, CO,, can absorb only its own peculiar rays, and as these constitute only a small portion of the spectrum their total effect is small compared with that of the aqueous vapor. Explanation of the formation of the two types of diurnal periods. Let us illustrate the formation of the double diurnal period at the earth's surface and the single period in the cumulus level by considering the behavior of the absolute humidity, that is the number of grams of water vapor per cubic centimeter. The first diurnal effect of the radiation from the earth is to raise the vapor content of the atmosphere from the low level occupied by it at night to a higher level during midday. This absorbing screen of water vapor, visible or not, rises and falls once daily through 1000 or 2000 meters, taken as a whole. While the warm air rises by convection from the surface to the level of 1500 meters, the vapor rises with it and endeavors to saturate the unit volumes of the higher strata at the pre- vailing lower temperatures, the depleted lower volumes being partially filled up again by fresh evaporation from the water and land surfaces. Thus, in fig. 5, which represents the humidity .Diurnal Absolute Humidify in tke Cumulus CXoual Level. Mte&t. 7p.m. ^Midn. Capacity -/or vapor contents per ettttt volume with change of tem JDiurnal 'Te FIG. 5. Illustrating the formation of the double and single diurnal periods of the absolute humidity. variations at the earth's surface and at the cumulus level, and the temperature changes at all levels up to a moderate elevation of probably 3000 or 4000 meters, we may consider the be- havior of the successive volume capacities arranged in vertical lines. There is a decrease in actual temperature with the elevation, and therefore the saturated unit-volume content decreases. The vapor sheet rises to higher levels, and this, together with the fresh supply by evaporation from the sur- face, can refill the depleted volume again, especially during 8 the forenoon hours. After the noon hour the continued in- crease of temperature gives rise to larger vapor capacity per unit-volume, represented by larger areas on the diagram which are shaded more thinly and decrease upward in dimensions. But while the rising vapor sheet keeps the upper volumes filled, the lower, which are drained by the ascension of the \\ater vapor, can not be supplied by evaporation at the surface at a sufficiently rapid rate to keep them full, because the prevail- ing surface moisture has been taken up at an earlier hour. The same remarks are true for the relative humidities. The result is that the upper volumes are always full, or relatively full, and have an increasing actual content up to the early afternoon, about 2 p. in., so that the diurnal curve at some distance above the ground has a single maximum and minimum as observed. On the other hand, while the 10 a. m. surface volumes are kept tilled, or relatively tilled, they are actually depleted in the afternoon and are not replenished by evapora- tion up to the original relative humidity of the morning, and therefore the curve shows a depression in the early afternoon, and is doubly periodic. The second maximum at the surface is due to a reversal of this process as the vapor settles back slowly to the ground during the afternoon and night. The additional lag of the evening maximum, being four hours in the evening to about 10 p. m., is due to the slow cooling of the ground after sunset, which continues to be a source of heat for several hours, and the slow conductivity of the heated atmosphere, which retains its heat even longer than the ground after the sun has set. This theory, if pursued into quantita- tive details will evidently account for the entire series of ob- served phenomena, and I hope to continue the study of this subject with such data as are now at the disposal of meteor- ologists. If we compare the areas of the complete actinometer curve of fig. 2 with that of tig. 1, as it is observed, the trun- cated portion must represent the heat energy that has been converted into work in carrying out these physical processes. Like an engine indicator-diagram, the difference between these curves can be translated as a function of the process concerned in the double diurnal periods in the lower strata, and thus become an important means of studying this function in the free atmosphere. If we could have suitable observations of the several elements at all levels up to 1 or 2 miles high, it would be a comparatively easy problem to discuss to a con- clusion. At present the serious difficulty is to secure the necessary data since we must resort to more or less indirect methods. The remaining elements may be treated for the change of period in a very few words. Analyzing the diurnal barometric pressure by volume contents we see that with the heating of the lower strata the denser air of night is replaced by contents of lower density after midday; taking into account the lag, the lower volumes are depleted and the upper are filled relatively, thus producing the two types of periods. This is entirely analogous to the barometric pressures of winter and summer wherein the summer pressures are lower at the surface of the earth, but greater at some such level as 1500 to 2000 meters, the summer pressure corresponding to that of the diurnal pres- sure in the afternoon. The later diurnal lag in the evening to 10 o'clock is a function of the cooling of the lower atmosphere by convection and radiation, and the settling back of the vapor sheet to the surface of the ground. The details of this phe- nomenon, as given in chapter 9 of the International Cloud Re- port, can all be shown to be in accord with this view, especially since the efficient vapor action caused by the lifting of the vapor sheet through radiation occurs outside the polar zones, and is greatest in the Tropics. It should be admitted that we do not yet understand the cause of the change of the phase of the diurnal barometric pressure which takes place in the polar zones. It is inferred from these considerations that since the double diurnal period is confined to a thin sheet near the sur- face, and does not extend throughout the atmosphere, Lord Kelvin's theory of a dynamic forced wave is not available for explaining this phenomenon. Dr. Harm's difficulties regarding the synchronism of the temperature with the diurnal barometric pressure will also probably disappear, because the local be- havior of the vapor sheet in dry and moist localities will impose strongly modifying conditions upon the efficient action of the surface temperatures in respect to the two types of periods. The fact that water vapor is a very powerful absorbent of given waves, and that this occurs chiefly in the cumulus level and not at the ground, indicates that it is the cloud temper- atures which must be studied for synchronism rather than those of the free air near the surface of the earth. It is evident that a large task in observations must be executed by meteorolo- gists before the details of these processes can be satisfactorily worked out. From what was written in my report on Eclipse Meteorology and Allied Problems regarding the iouizationof the atmosphere and the formation of electric potential, it becomes evident that temperature changes occur when the molecular structure of the aqueous vapor of the atmosphere undergoes modification by breaking up, at least temporarily, into atoms and ions. Since the transition from water vapor to liquid, in cloudy con- densation, marks a sensitive condition, and since it is just at this instant that the terrestrial (not solar) radiation is most absorbed, therefore all the conditions favor an excessive generation of ions and a change in the electric potential gradient. The fact that this element follows strictly the two type periods seen in the humidity and the barometric pressure makes it necessary that the absorption of energy and the ionizatiou should be resultant functions occurring together in one general process. I believe that all the complex details observed regarding atmospheric electricity will be explained along these lines. Finally, in fig. 2, it is indicated that the diurnal deflecting wind components and the magnetic deflecting vectors of the earth's field are in close synchronism through- out the twenty-four hours, but by comparing them with the diurnal radiation of the sun and the temperature it is seen that they are simply parts of the single period system which is common to all strata of the atmosphere, except the lowest, in the three elements described, namely, the barometric pressure, vapor tension, and electric potential gradients. We infer, then, that since the double period depends strictly on the con- vectional rise and fall of the vapor sheet, the magnetic field is primarily more closely connected with the effects of the solar di- rect radiation throughout the atmosphere. What we lack in this connection is a series of observations to determine the varia- tion of the magnetic components in the higher strata, which I doubt not will be found to be similar to those at the surface. In all respects it is evident that observation in the lower cloud region is as much demanded by the maguetician as by the me- teorologist, to determine the subtle cross connections between the gaseous contents of the atmosphere and the electrical and the rnagnetical variations. But it seems to me very probable that the magnetic diurnal variations are due to a set of phys- ical processes induced by the terrestrial radiation in the lower