728 ASTRONOMY: W. J. FISHER PROC. N. A. S. tude and mass, and thus to estimate the absolute luminosities of super- giant stars. 1 NATIONAL RuSIMRCH Fsixow. 2 Payne, Harvard Monograph No. 1, 1925 (137). 3 Payne and Shapley, Harv. Reprint, 28, 1926. 4 Maury, Harv. Ann., 28, 1900 (55). ' Milne, M. N. R. A. S., 85, 1925 (783). THE APPARITION DATES OF THE ANDROMEDE (OR BIELID) METEOR SWARMS BY WILLARD J. FISHER HARVARD COLLUGS OBSORVATORY Read before the Academy November 9, 1926 In a paper reviewing Quetelet's list' of meteor shower dates, H. A. Newton2 says: "IV. The December Periods. There appear to be two epochs in De- cember, each marking a distinct shower, viz.: Dec. 6th-7th, and Dec. 12th. There is no early date corresponding to the first epoh...." By "early date" he appears to mean dates of the eighteenth century and previous. The "first epoch" seems to mean the time of the shower now known as the Andromede or Bielid shower. This shower is traced by C. P. Oliviers back to 1741, when it appeared in early December. Its later apparitions came earlier and earlier in the year, but with a puzzling irregularity in the rate of advance of the date. In 1925 the question arose as to what was the proper date to suggest to a group of amateurs (the Bond Astronomical Club) for observation of these meteors. Finding the answer somewhat uncertain, the writer was led to apply to the data the method used by Newton, in the same paper, in forming his lists of the ancient shower dates of various swarms. Of his tables Newton says: "In the following tables are given the historic dates of star showers from Quetelet's list..... They are expressed in the Gregorian calendar, and therefore represent approximately corresponding dates of the tropical year.... To express these dates in a sidereal year there is given at the same time the corresponding day (and fraction of a day) of 1850; that is, the time when the earth's longitude in her orbit, measured from a fixed equinox, was the same as on the day of the shower. The following formula was used in the computation. "Let x be the number of days to be added to the recorded date, expressed in the Gregorian calendar, t the given year of the Christian era, n the Downloaded by guest on October 6, 2021 VOL. 12, 1926 ASTRONOMY: W. J. FISHER 729 number of leap years between the given date and A.D. 1850, and I the length in days of the sidereal year. Then, evidently, (1850 - t)l = x + 365(1850 - t) + N. To reduce this to a form better suited for computation, observe that N is equal to the integral part of 1/4(1851 - t), minus 12, plus the correction between the Gregorian and Julian calendars for the given date. Let c be this correction, e be the remainder after dividing 1851 - t by 4, 1 = 365.256374, and we obtain, by reducing, x = (1850 - t) X 0.006374 + 1/4(e - 1) + 12 - c. The integral part of (1899 - t)/100, minus the integral part of (1999 - t)/400, gives the value of 12 - c. "It will be observed that the secular variation in the value of 1, the motion of the apsis of the earth's orbit, the diminution of its excentricity, and the periodic perturbations are neglected. The terms dependent on these would together very rarely amount to one-tenth of a day. The equation of the center is therefore omitted...." Table 1 shows the data for all well-reported Andromede apparitions. The first column contains the serial number of the apparition, with suffixed a, b.... to indicate that, in the writer's judgment, the observations of different persons have to do with the same maximum. The second column contains the dates of maxima to tenths of a day, with the sign 'mdicating uncertainty inherent in the report, the sign < meaning previous to. The column headed 1850 shows the date, Universal Time, reduced after New- ton's method above. In this column ? means an uncertainty in the tenths, due either to lack of precision in the original report, or to doubt as to whether the actual maximum was seen. On account of the usual brevity of Andromede displays this latter uncertainty cannot be great. Only many observers reporting from numerous longitudes all around the globe can remove this uncertainty. Finally, a column of notes gives observer [, authority ( ), and other facts. To study the relations of reduced apparition dates, the calendar years of apparitions were plotted as abscissas, 1 yr. = 1 mm., and "1850 dates" were plotted as ordinates, 1 d. = 10 mm. The plot is reproduced, to smaller scale, in figure 1. TABLE 1 NO. O.M.T. OF MAXIMUM 1850 NOTES [OBSERVERI (AUmORroy) 1 1741 Nov. 25.44, 0. S. Nov. 27.3? St. Petersburg [Krafft]. (Quetelet; has N. S. date wrong.) Radiant? 