JC-NRLF 43D I.IHKAK'Y or TIIF. UNIVERSITY OF CALIFORNIA Gil""] OK S . Class w. is. XV :ur,. U. S. DEPARTMENT OF AGRICULTURE. WEATHKH r,F 1! F.AIT. STUDIES ON THE CIRCULATION OE THE ATMOSPHERES OE THE SUN AND OF THE EARTH. from the Monthly Weather Review, October and November, 1903, and January, February, April, May, and June, 11)04. FRANK H. BIGELOW. M. A., L. H. D. i. I -.-in; M| MM |'U Prepared under the direction of WILLIS L. MOORE, Chief U. S. Weather Bureau. 1 WASHINGTON: w BA-TH1 \ I . 1904. W. B. No. 316. U. S. DEPARTMENT OF AGRICULTURE, WEATHER BUREAU. STUDIES ON THE CIRCULATION OF THE ATMOSPHERES OF THE SUN AND OF THE EARTH. Reprints from the Monthly Weather Review, October and November, 1903, and January, February, April, May, and June, 1904. BY FRANK H. BIGELOW, M. A., L. H. D., PROFESSOH OF METEOROLOGY. Prepared under the direction of WILLIS L. MOORE, Chief U. S. Weather Bureau. WASHINGTON: WEATHER BUREAU. 1904. OOISTTElsTTS. Page. I. The circulation of the sun's atmosphere Historical review 1 Compilation of the prominence observations 2 Discussion of the observations 4 The differential circulation within the sun 6 II. Synchronism of the variations of the solar prominences with the terrestrial barometric pressures and the temperatures. . 9 Several opinions on the subject of synchronism 9 The unsatisfactory state of the observational data 11 Kesults of the observations ., 14 Discussion of the local inversions 15 III. The problem of the general circulation of the atmosphere of the earth 17 The canal theory 17 The general equations of motion Line integrals in the atmosphere 17 Equivalent expressions for the density p 18 P dr Development of the terms , V, and ^ To find the direction of the boundary curve between two strata . 19 Case I. Applicable to the temperate and polar latitudes of the earth 19 Case II. Applicable to the tropical zones of the earth .... 19 Case III. Applicable to the atmospheres of the sun, Jupi- ter, and Saturn 20 The interaction of Case I and Case II in the earth's atmosphere in the formation of local cyclones and anticyclones 20 IV. Values of certain meteorological quantities for the sun 23 The importance of these values to terrestrial meteorology .... 23 Nipher's equations 23 The astronomical constants for the earth and the sun 24 Application of the thermodynamic formula to the gaseous en- velope of the sun 25 Distribution of the pressure, temperature, and density in a solar hydrogen atmosphere 27 Discussion of the values derived from tables 12 to 14 29 The density 29 The pressure 29 The temperature and the gas constant 29 The mass of sun, the weight of one gram on the surface of the sun, and the transformation factor 30 Specific heats, energy of radiation, and contraction 30 V. Results of the nephoscope observations in the West Indies during the years 1899-1903 : 31 Methods of observation and reduction 31 Charts of the resulting velocities and directions of motion for the West Indies 31 The arch spanning the Tropics, which divides the eastward drift from the westward drift in the general circulation .... 32 The levels of maximum horizontal velocity 32 The winter and the summer circulations 33 The cause of the West Indian hurricanes 33 Approximate normal circulation in the West Indies during the winter and summer, respectively 34 VI. The circulation in cyclones and anticyclones, with precepts for forecasting by auxiliary charts on the 3500-foot and the 10,000-foot planes 35 The structure of the isobars at different levels 35 The geometrical construction of high and low pressure areas . 35 The cusp formation and its changes 37 Critical remarks regarding several theories of cyclones and anticyclones 38 The cause of the counter currents in the lower strata 38 Precepts for forecasting with the charts on the 3500-foot and the 10,000-foot planes as auxiliaries 39 1. Direction of the storm tracks 39 2. The velocity of advance 39 3. The areas of precipitation 39 4. Penetration into the higher levels 39 VII. The average monthly vectors of the general circulation in the United States 41 8549 TABLES. Page. Table 1. The prominence energy in zones as collected on the 26.68- day period, showing retardation in different latitudes . 3 2. Eetardation of the sun in different latitudes as derived from the prominence frequency in longitude ......... 4 3. Mean retardation by zones ............................ 5 4. Bigelow's rotation periods ............................ 5 5. Transformations of the daily angular velocity into sidereal and synodic periods ........................ 6 6. Several determinations of the rotation periods of the solar spots in different latitudes .................... 6 7. Astronomical constants ............................... 25 8. Constants for one atmosphere of hydrogen on the earth . 25 9. Transition to constants for a solar hydrogen atmosphere . 25 10. Fundamental constants for a hydrogen atmosphere on the sun ............................................ 26 11. Distribution of the pressure, temperature, and density in the solar hydrogen atmosphere ................... 27 12. Computation of the pressures, temperatures and den- sities at the surface and within the sun, by Nipher's formulas ...... ' .................................... 28 13. Transformation factor from perfect gases to the material of the sun within the photosphere ................... 28 14. Specific heats c p , c v , quantity of heat Q, and work W, in the surface stratum of the sun ...................... 28 15. Form for computing the coordinates of the resultant curve ............................................. 36 16. Average monthly vectors of the general circulation in the United States, 1896-97 ......................... 42 Figure 1.- 2.- 3.- 4.- 5.- 6.- 7.- 8.- 9.- 10. 11. 12. 13. 14. 15. 16. 17.- 18.- 19.- 20.- 21.- 22.- 23.- 24.- 25.- 26.- ILLUSTRATIONS. -Retardation of rotation in different zones of the sun as derived from the prominence frequency in longitude . -Periods of rotation of the solar photosphere derived from the prominence frequency in different zones ---- -Variable retardations in the periods of rotation of the solar photosphere ................................. -Formation of vortices in the solar mass by differential rotations ......................................... -Solar and terrestrial synchronism .................... -Variations of the annual pressure in the direct type . . . -Variations of the annual pressure in the inverse type . -Variations of the annual pressure in the indifferent type . -Variations of the annual temperature in the direct type. Variations of the annual temperature in the inverse type Variations of the annual temperature in the indiffer- ent type Distribution of the pressure types Distribution of the temperature types Component axes Case I -Case II -Case III -Cases I and II unmodified -Cases I and II as modified -Pressures at different latitudes (Ferrel) and altitudes (Sprung) -Distribution of the pressure, temperature, and density, in a solar hydrogen atmosphere -Chart XII A. Average monthly vectors of the general circulation, Havana, Cuba. -Chart XII A. Average monthly vectors of the general circulation, Cienfuegos, Cuba. -Chart XII A. Average monthly vectors of the general circulation, Santiago, Cuba. -Chart XII A. Average monthly vectors of the general circulation, Kingston, Jamaica. -Chart XII B. Average monthly vectors of the general circulation, Santo Domingo, Santo Domingo. iii 8 10 10 11 11 12 13 13 14 14 18 19 20 20 21 21 21 27 IV 27. Chart XII B. Average monthly vectors of the general circulation, San Juan, Porto Kico. 28. Chart XII B. Average monthly vectors of the general circulation, Basseterre, St. Kitts. 29. Chart XII B. Average monthly vectors of the general circulation, Roseau, Dominica. 30. Chart XII C. Average monthly vectors of the general circulation, Bridgetown, Barbados. 31. Chart XII C. Average monthly vectors of the general circulation, Willemstad, Cura9ao. 32. Chart XII C. Average monthly vectors of the general circulation, Port of Spain, Trinidad. 33. Chart XIII A. Average monthly vectors of the general circulation, Havana, Cuba. 34. Chart XIII A. Average monthly vectors of the general circulation, Cienfuegos, Cuba. 35. Chart XIII A. Average monthly vectors of the general circulation, Santiago, Cuba. 36. Chart XIII A. Average monthly vectors of the general circulation, Kingston, Jamaica. 37. Chart XIII B. Average monthly vectors of the general circulation, Santo Domingo, Santo Domingo. 38. Chart XIII B. Average monthly vectors of the general circulation, San Juan, Porto Kico. 39. Chart XIII B. Average monthly vectors of the general circulation, Basseterre, St. Kitts. 40. Chart XIII B. Average monthly vectors of the general circulation, Roseau, Dominica. 41. Chart XIII C. Average monthly vectors of the general circulation, Bridgetown, Barbados. 42. Chart XIII C. Average monthly vectors of the general circulation, Willemstad, Cura9ao. 43. Chart XIII C. Average monthly vectors of the general circulation, Port of Spain, Trinidad. 44. Chart XIV A. Average summer vectors of the general circulation in the West Indies, surface. 45. Chart XIV A. Average summer vectors of the general circulation- in the West Indies, stratus level. 46. Chart XIV A. Average summer vectors of the general circulation in the West Indies, cumulus level. 47. Chart XIV A. Average summer vectors of the general circulation in the West Indies, strato-cumulus level. 48. Chart XIV A. Average summer vectors of the general circulation in the West Indies, alto-cumulus level. 49. Chart XIV A. Average summer vectors of the general circulation in the West Indies, alto-stratus level. 50. Chart XIV B. Average summer vectors of the general circulation in the West Indies, cirro-cumulus level. 51. Chart XIV B. Average summer vectors of the general circulation in the West Indies, cirro-stratus level. 52. Chart XIV B. Average summer vectors of the general circulation in the West Indies, cirrus level. 53. Chart XIV B. Average winter vectors of the general circulation in the West Indies, surface. 54. Chart XIV B. Average winter vectors of the general circulation in the West Indies, stratus level. 55. Chart XIV B. Average winter vectors of the general circulation in the West Indies, cumulus level. Page. 56. Chart XIV C. Average winter vectors of the general circulation in the West Indies, strato-cumulus level. 57. Chart XIV C. Average winter vectors of the general circulation in the West Indies, alto-Cumulus level. 58. Chart XIV C. Average winter vectors of the general circulation in the West Indies, alto-stratus level. 59. Chart XIV C. Average winter vectors of the general circulation in the West Indies, cirro-cumulus level. 60. Chart XIV C. Average winter vectors of the general circulation in the West Indies, cirro-stratus level. 61. Chart XIV C. Average winter vectors of the general circulation in the West Indies, cirrus level. 62. Mean altitudes at which the westward drift reverses to the eastward drift in the Tropics 63. Chart XII. Sea level isobars for February 3, 1903. 64. Chart XII. Isobars on the 3500-foot and the 10,000- foot levels for February 3, 1903. 65. Chart XIII. Normal and abnormal isobars on the 3500-foot plane for February 3, 1903. 66. Chart XIII. Normal and abnormal isobars on the 10,000-foot plane for February 3, 1903. 67. Chart XIV. Typical normal sea-level isobars. 68. Chart XIV. Typical normal 3500-foot plane isobars. 69. Chart XIV. Typical normal 10,000-foot plane isobars. 70. Chart XIV. Typical abnormal sea-level isobars. 71. Chart XIV. Typical abnormal 3500-foot plane isobars. 72. Chart XIV. Typical abnormal 10,000-foot plane isobars. 73. Chart XV. Isobars and isotherms for February 27, Pago. Temperature components for February 27, Chart XIV. Chart XIV. Chart XIV. Chart XIV. Chart XIV. Chart XV. 1903. 74. Chart XV. 1903. 75. The general ellipse 76. Bight lines and circles where the gradients are twice as great on the circles as on the right lines 77. Chart XI. Average monthly vectors of the general circulation, St. Paul, Minn. 78. Chart XI. Average monthly vectors of the general circulation, Kansas City, Mo. 79. Chart XI. Average monthly vectors of the general circulation, Abilene, Tex. 80. Chart XI. Average monthly vectors of the general circulation, Vicksburg, Miss. 81. Chart XII. Average monthly vectors of the general circulation, Louisville, Ky. 82. Chart XII. Average monthly vectors of the general circulation, Detroit, Mich. 83. Chart XII. Average monthly vectors of the general circulation, Cleveland, Ohio. 84. Chart XII. Average monthly vectors of the general circulation, Buffalo, N. Y. 85. Chart XIII. Average monthly vectors of the general circulation, Blue Hill, Mass. 86. Chart XIII. Average monthly vectors of the general circulation, Washington, D. C. 87. Chart XIII. Average monthly vectors of the general circulation, Waynesville, N. C., and Ocean City, Md. 88. Chart XIII. Average monthly vectors of the general circulation, Key West, Fla. 32 36 36 STUDIES ON THE CIRCULATION OF THE ATMOSPHERES OF THE SUN AND OF THE EARTH. I. THE CIRCULATION OF THE SUN'S ATMOSPHERE. HISTORICAL REVIEW. That the solar atmosphere is circulating in accordance with the laws governing the convective and radiative action of a large mass of matter contracting by its own gravitation, is so evident that numerous efforts have been made to determine what these laws are, or at least to discover some reliable clue to a beginning of scientific research in that direction. The application by K. Emden' of H. von Helmholtz's method of adapting the general equations of motion to a solar mass, ap- peared to be a step in the right direction; further attention was called to the possibilities of this solution in my Report on Eclipse Meteorology, 2 pages 71-74. In June, 1902, Sir Nor- man Lockyer and Dr. W. J. S. Lockyer 3 published their sug- gestive curve of the percentage frequency of the solar prom- inences derived from the Italian observations for each 10 of solar latitude north and south of the equator. This curve in- terested me because it appeared to identify the distinctly solar phenomena with the short period curves which I had worked out in the terrestrial magnetic field and in the meteorological field of the United States, and first published in December, 1894, 4 af- terwards republishing them in 1898. 5 A study of the difficult sub- ject of inversion of periodic effects in magnetic and meteorolo- gical phenomena discovered at that time has been actively pur- sued by the Weather Bureau for the past ten years, and evidence is being accumulated, not only here but by others, of the exist- ence and importance of the fact of inversion in the magnetic phenomena, the pressures, and the temperatures of the earth generally. The solar prominence curve suggested also the pos- sibility of obtaining more decisive evidence of solar and terres- trial synchronisms than that afforded by the solar-spot fre- quency curve (which is apparently only a sluggish register of the true solar output of energy), because the terrestrial mag- netic field and the meteorological elements show minor varia- tions that are only feebly indicated in the solar-spot curve. The prominence frequency curves brought out distinctly for the sun the minor fluctuations that had been already found in the earth's atmosphere. My first computations on the amplitudes of the deflecting forces which disturb the normal terrestrial magnetic field were computed for the years 1878-1893, using the records of several European magnetic stations. To have extended the same com- putation to the years 1841-1900, inclusive, would have re- quired a vast amount of labor; as an equivalent, the de- flections of the horizontal force alone, without the declination 1 Eine Beobachtung uber Luftwogen. R. Emden. Wied. Ann. LXII p. 62, 1897, and Astrophysical Journal, January, 1902. 