atmosphere. This may explain the fact that the incoming solar radiation does not seem to be the cause of the ionizatiou which apparently precedes the generation of the electric and the magnetic disturbing forces. If this problem can be solved in the free air, it will probably also contribute important facts regarding our general knowledge of the relations between matter and ether. It is especially desirable to note that the facts which are now known indicate that the diurnal variation of the magnetic field of the earth is strictly a meteorological effect in the atmosphere, caused by the solar-terrestrial radiation, and that the orcler of production is (1) temperature, (2) electric potential, (3) magnetic deflection, somewhat as explained in Bulletin I, Eclipse Meteorology and Allied Problems. II. SYNCHRONOUS CHANGES IN THE SOLAR AND TERRESTRIAL ATMOSPHERES. Read before Section A, Astronomy and Astrophysics, American Association for the Advancement of Science. Washington, D. C., December 28, 1902. GENERAL REMARKS. Iii my paper, "A contribution to cosmical meteorology," published in the MONTHLY WEATHER REVIEW for July, 1902, evidence was given of the fact that the variation in the solar output, as registered in the relative frequency of the sun spots, has a marked synchronism with the variation of the areas in- closed by the curves representing the horizontal magnetic force of the terrestrial field. This is of course well known from many investigations, but the special features of the paper showed that the sun spots constitute only a sluggish register of the solar activity, and that the terrestrial magnetic force exhibits a set of characteristic minor fluctuations super- posed upon the general 11-year curve. These special varia- tions reappear with marked distinctness in the solar promi- nences as measured by their observed frequency, and also in the variations of the mean annual barometric pressures in all portions of the earth. The significance of this exhibit is its indication that the pressures in the earth's atmosphere are undergoing changes in short cycles of about three years average duration, which correspond with the changes iii the external work of the sun. A further study of our meteorological records during the past few month convinces me that these short cycles are produced by modifications in the general circulation of the earth's atmosphere, which produce alternate accelerations or retardations of general movements, and that these raise or lower the average annual barometric pressure over large districts of the earth's surface. There is also a sort of surging of the atmosphere with more or less stationary configurations or structures, and these involve the so-called seasonal climatic changes of weather by which one year dif- fers from another. Thus, the regions about the Indian Ocean and South America vary synchronously but inversely; the continental and the ocean areas appear to change in an inverse manner; there seems to be a tendency to generate a great cyclic change having a period of about eight years within which the pressure excesses begin, for example in India, pass through Asia, Europe, North America, and South America back to India. This synchronism between the solar and terrestrial variations is found in the United States to hold for the pres- sures, temperatures, the storm-track movements in latitude and longitude, the cold-wave tracks, and generally for all the elements of the atmosphere. I have elsewhere sufficiently described my views regarding the causes of this synchronism, and it must be evident to all that meteorology has a great in- terest in elucidating these fundamental problems of solar physics, since our hope of making seasonal forecasts of the weather will be fulfilled only by reducing our knowledge of the complex connections between the sun and the earth to a scientific basis. I can at this time present the result of only one portion of my work in this direction, with an indication of the nature of the problems that must be solved by astro- physicists in order to perfect our knowledge of terrestrial meteorology. DISTRIBUTION IN LONGITUDE. It is desirable to study the distribution of the effects of the solar activity at the surface of the sun in both longitude and latitude, and their variations in the 11-year period. Passing BIG 2 over the subject of the true period of the sun's rotation, which is now being discussed by scientists, and which would require a longer statement than is here possible, it may be noted that whatever period is adopted for an ephenieris, the frequency numbers for spots, faculse, and prominences collected in tables will show a drift to the right or left according as the period is too short or too long. For example, if in constructing an ephemeris one adopts as the mean period of rotation that which is proper to the sun spots at latitude

164 ill 72 x:i 4H 2 sr.i; 1895 1 4 29 131 169 212 194 166 124 171 167 135 101 2(1 3 7 6 1,640 Mean 2 7 28 110 143 172 221 191 186 196 224 224 196 121 68 38 32 21 2 183 (3) 1874 9 5 24 94 84 130 150 141 125 116 161 138 82 93 44 10 2 1 415 1885 3 3 17 139 181 139 229 208 175 201 232 299 242 148 48 /> 12 2 2, 284 1896 6 3 4 37 93 141 131 100 53 89 147 151 117 92 28 9 7 3 1 211 Mean 6 4 15 90 119 137 170 150 118 135 180 196 147 111 40 8 7 4 1,637 (4) 1875 10 13 15 87 60 46 78 81 55 26 61 52 44 61 137 19 5 6 856 1886 1 9 18 48 132 152 180 172 130 141 146 139 174 116 16 4 5 2 1,585 1897 4 6 8 90 81 52 91 85 74 138 139 126 41 76 80 11 6 5 1 113 Mean 5 9 10 75 91 83 116 113 86 102 115 106 86 84 78 11 5 4 1, 185 (5) 1876 40 29 19 76 75 39 50 43 41 66 84 65 44 66 77 19 20 23 876 1887 12 15 15 99 162 161 178 136 96 134 140 192 156 287 70 9 12 3 1 S77 1898 5 9 12 17 26 47 39 52 59 62 102 89 61 79 29 13 11 9 721 Mean 19 18 15 64 88 82 89 77 65 87 109 115 87 144 59 14 14 12 1 158 (6) 1877 25 18 17 33 78 53 62 57 39 43 52 60 54 64 50 13 13 11 742 1888 8 16 25 49 117 152 99 116 75 110 155 216 220 317 176 16 15 5 1 887 1899 5 10 11 16 23 13 17 24 24 31 56 57 54 82 31 17 21 6 498 Moan 13 15 18 33 73 73 59 66 46 61 88 111 109 154 86 15 16 7 1 042 (7) 1878 1 7 3 19 34 34 13 16 17 12 9 8 35 31 8 1 3 1 252 1889 2 2 6 21 62 51 36 32 30 38 52 65 104 174 39 6 4 724 1900 5 9 16 36 30 18 19 25 27 35 31 32 31 96 CM 31 24 10 543 Mean . ... 3 6 8 25 42 34 23 24 25 28 31 35 57 100 38 13 10 4 601 (8) 1879 1 5 13 46 85 49 33 29 10 9 4 24 45 101 27 5 3 1 490 1890 3 1 19 75 66 29 22 11 15 30 69 96 185 61 1 2 685 Mean . . . 2 3 7 33 80 58 31 26 11 12 17 47 71 143 44 3 2 2 588 (9) 1880 4 21 187 128 110 121 63 26 37 70 no 119 148 177 14 2 1 1 338 1891 3 5 16 199 215 146 182 107 69 34 91 160 183 220 178 17 7 4 1 836 Mean . 2 5 19 193 172 128 152 85 48 36 81 135 151 184 178 10 5 3 1 5S7 (10) 1881 5 13 143 169 107 132 175 153 93 76 126 197 191 116 170 115 15 2 1 998 1892 23 247 137 119 172 207 136 98 124 154 252 272 183 283 62 2 1 2 472 Mean 3 18 195 153 113 152 191 145 96 100 140 225 232 150 227 89 9 2 2 235 (11) 1882 21 146 177 56 108 160 196 193 133 114 168 198 157 172 118 141 63 g 2 327 1893 10 25 29 93 187 206 158 132 149 195 229 226 138 208 242 13 1 2 241 Mean 11 128 101 43 101 174 201 176 133 132 182 214 192 155 163 192 38 4 2 284 heat energy generated by gravitational compression. It is, furthermore, necessary to free the solar data from terrestrial meteorological effects before any type of least square analysis can be properly applied. To emphasize this point more fully, Tables 3, 4, and 5, derived from the original tabulation, give the sums for each rotation or month, respectively, for the entire solar surface, by summing up the numbers found in the several zones. It is seen that in the monthly means of the prominences there is a very distinct annual variation in the number of prominences observed. This can be due only to the annual change in the Italian climatic conditions which affected the making of the observations, and it shows that the recorded frequency numbers are not free from a strong terrestrial term which must modify all discussions in solar physics, unless satisfactorily eliminated. The tables for the solar faculse show the same seasonal variation as the prominences, but less con- spicuously developed, while the sun-spot means are practically unaffected by the climatic changes. This difference must be attributed to the relative length or duration of the three phe- nomena, the spots having a life sufficiently long to bridge over the gaps covered by cloudy weather in Italy, so that the true number of spots which occur on the sun is really counted. This is true of the facultc to a lesser degree becaiise their lives arc shorter than the sun spots, and some come and go in the intervals of stormy weather without being enumerated at all. The promi- nence numbers especially are subject to loss by not being ob- served continuously, because their life is usually very brief, so that the prominences which occur in successive meridian areas 13 Fio. 3. Mean variation of the distribution in latitude during the 11-year periods of the interval 1872-1900. and are seen only on the edge of the sun can not be fully counted under ordinary observing conditions. The Kalocsa observations exhibit similar disturbances due to the conditions. If the observations of 1884-1890 be collected in a similar mari- ner to that adopted above, we find that the numbers increase decidedly from 1884, which is a maximum year, to 1890 which is a minimum year, and this is contrary to the probable course of the events. The Italian observations decrease from 1884 to 1890, and the two series are opposite to each other in this re- spect, though they give similar zonal distributions so far as the maxima are concerned. Steadiness in observing and elimi- nation of cloudy weather was therefore indispensable in order to procure reliable data for these discussions in solar physics. So far from being independent almost all solar data are mutu- ally dependent upon adjacent events, and Professor Schuster's method of the periodogram is subject to this sort of limita- tion. The same is true of almost all the terrestrial meteoro- logical elements, and generally a negative result which is de- rived from the discussion of a periodic or cyclic curve is valu- able, only when it is certain that the data conform to the analytic presuppositions, such as are laid down in the theory of the energy curve. Schuster applied his theory to the Green- 14 TABLE 2. Mean observed dixtribulion in latitude during the 11-year aolar cycle. Solar spo< and faculce. Yi'lll'v .SO LA IS SPOTS. SOLAK KAfl'L^!. 40 30 30" Ml 20 10 10 10 10 20 30 30 10 Aunual sums. Above 40 40 30 30 m 20 10 10 10 10 -20 20 30 30 -40 Below J0 Annual MIIIIS. (l) 1883 .... 1894 .... Mean . (2) 1884 1 1 1 1 21 14 11 19 15 3 2 3 1 57 71 64 92 85 89 32 41 37 21 17 19 10 23 17 3 ff 5 4 2 13 45 85 65 93 93 93 80 115 98 63 73 68 85 61 73 38 28 33 17 52 35 10 45 28 14 15 15 5 21 13 1 8 6 7 22 44 33 38 55 47 58 56 57 109 44 77 75 29 52 32 58 45 30 38 34 35 25 30 15 18 17 3 7 1 4 12 16 14 37 67 52 107 129 118 113 82 98 80 89 85 25 42 34 20 74 47 10 40 25 3 14 9 3 33 27 30 79 89 84 68 148 108 20 33 27 22 24 23 6 19 13 2 2 2 313 387 350 432 315 374 236 208 222 98 171 135 71 180 126 62 86 74 34 57 46 61 158 215 187 319 368 344 298 510 404 7 6 7 4 9 7 2 7 5 4 25 15 5 32 19 1 15 8 2 28 15 15 85 33 59 109 27 68 ISO 29 40 68 64 66 44 69 57 20 56 38 8 62 35 9 70 43 2 36 19 6 65 36 45 244 152 198 253 100 177 161 110 136 175 152 164 135 161 148 97 100 99 39 129 84 21 122 72 9 75 42 6 112 59 31 150 155 153 279 156 218 188 189 189 154 166 160 143 145 144 99 96 98 47 181 114 32 181 107 37 103 70 15 171 !)3 6 45 37 41 121 112 117 107 148 128 117 154 136 174 121 148 164 129 147 70 207 139 53 226 140 71 130 101 30 211 121 11 21 12 17 58 61 60 85 154 120 159 199 179 168 167 168 169 209 189 63 197 130 39 200 120 38 118 78 19 168 N 16 124 71 98 196 169 174 163 238 201 89 139 114 69 104 87 40 156 98 23 96 60 7 133 70 2 62 32 12 90 51 44 146 83 115 187 167 177 120 173 147 24 53 39 11 14 13 2 45 24 3 27 15 1 53 27 793 941 867 748 791 77(1 594 809 698 258 946 609 169 1,044 607 160 582 371 94 937 516 183 908 554 731 1,341 869 1, 102 923 1, 1(17 1,015 3 2 1 1 7 4 1895 .... 1 1 Mean . (3) 1885 2 1 1896 .... 5 3 1 19 10 1 15 8 Mean . (4) 1886 1 1 1897 3 2 1 6 4 Mean . (5) 1887 .... 1 1 1898 Mean . (6) 1888 1 1899 8 4 1 15 8 33 17 2 57 30 14 60 19 40 92 72 82 37 57 47 2 1 1 20 11 1 14 1 8 32 11 22 9 6 8 Mean . (7) 1889 3 8 1900 Mean . (8) 1890 .... 2 20 24 57 41 52 34 43 35 39 37 4 21 32 33 33 61 78 70 40 79 60 () 1880 1891 6 3 6 5 19 1 10 15 4 10 3 3 3 Mean . (10) 1881 6 1892 .... Mean . (ID 1882 2 1 12 6 1893 Mean . 1 1 6 3 wich magnetic declinations taken from day to day, where the hourly variation is eliminated. It can be shown that the de- clination is a component which vanishes in theory, arid exists in practise only as a measure of the feeble variations of the earth's field which are distinctly accidental and only remotely connected with the solar action. VARIATIONS IN LATITUDE IN THE 11-YEAB CYCLE. \Ve will now consider the prominences, spots, and faculse in the 11-year cycle in order to discover whether there is some evidence of a periodic variation in the latitude at which the output from the interior of the solar mass becomes visible to us. An inspection of the details of the three cycles contained within the interval of time 1872-1900, shows that there is a triple repetition of similar variations in these elements, and suggests that the mean values of the years similarly placed in the 11-year period may be taken as a close approach to the law underlying these cyclical changes. The means of Tables 1 and 2 are plotted on fig. 3. The scale denotes the fre- quency numbers as counted from the Italian observations, and the zones are indicated by the degrees at the top of the chart. Dotted lines are drawn through the systems of the maximum numbers to mark the difference in latitude at which these develop. The prominences have two distinct maxima, generally, throughout the period, except that the one in high latitudes, 60-70, nearly disappears at the time of maximum spot frequency and the one in low latitudes, 20-30, practically disappears at the time of the minimum number of spots. After the minimum which has crests in high latitudes there is a vigorous recrudescence of the prominences in two distinct belts of maxima, 20-30 and 40-5(), with a tendency to di- verge toward lower and higher latitudes; the higher varies '25 in latitude and the lower less than 10. This swing in latitude of the maximum points is accompanied by a decided variation in the number observed, as indicated by the change in the areas included between the lines of prominence numbers and the axis of abscissas. The spots and the facuhu have each only one maximum in the same hemisphere, which gradually ap- proaches the equator from about latitude 25 at the time of re- crudescence just following the maximum number. The dying 15 TABLE 3. Italian observations. Observed mean monthly distribution of the solar prominences. Rotation. 1872. 1873. 1874. 1875. 1876. 1877. Mean. 1 202 150 91 37 13 40 89 2 229 200 135 69 51 75 127 3 214 130 140 60 51 59 109 4 157 188 98 55 26 37 93 5 219 180 97 65 51 55 111 6 229 139 107 45 42 95 110 7 281 215 96 48 47 54 124 8 315 229 105 124 107 115 166 9 287 105 111 131 114 82 138 10 143 190 163 51 105 42 116 11 129 89 75 71 83 31 80 12 130 98 115 46 88 54 89 13 110 140 35 54 59 3 67 14 52 39 Mouth. 1878. 1879. 1880. 1881. 1882. 1883. 1884. 1886. 1886. 1887. 1888. 1889. January 3 7 13 45 229 95 139 104 i in lie February 26 4 71 80 242 137 186 l')7 98 1117 March 39 7 145 88 184 97 317 146 126 107 April 33 54 109 146 133 212 111 82 129 9fifi 4.Q May 31 12 81 210 183 183 237 226 162 June 27 64 146 177 269 122 237 351 174 9*V7 9(1 July 59 57 260 299 288 219 364 328 233 9Q 1 ^ J. August 22 61 137 284 249 167 399 221 162 231 999 (HI September 80 137 187 169 133 233 177 140 1R1 October 4 100 120 121 137 233 269 104 68 CO 1 ^K November 8 58 77 258 139 135 152 126 138 141 70 4.7 December 40 97 140 92 142 111 193 77 108 7U 94 Month. 1890. 1891. 1892. 1898. 1894. 1895. 1896. 1897. 1898. 1899. 1900. Mean. January 25 60 83 145 87 28 134 60 53 AK jii QO February March 27 29 170 110 95 122 214 272 141 159 69 127 155 71 69 109 42 31 38 40 13 9O 104 1 1S April 38 138 158 324 104 131 77 85 60 AK 09 May 31 98 207 143 114 141 103 84 26 18 AQ 1 IK June 63 108 330 161 178 181 125 119 77 51 QC 14.7 July 60 256 323 167 157 257 143 81 64 K9 I',S 1 UO August 82 210 296 267 167 246 105 113 78 44 ^fi September 68 220 305 185 116 178 106 143 121 76 96 149 October . 175 217 186 138 78 93 102 101 86 \f> fin November . ... 36 98 216 70 104 114 55 95 27 28 9ft December 51 151 151 155 62 75 35 54 ^fi 1m' = constant, where or = the radius and u> = the angular velocity) holds BIG- -3 18 good in this case, then we have an explanation of the cause of retardation of the diurnal angular velocity of the motions of the photosphere in middle latitudes as referred to the equato- rial or polar belts. For if ,> & l then >,<<,, and since w, is the initial rotational velocity at the equator, the angular ve- locity in middle latitudes must be less than at the equator or at the poles. This agrees with the result of the surface ob- servations. Furthermore, the equatorial angular velocity is probably that of the interior mass, or micleus of the sun, and the poles should have the same velocity, a result in harmony with that deduced from my discussion of the terrestrial mag- netic field. This equatorial and polar angular velocity gives a 26.68-day synodic period for the rotation of the sun. Finally, the middle latitudes must give a slower angular velocity and a greater period, such as 27.30 days in the belts 12 to 15. Since the mass of the sun ought not by this theorem to have in any portion of it an angular velocity less than that of the equatorial plane, it does not appear to be reasonable that the short periods of about 25.80 to 26.00 days, which several inves- tigators have announced as that of the sun's rotation derived from a discussion of several different terrestrial phenomena, can be correct. It is very difficult to perceive how there can be any basis for a period shorter than 26.G8 days; on the contrary these authors seem to find a period at least one day shorter than the quickest period that can be derived from the obser- vations and discussions of surface solar phenomena. It is very probable that the problem of the circulation within the sun must be worked out before we can hope to bring that of the rotation of the solar mass to a satisfactory understanding. III. THE STRUCTURE OF CYCLONES AND ANTICYCLONES ON THE STATES. 