2 Eclipse Meteorology and Allied Problems. Frank H. Bigelow Weather Bureau Bulletin I. 1902. 3 On some Phenomena which suggest a short Period of Solar and Me- teorological Changes. By Sir Norman Lockyer, K. C. B., F. E S and William J. S. Lockyer, M. A., Ph. D., F. R. A. S. Received June 14 Read June 19, 1902. Addendum. Dated June 26. Proc. Roy. Soc. Vol.70 4 Inversion of Temperatures in the 26.68 Day Solar Magnetic Period Frank H. Bigelow. Am. Jour. Sci. Vol. XLVIII, December, 1894. 5 Report on Solar and Terrestrial Magnetism in their Relations to Me- teorology. Frank H. Bigelow. Weather Bureau Bulletin No. 21. 1898 and vertical components, were derived by the construction of a series of graphical curves covering these sixty years, from which the mean ordinates were computed. The result was shown in my paper on Cosmical Meteorology, July, 1902. 6 The same variation curve was found from the horizontal force for the years 1878-1893 as that previously given by the com- puted a curve, and it was therefore proper to conclude that this extension of the original computation in both directions was sufficiently correct for the purpose of the discussion. Furthermore, the prominence frequencies presented the ma- terial for studying the solar activity by zones, and the result of my compilation to determine the law of the movement of the points of prominence maxima in latitude was read before the American Association for the Advancement of Science on December 28, 1902, and published in the MONTHLY WEATHER REVIEW, January, 1903. 7 I there showed that in each hemis- phere the maxima of prominence frequency are grouped in two zones, and that in the zones near the equator, in latitudes about 20, the maxima of frequency approach that plane in common with the sun spots and faculse during the 11-year period, while in the zones in latitudes 50-70, the maxima simultaneously move toward the poles. This indicates a characteristic ten- dency of the solar circulation to spread from the middle lati- tudes toward the equator and toward the poles in two inde- pendent branches. In a paper 8 published in March, 1903, the Lockyers obtained a similar result for the same phenomena. They gave the life history of the sun in the separate 11-year periods between 1872-1901, whereas my paper had grouped these three available periods together for the sake of finding the average law. Dr. A. Ricco 9 has published similar studies of the movements of prominences in latitude for the years 1880-1902. The subject of the average distribution of the solar spots in longitude on the sun has been discussed by Dr. A. Wolfer, 10 and from it he derived some determinations of the solar rotation in different latitudes. In my paper of January, 1903, I stated that besides a study of the variable distribu- tion of the prominences in latitude, an effort was being made by me to discover some clue as to their distribution in longi- tude, in order to learn whether or not there was an accumula- tion on certain meridians, and it is the result of this work that is contained in the present paper. We have discovered an unexpectedly clear insight into the solar circulation, and this tends to strengthen the line of argument which I have been developing during the past fifteen years to explain the 6 A Contribution to Cosmical Meteorology. Monthly Weather Review July, 1902, Vol. XXX, p. 347. 'Synchronous Changes in the Solar and Terrestrial Atmosphere. Monthly Weather Review, January, 1903, Vol. XXXI, p. 9. 8 Solar Prominence and Spot Circulation, 1872-1901, By Sir Norman Lockyer, K. C. B., F. R. S., and William J. S. Lockyer, Chief Assistant, Solar Physics Observatory, M. A. fCamb.), Ph. D. (Gott) F R A S Received March 17. Read March 26, 1903. Proc. Roy. Soc. Vol. 71. 9 Le protuberanze solari nello'ultimo periodo undecennale. Mem Spett. Ital., Vol. XXXII, 1903. A. Ricco. 10 Publikationen dor Sternwarte des Eidg. Poly tech. Inst., Zurich A Wolfer. Bd. I, II, III, 1897, 1899, 1902. mysterious synchronism at the earth, of which numerous symptoms have been noted, in many kinds of observations. COMPILATION OF THE PROMINENCE OBSERVATIONS. The prominences which appear on the edge of the disk of the sun have been carefully delineated by the Italian observ- ers Secchi and Tacchini with stations at Rome and Palermo, also Kicco and Mascari, at Catania, working in cooperation, from March, 1871, till the present time in an unbroken series. Students of solar physics can not too gratefully acknowledge the value of the patient, laborious work which has been done by these observers, and the practical study of these data is likely to open up new and important lines of research. Be- ginning with March 1, 1871, the images of the solar disk have been published in the Memorie della Societa degli Spettro- scopisti Italiani, and they cover the time to the end of the century, except for a long gap from September, 1877, to Jan- uary, 1884. I am informed by Dr. Eicco that the drawings for these missing years are in the archives of the Catania Ob- servatory, and it is obvious that steps should be taken as soon as practicable to complete the published record, because the demand for the data is sure to increase, as can be inferred from the results indicated in this paper. On those graphical tables certain lines were drawn showing the position of the north and south poles and the equator of the sun, so that the disk could be readily divided into zones, passing first along the eastern limb from north to south, and then along the western limb from south to north. Flo. 1. Ketardation of rotation in different zones of the sun as derived from the prominence frequency in longitude. The diagrams on fig. 1 serve to illustrate the general situa- tion. Referring to fig. 4 of my former paper," Synchronous Changes in the Solar and Terrestrial Atmospheres, it is noted that the prominence maximum activity is central in the zones 10 to 30 and 50 to 70 of each hemisphere, and on- this ac- count it was decided to subdivide the solar disk into 20-degree zones, as follows: -f 90 to + 70, + 70 to + 50, _ 50 to 70, and 70 to 90, as indicated. A scale was prepared which when laid upon the published drawing of a given date would readily subdivide it into these zones on each side of the sun's limb. For the sake of recording the relative energy of the solar 11 Monthly Weather Review, January, 1903, Vol. XXXI, p. 17. output as registered in the prominences, a scale of estimation was adopted, as follows: = an undisturbed limb for the zone. 1 = a minor disturbance. 2 = a somewhat extensive disturbance. 3 = a disturbance pronounced in altitude or along a con- siderable extent of the zone. 4 = a very large, emphatic agitation of the limb. 5 = the largest prominences, occurring but rarely. The state of the limb was thus expressed in numbers of relative energy by estimation, care being exercised to make a similar relative number do duty whenever the style of the drawing changed from one draftsman to another. The com- putation sheets were arranged to allow the data for each of the nine zones to be collected together by years for the first compilation. For the second compilation the data belonging to the same zone for the successive years were brought to- gether. Hence, the work of tabulating the data was repeated twice throughout the series. For an ephemeris I used the one already constructed from my computation on the variations of the terrestrial magnetic field, having the period 26.679 days and epoch June 13.72, 1887, as given on page 120, Bulletin No. 21, Solar and Terrestrial Magnetism. This is known to coincide very closely with the period of the solar rotation at the equator, and as it was one purpose of this research to test prac- tically the working of this period, it was laid at the basis of the compilation. It makes no difference what ephemeris and period are adopted, since any periodic phenomenon not falling upon that period will show a gradual departure from it by the trailing of the numbers on the sheet from left to right, if the period is too short, or from right to left, if it is too long. An example of the use of the ephemeris and the result is given in Table 1. One point should be especially noted in this con- nection, and that is as follows : The same meridian of the sun is seen twice in a single rotation, first as the eastern limb, and second, thirteen days later, as the western limb. Whatever may be the intrinsic activity of the sun at a given zone and on a given meridian, that display becomes visible twice, first to the east and second to the west. During the passage of that meridian across the sun's disk the record is wanting so far as this series is concerned, though it could of course be studied otherwise by means of the spectro-heliographic photographs. Thus, as the successive meridians come to the edge of the disk, their output is recorded on the respective drawings. When these are collated with the equatorial period, whatever characteris- tics they may have which would imply special centers of solar activity will gradually emerge upon the numerical tables. As it is not possible to reproduce these extensive tables in this connection, two specimens of the second collection are shown on Table 1 for the years 1891 and 1892 in succession, and for the zones +50 to +70 and +10 to +30. Imagine that similar tables for zones +50 to +70 extend from 1871 to 1900, inclusive, except for the gap from 1878-1883, arranged continuously so that the prominence concentration and deple- tion flows without break on the sheet from year to year. This process is extended to the 9 zones, each 20 in width. In the first collection of the data the highest number was 5, and this was very rarely entered. Since the same area on the sun is seen twice, there may be two entries within the same tabular area on the first set of sheets. In the second set of sheets these numbers are added together and entered as one, so that occa- sionally the figures 6, 7, 8 occur, as in Table 1. They repre- sent the largest disturbance occurring in one small area of the sun, as defined by the latitude and longitude thus pre- scribed. If now the maxima show a tendency to trail across the sheet as indicated by the continuous lines drawn athwart the table, instead of being scattered at random, then this is evidence that the center of eruption itself rotates about the sun at a different rate from that laid down in the assumed TABLE I. The prominence energy in zones as collected on the 26.68-day period, showing retardation in different latitudes. Period 26.67&daiss,. JZpocA June 13. 72, 1887. Zone + 6O to + 7O. 7 2 3 4 5 6 7 8 ff 10 11 12 13 ]4 15 16 17 18 10 20 21 22 23 24 26 26 27 18.91 'Jan. 11 1 3 Q 1 1 . "*-, Feb. 6 2 / 1 2 2 2 4 o 2 4 4 <7 3" ^ .2 2 Jtfch. 3 ,? ^4 3 2 1 2 ^^ ^^ v4pr: 1 4 2 ~~S-~ - 4 3 2 1 1 1 2 2 / Jlpr. 27 S> >, / 2 1 -, 2 16 Dec. 23 /4 7 2 3 7 J 7 ^ f> / ^**n . 1892. Jan. 79 1 1 2 1 1 2 2 1 S 3 J 1 1 1 1 Fed. 15 2 4 1 2 3 1 4 J 2 3 2 .Mch.12 3 -9- 3 3 2 1 2 3 2 3 4 2 2 2 / 1 1 2 2 / 2 4 17 JJpr. 8 4 6 6 V -^ 4 3 3 1 1 1 4 S 2 1 3 2 3 1 6 3 S 2 tACair S 3 1 2 3 iT -~ , ^ 2 4 3 3 3 2 3 3 ] J 2 2 3 tMay 31 6 1 2 2 2 3 3 "9- -^ 4 6 5 2 4 1 1 4 3 3 3 o J 1 J 1 2 June 27 7 4 3 2 1 2 2 3 3 3^ -#- 2 3 7 1 3 2 S 6 5 2 4 2 1 Jiziv 24 8 3 1 1 3 2 1 5 3 4 1r- >^ 4 4 6 3 4 3 2 3 2 3 2 ^9ucr.J9 9 3 3 J / 1 2 2 4 1 s S - *> 4 4 4 4 4 2 2 2 3 1 jSejo. IS 1O 4 3 3 1 2 1 1 i 5 3 4 3" T- f" 4 1 1 1 1 Oct. 12 11 3 3 1 1 5 4 2 2 1 2 J 2 3 5 2 ^ **. 3 1 2 2 6 JVbir 7 12 6 3 1 2 3 1 2 2 3 6 3 3 4 y- ~~~. 6 4 3 Dec. 4 13 3 3 3 4 2 2 2 2 2 2 "-. . Zon e +JO toi-3O . 1891 Jan 11 1 J 2 2 S 3^ ^ 2 2 / / 14 Feb 6 2 X 5 2 1 / 1 I I / 2 2 1 ^ (,/ / 2 I I J 4 3 / Jtfch 5 3 2 ^. 1 1 2 1 6 6 X 6 3 2 2 ,j3pr*. 1 4 1 ^\ s? 1 3 2 4 3 I 1 2 I I / "^ 2 2 r tApr. 27 S 1 7 s V 8 1 3 2 1 3 / ; *x 1 3 J I f 3 1 r. 8 4 1 2 6 5 3 2 1 4 3 / V s 7 2 4 4 3 7 Jfyfcti/ 5 A' X 2 J 3 1 \ ^2 J 3 7 7 f) 7 s. ,5 *Aaif3J 6' 5 \ 1 3 2 2 3 4 3 2 3 4 X 3 P. 3 ?, 3 g 7 7 June 27 7 3 6^ ^ 1 4 / 6 / 2 4 3 4 ,5 .? 2 X I 7 2 2 3 3 G ?, 3 7 July 24 y 1 4 2\ / 3 4 2 I 4 2 3 4 f 4 ^ 3 ?! 7 ,? ,? e 3 ttfitff.ld 9 4 4 3 *s, 2 ! 3 / 2 3 2 3 4 2 3 6 V ?. 7 7 ft 1 4 Sep. 15 10 2 2 3 3 \ 3 3 1 7 7 4 7 3 5 4 7 s V? ?, ,f 3 ,? ?. 7 Oct 12 11 3 2 J 2 s? 2 I 3 3 7 3 3 4 2 ,? ? e I g ,f JVbv. 7 12 3 1 % ^ 3 1 4 2 1 / 7 4 6 4 E .6 S f Dec. 4 13 2 4 5 5 2 I 2\ J. / 2 ?, 7 2 3 7 2 f> Si 9 16 "VT ephemeris. From such trails the angular retardation in dif- ferent zones can be computed with considerable exactness. The reader will not receive a satisfactory impression of the distinctness with which this trailing at different rates in the several zones occurs, without an inspection of the entire series of tables, and it is hoped that they will be published in a special report, as the subject matter is evidently very im- portant and suggestive for the solution of the fundamental problem of the mode of the internal solar circulation. An examination of these sheets indicates that there is a marked tendency for the numbers to bunch themselves to- gether in a very special manner. Between the successive years there is generally a depletion corresponding with the winter months, while the summer months are relatively full and com- plete. As pointed out in my paper on Synchronous Changes, this is evidently due to the fact that the relatively cloudy weather in Italy during the winter months made it impossible to secure so many days of observation as during the summer, and I conclude that the apparent concentration of the tables in the summer season is a meteorological effect, and should be treated as such in interpreting the results. At the same time there is a very similar concentration of the numbers along the days of the period, corresponding with a solar rotation, which can not be explained in that way, since it occurs as prominently in summer as in winter. It must apparently be referred back to some solar activity producing prominences on the two op- posite sides of the sun. The maximum numbers not only trail downwards and to the right on the tables, but the lines of maxi- mum also drift across the tables to the left, thus indicating retardation in the higher latitudes relative to the adopted equatorial period. It may be mentioned in passing that this increase of activity of the sun on two opposite sides of its mass, as if a certain diameter had greater energy than the one at right angles to it, has already been detected by me in the meteorological field of the earth's atmosphere, and also in the terrestrial magnetic field, as shown on pages 91 and 92 of my Eclipse Meteorology and Allied Problems, and elsewhere. This persistent excess of outflowing energy on two opposite sides of the sun suggests the possibility that the sun should be regarded as an incipient binary star," where the dumbbell figure of revolution prevails instead of the spheroidal. If this is really the case, and the evidence suggests it, then there would be a reason for the existence of the two primary centers of activity in the sun, instead of its having a single center. Some double acting system appears to impress itself generally upon the solar cos- mical relations. From this we should expect to find that the sun has two magnetic and two meteorological systems, inter- acting so as to form the configuration of the external field as measured at the earth. There would then be sufficient ground for a differential action in the terrestrial pressures and temper- atures, as detected in the discussion of such data by many students. This view is quite in harmony with the well known fact of the existence of numerous binary systems of suns more or less widely separated, and it can not be regarded as unlikely that the sun is actually developing in this way. The enormous mass of the sun would seem to entice its constituents to group themselves preferably about two centers for the physical pro- cesses involved in circulation and radiation, rather than about one, and I suspect that this is the correct explanation of sev- eral well known phenomena. DISCUSSION OF THE OBSERVATIONS. On Table 1 are given some examples of the slope of the line of maximum frequency numbers in successive years. These 11 Compare Figures of Equilibrium of Eotating Masses of Fluids. By G. H. Darwin, Proc. Roy. Soc. Vol. XLII. 1887, p. 359. Thomson and Tait, Nat. Phil. Vol. I, part 2, pp. 330-335. were drawn originally by a careful examination of the entire set of figures, and an effort was made to locate the line along the maximum numbers so as to balance as nearly as possible the entire system on either side of it. Some regard was paid to the average trend of the lines in the other portions of the same zone, whereby one's judgment was guided in cases of doubt. Entire impartiality was exercised as far as practicable, and the results now about to be described were entirely un- expected. It would perhaps be preferable to utilize least square methods, if one could afford so great labor. The lines are all numbered, as 16, 17 in the zone + 50 to + 70, which are complete; those in zone + 10 to -f 30, namely 14, 15, 16, are fragmentary on Table 1. We now count the number of days which have elapsed for a certain number of periods, in order to find the average rate of retardation per rotation of 26.68 days. Thus, for the line 16, zone + 50 to -f 70, about 12 periods elapsed, beginning with period 2 and ending with period 14, while the line was trailing, or the period was retarded, 26.7 days. Hence, 26.7 -=- 12 = 2.225 days retardation per period of 26.68 days, so that the rotation period in that zone is 28.905 days. Similarly, line 17 gives a retardation of 26. 