3500-FOOT AND 10,000-FOOT PLANES FOR THE UNITED The reconstruction of tlie theory of cyclones and anticyclones depends upon the determination of the velocities and directions of the air movements, the form of the isobars, and the distribution of the iso- therms at several planes above the sea level. My re- port on the International Cloud Observations of 1898-99 gives the result of the survey of the upper air for the vectors of motion ; this was supplemented by a series of papers in the MONTHLY WEATHEK REVIEW, January to July, 1902. My report on the Barome- try of the United States, Canada, and the West Indies, 1900-1901, has provided the necessary means for reducing the observed station pressures to three standard planes. The observational requirements of the problem will be completed by the discussion of the temperatures and vapor tensions, which has been already begun, though it will take considerable labor to finish the research. Meanwhile, it is profit- able to make use of the material at hand in a series of studies on the circulation of the atmosphere at different levels up to two or three miles above the sea level. Beginning with January, 1903, the succes- sive MONTHLY WEATHER REVIEWS will contain charts showing the mean monthly isobars on the sea-level plane, the 3500-foot plane, and the 10,000-foot plane. By comparing these pressures with the series of normal pressures given on the charts of chapter 7, Baroinetry Report, we can find the departures for each month on these three planes, and a discussion of such departures from year to year, when studied in connection with other phenomena, will have an important bearing upon the discovery of the laws for use in seasonal forecasting. Similarly, monthly temperature charts are given, and these are con- structed by means of the temperature gradients which can be obtained from the data in Table 48, of chapter 8, of the same report, by subtracting the values of t from t (sea level), /, (3500-foot), t t (10,000- foot) in succession. The latter temperatures were found by a process which eliminated the local ab- normalities contained in the observed station tem- peratures, and they have permanent value. The surface temperatures of the several stations need to be further revised, and so we can claim at present for the temperature gradients only an approximate correctness. This imperfection will not greatly in- fluence the position of the mean isotherms, but the reduced temperatures of neighboring stations do not appear on the maps quite as harmonious as we hope to make them by means of the revision just mentioned. 21 /<*> JO'- 7O" 6V Of* &) EXAMPLES OF SELECTED CYCLONES. The construction of average vectors of motion and of mean isotherms as contained in the two reports on Clouds and Baronietry produces a composite or result- ant chart, and this is of value in discovering general relations and laws of structure in cyclones and anti- cyclones. It is, however, essential to determine the conditions prevailing in individual cyclones and anti- cyclones if we wish to apply the theories of hydrody- namics and thermodynamics in detail, so as to com- pute the relations between the dynamic and thermal energies on the one hand and the resulting forces that characterize the actual storm. For this pur- pose the station reduction tables of chapter 9 have been expanded, and tables have been furnished to the several stations for practical service. By means of these the observers at 175 stations are enabled to mail postal cards daily to Washington containing the (B, t, i') at the station and the reduced values of the pressure for the three planes, respectively. With this data, beginning December 1, 1902, we have prepared daily charts of pressure for the United States and Canada on the sea level, the 3500-foot plane, and the 10,000-foot plane, and we propose to discuss this material briefly in the MONTHLY WEATHER REVIEW preparatory to making a suitable general report on the entire subject. Prof. E. F. Stupart, Director of the Canadian Meteoro- logical Office, is courteously cooperating with the United States by furnishing the daily postal cards for Canada. For the month of January, 1903, we present two cyclones that of January 2, central in the west Gulf States, and that of January 7, central in the Lake region in order to illustrate typical configu- rations of the isobars on the upper planes. It is our intention to merely mention some of the salient features of these charts, since an inspection of them will doubtless suggest their true meaning to mete- orologists better than any verbal description. They have special scientific interest from the fact that this is the first exhibit of the isobaric systems in the upper air surrounding individual cyclonic and anti- cvclonic centers. 22 January 2, 1903. Charts 1, 2, and 3 are transcripts of the isobars as derived by computation in accord- ance with the system contained in the Barometry Report. We note (1) that the closed isobars of the cyclone at sea level tend to diminish in number and intensity at the upper levels and that they finally open out into shallow, inflected curves at the height of about two miles; (2) these curves in opening out first form cusp-shaped curves, joined together by a pressure which is higher than that north or south of it, whereby one closed isobar and one long or open isobar of the same name occur above and be- low the line of the cusps; (3) the high pressures to the east and west of the cyclone diminish in area and soon fade away into the long, looping isobars of the upper strata. We now find the general normal and the local departure components of these observed isobars as follows: (1) The normal isobars for the month are copied on tracing paper in black lines, being ex- tracted from the January charts of chapter 7; (2) these lines are laid over the observed isobars, and a new system of lines is constructed by tracing the diagonals of the quadrilateral figures thus formed, and these new lines are shown in red lines on Charts 4, 5, and 6. These curves give us in tenths of an inch the values of the local pressure disturbances which deflect the normal isobars, and they therefore measure the pressure effect of the local cyclone proper. The causes that produce these local departures of pres- sure must be the same as those that produce the cyclone itself. We may assume that the upper vec- tors of motion are parallel to the observed isobars, and we conclude that in this particular storm a cur- rent of air from the southeast is flowing upon the United States ; that a part of it curls to the left and enters the vortex of the closed isobars, which gen- erates a vertical component, and that the rest of this stream flows away by uniting with the normal general circulation. There seems to be also a minor stream of air from the northwest, and a portion of this enters the vortex. w AJSt-_j>Jt!__ x- as- *i_ E < 23 .Iitituari/ 7, 1002. Charts 7, 8, and 9, are trans- cripts of the reduced pressures obtained in the same wav; Charts 10, 11, and 12 give the normal monthly isobars, and the local isabuormals of pressure of a typical cyclone central in the Lake region. Here, again, the central closed isobars open out first into cusps with a feeble high pressure bridge, and then into loops which become flatter with the height, and finally disappear by merging in the normal lines. It is apparent that on the west side of the center a strong current from the north is chiefly concerned in building this cyclone, a part of it curling into the central vortex which has a vertical component, the remainder escaping eastward into the normal circulation. By comparing the vectors of Chart 23, International Cloud Report (blue arrows), we see that those vectors conform very closely to these iso- bars, and that they are generally parallel to each other. The component vectors of figs. 6 and 7, MONTHLY WEATHER REVIEW, March, 1902, show that the deflecting vectors also follow closely parallel with the isabuormals of pressure. The agreement of these three independent researches assures us that the analysis of the structure presented in my previous papers harmonizes closely with the observed facts. It is evident that if a series of coaxial circles about the center of the cyclone be superposed upon a system of parallel lines representing the general isobars, we should obtain resulting curves similar to those that have been produced by reduction of the pressures from the surface data. This involves an equation of three degrees and three characteristic areas, one central, one above the cusp lines, and one below them. (Compare fig. 11.) This analysis will therefore enable us to pursue the mechanics of cy- clones into remote details, and so we shall at length be able to compare theory and observation with much precision. The subject will be further illustrated and discussed in later papers. IV. THE MECHANISM OF COUNTERCURRENTS OF DIFFERENT TEMPERATURES IN CYCLONES AND ANTICYCLONES. THE WEATHER BUREAU CLOUD OBSERVATIONS. The report on the international cloud observations of May 1, 1896, to July 1, 1897, Report of the Chief of the Weather Bureau, 189899, Vol. II, contained an outline description of a theory of the structure of cyclones and anticyclones, which was thought to be indicated as the probable interpretation of the motions of the air in cyclones and anticyclones. It was evi- dent that a more complete insight into the mechanism of this type of motion in a fluid under atmospheric conditions would be afforded by the construction of systems of isobars on at least three planes having different elevations. For this pur- pose the sea level, the 3500-foot level, and the 10,000-foot level were selected, and suitable reduction tables have been made as described in the report on the barometry of the United States, Canada, and the West Indies, Report of the Chief of the Weather Bureau, 1900-1901, Vol. II. Since December 1, 1902, we have received daily reduced pressures on these planes from the regular stations of the United States and Canada, and the corresponding charts have been drawn with care by Mr. George Hunt of the Forecast Division. A definitive treat- ment of the problem evidently requires charts of the isotherms on the same planes, but it will not be necessary to wait for the completion of our discussion of the temperatures, because we have already obtained the approximate gradients needed in a preliminary study of this question. It is proposed to sum- marize the present status of the research, previous to working out an analytic treatment of the mechanism of tornadoes, cy- clones, hurricanes, and the general circulation, from the data now in possession of the Weather Bureau. THE GENERAL CIRCULATION. The circulation of the atmosphere has been analyzed by meteorologists into (1) the general cold center cyclone, which covers a hemisphere of the earth from the pole to the equator, and (2) the local warm center cyclones and the anticyclones, which drift eastward in the temperate latitudes. Ferrel worked out his well-known canal theory for the general cyclone, with northward motions in the upper and southward motions in the lower strata of the atmosphere. This theory was adopted by Oberbeck and carried out with difference of details, and it has been the prevailing view till the discussion of the Weather Bureau observations of 1896-97 in the United States proved that it is incorrect and must be greatly modified. No northward movement of importance exists in the upper strata, and there is no calm belt separating the eastward drift from a westward current in the polar zone. In the Tropics the motions are substantially those deduced by Ferrel, and they result naturally from the equations of motion on a rota- ting earth heated in the equatorial belt. Professor Hilde- brandsson's report on the International Cloud Observations confirms these facts for Europe and Asia generally, and there- fore we conclude that they are fundamental, and that the canal theory must be finally abandoned. The Weather Bureau report showed that the incoming solar radiation of short waves heats the atmosphere only a little, but that it does heat up the earth's surface. This latter radiates much longer heat waves at terrestrial temperatures, and thereby the lower strata of the atmosphere are heated up by convection currents to a distance of two or three miles. This heat energy is very vigorous in the BIG 4 Tropics, and produces currents of warm air which leak outward and flow toward the poles only in the lower strata instead of in the high levels, determining by their motion the local distribu- tions of pressure near the surface of the earth. By an analo- gous process cold currents flow from the higher latitudes toward the equator at low or moderate elevations. These counter currents meet in the middle latitudes, as over the United States, and we have now to study the action of the resulting mechanism. THE LOCAL CIRCULATION IN CYCLONES AND ANTICYCLONES. In order to account for the phenomena observed in cyclones and anticyclones, there have been two distinct lines of discus- sion, (1) the thermodynamic theory and (2) the hydrodynamic theory. The former required a warm central current of rising air to form a vortex. The Espy hypothesis, that the heat neces- sary to drive the vortex is derived from the latent heat of con- densation evolved in changing aqueous vapor into water of pre- cipitation, has been strenuously maintained by many students. There are, however, numerous serious objections which can not be set aside, and these have caused during the past few years a general abandonment of the theory as a true account of the primary cause of cyclones. Ferrel worked out his theory by means of a special type of vortex with closed boun- daries, but this does not, unfortunately, in the least satisfy the observations, and it has been rejected as the result of such discrepancy. The equations of motion admit of solution by a different vortex, which more nearly conforms to the require- ments of the problem, but no driving force sufficient to sustain a cyclone was discovered before the one suggested by the Weather Bureau research, so that up to recent times the local vortices remained to be fully accounted for on a sound physical basis. The second theory of the local circulation considers it as simply a question in hydrodynamics, where the local thermal force is subordinate to the driving action of the great whirl which gyrates about the pole as a center. In this view the eastward drift simply curls up at places and forms eddies in the great current, and they are borne along by it. This seems to be the general idea adopted by Professor Hil- debrandsson in his recent report. There is undoubtedly a certain amount of dynamic action which enters into the con- struction of cyclones, but there must also be a powerful me- chanical force derived from the effort to restore the thermal equilibrium between currents of different temperatures. We shall, therefore, endeavor to trace out these processes more fully than it was possible to do a few years ago and explain a very probable theory of the interaction of the forces that gen- erate and sustain these local storms. THE ISOBARS AND STREAM LINES ON THE SEA-LEVEL PLANE, THE 3500-FOOT PLANE, AND THE 10,000-FOOT PLANE. It is first necessary to recall briefly the results derived by the Weather Bureau in its research into this problem. A con- sideration of the available meteorological observations above the surface of the ground convinced me that it would be nec- essary to depend upon computations rather than upon direct observations, in order to obtain the daily synoptic pressures and temperatures upon any given reference plane. Observa- tions by balloons, kites, theodolites, or nephoscopes are indis- 25 26 27 /JJ* 12V' 28 //a* /os m /a?" AS* SV' as 29 30 pensable in order to secure the necessary data for making the reductions and for checking the results, but it is not possible to make observations on any elevated plane in sufficient num- bers to construct a daily map of the weather conditions with- out adding many laborious corrections. It was, therefore, apparent that suitable methods of computation must be de- vised for this special purpose in order to reduce the problem to practise. The Weather Bureau now possesses complete ba- rometry tables for the isobars on three planes, and is working out the data for the corresponding isotherms. We have, how- ever, approximate temperature gradients which can be used for the present, in all the preliminary discussions. The ther- modynamic formulse for the a, /J, y, d stages have been adapted to tables for the computation of B, t, e at different elevations. It was indispensable to substitute these tables for the Hertz diagram, because that is liable to an error as large as 7 milli- meters, owing to the neglect of the vapor tension in evaluating the numerical data. Since we require vertical gradients of pressure to within 0.01 millimeter, it is practically impossible to secure that degree of accuracy if the vapor tension is rejected. In the MONTHLY WEATHER EEVIEW for January, 1903, charts of the isobars, figs. 1 to 6 for January 2, and figs. 7 to 12 for January 7, are given on the three planes; the two compo- nents into which they were resolved are also charted, namely, the normal isobars for the month, as given on Charts 28, 30, and 31 of the Barometry Report, and the local disturbing iso- bars, which are approximately circular in form at the center, the other lines having special curvatures which will be ex- plained. In the present paper there are similar charts, figs. 13 to 15 for February 7, 16 to 18 for February 8, and 19 to 24 for Feb- ruary 27. In order to resolve the observed isobars into the com- ponents, the normal isobars of the month were copied on trac- ing paper; these were superposed upon the computed isobars of the given date, and the diagonals were then drawn to form the second system of components. Attention should be fixed upon one characteristic feature in these charts of isobars, which is readily recognized on nearly every map. To the north or northeast of the closed isobars around the low center, there is a cusp-shaped set of isobars forming a saddle between two isobars of the same name ; thus, on fig. 19, the cusps 30.0 be- tween isobars 29.9; on fig. 20, 26.4 forms the cusps of a sad- dle between 26.3; and on fig. 21, 20.2 forms the cusps to 20.1. By referring to Maxwell's Electricity and Magnetism, Volume I, Plate III, an analogue to this typical construction in electro- statics is to be found; his Plate I is an analogue to a cyclone in relation to the general circulation around the pole, and Plate II is an analogue to an anticyclone. These figures are con- structed by the precepts on page 169, so that the resulting isobar is by analogy B= B^ + E v where B t refers to the gen- eral isobars and B 2 to the local isobars. In the electrostatic analogue the potential is found by the law V= , where the successive values 1, 2, 3 are assigned to V, and r is computed from a given value of e. In the case of the isobars, the dif- ferences are nearly equal to each other in the general system, and in the local system the gradients may be taken, for example, about twice as great. Specifically, on the normal charts the pressure difference is O = 0.1 inch for about one and three-fifths degrees in latitude, or 180,000 meters, or 112 miles. A vigor- ous cyclone is formed by superposing about eight circles, with the gradient O = 0.1 inch for four-fifths