2 days in 11 periods. Hence, 26.2 -4- 11 = 2.382. These two values are entered in the proper place on Table 2. The results have been grouped by years where the solar energy TABLE 2. Retardation of the sun in different latitudes as derived from the prominence frequency in longitude,. Years. Slope. OJ 3 A Periods. CO ft Retarda- tion. d i 3 Periods. IK :>> s ft Retarda- tion. 1871-1877 1884-1888 1889-1893 1894-1900 Max.-Min. Max.-Min. Min.-Max. Max.-Min. Zone + 10 to 10. 1 2 3 4 5 6 7 8 90 90 69 69 68 68 96 69 9.0 9.0 6.5 7.4 5.2 6.0 11.4 8.2 0.100 0.100 0.094 0.107 0.077 0.088 0.119 0.119 Me in ... 0.101 1871-1877 1884-1888 1889-1893 1894-1900 Max.-Min. Max.-Min. Min.-Max. Max.-Min. Zone -f 10 to + 30. Zone 10 to 30. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 18 41 39 35 25 26 9 19 34 35 35 10 18 31 31 23 33 37 35 34 28 12.8 28.2 26.1 25.3 20.2 17.8 6.0 14.0 26.0 26.0 25.0 7.2 16.2 26.7 26.2 19.0 26.3 26.7 27.8 26.6 20.7 0.711 0.688 0. 669 0.723 0.808 0.684 0.666 0.737 0.765 0.743 0.714 0.720 0. 900 0.863 0.845 0.826 0.797 0.722 0.794 0.783 0.739 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 15 28 38 39 37 26 10 16 31 33 35 17 16 34 34 27 33 35 34 36 35 34 13 12.5 22.1 26.5 27.0 27.0 19.0 7.3 14.0 27.0 26.7 26.5 14.0 13.6 26.8 26.7 22.0 26.4 27.0 26.6 28.0 26.8 24.0 9.8 0.833 0.789 0. 697 0. 692 0.729 0.731 0. 730 0.875 0.873 0.809 0.803 0.824 0. 850 0.788 0.785 0.815 0.800 0.722 0.783 0. 778 0. 766 0. 706 0.753 Mei in 0.757 Mes in . . 0.782 . TABLE 2. Retardation of the sun in different latitudes as derived from the prominence frequency in longitude Continued. Years. Slope. ^^ --""M" 3 fl / / ^ &. eta 1 "*" I ! / '','& c 1 ' LProjnin / 7 *naf , / / Spots^. "'' /' Rftartt'n ? a 50 J TO 1 50 2 w 2 50 3 OOdaj-s KrixfZS 68 27 1.1 27 G8 26 /a zs SS 29 /S 29 fiSdayS. FIG. 2. Periods of rotation of the solar photosphere derived from the prominence frequency in different zones. It should be noted that the mean retardation does not fol- low a regular slope, or a simple curve that can be reduced to an analytic function. From latitude 20 to 40 there is a smaller inclination than on the slopes between and 20, or on those between 40 and 60. In fig. 2 the line has been extended to 90, that is to the pole, but it is unknown beyond 70, since the polar zones were too irregular to permit any use of this method. It is probable, that a continuous line, as indicated, is nearly correct. In order to compare my result with some well known rota- tion periods, (taken conveniently from Miss Clerke's Problems in Astrophysics, p. 146), the following compilation is intro- duced: Heliographic latitude. Spots. Prominences. (Bigelow). Faculee. 25.09 24. 86 24.66 15 25.44 25. 36 25.26 30 25.81 25.66 25.48 From this it appears that my prominence rotations lie mid- way between those of the spots and the faculse. Duner's ro- tations for the reversing layer, as quoted by Miss Clerke, are apparently impossible. The determinations of the rotation period as given by the well-known formula) of Carrington, Spoerer, Faye, and Tisserand are found in Table 6. These periods begin to depart from the rotations as found from the prominences after leaving the latitude of 20. TABLE 6. Several denominations of the rotation periods of the solar spots in different latitudes. Carrington. Spoerer. d X T S X T S o , , 865 24.97 26.80 877 24. 65 26.42 5 863 25.03 26.90 864 25.00 26.83 10 857 25.20 27. 07 853 25.32 27.21 15 849 25.44 27.35 842 25.65 27.59 20 840 25.71 27.66 833 25.93 27.91 25 828 26.08 28.09 825 26.18 28.21 30 816 26.47 28.54 819 26.37 28.43 35 803 26.93 29.04 814 26.53 28.62 40 789 27.38 29.60 810 26.67 28.77 Faye. Tisserand. d X T 8 X T 8 , , 862 25.06 26.90 858 25.18 27.04 5 861 25. 09 26.93 857 25.20 27. 07 10 856 25.23 27.11 853 25. 32 27.21 15 850 25.41 27. 32 847 25.50 27. 42 20 840 25.71 27.66 840 25.71 27.66 25 829 26.05 28.05 830 26. 02 28.01 30 815 26.50 28.58 819 26.37 28.43 35 801 26.97 29.11 806 26.80 28.92 40 785 27.52 29.76 793 27.24 29. 43 It is proper to remark that the agreement in low latitudes, between the periods obtained from the prominences, the spots, and the faculse is not unfavorable to a feeling of confidence in the results obtained by the prominence method in higher lati- tudes. This is perhaps strengthened by the further develop- ments which are indicated in the next section. THE DIFFERENTIAL CIRCULATION WITHIN THE SUN. In order to study more minutely the meaning of the fluctua- tions in the relative retardations given for successive lines in Table 2, it is seen that we have practically obtained a value of the retardation for each year of the interval 1871-1900, except for the gap 1878-1883, and that by plotting these as ordinates on a diagram whose abscissas are the years, a curve of relative retardation in the several zones can be constructed. Fig. 3 exhibits these data in a graphical form. Thus, in the northern hemisphere, for the zone -f- 50 to + 70, the ordinates in Table 2, beginning with that for 1871, read 2.13, 2.08, 1.93, 2.25, and these form the successive points of the retardation curve. In the upper section of the diagram marked " Prominence fre- quency " is reproduced the curve of average prominence fre- quency for the entire sun, which is the mean curve of the zonal system shown on fig. 2 of my paper on Synchronous Changes, 14 and is also reproduced at the head of fig. 28 of my paper, A Con- tribution to Cosmical Meteorology. 15 An inspection of the curves of fig. 3, shows plainly three important facts of fundamen- tal significance: (1) the retardations relative to the equatorial period of rotation, 26.G8 days, increase toward the poles; (2) the irregularities in the observed retardations are very much greater in the polar than in the equatorial zones; (3) these irregularities in the retardation do not appear to be accidental, but they synchronize closely with the variations in the fre- quency of the prominences. The value of this last inference is very great, in view of the other facts brought out in various portions of my research. Using this prominence curve as the standard of reference we have already proved the following facts: (1) The elements of the earth's magnetic field fluctuate with it annually in synchronism; (2) the terrestrial tempera- tures and barometric pressures synchronize with it, as will be shown conclusively in my next paper, in the MONTHLY WEATHER EEVIEW for November, 1903; (3) the internal circulations of the sun, as recorded in the rotational velocities of the photos- phere, also synchronize with the same curve. This exhibit binds the entire solar and terrestrial atmospheres in one syn- chronous circulation, and it therefore places the entire subject of cosmical meteorology upon a satisfactory basis, entirely in harmony with the procedure marked out in previous papers. While it can not be supposed that this discussion of the solar prominence frequency in longitude gives us final quanti- tative results on the rotation phenomena of various zones, yet the line of argument is sufficiently sustained to warrant further extensions of the research. We have shown that the solar angular velocity diminishes from the equator toward the poles at a certain rate, as on fig. 1 for example, or as on fig 4. This is in harmony with the von Helmholtz-Emden equa- tions for a rotating mass hot at the center and cooling toward the surface. 16 In such a mass there are discontinuous concave cylindrical surfaces coaxial with the axis of rotation, the equa- torial parts being nearer the axis than are the polar parts. This also implies that the polar regions of the sun are warmer than the equatorial by reason of the currents from the center toward the poles. At a surface of discontinuity, on each side of which the pressure is the same, but the temperature and angular momentum different, as where a rapidly moving cur- rent flows over a more slowly moving current in the earth's atmosphere, the conditions are favorable for forming vortex tubes, terminating on the surface, but extending through the mass of the sun. They are right-handed in the northern hemisphere and left-handed in the southern hemisphere, for convective actions from the equator toward the poles. If vor- tices are thus formed in the sun, so far as the state of its ma- terial permits, then the solar mass is in fact in a polarized state, the internal matter tending to rotate throughout the globe around such lines as are the generators of the required discontinuous surfaces. The turbulent conditions of internal circulation tend to a lawful disposition by the regulative action of a hot mass gravitating to a center by its own internal forces and emitting heat through these processes of circulation ac- companied by polarization and rotating vortex tubes. The contents of a tube must be made up of molecules and atoms more or less charged with electricity, and the necessary rota- tory motion produces Amperean electric currents which are a sufficient cause for the generation of a true magnetic field, positive on the northern and negative on the southern hemis- phere of the sun. This conforms to the result reached years 14 Monthly Weather Review, January, 1903, Vol. XXXI p 10 15 Monthly Weather Review, July, 1902, Vol. XXX, p. 352 16 See Eclipse Meteorology, pages 70 and 71. ago by my analysis of the terrestrial magnetic field, which showed that the earth appears to be immersed in a magnetic field perpendicular to the plane of the ecliptic and positive to the north of it. Variable circulation within the solar mass would display itself in corresponding changes in the rotation of the discontinuous surfaces, in the vortices carrying electri- cal charges, in the external magnetic field, in the number of prominences, faculae, and spots, in the earth's magnetic and electric fields, and in the terrestrial temperatures and pres- sures. Synchronism having thus been established through- out this vast complex cosmical system and referred back to fundamental thermodyuamic and hydrodynamic laws, it be- comes possible to make further advances in the problems of solar physics. Thus, the curvature of the internal lines can J870 J87S 2.50 1.50 JOO OSO 2.SO 2.00 0.60 J88S J890 1S95 1906 Northern Hemisphere. Southern Hemisphere. Zone-7Oto-5O: Zone-50to-30. Zone-3Oto-JO. Zone-lOtoO T FIG. 3. Variable retardations in the periods of rotation of the solar photosphere. 8 be studied in different parts of the meridian section on pass- ing from the surface of the sun to internal parts by means of the vortex law of constant angular momenta, Q = u> va 2 , under the assigned thermal conditions. We shall make an attempt to do this in a report which will contain the tabular data in full upon which^ these deductions are based. If it is true that large cosmical cooling masses in rotation N Pole. S Pole. FIG. 4. Formation ol vortices in the solar mass by differential rota- tions. contain u polarized or vortical internal structure which is the basis of a magnetic field, then it follows that this is the ex- planation of the earth's magnetism as well as of the magnetism of the sun. Hence, all stars are magnetized spheres, and their relative magnetism would be a measure of the activity of their internal circulations. Thus, the relative intensity of the earth's and the sun's magnetization becomes a measure of the internal vortical circulation in polarized tubes, and the variations of the earth's magnetic field have a cosmical significance, not only as to the direct action of the sun as a great rotating variable magnet, but as a measure of the forces which go to make up the solar output in several manifestations of energy. The summary of this line of thought may be found in chap- ter 4 of my "Eclipse Meteorology." It is proper to renew my objection to the results derived by other investigators for any solar rotation period which is shorter than 20.68 days, because it does not seem to be possible in view of the above analysis of solar conditions. Thus, we must reject Spoerer, 26.32; Broun, 25.92, 25.86, and 25.83; Hornstein, 26.39, 26.03, 26.24, and 25.82; Liznar, 26.05 and 25.96; Muller, 25.66, 25.79, 25.86, 25.87, and 25.47; von Bezold, 25.84; Hamberg, 25.84; EkholmandArrhenius,25.93; Schuster, 25.809 or 25.825. The numerous computations, giving results so widely different from that apparently ruling in the sun as derived from observations upon its own material, seem to indicate that the application of these several methods of computation to terrestrial data raises grave doubts as to their value. There are numerous difficul- ties in applying least square methods to solar-terrestrial data in the present state of our science. The great fluctuations going on within the solar mass tend to mask the fundamental law until it has been derived, at least approximately, by sim- pler methods. But the evidence is very positive that the equa- torial period of 26.68 days is the shortest one actually prevailing in any portion of the mass of the sun. II. SYNCHRONISM OF THE VARIATIONS OF THE SOLAR PROMINENCES WITH THE TERRESTRIAL BAROMETRIC PRESSURES AND THE TEMPERATURES. SEVERAL OPINIONS ON THE SUBJECT OF SYNCHRONISM. The numerous studies during the past fifty years into the ap- parent synchronism between the solar variations of energy and the terrestrial effects, as shown in the magnetic field and the meteorological elements, have been on the whole unsatisfactory, if not disappointing. Just enough simultaneous variation has been detected in the atmospheres of the sun and the earth to fascinate the attentive student, if not to justify a large expendi- ture of labor, in view of the great practical advantages to be obtained in the future as the result of a complete understand- ing of this cosmical pulsation. The attack upon the problem has really