of a degree, or 56 miles. The irregularities arising from the distortion of either typical system give rise to problems on the conditions of cyclones and anticyclones which are of much interest. In the case of elec- trostatic force we deal with potentials and lines of force; in that of pressure with stream lines and gradients, since in the frictionless upper strata of the atmosphere the lines of motion are parallel to the isobars unless under special dynamic con- ditions. Now, on Charts 36 and 39, of the Cloud Report, are shown isobars after Teisserenc de Bort, drawn about the pole at the elevations 1500 and 3000 meters, respectively. This cor- responds with the system of large circles in the electrostatic analogue. On Charts 30 and 31, of the Barometry Report, giving the normal pressure for the 3500-foot and the 10,000- foot planes, we have constructed the lines accurately for one special area in the general system of isobars, namely, that covering the United States, and these are similar in form .to those from Teisserenc de Bort, though numbered differently in the inches on account of changes in the adopted heights. They are drawn as perfectly as possible and may be trusted to rep- resent the result of eliminating the local cyclonic circulations. The maps of pressure and temperature given as Charts VIII and IX of the MONTHLY WEATHER REVIEWS for January and Feb- ruary, 1903, agree closely together in their curvature relative to the pole. By comparing with these high level isobars and isotherms the wind directions determined for the upper cloud system, as shown on Charts 20 to 35 of the Cloud Report, it is possible to infer that the stream lines of the general circulation are parallel to the lines of equal pressure and temperature in the higher strata of the atmosphere. The divergences from this system, which occur at any place, are, therefore, not due to the action of the forces of sliding friction such as produce eddies, but to the interplay of dynamic forces of motion de- rived from other sources. Furthermore, it is simpler to de- termine the direction of these common lines, the isobars, iso- therms, and vectors of motion in the upper atmosphere by computing the isobars and isotherms from the surface data than by the laborious compilation of wind directions and ve- locities by means of cloud observations, from which the result- ants may be deduced. That is to say, we may have daily stream lines on the upper planes by computation from surface data, which are as reliable as those which would be obtained from a long series of cloud observations reduced to annual or monthly means. This is a practical conclusion of much value in meteorology. The isobars on Charts 37, 38, 39, 40 of the Cloud Report, from the data of Teisserenc de Bort, show that there is a greater density of the gradient lines from latitudes 25 to 60, than nearer the equator or the poles. Therefore the pressure gradient is stronger over the United States than in the tropical or in the polar zones. Such a diminution of the general gradient in lower latitudes is in accord with that theory of the general circulation which drives the currents westward in the lower strata of the Tropics; in the higher latitudes the decrease in gradient indicates a feeble tendency to form a belt of winds flowing westward near the pole. It is a tendency only, because the gradient does not reverse but continues to diminish to the pole, and the motion is everywhere eastward. This is another fact in contradiction to the canal theory, and it also implies that the return circulation of cold air from the poles to the Tropics sets in near the latitudes of 50 to 60 in the descending anticyclonic structure, where the cold streams originate in connection with local areas of high pressure, rather than in the polar zone. The cyclones and anticyclones in middle latitudes are the natural products of the thermal inter- change of heat between the "sources" which are in the warm currents and the " sinks " which are in the cold currents. This is not brought about through cooling a northward current in the highest strata of the atmosphere by its radiation of heat into space, or by vertical expansion in the Tropics, as the canal theory requires. The hot and cold masses of air, so far as they are produced by the differences of insolation in the lower layers of the atmosphere, are brought together into physical contact through the low level countercurrents, which are the winds from the south and from the north, respectively. These currents of different temperatures form the natural equivalents to the boiler and the condenser in a thermal en- gine, and the Carnot cycle is applicable to the analysis of the cyclic processes. The stream lines observed in the motions of 31 FIG. 25. The formation of local anticyclones and cyclones in the general circulation about the poles. the atmosphere as local circulations are built up by the struggle there going on to restore the thermal equilibrium and uniform temperatures. This countercurrent theory is an effective one, in that it brings the abnormal temperatures of the atmosphere into contact through the streams of different temperature, so that they can work mechanically upon one another. The canal theory keeps the currents separated throughout the en- tire circuit, so that the assumed cooling and heating in the circuit is more like the local heating of a closed current at one portion, while it cools in traveling through the remainder of its course. There is little mechanical efficiency in that pro- cess, and it is not useful as a meteorological theory, nor in ac- cordance with" the facts of observation. A certain average excess of heat in the Tropics is required to keep the general cyclone moving at its observed rate of gyration in the upper strata. The thermal equator of such motion moves annually in latitude northward and southward, and this carries with it the entire thermal engine in its annu- ally changing configuration. In the northern winter the thermal equator is far to the south, the contrast between the north polar cold and the tropical heat is much increased, and the general cyclone is relatively efficient; in the northern sum- mer the thermal equator is far to the north, the difference of temperature between the boiler and the condenser of the northern engine is less, so that the circulation is relatively feeble. This oscillation of the heat energy northward and southward, carrying with it the thermal structure toward one pole or the other, just as the astronomical zones of day and 32 night move up and down the earth in latitude, is depicted in the series of diagrams of normal pressure shown in Charts 28 to 31 of the Barometry Report. The corresponding variations of the temperatures are given on Charts 18, 19, 20, and of the vapor tensions on Charts 23, 24, 25 of the same report. The functions of B, t, e, which are involved in these variations, constitute the basis for a complete solution of the forces that generate and maintain the general circulation in middle latitudes. If we could extend this sys- tem of pressure and temperature charts to the pole, and to the equator on the American Continent, and also obtain the vectors of motion, it would afford the required data for the discussion of the dynamics involved in the circulation of the entire atmosphere, and this is the ultimate problem of our meteorology. The variations of this general circulation from season to season should be extended to include its average changes from year to year, and also the connection of these with that part of the solar energy which is expended as radiation, and is variable in long and short cycles. This will form a science of cosmical meteorology upon which long range forecasting of the seasons can be based. Unless the subject proves to be too complex for human skill to classify, we shall eventually con- struct a meteorology rivaling other branches of astrophysics in interest and value to mankind. THE MECHANISM IN CYCLONES AND ANTICYCLONES. Turning now from these considerations regarding the gen- eral circulation to the mechanism of local circulations, we will further illustrate the separation of the local components from the general normal isobars by the six diagrams of fig. 25, the formation of local anticyclones and cyclones in the general cir- culation about the pole. We draw 18 concentric circles about a pole as a center, where the common difference is 5 millimeters, except in the polar zone where the difference is greater. The outer circle extends to latitude 23, that is to Havana, so that these circles cover the latitudes in which the cyclones are pro- duced in northern latitudes. Diagrams 1, 2, 3, show the method of constructing a low pressure area, and 4, 5, 6, that for a high pressure area; diagrams 1 and 4 give examples of the draw- ing of a few individual resultant curves; 2 and 5 are com- plete for isolated low and high areas; 3 and 6 exhibit the con- nection between a high and a low area, and this diagram is com- parable with the isobars found on the charts of reduced pres- sures, as figs. 13, 14, 15, 16, 17, 18, of this paper. In making these specimen diagrams a system of local circles is superposed upon the general circles, but the common difference between them is taken half as much linearly, that is the gradient is twice as steep. On the general circles 5 millimeters is equivalent to 0.10 inch of pressure, on the small circles 2.5 millimeters is equivalent to 0.10 inch of pressure. These relative dimensions serve approximately to illustrate a