consisted in rather blindly groping for the most sensitive pulse in the entire cosmical circulation, and in disen- tangling the several interacting types of impulses. It is evi- dent that the partial failures hitherto attending this work have been due to two principal causes: (1) The comparison was made between the changes in the spotted areas of the sun and the terrestrial variations, but these solar changes were not sensitive enough to register a complete account of the action of the solar output. Discussions of the spots are being replaced by others upon the solar prominences and faculse, which respond much more exactly to the working of the sun's internal circu- lation. (2) The magnetic and the meteorological observations have not been handled with sufficient precision to do justice to the terrestrial side of the comparison. It is evident that all these physical data at the sun and at the earth must be com- puted with an exactness comparable to that of astronomical ob- servations of position, if meteorology is to be raised to the rank of a cosmical science. When one considers the crudeness of the meteorological data, taken the world over, due to the character of the instruments employed, the different local hours of observation, and the divergent methods of reduction, it is no wonder that the small solar variations have been swal- lowed up in the bad workmanship of meteorologists. The prevailing methods have been sufficient for forecasting and for climatological purposes, but they are entirely inadequate for the cosmical problems whose solution will form the basis of scientific long-range forecasts over large areas of the earth, that is, for forecasting the seasonal changes of the weather from year to year. It is perfectly evident that if secular varia- tions of any kind, such as the annual changes in terrestrial pres- sure, temperature, or magnetic field, are to be attributed to solar action, the original observations must be finally reduced to a homogeneous system. The local peculiarities of each station must be carefully eliminated, and the data of numerous sta- tions must be concentrated before anything like quantitative cosmical residuals can be obtained. When we consider that there have been numerous changes in the elevations of barom- eters, various methods of reducing the readings, and many groups of selected hours of observations entering into the series at the same station, how could it be expected that any thing better than negative results in solar problems would be obtained? The skeptical attitude of conservative students, who declare that the many indecisive results already obtained mean that there is no true and causal solar-terrestrial syn- chronism, is, of course, quite fallacious until it has been demon- strated by the use of first-class homogeneous data that the suspected physical connection is imaginary. There is but little question that the existing uncertainty is in fact based upon the use of the very imperfect methods of observation and reduction which have prevailed in meteorological offices, rather than upon the unreality of the phenomena in nature. At present the difficulties of the research are diminishing by reason of two improvements; (1) a better knowledge of where to make the comparison, and ( 2) the gradual acquisition of reliable secular data. Thus, the prominence data are super- seding the sun-spot numbers, and it has now become compara- tively easy to traverse the magnetic and the meteorological fields with our improved standard curve of comparison, and to bring out the fundamental typical synchronism in nearly every series of observations, so far as the annual means are concerned. The importance of emancipating this subject from the pre- vailing skepticism is evidently in the interests of advancing cosmical science. If we can prove that other forces than the Newtonian gravitation and radiation are interacting between the sun and the earth, it becomes a conclusion of vital interest to astronomers. As an example of the present state of opinion, we note Prof. Simon Newcomb's address" before the Astro- nomical and Astrophysical Society of America on December '29 1902, in which he says: The conclusion is that spots on the sun and magnetic storms are due to the same cause. This cause can not be any change in the ordinary radiation of the sun, because the best records of the temperature show that, to whatever variations the sun's radiation may be subjected, they do not change in the period of the sun spots. We shall, on the other hand, show in this paper that ter- restrial temperatures do, as a whole, change with the varia- tions of the solar prominences, and this will tend to modify Professor Newcomb's inference. The question whether the connection is direct or indirect, by a magnetic field or by some special action of radiation, is to be decided finally by an appeal to the observations. Dr. J. Hann writes in his Lehrbuch der Meteorologie, pages 626, 627: These can lead to the discovery of the period, but it is very difficult to find the true length of the period, since the amplitude of the variation of the meteorological elements within the period is not very great, because so many other influences are present, which stand in the way of deriving more accurate mean values out of long intervals of time. As yet no one has succeeded in surely deducing for any one meteorological element a cyclic variation of considerable amplitude. These efforts have been applied to variations of tempera- ture, clouds, rainfall, thunderstorms, hail, barometric pres- sures, cyclones, and winds, especially with the view of finding an 11-year period synchronous with that of the sun spots. It should be noted that a shorter period, of about three years, is probably the better period of synchronism to be studied. Also, synchronous movements need not be truly periodic. Indeed, there may be true correspondence with very irregular and aperiodic changes. It is easier to connect loosely constructed variations in the prominences of about three or four years duration with terrestrial variations than to establish synchro- nism in the 11-year sun-spot period. Dr. A. Sprung, in his Lehrbuch der Meteorologie, pages 366, 367, writes: Therefore, a connection between the sun-spot frequency and the changes in our atmosphere can not well be denied. It is probable that the pe- 17 Science, January 23, 1903. 10 riodic changes in the atmosphere are not caused directly through the sun spots, but that both phenomena are brought about through one common or by several interacting causes, whereby a displacement of the periods relative to one another becomes possible. Prof. Cleveland Abbe has frequently expressed in the MONTHLY WEATHER REVIEW a very doubtful view regarding the advisability of such researches, with the object of discouraging further efforts to unravel the solar-terrestrial net. Thus, in the MONTHLY WEATHER REVIEW for June, 1901, page 264, he writes: As the periodicities in sun spots, the width of the spectrum linos, the magnetic and auroral phenomena are sufficiently well marked to be satis- factorily demonstrable, while corresponding variations in pressure, tem- perature, wind, and rainfall are small, elusive, and debatable, we must caution our readers against being carried away by optimistic promises. It is certainly impressive to the thoughtful mind to realize that there is even a slight connection between solar and terrestrial phenomena, but the delicacy of this connection is such that it still remains true that the study of meteorology is essentially the study of the earth's atmosphere as acted upon by a constant source of heat from the sun. None of these astrophysical studies should tempt the meteorologist to wander far from the study of the dynamics of the earth's atmosphere and the effects of the oceans and continents that diversify the earth's surface. f.OO f.ZO "60 3.40 9. fq 3.0O 8.80 (2SJ (10) ^ of 200 ISO too Cu of J90? FIG. 5. Solar and terrestrial synchronism. We have, nevertheless, merely to recall the works of many scientists in order to realize how strong a hold this problem has upon the astrophysical meteorologist: Herschel, 1800; Gautier, 1844; Fritsch, 1854; Arago, 1855; Zimmermann, 1856; Wolf, 1859; Meldrum, 1870; Koeppen, 1873; Hill, 1880; van Bebber, 1882; Blanford, 1889; Bruckner, 1890; Lockyer, 1898; Carrington, Spoerer, Wolfer, and many others. The number of students who are taking up the problems of cos- mical meteorology is rapidly increasing, and this shows that there is encouragement for such work. The present paper continues the discussion of an investi- gation first published in 1894, 18 which brought out the fact that there is a synchronous variation in short cycles of about three years duration superposed upon the 11-year sun-spot period. In Bulletin No. 21, Solar and Terrestrial Magnetism, page 127, it was said: A comparison of the mean American meteorological curve with tho European magnetic curve certainly shows conformity to such an extent as to exclude merely accidental physical relations. Should such a result be obtained also in the future, it will bo a demonstration of the synchro- nism of tho two systems of forces under consideration. JS72 J87S JS90 J83S 1O9O J895 l&OO 2OO 100 T \ jT\ r- / \X^\ / ^ \ ^ fV/ V / ^. ^^-^.y \. Pffjmincr ices on th e Sun. "^ ^ +20 o -20 HO O -10 +10 -10 +10 -10 +20 o -20 +10 -10 +20 o -20 +20 -20 +20 O -20 +3O O -30 /\ M A / ^ / \ f\ ~^\ / \ \ / V7 V > \ - -^^ \ \ " *' , \ s "N V. / \J ,VfH' A/ft 'A Wales. ( $1 \/ /\ (\ s~\ f / \ f\ ^ / \ \ / \ I ~ W \ / "^^ V L \ S ^JjVor "tk India. (3j X-V /- ^ /\ --> / \ /\ / \ ^-^ / ^ \-S V / Vx \J Centn *l India. (4J \s A / 17 \ /\ A 7 \ n t \ / \ H /I ^ 1 J \ J V-x- , v ; \ } \^r Soub ^. India, (51 f~\ x s. J V -, A. /\ Z^. \ y\ _ ^ V A -S~ U \ / X \- ' JVort h China. (3) Qk r\ r\ x ^~ - s\ ^ ^~S \ A / V / \ o \ f\ / 2 v / V^ J a naj?,. f-^A } -\ /^ V^ / N / "~\ ^\^s \J_ \S \. ;C\ / Coast Cape Co font/ J 4 r* v y-v "- -^ /\ ^ / v/\ ^^ ^_^ ~ / \^s Inland G. 'woe ColonirJ37*-^ Plateau. Cave Colonu.(2) ^^r\ ^ /~~^ j \ ^ , \y \ * \ x ' ^~"^ i V r\ * f\ \ A / \ \ / \ 1 \ / \ / \ , ^ \ , \ / \ \ I \ / , / v/ \ / ^ I / \ \I s / \ J 1 /A \J /< '('/(ffir/. '(Jrf ^ ^ / v/ \ / v^^ x^ J V / N^ *^ Promine* tcqs on the i^fifn *Ss +2O -20 + 20 O 20 +20 O -2O +30 O -30 +30 -30 +SO O 20 France. ^ /~\ /~\ A / \s / 2 \ / Llx^ ^ f\ / ft 1 1 / \ V / s z H V / s / \ Spain. r\ / ^ r \ f 1 / \ / A A \ / / Nl7 u \ 7 V Q / _E .^ ' Vy ) \ f \f\ A /A / X / f\ j \ A f \ V /" , / > / w / \ ^ / &au.ffa wz uro oe. V / / r> v J. 'X 2S s / _ . s^~\ O x^ \ / N^ , _ \ 1 P 1 / \ z. \ / 1 j JVor gg Russ /a;. ^^ \ / r\ / rJ\ A ^y^ /\ 5 ' ^ i ) v \ v w 2E -t J t. 1 /~\ 'N / ^^^ ~\ ^~ \ / VA ~^\ \. ^- vX ' Pf \ +30 o -30 33 Russi cz _^ \ -. \ ^^^ Q /\ / \ /A / ^_/ \ ^y \ / \y \y w^ ^ i*V? ff*(7^ iSf&(*2*CCK FIG. 1. Variations of the annual pressure in the inverse type. In the present paper we shall show the results of a discussion of the annual residuals of pressure and temperature in all parts FIG. 8. Variations of the annual pressure in the indifferent type. use some simple devices for the sake of arriving at approxi- mately homogeneous residuals. The work for the United States is complete for the pressures, and is in progress for the tem- peratures. By inspecting my Barometry Report 19 it is easy to see the reason for the necessity of the reduction. In order to give some idea of the state of the data in other countries, we note the following with respect to the barometric pressures: For Russia-Siberia, several stations changed elevation more than once. India, there are numerous changes of elevation. South Africa, numerous changes of elevation, and also of the hours of observation. New South Wales, the monthly means of observations alone 19 Eeport of the Chief of the Weather Bureau, 1900-1901, Vol. II. 12 ta-rr rsrs 2880 laas 1090 lays ixo / X\ 200 / _5^5_\ / ^^ c ^ \^x \ / ^-^ 100 "V^ i V Promint >nces on /ie Sim. ^^^ o t. x-^ t-J.O / N r- ^ "\ / \ * ** ^^ o . _ \ 7 v ^ v ^ r' UO v ^Wew iSoittA Wa6es. (JOI +1.0 r\ . / ^ . o >v_ v/ ^^ l.O /SotitA^ 4_ustml(a ( ' J3a.ta.vi z and lA^otniilcc. . 25 ^_^ ^ ^^ S~*\^ ^ ""*' - V. - ^fncfcfjyof^i a /4) ^^ _^-^ ^^^ / r \/ / ^**-S ' / +1.0 o /i aur"tttiu -.13) y~\ ^^^^ ^^ ^x v^ "* ^" ^^ " N ~^^_X^ 1.0 +1.0 o -W +1.0 o Cei/iojz.(6i _ - x* V _ \^ \_x \ -/ 1 \/ In 2ia,JJow /W^ v _^. . JU adagasci r>.(2) W +1.0 o -1.0 +J.O -1. ^-*^ a ntralAl ricccJ6t~ / \ / \ / /"\ V / "* West Africa. (S) M72 1875 J880 23SS 289O 1895 1$OQ f \ /^V r- 1 ^^\ / s ^^ ^^ f\J Y / wo N ^ J ^V Prominences art the >u.n. >s - *. F +!.0 -7.0 +1.0 South Africa. .(20) ^/~\y "X j^^~\ y^^^ -^ ^^ \ / ^~~^ South Americ *,.(J5) /\ XN ~->k f\ y^v ^-v zs / \ / Vx U \S- \ X ^~ X / +1.0 -1.0 +1.0 -1.0 +1.0 -1.0 +w -1.0 +1.0 -1JO +1.0 -1.0 V.o 1.0 +1.0 o rvx-s Santia. 5> ^9 CAilt. / ^\ Q /" /~^*^, \^r-*^ */ \J \s West Indies. < ^ r~ ^**s r ^Azores crnd Jtfadeirvt, . 13) "11 ^ x\ ^X ^^" " \^^ ^X^ ,^v S\ North Africa (J2) x 2 2 V y^ Vz \ / ' s~ \^s \ z \_ X ,-N South West En rvp>e.(12i ^ x- .^^^.^ <\ x v r\ r / ~ v> \^~- \ , -s\f w \y r^ VestJ5ur>t 7ve. rf$) /^N _x^"~X \j^J^ r / \ / \ , "x /n^^ w ~ 1 i ^. West Given land. i~i4) i \ /\ ( \ r\ / \ - \ r\ I P / / f * \ r\ V / J f\ I 2-4 \J LJ \AJ \. \y y-*v S~ "* 23 -4 \ s - X\ r r ^^J \x +1.0 -1.0 _ Pacific States .(fO) ^^ < ^ ^ s. ,^-s. ^ \-x v -v_ 'ffonolirfu FIG. 9. Variations of the annual temperature in the direct type. were published. These had to be collected before the annual means could be computed. Argentina, the monthly means of observations alone were pub- lished, and these also had to be collected before the annual means could be computed. The stations have quite short records. Iceland and Greenland, very few changes in elevation, but not long records. In general all the annual pressure curves were plotted, and a mean pressure and normal gradient were determined, from which the amplitude variations were taken off as residuals. Since our purpose was simply to secure the most probable annual residuals this graphic method was substituted for the exact computations which ought to be made. Frequently the secular gradient slope was so prominent throughout the series for a single station as to suggest a gradual change in the cor- rection of the barometer relative to a normal standard. With respect to the temperatures, the annual means were extracted from the reports, and the mean values for the several series were computed, so far as they were apparently homo- geneous, and from these the residuals were formed. As the cosmical annual variation of temperature is only 1 to 2 F., it was often possible to break up a long series at the same station into homogeneous sections; but this was done cau- tiously, and only after clear evidence of a discontinuity in the local conditions. The great difficulty with the temperature data consists in the numerous hours of observation that have been adopted, or in the numerous selected groups of hours from which the means were derived. Many of these differ- 13 ences arose from artificial attempts to obtain an approximately correct 24-hour mean, to which in fact all meteorological data should be very carefully reduced. Some of the combinations of hours used are as follows: United States, Washington mean time, 7:35, 4:35, 11:35; 7:35, 4:35, 11:00; 7, 3, 11. Seventy-fifth meridian time, 7, 3, 11; 7, 3, 10; 8, 8; maximum, minimum. 1872 1S75 1880 1685 189O 1895 19OO 200 100 z_ \ ^\ / ^zrs / V " \ x C\J \ / V x \ y v s ^V " ' ^^ _ Prominences on ii re Sun. F. -l.o o -1-1.0 -1.0 +1.0 -1.0 o + 10 -1.0 o +1.0 1.0 +1.0 -1.0 o +1.0 -1.0 o +1.O -1.0 o +1.0 l.O o +1.0 -2.0 +1.0 -1.0 o +10 75 JaDOJi.llSI ^^ ~ / c A \ ^ s^ ' \_^ \ Z_AJ ^/ \ / -* 132552! tna.J2) s~*\ _ / \ /-^ Z-JuZ \-~. v / 2 V^ / v^ -5^7 \ y Q V """ ^ SJl. Chin i3S Z_j A, 2_S \ ^_ ^/ ^ ~^^^_^ S.W. Russia.. I 191 ' \ y ^ /-\ ,^\ 1 V / \ ^ / V - / \ A r- / \ / \J ^ _ y \/ 3 ' vy ^_ z / L \ / ' \ \ ... Centr ^ Russia. I 101 S r \ /"*- - A Q ' V \ f E2_ \J \ /" V- v / \ \J ^^ \X V / \ 3 /> s A i / \ \ r- \ / r~ / ^ \ / /" \ j V / / v / \J vx ^ \ /. V/ vy ,yK W.Ru^ta.:t.9l A f. / v / V \ - / v - " -- * "^^^ / \ / *"v-J V ' \y v/ HI^^^ \/^ / Centr (T Enron e.(17) \> (\ A \ \ / \ zs 3 / \ / \ \ j y \ / \ ' - " N. ' v_y U x V/ Faroe /s-< and&i let iia.nct.- E. GreenLa rut. (4-) x / ^ 1 vy s J v_ /-\ / \ \|y V v /-\ Souths ltlcmtic"States . 1 g / -\ \ y ^ \r\ ^ / \ "i vy \ / A / ^_ V \ y v Wfe5-l =J ( dv dw The usual method of development proceeds by taking dx dy dz = > W = > S that f _ dP = C(udu + vdv + wdw) +V0 = J?' + V-C. This is the ordinary form of the equation of motion on the rotating earth as given in treatises on hydrodynamics, as in Lamb, p. 22, and Basset, Vol. I, p. 34, and is known as Ber- noulli's Theorem. G is not an absolute constant, but is the func- tion of the parameter of a stream line; and in the atmosphere, where the flow takes place in stratified layers having different temperatures and angular momenta, it changes from one stra- tum to another. It is also possible to integrate these terms along an arbi- trary line, s= I ds = I (dx, dy, dz), and in this case the deriva- tive relative to the velocity will give acceleration along ds ; that is, we have qds instead of qdq, and under some circum- stances this may prove to be an advantageous method. In meteorology this will depend, however, upon whether the one 22 Monthly Weather Review, Vol. XXX, pp. 13, 80, 117, 163, 250, 304, 347. or the other set of terms that are required are most practically observed, as line integrals may be readily computed for either of these systems. LINE INTEGRALS IN THE ATMOSPHERE. The principles of the canal theory of circulation have been applied by V. Bjerknes 23 and J. W. Sandstrom " in their papers on circulation, under the form of line integrals around arbi- trary closed curves in the atmosphere. Thus, the circulation is expressed by them, with the vertical and horizontal compo- nents of the total enclosed curve, as Total circulation. Relative component. Earth's component. (5) C7 a = + G e (6) fqds =jVs +2. dt ds = (7) (8) _ (9) _ f*l = C q J P */ ds dS Equation (7) is the time rate of change. (7 a = the line integral of the tangential component of total velocity. G = the line integral of the relative velocity (tangential). C = the line integral of the velocity of a point on the moving earth itself (tangential). (9 a > 1> ?e) = ^ e velocities; (q^ q, q e ) = the accelerations. R = friction; <"= the angular velocity of the earth. P = pressure; p = density. i = the angle on the plane of the parallel of latitude that ds makes with the direction of a moving point of the earth. S 1 = the projection of the closed curve S on the plane of the equator for the polar distance 0. These integrations involve an accurate knowledge of the pressure, density, and acceleration at numerous points along the chosen closed curve, and this it is very difficult to obtain by practicable observations. The variation of 9 can be found more readily. Several illustrations are given by the authors in ap- plying the theory to the general circulation of the atmosphere and to the local cyclones and anticyclones, but these illustra- tions do not seem to conform satisfactorily to the conditions observed in North America, as will be set forth in the other papers of this series and in a full report on the subject. There arises no question with respect to any of the terms of the equation except the one containing -jp which appears to be an addition to the usual form of the equation of motion on the rotating earth. As has been shown by V. Bjerknes, if the angle can be taken constant for a given relatively small closed curve, we have = 2 j , cos 6 ,, /* J cos i ds, where i is the angle that the element ds makes with the par- allel of latitude, or the angle between the two radii of an ele- "Meteorol. Zeitschrift, March, 1900; April, 1900; November, 1900; March, 1902. 24 Ron. Svens. Vet. Ak. Handlingar, Bd. 83, No. 4; Meteorol. Zeit- schrift, April, 1902 ; Vetens. Ak. 1902, No. 3. 17 18 nientary area, as shown in fig. 14. Hence, for a line integral we have, y (15) FIG. 14. Component axes. (IV) d C C dw C di ' j \ \ m cos i. ds= %J -^-. cos i ds | J ^-^- sin i as = \(udy vdx\, since = u, m =v, dscoai = dy, dseini=dx. dt dt We have in the case of a velocity potential, u dy v dx = 0; and, as is well known, the only influence of the rotation of the earth is to add a deflecting force always at right angles to the direction of motion. The integral of the work done in moving a particle, I -J . ds, receives no additional term from the fact that the earth rotates, any more than a planet alters the velocity in its orbit from a force perpendicular to its path. We thus obtain 2 oi -,^ = 0, and all the developments derived from its use must be carefully interpreted. It seems impor- tant to have made this fact clear, in order that the equation used as the basis of the following analysis may be taken with- out modifications. If the gravity potential F= gz is added we obtain the complete equation. The line integral of a gravity force around a closed curve is, also, always zero. EQUIVALENT EXPEESSIONS FOE THE DENSITY p. 1 P The specific volume or isoster, = v, in the term , can P P. be discussed in four different ways, and substitutes for it can be introduced into the equation. 1. From Bigelow's equation (47a), Cloud Report, we have P T P ^ '* where the variations are expressed in terms of /> , P , P and the thermometric temperature t. This is the common pro- cedure among meteorologists. 2. From equation (75), the Boyle-Gay Lussac law of gases, (13) 1 RT __ P ~ p ~ v> where R is the gas constant, and T = # the potential tempera- ture. This form was employed by H. von Helmholtz, and it has several advantages over the others in applications to the atmosphere. 4. By reducing the volume to unit density so that /> = 1, we shall find that P ~ k-l J k r which is the form used by Emden in his paper on the solar circulation. 5. The potential temperature is found practically from the formula (") /-v**- 1 , B Pi or in logarithms, (18) ' log = log + 0.2889 (log B - log B,). o> dr DEVELOPMENT OF THE TEEMS , V, AND , . Since the pressure P in units of force = g p, we have from (15) (19) P *-* _! i-* fc-i = <7 * R .B . n k r> = Q TO * R. 9 . n k f* ifO*0 + - i'O* * (20) P_ p (21) dP dr. . = A . 9 . I for . dm d - P - = A 9 ^ fidr ' dr A = g p a k R. = constant. /p\l=* (*)' k-l " = The gravity potential, including the centrifugal force of rotation about the axis z, with the angular velocity 2 + ^- + C. where the variations are given in terms of R, T, p- the gas constant, the absolute temperature, and the weight and this has been used in some discussions. Since the atmosphere is not arranged upon the adiabatic law, but diverges from it * ^<> K __ ^ + 1 ( considerably, this method must be cautiously introduced, # : r though there is a strong temptation to use the absolute tern- (29) Second stratum: perature on account of its convenience. i 1 / 50 \ * 1 3. Since we have = ( ^ I , by equation (84), and P \P / Po 1 72 V 7 = 9 , by (75), we obtain the third form, Po Po \ i 1 / \ *~ p T The equations of motion for two strata flowing over each other, and having different potential temperatures and angular momenta, become, (28) First stratum: H' 1 At the discontinuous surface of flow the pressure r l = K V hence, (30) /_!_ l\g R' , K'+O , (V+V) e. ' Po C C e, . , "' (u' 19 The terms in u and w may not always be neglected where there are strong meridional and vertical currents, as in cyclones and anticyclones. TO FIND THE DIRECTION OF THE BOUNDARY CURVE BETWEEN TWO STRATA. 1. Differentiate (27) for r with m constant. Then, in crossing the boundary from the first to the second stratum, (32) dr 2. Differentiate for m with r constant, at the same time holding the angular momentum (via) constant in each stratum. Equation (27) can be written: Differentiating, (34) Q = du udu wdw\ 1 ). dm dm I wdw dm For the two strata, (36) \ 1 ~ + omitting terms of the second order. 3. Finally, dividing (36) by (32), we obtain, (37) dr 1 gw This equation defines the slope of the curve which separates the two stratified currents that flow past each other, preserving their angular momenta, Q = vm = v.~l eastward and IT, for relative velocities. (38) + dr + dr r(v 2 2 v 2 ) 0, (y, 2 i> 2 ) i dis \_ #j 8 t The second member of the equation is positive if where v a > v , v 2 > v , v 1 > v v and 6 1 > # 2 , that is to say, if the higher strata have a higher potential temperature and greater eastward relative velocity than the lower, the quantities being arranged as in fig. 15. Fia. 15. Case I. Take a point in the atmosphere defined by (r, m) the radius and the radius of rotation, respectively. The next successive point on the line of separation of the two gyrating strata is given by (r + dr), (m dm) as indicated, so that the curve continually rises above the successive tangents to the horizon, but approaches the axis of rotation in the direction of the celestial pole. Since (D* v 2 ) is the square of the relative linear eastward velocity, it follows that the strata in the atmos- phere subject to this law have a continually greater eastward drift and greater potential temperatures with the increase in altitude above the surface. These conditions are character- istic of the earth's atmosphere beyond a certain latitude which varies with the height above the surface. The Weather Bureau Cloud Keport, 1898, proved that the velocities and also the potential temperatures for the United States conform to Case I, as in chapters 12, 13, and 14, which contain a discussion of the departure of the temperatures of the upper strata from the adiabatic law in the sense that these strata are overheated. Those velocities have been properly prepared for immediate introduction into the above formula. CASE II. APPLICABLE TO THE TROPICAL ZONES OF THE EARTH. ,< (39) dr and- .v-v for K h K < u ~| westward < o relative > i> 2 J velocities. The second member of the equation is negative if , 2 L , where t\ < , u, < v a , w, > v v and 0, < 2 , that is to say, if the higher strata have lower potential tem- peratures than the lower, and the lower strata a greater west- ward relative velocity than the higher, the quantities being arranged as in fig. 16. Take a point in the atmosphere defined by (r, GJ) and the next successive point on the line of separation is given by (r dr), (m dm), as indicated, so that the curve continually falls below the successive tangents to the horizon, and ap- proaches the axis of rotation in the direction of the celestial pole. The relative velocity is westward, since v is greater than v l and v 2 , so that v*v a * and v 2 2 1' 2 are both negative quantities. Since u, 2 u 2 is a smaller negative quantity than r 2 2 2 , the numerator is negative. Also, the denominator is negative, for 6 l < # 2 . These conditions are fulfilled in the tropical zones where the westward drift is greater in the lower strata and diminishes upward, while the potential tempera- 20 FIG. 16. Case II. tures decrease upward. Chapter 8 of the full report will discuss the velocities in the tropical zones of the West Indies. The potential temperatures in the Tropics still remain to be computed. CASE III. APPLICABLE TO THE ATMOSPHERES OF THE SUN, JUPITER, AND SATURN. _ v'-v 1 [ v i > VI eastward 9 l > # 2 and ' g - < * g - for u 2 > relative 1 * L v i < v zJ velocities. (40) j-dr = _ T^ r-<) g. -(V-Q 2 "| = _ The second member of the equation is negative if _,, v'v' g > g where w, > , t;., > , v, < u,, and 0, > 2 , that is to say, if the higher strata have a higher potential temperature and a smaller eastward relative velocity than the lower, the quantities being arranged as in fig. 17. FIG. 17. Case III. Take a point in the atmosphere denned by (r, m), and the next successive point on the line of separation, which has vary- ing temperatures but angular momenta that are constant within the thin layers, is given by (r+dr) (uo + dvo), as indicated, so that the curve continually rises above the plane of the horizon, and recedes from the axis of rotation in the direction of the celestial pole. The warmer strata are nearer the axis, and the potential temperature increases in the direction parallel to the axis of rotation, and at the same time the relative velocity is such that the strata near the pole rotate more slowly than those at greater distances. These conditions are found to prevail in the atmospheres of the sun, also of the planets Jupi- ter and Saturn, as attested by the belt formations and the systems of vortices penetrating to the surface. On the sun the granules of the photosphere are the ends of vortex tubes between adjacent strata having different velocities. Similar vortex tubes are seen on the two planets. THE INTERACTION OF CASE I AND CASE II IN THE EARTH 's ATMOS- PHERE IN THE FORMATION OF LOCAL CYCLONES AND ANTICYCLONES. In the earth's atmosphere the boundary between the east- ward drift of the temperate zones and the westward drift of the tropical zones is an arch spanning the equator high up into the cirrus cloud strata, and resting on the surface at lati- tudes 30 to 25. On the poleward side Case I applies but on the side toward the equator Case II prevails. If the circulations of Case I in the temperate and polar zones, and of Case II in the tropical zones, are applied without further conditions, the isobars in the atmosphere will be dis- tributed, as in fig. 18, so that they rise from the arched boun- dary of the eastward and the westward relative velocities toward the pole and toward the plane of the equator re- spectively. This, however, is not the course of the surfaces of pressure in the atmosphere as determined by the observa- tions near sea level, and by computations at higher levels. To illustrate the actual conditions, in fig. 20 Ferrel's values of the isobars on the sea level are given from pole to pole, and Sprung's isobars for the 2000-meter and the 4000-meter planes. The practical problem is, therefore, to account satis- factorily for the modifications of the types. In the present state of meteorology we enter upon a field that is incompletely explored, so that the following remarks are suggestive of the solution rather than final, but there will be much material that sustains them in the complete report, Volume II, Report of the Chief of the Weather Bureau, 1903-1904. There are two conditions that modify the solutions of Case I and Case II very decisively. (1) The first is that the as- sumption that the angular momenta in the several strata re- main constant around the earth, or that the air rotates in unbroken rings, does not hold good even approximately. Be- sides the waves and vortices engendered between discontinu- ous strata, as von Helmholtz explained, there is a yet more pow- ful cause for the breaking down of the vortex law, v as = con- stant, namely, in the cyclones and the anticyclones of middle latitudes, and in the convectional vertical circulation near the equator. (2) The second is that the boundary between the eastward and the westward drift does not girdle the earth uniformly, but is broken up into sections by the intrusion of Case II into the region of Case I, and the extension of Case I into the region of Case II, so that the high pressure belt which this solution assumes to encircle the earth is broken up into large isolated high areas or centers of action, as those lying over the oceans in summer, or over the continents in winter, in the lower strata of the atmosphere. To work out the theory of these details will be a large task for the meteor- ologist of the future. These two types of disturbance oper- ate together, somewhat as described in the Weather Bureau Cloud Report, 1898-1899, so that the present paper is merely an extension of the analysis there suggested. The following descriptive statement attempts to outline the probable course of the modifications of the pure vortex theory contained in the system of equations given above. Referring to figs. 18 and 19, the "unmodified" and the "modified" systems, respectively, it is evident that the solar radiation in the Tropics, if unrelieved, will by accumulation raise the isobars of Case II, by increasing the potential tem- perature # 2 and the westward velocity v 3 v in the lower strata. In a circulating atmosphere the relief comes in two ways, (1) by forming a vertical convection near the equator, and (2) by forcing a horizontal convection into the lower strata 21 Case I. Case IT. CaseJT. Cause. I. FIG. 18. Cases I and II unmodified. of the temperate zones. The first transports heat into the upper strata, reducing # 2 and increasing #,, so that the west- ward drift diminishes. At the same time the intrusion of masses of air having one value of momentum (mv) n into those having another value (mv).