strong winter cyclone, but they should be modified according to the observed conditions of the individual cyclone. When the monthly normal iso- bars are subtracted from the observed map of a given day, we have at once the small circular system, together with its varia- tions from the normal type according to the prevailing circum- stances. Looking at diagram 1, of fig. 25, we see that in passing from the pole outward each circle is + 0.10, one-tenth inch higher, beginning for example with 25.4 and extending to 27.1. The small circles are numbered .1, .2, .3, .... for the low area, and + .1, + .2, -f- .3, for the high area. At the point A we have 26.1 on the large circle; on the next circle it becomes, 26.2 0.1 = 26.1, by uniting the two gra- dients; on the next it is, 26.3 0.2 = 26.1. In this way, draw- ing the diagonal lines, we pass around a U-shaped curve hav- ing a certain concavity. Other curves are formed outside and inside of it, a few of the inner curves making closed ovals, ec- centric to the center. The dotted curve on diagram 2 shows where the cusp-shaped curves unite over the saddle of higher pressure. The diagrams 4 and 5 are drawn in a similar way, by using the plus system of circles. At B we have 26.7 + 0.1 = 26.8; 26.6 + 0.2 = 26.8; 26.5 + 0.3 = 26.8 Similarly the other lines are drawn. Finally, in diagrams 3 and 6 the two systems are united, so that the lines flow from one to the other continuously. It should be noted that in fixing the centers of the two systems of component coaxial circles, that for diagram 3 was placed on the isobar 26.5, and that for diagram 6 on the isobar 26.4. That is to say, the center of the anticyclone must be nearer the pole than that of the cyclone, in order to make the isobars continuous, otherwise some of the ends of these systems of high and low areas are left un- connected and without natural continuity. A comparison of these typical isobars with those constructed from the daily observations, see figs. 1 to 24, proves conclusively that they are substantially of the same type. We find the cusp formation on each with the opening of the U-shaped figure toward the pole in the cyclone, but toward the equator in the anticyclone. The closed curves of the cyclone are more nearly elliptical than those of the anticyclone, as is commonly the case on the weather maps. The flow of air from the northern quadrants of the anticyclone toward the southern quadrants of the cyclone is necessary to the structure. COMPARISON WITH OTHER OBSERVED CONFIGURATIONS. In order to recall the results of the research which are in- cluded in the Cloud Report, the following drawings are intro- duced. Fig. 26 shows the vectors of motion and their com- ponents as observed in anticyclones and cyclones at the 1000 meter (3280-foot) level, and the 3000 meter ( 9843-foot) level, so that these are comparable with the isobars computed on the 3500-foot and the 10,000-foot planes. The direction of the original vectors is evidently parallel to the isobars, the long vectors which indicate greater velocity are to the north of the anticyclone where the isobars are closer, and then to the south of the cyclone where the closeness of the pressure lines is a maximum. Comparing the anticyclonic and cyclonic compo- nents with the resolved local isobars on the charts of observed pressures, figs. 1 to 24, the opening of the stream lines marked .4 on the cyclone corresponds with the opening in the U-shaped clone, similar conditions are found to the south of the anticy- cusps. Furthermore, in fig. 27, 1, II, III, three charts are repro- duced from the Cloud Report; Chart 23, the mean winter Lake region low; Chart 29, the mean west Gulf low, each for the lower clouds; and Chart 35, the mean summer hurricane low for the upper clouds. The stream lines flow uninterruptedly to the center on spiral or disturbed spiral curves, one stream from the northwest and another from the south, and to the north of the center the same U-shaped cusp formation is described by the vectors of motion as are found on the charts of isobars. It is remarkable that in the case of the hurricane this formation is found in the cirrus levels, just such as in ordinary cyclones is produced in the cumulus levels, showing that this funda- mental typical construction penetrates to the height of 5 or 6 miles, when the forces of motion producing it are sufficiently intense. The relative penetrating power of the cyclonic action is a very important feature, which is brought out by these isobars and stream lines in the higher levels. Furthermore, consider the component local isobars in dotted lines on figs. 4, 5, 6, for January 2; 10, 11, 12, for January 7; 22, 23, 24, for February 27. On January 2 it is evident that the principal feeder is a current of warm air flowing over the South Atlantic States, which curls into the closed isobars from the northward; here the cusp formation is somewhat obscure, and this usually happens while the center is so far to the south. On January 7 the main stream feeds into 33 the vortex from the northwest, and on the western and southern sides, where the isobars are dense, the stream curls into the center. On February 27 there is a strong stream from the southeast and another from the northwest, both of which curl strongly into the central vortex. Hiffh urea, vectors. ^Anticyclonic Cbmponents. 1.86 O.62 Jjcnv area vectors-. Cyclonic Components. miles. FIG. 26. The vectors of motion and their components in anticy- clones and cyclones at the 1000-mile and 3000-mile levels. It should be particularly noted that the stream curls into the central vortex at all levels from the ground upward, cross- ing the closed isobars at some angle, but running parallel to the open isobars, thus confirming the results of the Cloud Report. It should be observed, also, that the U-shaped opening in the northern cyclones is swung around to the northeastward, thus distorting the lines from their primary position of sym- metry, which is toward the pole. This is due to the fact that the cyclone has vertical and gyratory components which pene- trate from lower to higher levels, and therefore into the upper layers, drifting more rapidly eastward than the lower, BIG 5 Such distortion is accompanied by an interchange of the inertia of motion, and this is the part of the thermal machine of the atmospheric circulation which acts as a brake upon the swiftly flowing eastward drift. This is the means by which the eastward velocities are slowed down from the excessive III. Summer hurricane low. Chart 35, International Cloud Eeport. II. Winter west Gulf low. Chart 29, International Cloud Eeport. I. Winter Lake region low. Chart 23, International Cloud Eeport. Fia. 27. The stream lines at cumulus levels for cyclones and at cirrus levels for hurricanes. motions required, in the general theory by the law of the pre- servation of vortex areas, into the moderate motions actually ob- served. Since this penetrating power may extend to the cirrus levels, the total energy of retardation is evidently very great, and therefore this portio'n of the problem of the general cir- culation should be developed on the lines already outlined in my papers, rather than on those followed by Professor Ferrel. Furthermore, we remark that my construction is not in accord with the theory of the German vortex, as also explained in that report. This vortex requires a local center of beat and a vertical current, with zero velocity at the center and maximum velocity at a circle on the edge of the closed curves, from which locus it gradually falls away to zero again at a considerable distance. In nature we have, on the other hand, individual stream lines of different temperatures curling into a common center, with velocity increasing up to the very center, as indicated on Chart (!9 of the Cloud Report. The German vortex is much nearer the natural type than the Ferrel vortex, but there are features in it which are not compatible with the observations them- selves. The disturbance of the eastward drift by the penetra- tion of a cyclonic vortex into the upper strata is further illus- trated by the scheme of fig. 28, where the successive levels are Cirrus FIG. 28. Scheme of the disturbance of the eastward drift by the penetration of a cyclone vortex into the upper strata. shown with the isobars bending away from their normal east- ward direction, first into U-shaped curves about the axis, then to cusps and closed curves, and finally to simple closed curves at the surface. These closed curves always imply a vortex with its vertical component governed by the usual vortex laws. The boundary of the true vortex action diminishes in size, and loses itself in the upper strata as a simple sinuous deflection. The vortex throws up a vertical component all over its area in proportion to the gyratory velocity, and in the center this forms a rising current, continuous and undisturbed, till high levels are attained. On the edges, however, the vertical com- ponent is stripped off by the action of the eastward drift, which also acts more powerfully in proportion to the elevation. This depletion of the surface of the vortex in proportion to the height is the mechanical mode that controls the escape of the upward current, which loses itself to the eastward by merging in the general circulation, whence it passes through other anti- cyclones and cyclones in succession. The radial horizontal component is inward toward the center in all levels of the cyclone, as was indicated in my Cloud Report. Thus, the en- tire complex of the