^ will change their velocities. These two causes lower the lines of Case II 011 the equator side, and in the lower strata may even reverse them. Accompanying these changes a component on the meridian toward the equator sets in, so that the trades from the northeast and southeast are de- veloped, and the first minor circulation is maintained in the sense indicated by the arrows over the tropical zone of fig. 19. The rise and fall of the isobars of Case II, with the relief of the incoming solar heat through this circulation, is a complex but sensitive form of natural heat governor which is self- regulating, and preserves the normal state of equilibrium proper for the season of the year. This special action is chiefly due to the mutual movement among the terms of equa- tion (39) for Case II. A still more complex system relates to the temperate zones and Case I. To some extent the terms within equation (38) for Case I go through a similar self-adjustment in response to the local insolation, but this is by no means the primary Case I + Ca.se H Oasel . Ca.se H+ Ca.se! . Casel+Ca-Bett. FIG. 19. Cases I and II as modified. cause for the depression of the isobars of fig. 18 to those of fig. 19. As explained in my paper, " The mechanism of coun- tercurrents of different temperatures in cyclones and anti- cyclones," MONTHLY WEATHEH REVIEW, February, 1903, cyclones and anticyclones are formed by horizontal currents under- flowing the prevailing eastward drift. Thus, as shown on fig. 19, warm currents flow from the Tropics into the Temperate Zone, as from the Gulf of Mexico into the United States, underneath the eastward drift, and this stratification of warm air beneath cold air produces two changes. The potential temperature # 2 is increased, the value 9 l #, is diminished, the velocity is checked and the isobars fall, because the angular momentum is diminished. At the same time that the air rises on the east side of the cyclone, a cold current from the north flows to the west side, and this decreases its # 2 but increases the difference #j 2 , so that the velocities are increased. It is known that the eastern warm current tends to curl westward and the western cold current tends to curl eastward about a cyclonic center; inverted conditions prevail around an anti cyclonic center. Furthermore, the dynamic action of intruding cy- clones and anticyclones from the lower to the higher strata, by their interchange of inertia with the eastward drift, must diminish the eastward velocity and lower the isobars of Case I. 7Z772. 47O 4OOO }6O tte 20OO .Surface 60O 590 seo 76O 7JO -140 +70 +6O +SO +4O +30 +20 f-JO" O JO" ZO -JO - 5O -6O 7O -8O 9O Fio. 20. Pressures at different latitudes (Ferrelj and altitudes (Sprung). 22 This effect of the interchange of components may be seen by combining the terms of Case I and Case II algebraically. Thus, we have, symbolically, _-dw_ Case I ~" [= -dr Jrdecrease of (+dr) Case II Lincrease of ( dnj) 1 so that the lines of Case I are plotted nearer the axis, and lower in the atmosphere above the horizon than in fig. 18. There are instances in which, by this intrusion of the warm air of Case II from the Tropics into the region of Case I, the potential temperature of the lower strata is greater than that of the higher strata, so that Case II supersedes Case I in the temperate zones with local westward winds. Similarly, the interplay of these cases outside their normal regions is a suf- ficient cause for the manifold local circulations found in the lower strata of the atmosphere up to about 3 miles from the ground, beyond which the circulation is more regular. The amount by which the normal lines of Case I are depressed through the intermixture of Cases I and II, in consequence of temperature and inertia interchanges in the lower strata, measures the amount by which the vortex law ceases to be complete in its application, and by which the Ferrel theory of the general circulation becomes an untenable hypothesis. In effect these interchanges are attended by secondary currents along the meridian so that there is a second minor circuit in the temperate zones, somewhat as indicated on fig. 19. The H, L, H, of the vertical section should be understood to stand over H, L, H, on the horizontal plane of the given latitude; that is, they are not distributed in latitude but in longitude, and should be superposed in a correct projection. So far as I understand the facts, this circulation, taken in connection with the tropical circuit, conforms to the results of the International Survey, as stated in H. H. Hildebrandson's Keport, which need not be here recapitulated. In the polar zone our information is too meager to afford us very definite knowledge, but I suspect that there is a third circuit as shown in fig. 19, though it may not be very pronounced and well defined. It is my purpose to work out the data for the temperate and the tropical zones now in the possession of the Weather Bureau and applicable to the North American Continent, along the lines here indicated. The attempt to bring these laws of the general and the local circulations into a harmonious numerical scheme will require considerable labor, but it is believed that it can be accomplished. The data contained in my reports, while apparently somewhat disconnected, are in reality all contributory to my solution of the problems of atmospheric circulations both of the earth and of the sun, together with the connections between them. It is proper to determine care- fully the separate portions of the work, i. e., the velocities and temperatures of the strata in motion as dependent upon obser- vations, before trying to put them together in a final synthesis. It is only necessary to have in mind the general plan of development, as here outlined, in order to keep the several portions in harmonious relations with each other. IV. VALUES OF CERTAIN METEOROLOGICAL QUANTITIES FOR THE SUN. THE IMPORTANCE OF THESE VALUES TO TERRESTRIAL METEOROLOGY. The most important data needed for use in studies in solar physics are the correct values of the pressure, the temperature, the density, the gas constant, and their many derived rela- lations, at the surface of the sun, within its mass, and through- out the gaseous envelope. In the present uncertain state of our knowledge of these quantities, even an approximate deri- vation of these data is important, and this forms the justifica- tion for the studies contained in this paper. The problems of the circulation within the sun's photosphere, the transitions and the transformations in the atmospheric envelope with the attendant radiations and absorptions, the heat and light re- ceived at the outer surface of the earth's atmosphere, the re- sulting absorption and transmission of energy in the air, and the dependent circulation, are all languishing for the lack of a sound footing for our computations and deductions. The computations for the surface temperature of the sun give results ranging from 5000 to 10,000; using Bitter's Law, Professor Schuster computes the temperature at the center of the sun as 12,000,000, assuming that it is composed of hy- drogen split up into mouatomic elements. But it is evident that any such range of temperature would simply explode the sun, whereas it now circulates in a moderate manner. Unless some value for the temperature of the solar photosphere can be found, it will be impossible to determine what percentage of the total solar radiation is absorbed in the solar envelope, even though the radiant heat be computed successfully on the outer surface of the earth's atmosphere from radiation meas- urements at the ground. Should the following remarks prove to be merely suggestive it will be proper to make them as a contribution to the problems in solar physics. I have been interested in the paper by Prof. F. E. Nipher, on the "Law of contraction of gaseous nebulae," 25 because it seems to offer a way of escape from the impossible results which follow from Bitter's equations, where the exponent in P v n = B is 1.33 -f . Nipher makes the value of n = 1.10, and from this exponent the entire system of relations seems to be more probable. I will recapitulate Nipher's equations, after making the following changes in his notation to reduce them to the symbols used in my papers: Nipher. Bigelow. Gas constant change C to R Density " S " /> Distance from center " R " r Mechanical equivalent of heat J " A' 1 Heat equivalent of work 1 A J * 1 Constant " A " B Batio " p " b Constant " k " k' "Transactions Academy of Science, St. Louis, October 1, 1903. NIPHER S EQUATIONS. Adiabatic law for perfect gases: 741) Pv=RT. Heat relation: Assumed laws for non-perfect gases: (43) Pv n =P a v"=B. (44) IV--*. (46) js=i = Specific heat: AR Gravitation : (47) ~-=k t ^ f p = k' 1 - ar r' ' Pressure : (48) P 4.19 x 10' _ 1.5173x10' [2 -1 n r -il. *"- 3 ' . Bn r " - 9551 ' 8 ' (2-n)' 2TF~?J l^FpJ T' 0.636 M ' k' Density: [In Sri* B 1J_ f 0.955 I 1 - 11 (49) /) = -r~ r? , 2 -"= jj. = 0.95 Temperature : R T 0.78 M (50) T 11 / 0.95 W" = 0.818 5 | (2-n) s 2^/P Jf* R Mass : 2-n n - 3n 2 ) 1 -A P(2 3n 2 ) 1 -A- J -n)'J '''' 0.955V-" 0.77 2-n 1.22 Tr 23 24 Weight of one gram at the surface: k* M 1 2 n \\ B(4:n 3n') h-n 1 . T 2flr Auxiliaries. /dQ\ "( dv \ ( dP \ dP d " R M R M - c P -A lp v , f ,- AKit - ? r^.* dy 2 dr -S+*^* V= + 2-n-r' A R - 2 -n r L22 r Auxiliaries : ,3) n-r- 2n ^_ 3 j ( R 1 ?i 2c.. -f 4^4 7J 6K 4 / r-,7 \ 8_J . 1 10 ^(4 3n)>i J f(4/t 3/i*)lf"| 2<- p + 3A R 5/c 3 3;z 4 K 4 3c (68) Cj, = A R g _ 2ft = .4 7.' K _ l = A R ^ _ l . 4 2 n M L* M /c 2 (initial) Contraction ratio o . ("final 1 ) ' f /r V (55) P=P (^j =P 6*. /r \ 3 (56) p=r\-?) = />.* \oi ) -f * \ r / ' Mass : 4 , 2 n j [58) Jf=ij- -r />= ="4_3 ft ^'' Average density: f ro\ T ^ ^ n 3 86 n (OJ) 11 J. 1 V r. X 1 2 o U.O1O n . Heat: (70) = (%y\ (T - T ) = - (c, + 4J 7?) (T - 2 T ) (c, + A R) T (b - 1). Work: (71) W= CP do=P 'i^J*" ^ = r ^ n (b - 1) />oo , 4 3n M'li* 3f'^ = 4 -J r '- 2pd? '= 2r =- 636 2r ' Ratios : /7O\j-i. _ Z P' 07^ l"^ ia 4 3^ 2-n 4 on Distance from center to stratum where the density /> = aver- age density p a : - w ' c v + c p + A R 2c v +3A11 5/c 3 C B -f 4^ R c v + 4A R /7Q\ _ P ' - ' Q AA 4 3 W j r 0.545?-. T^ (74) n 5K 3 400 3 (2 n) Average pressure: 4s j r 2 P dr (611 P ^ 3P f>40 P Differences: /7K\ /IP A1 8 A A T> v *"* / s*f * Kj, 4- J r 1 dr J o Distance from center to stratum where the pressure P = average pressure P : [~| 2-" 1 6 5n 2 Q 502 (75) c p ^- 3(2 -n) J 5/c -3 J *' K 1 4 3n 3/ >P J ~ 5*c 3 n %r T a For a rise of 1 C., energy equivalent to 2c p + 3^4 R heat units must be applied to the unit mass, of which c p + 4^4 R heat units are radiated per unit time, and c p A R = c v heat units are used in raising the temperature. THE ASTRONOMICAL CONSTANTS FOB THE EAETH AND THE SUN. It is difficult to select from the available astronomical data a system of constants that is rigorously self-consistent, and in this preliminary discussion it is not necessary to make com- plete adjustments between the several quantities. The fun- damental units employed are conveniently the C. G. S. system, and not the C. S. system, because in the thermodynamic for- mulae the unit of mass is the gram. In the C. G. S. system the gravitation constant is found from the formula, M m R 1 n /rff*\ 7,2 1 C3r\ 4-V o 4 1 /-'^ 1 i'O ~R~f ~M^n' The constant for transformations from the C. S. system to the C. G. S. system is ; i. e., (mass C. S.) = (mass C. G. S.). K 1C 3 2-nJ Average temperature: (63) T 3 ' T 1.08 T. Distance from center to stratum where the temperature T = average temperature T a : (64) r . ~ l> r 707 r Specific heat: dP dv dO ** P ^ u c 71 c c /K ?i\ ^ ' dT dP do 1 n K \i n)' ~T + v 25 TABLE 7. Astronomical constants. Hence, Numbers. Logarithms. K R t zz mean radius of earth, Bessel's 6370 19100cm. 8.8041525 ~ m ^' spheroid R^ = 17. 6083050 This asserts that if remains constant, v = also remains R* = 26. 4124575 m f> p al zz average density of earth, 5. 576 0. 746323 constant. If a gas, as hydrogen, /> = 0.000089996, is sub- Harkness jected to the same relative increase in P and T, it remains at the 4 4. 1888 0. 622089 K 3 " i same density as that for which its gas constant was computed. MI ~ ~ir Rf p a , zzmass of the earth 6. 0377 X ISO 27 27. 78070 We can, therefore, transform hydrogen, or other perfect gases, in grams from terrestrial to solar conditions by simply multiplying by m 1 gram 1. 00 0. 000000 the proper factor. In this case it will be x = 28.028, the ratio <7 zz acceleration per second at 980.60cm. 2.991492 of g at the surface of the sun to g at the surface of the earth. surface of earth In Eclipse Meteorology and Allied Problems, chapter 4, R * n i Table 14. "Fundamental constants," a series of values was 1? 5j Jo constant 2 818927 computed depending upon assumed values of r, the sun's J/, m 1. 5173 x 10' j radius, and G, the ratio between gravity at the surface of zz transformation constant ft 2 1. 5173 X 10' 7. 181073 of Mie sun and gravity at the surface of the earth. Since these values have been changed a little in the preceding computa- ratio of mass of sun to mass of 333432. 5. 523008 tions, it will be necessary to reconstruct the numerical values J i earth, Newcomb of that table, although the effect upon the dependent quanti- M = mass of the sun 2. 0132 X 10 33 33. 303878 ties is not important. In order that the transition from ter- r zz radius of sun for Auwer's di- 694800 80000cm. 10.8418603 restrial to solar conditions may be made as plain as possible ameter (31' 59.26") to the reader, we will compute the fundamental constants on r 2 zz 21. 6837206 the supposition that the earth is surrounded by a hydrogen r i 32. 5255809 atmosphere instead of the common air, making allowance for p parallax of the sun, Newcomb 8.7965" 0.9443099 the change in density. D zz distance from sun to earth 1493 40870 00000 cm. 13. 1741786 r/D i-'ti ir. r\f voflii -i r\n rv+1 n /-vorrrrrvfTo TABLE 8. Constants for one atmosphere of hydrogen on the earth. /rt[ Liino oi rauii S/S, ratio of surfaces (109. 071 ) 2 iuy.u/j. a.uoMUfo 11896.4 4.0754156 Formulae. M. K. S. system. C. G. S. system. V/ F, rz ratio of volumes (109. 071) 3 1297548. 6. 1131234 ^, gravity at surface of sun . ' 28 028 1 4475924 Loga- Loga- gravity at surface of earth j Numbers. rithms. Numbers. rithms. p n zz mean density of the sun zz M /J, 3 J/! ' r< 1.43287 0.156208 ( 18. 5212 miles/sec, velocity of the earth in its orbit ) I 29.80670 cm./sec. 1.267670 6. 474314 zz acceleration at the dis- tance of earth (check) zz J/ = rate at which earth falls toward sun 0. 59491 cm./sec. 9. 77444810 0. 23422 inch/sec. 9. 36961510 0. 29746 cm./sec. 0. 11711 inch/sec. 9. 7744810 9.47341810 9. 06858510 APPLICATION OF THE THERMODYNAMIC FORMULAE TO THE GASEOUS ENVELOPE OF THE SUN. The evidence from the action of the lines in the solar spec- trum, as regards shifting, broadening, and reversals, shows that in the envelope resting upon the photosphere, comprising in its contents the reversing layer, the chromosphere, and the inner corona, the gases may be treated as approximately per- fect gases and tending to conform to the Boyle-(Mariotte)- Gray- Lussac law, P v = --- T, where P is the pressure in units of force, v the volume, K the absolute gas constant, m the molecular weight, and T the absolute temperature. I propose, also, to apply the same law to the solar mass within the pho- tosphere, with a suitable modification, and to compare the results with the data obtained from the use of Professor Nipher's equations. We can first multiply the equation by any numerical value, x, and distribute the variation between P and T alone, holding the density identical in the two conditions. Formulae. M. K. S. system. C. G. S. system. Loga- Loga- Numbers. rithms. Numbers. rithms. do = gravity 9. 806 m. 0. 99149 980. 6 cm. 2. 99149 p m zz density of mercury 13595. 8 4. 13340 13.5958 1. 13340 B u zz mere. col. for 1 atmos 0.760 9. 88081 76.0 1. 88081 p b zz density of hydrogen 0. 089996 8. 95422 0. 000089996 5. 95422 Po = Pm B = Ph ' (weight) 10333. 4. 01421 1033. 3 3. 01421 TJ 114815. 5. 05999 11481500. 7. 05999 i ( noiti. t u iiios) Ph jf temperature 273. 2. 43616 273. 2. 43616 I R a zz gas constant -"o 420. 56 2.62383 42056. 4. 62383 v zz zz: specific volume Ph 11. 112 1. 04578 11112. 4. 04578 Po f'o = l 114815. 5. 05999 11481500. 7. 05999 ^r.= 114815. 5. 05999 11481500. i 7.05999 TABLE 9. Transition to constants for a solar hydrogen atmosphere. Formulas. M. K. S. system. C. G. S. system. Loga- Loga- Numbers. rithms. Numbers. rithms. G = gig. 28. 028 1. 44759 28. 028 1. 44759 Gp = p (weight) 289600. 5. 46180 28960. 4. 46180 i' v (same density) 11.419 1.04578 111112. 4. 04578 p v 1 3218000. 6.50758 321800000. 8. 50758 G T = T 7651.6 3. 88375 7651. 6 3. 88375 Ro = R 420. 56 2. 62383 42056. 4. 62383 RT=l 3218000. 6. 50758 321800000. 8. 50758 26 TABLE 10. Fundamental constants for a hydrogen atmosphere on Hie sun. Data. Formula). Meter-kilogram-second . Centimeter-gram-second. Number. Logarithm. Number. Logarithm. Radius of the sun r 694800800 m 8. 8418603 694800 80000 cm 10. 8418603 Gravity acceleration at the surface g Gg a = 28. 028x9- 806 274. 843 2. 4390843 27484. 3 4. 4390843 Modulus of common logarithms M 0. 4342945 9. 637784310 0. 4342945 9. 637784310 C Mercury Water Density \ 1 Air Pm Pi Po 13595. 8 1000 1. 29305 4. 1334048 3. 0000000 0. 1116153 13. 5958 1. 0000 0. 00129305 1. 1334048 1.0000000 7. 111615310 I Hydrogen Ph 0. 089996 8. 954223210 0. 000089996 5. 954223210 Height of standard barometer Height of homogeneous atmosphere Barometric constant B u P = 0. 760 X 28. 028 21. 3013 3218012 7409746 1.3284060 6. 5075876 6. 8698033 2130. 13 321801200 740974600 3. 3284060 8. 5075876 8. 8698033 1 p m B u R T K M Ph M M Pressure in units of weight P 289608. 1 5. 4618108 28960. 81 4. 4618108 Pressure in units of force p J v _ RT _ K i c v 79596670. 9 7. 9008951 795966709 8. 9008951 Press, of one terrestrial atmosphere Volume (specific) of hydrogen Gas constant for pressure p 1 101323. 5 11.1116 420. 565 5. 0057103 1.0457768 2. 6238330 1013235 dynes 11111.6 42056. 5 6.0057103 4. 0457768 4. 6238330 n* ,^ T Ptt * Gas constant for pressure P R P"h 9 _ Pm B n 9 1. 15589X10 5 5.0629173 Lifitttyte 1 9. 0629173 Temperature at the photosphere Temperature gradient T = 28. 028 X 273 d'f_ A _ 1 7651.6 C. 1. 2563X10- 8 3. 8837546 2. 099104910 7651. 6 C. 1.2563X10- 9 3. 8837546 1. 099104910 Specific heat at constant pressure Heat equivalent of work Coefficient from specific heats Ratio of the specific heats c p =gp^ART 1 1 186503 0. 00234302 189261. 5 1.000005 5. 2706707 7. 369775610 5. 2770621 0.0000021 18. 99G8 2. 38G63X10- 8 18926. 15 1.000052 1. 2791478 2.378252710 4.2770621 0. 0000228 426. 8 a 4. 1855 X 10 ; " 9f > T ~c v The constants are worked out for the meter-kilogram-second (M. K. S.) system and for the eentimeter-gram-second (C. G. S. ) system, respectively, the formulae, which are well known, being found in Table 64 of the Report of the Chief of the Weather Bureau, 1898-99, Vol. II. If hydrogen, as a perfect gas, conforms to the Boyle-Gay Lussac law at so high a temperature as 7651.6, then there must be some stratum in the sun's atmosphere where the density is the same as it is under the standard conditions on the earth. If the gas ceases to be perfect to some extent, this statement must be proportionately modified, but in any case even approximate conditions will be very valuable as giving a general view of the prevailing state of solar physics, in which a footing of some sort is a desideratum for meteorology in general. We next determine the temperature gradient by the computation in Table 10, in which the same constants are em- ployed as above, except that their values have been determined with greater precision. To obtain the temperature gradient per meter, or the adia- in the M. K. S. system must be multiplied by 1000, and in the C. G. S. system it must be multiplied by 10000 so that they both give : 0.000012563 C. per meter, or, dT (79) dh = 0.012563 C. per 1000 meters. This can be checked from the terrestrial adiabatic rate, which is 9.86938 per 1000 meters, by multiplying by (80) dT 'dh ^ X sw (81) 0.012563= 9.86938 x 7 batic rate of fall of temperature per meter, the value of dh (28.028) a The rate of the fall in temperature in the atmosphere of the sun is very slow according to this computation, so that varia- tion in the density of the gases is not due so much to changes in temperature as to changes in pressure, which are very rapid, as is shown in Table 11 and fig. 21. The approximate formula 27 is all that is necessary in this discussion because of the steady state of the temperature just indicated. Let P =the pressure of 28.028 atmospheres, where h a , height, is assumed to be zero. P = the pressure in atmospheres at the height h. K = 7409.746 kilometers, the barometric constant. Then we shall have the reduction formula: (82) logp= ;i ~\ and logP = log P t - ~ The value of A in seconds of arc is found from radius of sun in kilometers ( 83 ) 1 ' (second of arc) = the of 8un in seconds 694800.800 16' X 60 =960' ; 723.751 km. DISTRIBUTION OF THE PRESSDKE, TEMPERATURE, AND DENSITY IN A SOLAR HYDROGEN ATMOSPHERE. P Since in a perfect gas Pv = = RT, we shall have for the f> i * P density, p = . In order to compute 11, the gas constant, we take R = - , where, I' 1 P = 28.028 atmospheres, P = 0.089996, T= 7651.6, whence we obtain R = 0.040702 [logarithm = 8. 6096146] . The values resulting from the computation are given in Table 11 and fig. 21, "Distribution of the pressure, tempera- ture, and density in a solar hydrogen atmosphere." The indi- cations regarding the prevailing pressure, derived from the behavior of certain lines in the solar spectrum, are that the reversing layer is under a pressure of about 5 atmospheres, or possibly as little as 3 atmospheres (Astrophysics, February, 1896, p. 139; May, 1898, p. 327; April, 1900, p. 240). Accord- ing to Table 11 the pressure at the height 8" above the stratum TABLE 11. Distribution of the pressure, temperature, and density in the solar hydrogen atmosphere. h" h in arc. in km. h K P T p Height of layer (A 1)" above photo- sphere. 45 32568. 75 4. 39539 0.001 7242. 4 0.000004 38 Top of inner corona. 40 28950. 00 3. 90702 0.003 7287. 9 0. 000012 33 35 25331.25 3.41864 0.011 7333. 4 000036 28 30 21712.50 2. 93026 0.033 7378. 8 000110 23 25 18093. 75 2.44189 0.101 7424. 3 000335 18 20 14475. 00 1.95351 0.312 7469. 7 0. 001026 13 18 13027. 50 1.75816 0.489 7487. 9 001605 11 16 11580. 00 1.56281 0.767 7506. 1 002510 9 14 10132. 50 1. 36746 1.203 7524. 3 0. 003927 7 Top of chromo- sphere. 12 8685. 00 1. 17210 1.886 7542. 5 0. 006143 5 10 7237. 50 0. 97676 2.957 7560. 7 009609 3 9 6513. 75 0. 87908 3.703 7569. 8 0. 012018 2 8 5790. 00 0. 78140 4.636 7578. 9 0. 015031 1 Reversing layer. 7 5066. 25 0. 68380 5.805 7587. 9 0. 018796 Top of photo- sphere. 6 4342. 50 0. 58605 7.270 7597.0 0. 023512 1 5 3618.75 0. 48838 9. 104 7606. 1 029406 2 4 2895. 00 0. 39070 11.400 7615.2 0. 036779 3 3 2171.25 0. 29303 14.275 7624. 3 0. 045999 4 2 1447. 50 0. 19535 17. 875 7633. 4 057532 5 1 723. 75 0. 09768 22. 383 7642. 5 0. 071955 6 28. 028 7651.6 0. 089998 7 Within the photosphere. Fro. 21. Distribution of the pressure, temperature, and density in a solar hydrogen atmosphere. having a pressure of 28.028 atmospheres is 4.636, and this may be adopted as the height of the reversing layer. If the top of the photosphere is 1" below fche reversing layer, the top of the chromosphere 5" above it, and the top of the inner corona 35" above the top of the photosphere, then the layer at pres- sure 28.028 atmospheres is 7" below the top of the photosphere, and is probably in the midst of the photospheric shell. The temperature gradient is a straight line, 26 but the pressure and density are distributed on curves of the logarithmic type. From 28 to 5 atmospheres the pressure and density change very rapidly, but from 2 to atmospheres they change very slowly. There is a quick transition in the rate of change dT 1 26 Since the temperature gradient, -jr- = -=- , was computed for the stratum within the photosphere, where P = 28.028, it follows that in the higher strata, in which P has smaller values according to Table 11, the / dT\ P n gradient will be greater in the proportion, I dh/P' ass 'g n i n g suc- cessive values to n in the several strata. Hence, the temperature fall is C I dT\ (dT\ A T u = I I -sir- I dh, where ITT") increases toward the top of the solar atmosphere. Computations for the successive layers show that the temperature fall is slow up to the level of P= 1 atmosphere, beyond which it increases very rapidly as the density diminishes, so that the temperature of space is reached at the top of the inner corona. We obtained the following temperatures: Initial stratum in photosphere P=28.028, Tr=7652 Top of the photosphere P= 5.805,7=7500 Top of the reversing layer P= 4.636, T= 7450 Top of the chromosphere P= 1.500,7=6950 This law gives too low temperatures at the top of the inner corona to be acceptable at present. Eeferring to the earth's atmosphere, the law of cooling is not the adiabatic rate, but the gradient is nearly the same as that found for the lower strata in all levels up to 16,000 meters; that is to say, cooling takes place at a uniform rate. The law of cooling in the solar atmosphere is a function which is not now known, and it may fall be- tween the two extreme types indicated above. The entire subject de- mands a careful research. 28 between 5 and 2 atmospheres, and in the midst of this the reversing layer and chromosphere are located. It is, there- fore, probable that the action in the reversing layer which sends forth visible light waves is due to rapid transmissions in pressure and density, rather than to any changes of tem- perature. This favors the theory proposed for the explanation of the reversing layer by Becquerel, Wood, and Julius, namely, that it is due to contrasts of density, and in accordance with which the phenomenon has been reproduced in the laboratory. Compare pages 65 and 162, Eclipse Meteorology and Allied Problems, Weather Bureau Bulletin I. The shifting and the broadening of the lines in the spectrum are due to a variation of pressure and density rather than to a change of temperature. It is also seen that the density of the hydrogen approaches zero at the height of the top of the inner corona. The coincidence in the observed boundaries TABLE 12. ComptUation of the pressures, temperatures, and densities at the surface and within the sun by Nipher's formulae. Fundamental constants. of these layers in the sun's atmosphere with the results of this computation on the physical state is evidently so perfect as to argue strongly for the correctness of the physical con- stants employed. The outcome goes to show that the photo- sphere is the region where great changes in pressure are taking place, so that violent circulations, explosions, and chem- ical and electrical combinations must prevail, and observations show that this is the case. From the values here employed we can readily compute many other important thermodynamic relations. It may be observed that the Smithsonian Astrophysical Ob- servatory computes from the Washington observations a tem- TABLE 13. Transformation factor from perfect gases to the material of the sun within the photosphere. Formula P l rz-s P s resurface pressure by Nipher's formula p h = density of hydrogen at surface of sun Numbers. 2.9004x10" 0. 000089996 5. 95422310 Logarithms. 14. 462460 M 1 Numbers. = total mass of the sun 2. 0132X10 33 Logarithms. 33. 303878 p f = surface density by Nipher's formula P 2 = corresponding pressure from inside 0. 37255 7. 0065 XlO 10 9. 57118210 10. 845501 T? i= gravitation constant 1. 5173X 10 7 7. 181073 P, := pressure found from outside conditions 7. 95967 XlO 8 8. 900895 r =: radius of the sun in centimeters 694800 80000. 10. 841860 F transformation factor 88. 025 1. 944606 T =: absolute temperature at surface 7651. 6 3. 883755 .R 2 = gas constant for Pfrom Nipher's for- 1.0175X10" 11. 007523 Density at surface and within the sun. mula f 0.78 M R l = gas constant for P from hydrogen 1. 1559X10 9 9. 062917 P i -j- surface density 0. 37255 47T ?"*^ 9. 571182 F := transformation factor 88. 025 1. 944606 r Pa 1.43287 1]r fn/-Arlnnaii"ir 037121 9. 569621 Some such factor as 88 is required to change the conditions ~ 3. 86 3. 86 surface density * average density from astronom- 1.43287 ical data 0. 156208 outside the photosphere for perfect photosphere for nonperfect gases or gases to those inside the liquids. *. = 0. 545 r = distance of stratum p a 3. 7867X 10' 10. 578257 TABLE 14. Specific heats c , c,, quantity of heat Q, and work W, in tlte from center surface stratum of the sun. rzspeciflcvolumeatthesurface 2. 6842 0.428818 i K 3n 4 Numbers. 3c Logarithms. Pressure at the surface and within the sun. e p \ K 1 2 2n ( = assumed value . D 3.4615 0. 539264 0. 636 M 2 A? 1 P 14. 462460 A = heat equivalent of work 9 ^789^^ 1 O ~ o j zi: surface pressure 2. 9004 XlO 14 4.1855X10' p a 5. 40 P z= average pressure 1. 5662x 10 15 15. 194854 R = gas constant 1.0175X10 11 11. 007523 r. = 0. 502 r =. distance of stratum P a 3. 4879X 10 10 10. 542564 AR 2431. 3. 385776 from center 3w 4 i j- Or 4 T~* R T at the surface of the sun. c f AR 2 _ 27i - : 3 - 5 AR 8414. 8 3. 925040 l Mk* Assume 3. 4615 AR = 0.818-^- 7.8103X10" 14. 892668 2c p 16829. 6 RT 3AR 7293. = Pu (The coefficient should be 7.7854x10" 14. 891278 more fully developed) AR 9724. R Pi) -y the gas constant 1.0175x10" 11.007523 /dQ\ _ specific heatdue ~ \d T/ n ( f "i" to contraction 18138.8 4. 258609 Temperature at the surface and within the sun. n - (\ | ' Q A j3 A* -L ciosGiy 1.1008 0. 041699 T 273X28.028 7651.6 3. 883755 p"r T. =. 1. 08 T 8263. 8 3.917179 c - W~ y+SXR 0.7519 9. 876184 r t = 0.707r 4.9122X10 10 10. 691279 0. 75 closely A T= 8263. 8 7651. 6 = 612. 2 612. 2 2. 786893 + Ar 1.000 r 0.707 r = 0293 r in km. 203577. 5. 308728 TB- i CQA M ^ work of compres- 1.2225X10 48 48. 087250 2r - sion AT 1 _ temperature gradient within the 0.0030072 7. 