circulation has dynamic components, and the energy thus expended must be referred back finally to the source of heat in the Tropics, where the absorption of radiant energy from the sun goes on vigorously at the surface of the earth. The great general cyclone is perpetuated by the vertical uplift of the strata, due to the residue of the tropical heat which does not leak out toward the poles in horizontal warm currents of air near the surface, and its motion is in general nearly inde- pendent of the counterflow of these lower currents, except for the distortion due to the penetration just described. We have therefore established the existence in the cyclone of the inter- action of three practically independent currents of air, (1) the great overflowing eastward drift, (2) the underflowing cold current from the northwest, and (3) the underflowing warm stream from the south. THE INTERACTION OF THE THREE THERMAL CURRENTS. It is necessary yet further to consider the thermal action of these currents which have very different temperatures. For it is evident that the formation of local closed isobars with vortex action and vertical currents, while accompanied by dy- namic forces must yet depend upon a powerful and persistent thermal source. We have elsewhere shown that this energy is not to any great extent the latent heat of condensation of aqueous vapor, this being a secondary product; nor is the effect purely dynamic as the eddy theory implies. Where, then, shall we find a true efficient source of heat that is competent to account for all the conditions observed in the circulation phenomena of the atmosphere. It seems to me that this is to be attributed to the thermal action due to the overflow of layers of cold air upon masses of warm air. Abnormal stratification of air currents, where the relatively cold is above the warm, necessarily involves an upward current having an energy pro- portional to the difference of temperature. It is not necessary to say more about the truth of the view that this stratification exists, because such an overflow is really one of the most com- mon conditions to be observed in meteorology. If a warm current leaves the latitudes of the high pressure belt, 35 more or less, and runs northward, it begins to underflow the eastward drift. If a cold area slides down from the northwest into warm latitudes, its upper portions are drifted forward over the warm lower strata. If two currents counterflow to- gether the cold western masses are drifted forward upon the warmer at moderate levels, also warm masses are carried east- ward over the next anticyclonic area. The instant the normal thermal equilibrium of the atmosphere is disturbed by such stratifications, thermal energy is present for the formation of dynamic vortices. Thus a hurricane begins in the late summer when the sun retreating southward brings the first layers of cool air to overspread the Tropics in a sheet. The warm surface air then begins to flow under this and penetrates it in a vortex, and this continues to operate as long as the flow of current sheets of two temperatures from the different sources continues. The track of a hurricane can thus traverse thous- ands of miles, because the cold overflow sheet covers the tem- perate zone, and the warm underflow current is directed in streams depending upon the general circulation of the lower air about the permanent anticyclonic centers of action. A specific example will make these remarks more definite. In the Cloud Report we took great pains to construct the abnormal gradients of pressure, temperature, and vapor ten- sion, such as are observed when the cumulus clouds are in the process of formation. These gradients are to be found in Tables 147, I to VII, for the metric system, and in Tables 153, I to VII, for the English system. By entering these tables with the prescribed arguments we can find the gradients which are prevailing at a given level in a cyclonic circulation. These tables are constructed primarily in reference to the 3500-foot 35 plane, but they can be extended to other levels by the adjoin- ing precepts, if some judgment is exercised. Furthermore, it was essential to establish the normal conditions which prevail iu the atmosphere at two higher planes, so that the difference between the normal gradients, which may be readily computed from the mean monthly values as given in the Barometry Re- port, and the abnormal gradients, which pertain to the differ- ent subareas of cyclones and anticyclones, may be obtained. This was one of the purposes that was kept in mind in con- structing the Barometry Report, and the data for such normal gradients are given in Table 48. By subtracting the numerical values for B, t, e, on the different planes, and dividing by the difference in elevation, these normal gradients are found. By using the surface data in connection with the three selected planes, we obtain several systems of gradients which can thus be computed for mutual comparison. As to the abnormal gradients of temperature, for example, we may take from Table 153, II, of the Cloud Report, the values for the different sub- areas in a cyclone, the table being quoted only in part. TABLE 1. Pressure and temperature gradients in English measures. FALL OF PRESSURE IN INCHES PER 100 FEET. e B .0100 .0120 .0140 .0160 .0180 .0200 .0220 .0240 t F. 90 095 0.095 0.095 0.096 0.096 0.097 80 096 097 .097 .097 .097 .098 .099 70 098 099 100 .100 .101 .102 .102 .103 60 102 103 104 .104 .105 . 106 .107 .108 50 105 106 107 .107 .108 .109 .110 40 107 108 109 .109 .110 .111 30 109 110 111 .111 .112 20 113 114 115 .115 10 117 118 120 FALL OF TEMPERATURE IN DEGREES PER 100 FEET. e B .0100 .0120 .0140 .0160 .0180 .0200 .0220 .0240 t F. 90 0.88 0.82 0.74 0.240 80 0.85 0.82 0.74 .65 .58 .52 .47 70 0.79 .68 .59 .51 .43 .37 .34 .31 60 .59 .48 .40 .33 .30 .28 .27 50 .41 .33 .25 .20 40 .26 From Table 153, International Cloud Report. In the eastern subareas we have high temperatures and high vapor tensions (t v e,) so that the temperature gradients are large ; in the western areas the temperatures and also the vapor tensions are lower (t v e 2 ). Then (t v e,) will give larger values of G. t l than (f 2 , e 2 ) will give for O. t f If the Q. t t exceeds the normal gradient of the season, we have the mechanical cause for a vertical current. This principle can be applied through- out the cyclonic field with unfailing results of the right kind. In general it may be stated that the normal temperature gra- dients are about three-fifths the adiabatic rate, and this occurs when the strata are in atmospheric equilibrium and no cur- rents are distinctly rising or falling. In cyclones and anti- cyclones, where the vertical currents are pronounced, the tem- perature gradients are about the same as the adiabatic rate. This remarkable theorem regarding gradients is very signifi- cant in the physical thermodynamics of the atmosphere. Hence, we conclude that air is rising to the east, but falling to the west of the center of the cyclone. It seems almost a paradox that in the warm current of air the air should be rising to a region where the pressure is higher than it was before the movement began. But rising air always increases the pressure in the stratum to which it is moving, and this hardly needs to be reaffirmed. The overflowing cold air in the strato-cumulus level, therefore, in itself generates the power which raises the warm air underneath it by the usual thermo- dynamic laws. Hence, if a relatively cold layer is thrust into a column of air otherwise normally disposed, the warm lower layers will rise to meet the cold stratum, and the higher strata which are also relatively warm will fall toward it. Relatively warm air flows to the place of relatively cold air. If the surface layers are cooled by radiation in anticyclones the air of the upper strata will settle down upon them by this law, namely, that relatively warm air seeks relatively cold air. The currents of transfer thus set up have an adiabatic system of gradients; on the other hand, the normal layers of the atmos- phere do not dispose themselves into adiabatic strata, as was proved in my Cloud Report. Some specific examples of the operation of these processes will now be mentioned. EXAMPLES OF THE INTERACTION OF ABNORMALLY COLD AND WARM STRATA. A survey of the conditions prevailing at the time of the water- spout photographed on August 19, 1896, off Cottage City, in Vineyard Sound, Mass., leads me to the results contained in Table 2, extracted from a report now in preparation on this important phenomenon. It contains for the a, {3, j-, 3 stages the heights on the photograph in millimeters and inches, the actual height in meters and feet, and the pressure, tempera- ture, and vapor tension at the beginning and end of each stage. Thence the gradients are found per 100 meters, or per 100 feet, viz: (1) (O ) Observed, according to the actual observations, (2) (O s ) Cloud, according to the Cloud Report Tables 147 and 153, and (3) (G b ) Barometry, the normal gradient prevailing in the air for that month as deduced from Table 48 of the Barometry Report. This waterspout was formed under re- markable conditions. The pressure was a little high, 30.05 inches; the temperature was exactly normal for the month of August, 67.5 F., and the vapor tension was low, correspond- ing to a relative humidity of 64 per cent. This gives the ratio g j. = 0.0143 from which the gradients (G c ), cloud, were obtained. Comparing (G ), (G c ), and (G b ) we note that (G b ) is less than (G ) and (