47816510 Q ~ 0.7519 W = heat radiated 0. 9192X10 48 47. 963434 sun per 1000 meters TT Q rr excess of work energy over 0.3033 XlO 48 47. 481872 Mass of the sun. heat energy I M ZRTr 33. 302991 Q 3.03 0. 481562 = 1.22 IT, rzmass 2. 0091X10 33 WQ W 4riq ; Adopted value from Newcomb 2. 0132X10 33 33. 303878 W-Q . Uo Weight of 1 gram at the surface of the sun. (8 _5n)(4-3n) 7077 9 3 o p m 7.2 c ' - c f 3 (2 n) 2 (5 3)' ' ( p ' ( ( . t ' f\/ A _ _ IV 4. 438178 c p 0.180 AR 9 * r = 980. 6 X 28. 028 27484. 4. 439084 c f 8414. 8 1. 0548 0. 023190 - c v 7977. 2 29 perature of about 6000 for the atmosphere of the sun, although it is quite certain that a higher station, as Mount Whitney, would give a greater temperature, say 6500. This, of course, takes account of the absorption in the earth's atmosphere, but not of that in the sun's atmosphere. It seems probable that the equivalent of 1000 C. may be absorbed from the stratum included between the midst of the photosphere and the top of the inner corona. If this is not the case, then the outgoing radiation of the sun must be such as to give nearly 4.0 gram- calories per square centimeter per minute on the outer surface of the atmosphere of the earth. The relative absorption in the atmospheres of the sun and the earth, respectively, will be much more readily determined if it can be admitted that the temperature of the sun about 7" within the photosphere is approximately 7652. In the following discussion the sur- face stratum is that which is 7" below the visible boundary of the photosphere, where the pressure is taken as 28.028 at- mospheres. The various comments made by Buckingham and Day as to the value of temperatures extrapolated from ter- restrial to solar conditions have their importance, but it is believed that we shall be able to gain a footing by other processes, such as thermodynamic relations, and thereby de- termine the thermal condition of the sun without such an overstepping of the limits of the actual practicable experi- ments of the laboratory. We will proceed, in Tables 12 to 14, to consider the conditions within the solar mass, with the aid of Nipher's formulae, and to show that here, too, there is ground for encouragement, because of the numerous agreements be- tween two independent sets of data, namely, the astronomical quantities and the thermodynamic values. DISCUSSION OF THE VALUES DERIVED FKOM TABLES 12 TO 14. Table 12, " Computation of the pressures, temperatures, and densities at the surface and within tke sun by Nipher's for- mulae," contains a series of values at the surface stratum in the photosphere, where the pressure has been taken at 28.028 atmospheres as the result of external conditions. These have now been computed from astronomical data M, k*, r, and the assumed temperature 7G51.6. The purpose is to compare these two sets of values, one computed from external conditions, and the other from the internal conditions, the former for strictly perfect gases, as hydrogen, and the latter from such non-per- fect gases or liquid material as makes up the body of the sun. While the law Pu = RT applies to perfect gases, we may yet obtain some approximate idea of the state of the sun in- side the photosphere if a transformation factor can be found by which to pass from the first system to the second. In a circulating mass like the sun it is probable that something like this law applies throughout the mass. At any rate the view can be tested to some extent by studying the two sets of data. There is, of course, some danger of arguing in a circle through so complex a system of formulae, but I think that the general conditions herein exhibited conform more closely to a natural solar mass than the results heretofore derived by the use of Eitter's formulae. The density. The average density of the sun from astronomical data is 1.43287, and it is a denser liquid than water. The surface density is 0.37255, or about one-fourth the average density. This latter occurs at the distance 0.545?- from the center of the sun, and if anything like the same gradient of density is main- tained throughout, the density near the center of the sun is not far from 5.7, which is about the mean density of the earth. We may, therefore, assign a more or less solid nucleus to the sun, which becomes viscous at a distance of about one-third the radius from the center, and soon thereafter mobile. The transitions within the aun are gradual, but at the photosphere there is apparently a mixture of liquid and gaseous masses in active transitions, and these seem to be the conditions indi- cated by the phenomena observed in the sun spots. The prominences, faculse, and chromosphere are strictly in a gaseous atmosphere; the photosphere is a mixture of gases and liquids, and the interior consists of a circulating liquid passing into a solid nucleus near the center. While the sun's pressure by gravitation alone would increase the density of its constituents, the temperature is at the same time high enough to balance this tendency to compression, so that the material in the sun is in about the same state as the material of the earth, except that here the outer layers have advanced toward solidi- fication under the prevailing low temperature. A contracting . sun, in order to keep up its radiation, must be circulating freely, and this precludes a very high degree of viscosity, ex- cept near the center. The pressure. Beginning with a pressure of 28.028 atmospheres in that layer of the photosphere where the temperature is 7652, which on the sun is equivalent to 7.96 x 10 s dynes, we compute that for a hydrogen gaseous envelope the pressure practically vanishes at the top of the inner corona. Beyond this layer, into which hydrogen is ejected in the prominences, the condi- tions are favorable for all the electrical and magnetic phe- nomena belonging to the cathode rays in rarefied gases. At the photosphere, where the materials change from gases to vapors and liquids, there is a corresponding equivalent increase in pressure up to 2.90 x 10' 4 dynes. It would take this increase in pressure to pass from the gaseous to the fluid state at the high temperature there prevailing. If a fluid may be consid- ered as a gas brought by pressure at a given temperature to the liquid condition, then this pressure difference also repre- sents the explosive energy when the liquid changes to a gas. If the liquid is elevated from the interior to the surface of the sun by convection currents, then, on reaching the surface, it may greatly expand and even explode when vaporization takes place, as is commonly observed on the edge of the sun through the enormous velocities measured by the change in wave lengths, by the Doeppler principle, or by anomalous dispersion. Within the body of the sun, at the distance 0.5 radius from the center, the pressure is 1.57x 10 15 dynes, which is 5.4 times as much as at the surface. By the same ratio, the pressure would be eleven times as much at the center, though this law doubtless changes within the nucleus. The pressure is comparatively uniform below the sun's surface, and widely discontinuous at the sur- face. Hence, the convectional currents and the dependent phenomenon of rotation in latitude are leisurely motions com- pared with the explosive action at the surface layers. The temperature and the gas constant. Nipher's coefficients are carried to only three decimals, which is doubtless sufficiently accurate for the determination of the value of the contractional constant n. It is not quite suffi- ciently accurate, however, to give proper check values from one formula to another, but I have not thought it worth while to carry this computation beyond the approximate stage. If we pass from a perfect gas to a fluid, the value of the gas constant adopted must be interpreted as merely suggesting important re- lations, and too much emphasis must not be laid upon certain obvious criticisms which naturally arise. We may suppose that the mass of the sun beneath the photosphere, while apparently fluid or viscous, yet moves in accordance with the general law, by reason of convection, so that it is continually readjusting itself to conform somewhat closely to this general law of gaseous elasticity. At any rate, this is the theory upon which we have proceeded in the discussion. We compute the product p E Tbj Nipher's formula, and check it with the product found from the pressure and density, and then with the temperature T = 7651.6 find K = 1.0175 x 10" for the fluid of density 0.37255 in the surface layer. The temperature within the sun 30 at the distance 0.707 radius from the surface becomes 8264, and at this rate, an increase of 612 in 0.293 radius, the total increase from the surface to the center is 2089, making the central temperature 9741. This gives an average gradient of 0.0030072 per 1000 meters from the center to the surface. We find, also, the gradient from the photosphere to the top of the inner corona to be 0.012563 per 1000 meters. The gra- dient of the temperature is about four times as great in the at- mosphere of the sun as inside the photosphere. The cooling is, therefore, more rapid outside than it is inside the photosphere. ' The mass of sun, the weight of 1 gram on the surface of the sun, and the transformation factor. The mass of the sun is 2.0091 x 10 33 by Nipher's formula, agreeing closely with that adopted from Newcomb, 2.0132 x 10 SS , the former being computed through the product RT, and thus checking all the quantities. The weight of 1 gram at the sur- face of the sun is 27428 by Nipher's formula, through the product RT, and this agrees with the simple product g = 980.6x28.028 = 27484, thus checking again. The transition factor from a perfect gaseous system to that actually existing at the surface, where the density is 0.37255, is found as indi- cated. We find the pressure corresponding to 0.37255 instead of that for which the computation was made in a hydrogen atmosphere of density 0.000089996, and obtain P t = 7.0065 x 10' through Nipher's formula, as if the atmosphere were of the greater density. For the actual hydrogen atmosphere we com- puted (Table 13) P l = 7.95967 x 10". Hence, P t = 88.025 P v so that 88.025 is the required factor. Similarly, the gas con- stant from Nipher's formula is R 3 = 1.0175 x 10". It was com- puted for the actual hydrogen atmosphere (Table 13) to be R 1 = 1.1559x10'. Again, R 3 = 88.025 ,, so that there is mutual agreement. Some such factor as 88 is required to pass from the law for perfect gases, P l v = ^ T, to that for solar liquids, P 2 v = M t T. It will not be advantageous to speculate as to what this factor 88 signifies, but it is not so large as to be improbable in passing from a gaseous to a fluid state, as it may stand for the internal forces of viscosity or friction and molecular cohesion, and pos- sibly for some unknown forces of electricity and magnetism. Specific heats, energy of radiation, and contraction. Carrying the values of the several quantities through the various formuL-e we find that they conform to the prescribed conditions, as follows: Specific heat of contraction Exponent and coefficient Heat energy of radiation Work energy of contraction heat radiated n Q w Ratio Ratio Ratio work of gravitation heat radiated excess work of compression w Q W Q W excess " W Q Specific heat at constant pressure c p Specific heat at constant volume r-^ A.Sf. *t=-> 7 A.Ou. 7r ~7 1*r- Cts. 3. Wtnct XXXII 48. Chart Xn B. Average monthly vectors of the general circulation in the West Indies at the various cloud levels. First arrangement. 2*1(7.26'. Sctrtto jDomingo. Fig. 27. , Porto Rico . <7 F Jif ^4 A SO . 1 at I I s to 10 2 70 19.5 18.5 86 25 2 19.8 76 November 5.0 2.3 102 18 4 12 82 21.0 19.5 90 32.4 25.2 83 December 5.2 2.8 109 20.4 14 4 93 23.0 20.0 94 37.8 30.7 85 8. BUFFALO, N. Y. January 5 7 4 2 84 27 4 17 86 59 44.5 89 51.3 51 3 7E February 5 7 4 1 87 26 4 16 4 84 58.5 43 88 53.2 47.7 75 March 5.7 3 7 93 24 15.0 87 54.0 36.0 88 36.0 38.7 7 April 5 4 3 2 104 20 6 12 8 91 45 30.5 89 33 32 4 8( May 5 3 2 9 112 16 8 10 2 96 31.5 23. 5 92 33.3 29.7 9( June 5 2.6 121 14 9.6 102 25.0 18.0 97 35.1 29.7 M July 4 9 2.3 126 12 9 8 104 20 15.5 105 36.9 30 6 105 August 4.7 2.3 127 13. 2 10.0 105 19.5 16.5 108 41.4 33.3 104 September. . . 4 8 2 3 126 17 10 8 102 17 19 5 104 45.9 38.7 10( October 5.0 2.2 119 22 12.2 96 27 23 5 96 52.2 45.0 9E November 5. 1 2.4 110 25.4 14.4 91 36.0 30.5 94 54.0 51.3 9( December .... 5 4 3 2 105 27 2 16 4 87 48.0 39 91 55 8 52 2 l 44 TABLE 16. Average monthly vectors of the general circulation, etc. Continued. 9. BLUE HILL, MASS. 1896-97. Velocity in meters per second. Wind. St., Cu., S. Cu. A. S., A. Cu. Ci. Cu., Ci. S., Ci. v, V r V, V 9 Fi V f v, F 9 January "... 7.6 7.2 6.8 6.4 6.2 6.1 6.2 6.3 6.8 7.0 7.3 7.6 4.6 4.5 3.7 2.6 2.4 2.3 2.3 2.3 2.3 2.5 2.8 3.6 68 62 61 88 116 126 129 130 125 114 98 80 24.2 23.6 22.0 20.4 19.2 18.0 17.6 17.6 18.6 20.2 22.0 23.4 12.4 12.2 11.4 10.6 9.6 8.4 8.4 9.4 10.2 10.0 9.4 10.8 o 73 75 76 80 84 89 101 117 124 120 90 74 38.5 35.5 32.0 28.0 24.0 22.0 19.0 20.0 25.0 31.0 36.0 38.5 32.0 30.5 26.5 22.0 19.0 17.5 16.5 18.5 22.0 27.0 32.0 32.5 O 97 92 89 87 85 88 93 103 109 113 111 106 54.0 49.5 41.4 35.1 28.8 27.0 27.0 27.9 31.5 38.7 45.0 52.2 46.8 45.0 38.7 32.4 26. 1 23.4 22.5 22.5 27.0 33.0 40.5 46.8 87 83 80 83 87 91 98 99 101 99 96 93 February March April May June . . July August September November December 10. WASHINGTON, D. C. January 4.1 2.0 34 14.0 8.6 101 27.5 25.0 90 47.7 45.9 91 February 3.9 1.7 23 14.0 8.4 106 28. 5 24.0 97 50.4 45 9 92 March . 3.6 1.4 39 13.4 8.0 108 26.5 22.5 101 45 43.2 92 April 3.2 1.0 49 12.0 7.4 111 22.5 19.5 104 36.0 35 1 91 May . 2.8 0.6 73 11.0 6.0 111 18.5 16.0 107 27.0 26. 1 90 June . . 2.5 0.5 110 10.0 5.2 104 15.0 12.0 100 23.4 19.8 90 July . 2.3 0.5 117 8.8 4.6 95 13.5 10.5 95 19.8 17.1 90 2.3 0.5 117 8.2 4.8 81 13.5 10.0 90 19.8 18 88 September . . 2.5 0.5 90 8.8 5.8 72 15.0 11.5 85 21.6 20.7 87 October 2.9 0.7 65 10.2 7.4 73 18.0 15.0 81 27.0 24.3 87 November ' 3.2 1.2 50 12.2 8.4 76 21.0 14.5 79 31.5 31.5 90 December 3.6 1.7 40 14.0 8.0 85 25.0 17.5 82 37.8 38.7 90 11. WAYNESVILLE, N. C. 12. OCEAN CITY, MD. 2.9 1.6 62 15.8 11.6 91 36.0 35.0 108 53. 1 51.3 94 February 2.7 1.4 59 15.2 11.2 92 35.5 35.0 107 54.0 51.3 94 March 2.3 0.9 57 13.2 10.0 90 34.0 31.5 109 45.0 45.0 92 April 1.9 0.5 56 12.6 8.0 88 30.0 26.5 108 36.0 35.1 91 May 1.6 0.1 107 8.4 6.0 80 25.0 19.0 103 27.0 25.2 91 1.4 0.3 180 6.8 4.8 70 18.5 15.0 95 18.0 14.4 90 July 1.3 0.5 180 6.0 4.6 63 13.0 10.0 91 10.8 9.0 84 August . 1.3 0.4 167 6.0 4.8 68 11.0 10.5 90 9.0 9.0 84 September 1.4 0.4 120 8.0 6.4 67 14.0 14.0 94 11.7 14.4 86 October 2.0 0.6 78 10.4 8.0 85 20.0 20.5 98 18.9 26. 1 88 November 2.6 1. 1 68 13.6 9.8 87 26.5 27.5 102 28.8 36.0 90 December . . ... 2.9 1.5 63 15.6 11.2 91 34.0 32.0 105 39.6 45.0 92 13. KEY WEST, FLA. January 4.6 2.3 318 14.4 2.4 215 20.0 8.0 97 28.8 26.1 90 February . ... 4.5 1.8 294 15.2 4.6 193 20.0 9.5 106 27.9 24.3 91 March .... 4.3 1.9 265 14.8 6.4 197 17.0 7.5 106 25.2 19.8 86 April 4.1 2.4 251 13.6 8.0 210 13.5 4.0 104 18.0 14.4 69 May . . 4.2 2.7 249 12.0 9.0 221 10.0 0.5 135 11.7 10.8 49 June 4. 1 2.9 248 10.4 8.8 228 8.5 2.0 270 17.1 7.2 7 July 4.0 2.9 253 9.4 11.0 244 7.5 5.0 259 15.3 5.4 321 August 3.8 2.9 261 8.4 10.0 254 7.5 5.5 255 15.3 4.5 308 September 3 8 2 8 274 8.4 8.6 262 8.5 7.0 249 9.0 1.8 227 October . . . . . . .... 4.1 2.7 289 9.2 4.8 267 10.5 5.5 246 12.6 7.2 120 November 4.5 2.7 306 10.2 2.4 260 14.5 4.0 235 18.0 15.3 107 December 4.6 2.7 318 12.2 1.8 229 17.0 3.0 211 23.4 19.8 100 XXXII 81. Chart XI. Average monthly vectors of the general circulation. Paul, Minn. Fi r~-5 1 \A 7-7-ariffeme i 'r-&tJ4rr--..x.