2 1798 Dec. 7, <10 P.M. Dec. 7.7 Near Bremen? [H. W. Brandes.] 7 per min., 480 total. Radiant? 3 1818 Nov. 19.54 Nov. 19.7? Gosport, Eng. (Kaemtz, from Chladni.) "Many." Radiant? Downloaded by guest on October 6, 2021 70- ASTRONOMY: W. J. FISHER PR3c. N. A. S. TABLE 1 (Continued) NO. G.M.T. MAXIMUM 1850 NOTES (OBSSERV"R (AUTHORUTY) 4 1822 Nov. 25, <10 P.i Nov. 25.6 English Channel [Duke of Wurtem- berg]. (Gruithuisen.)". saheine bedeutende Zahl,von S. nach S.W. fallen." Probable rqdiant, 2 hrs; 20 min. +500,within 100. 5 1830 Dec. 7.54 Dec. 7.6? France [Raillard]. "Apparition extraordinaire." Radiant? 6a 1838 Dec. 6, 8.55-9.15 P.M. Dec. 6.5? Toulon [Flaugergues]. 42 in 20 min. Radiant in zenith, probably about 2 hrs. 04 min. + 430. 6b 1838 Dec. 7, 6-7 P.M. Dec. 7.4? England [T. W. Webb]. 40 in 30 mm., 1-3 observers. Radiant seems to have been somewhat southwest of zenith, say 23 hrs. + 400. 6c 1838 Dec. 7.44, "evenLing" Dec. 7.5? Parma [Colla]. "Un grande nom- bre." Radiant? (Id 1838 Dec. 7, 8- P.M. Dec. 7.7 New Haven, Conn. [Herrick]. 93 per hour. (H. A. Newton). Ra- diant about 3 hrs. 15 min. + 500. 6e 1838 Dec. 8.4d, "evening" Dec. 8.5? Brussels [Quetelet]. "Beaucoup." Radiant? 7a- 1847 Dec. 8.5 Dec. 8.3? Aachen [Heis]. 149 per hour. Ra- diant 220 + 55°. 7b 1847 Dec. 10.44 Dec. 10.2? Aachen [Heis]. 140 per hour. Ra- diant 220 + 550. 8 1850 Nov. 29A-4 Nov. 29.4 Aachen [Heis]. "Ausserordentlich viele," but only 5 in Resultate. Radiant probably 150 + 62°. 9 1867 Nov. 30.4i= Nov. 30.0 Bergamo [Zezioli]. 7 -meteors, 170 + 480. (Schiaparelli.) 10 1872 Nov. 24.6 Nov. 24.0 New Haven, Codn. [Newton]. "250 before midnight," "three- -fourths of them from Biela." "Very few morning and evening of the next day." Ila 1872 Nov. 27, 11.00-11 .35 Nov. 26.7 Mauritius (Meldrum). 1160 per hour, 2678 total, between clouds. Radiant close to o and 3 Persei. 1lb 1872 Nov. 27.4 Nov. 26.8 Europe and U. S. (A. S. Herschel, Nature, 7, 185-188, 1873). 12a 1885 Nov.26.44, "ever iing" Nov. 25.4? Bristol, Eng. [Denningl. 100 per hour, mostly Bielids. 12b 1885 Nov. 27, 8-9 P.M. Nov. 26.0 Zi-Ka-Wei, China [Marc-Dechev- rens]. 100 in 15 min. Radiant? Was not over at Nov. 28th, 4 A.M. The most easterly observation? Also observed at Mauritius, radiant about y Andromedae, and off Cape Palmas. Downloaded by guest on October 6, 2021 VOi. 12, 1926 ASTRONOMY: W. J. FISHER 731 TABLE 1 (Conduded) NO. O.K.T. MAXIMUM 1850 NOTES [oM]stvnRi (AUTIolom) 12c 1885 Nov. 27, 6.15 P.M. Nov. 26.25 Europe and England generally, Rio and Eastern U. S. (Summary by H. A. Newton, Am. Jour. Sci. (3) 319 78-79,409-426, 1886). 75,000 per hour or more. Radiant 24.54° + 44.74°, average (Oli- vier). 13 1892 Nov. 23, 11.25 P.m. Nov. 22.8 Washington (Horigan), and as far as Albuquerque. At Princeton, N. J. (C. A. Young), estimated 80-100 per min. Radiant shifted, from 1 hr. 20 min. + 40030' to 1 hr. 40 min. + 400. 14 1892 Nov. 27, 8 to 11 P.M. Nov. 26.9 Mexico, en route Torreon-New Orleans (H. A. Newton), "hope- less to count;" through railway car window. Radiant? 15 1899 Nov. 24.2 Nov. 23.6 Europe generally (DIenning), 90 per hour; Eastern U. S. (Olivier). 2-3 per min. Radiant at Prince- ton 230 + 421/40. The change of 1850 date, from apparition to apparition, is due partly to changes in the position of the X node where earth and meteors meet, partly to the fact that the 2 \ meteor stream is not single and a.\\___ homogeneous, but multiple and condensed into swarms. In the figure it is seen that the points \ . mostly lie within a slender strip' " - 0 narrowing downward to the right, or as the dates increase; and that l i--lb many of these fall by groups quite '\ 4 * __42_ accurately on straight lines con- \0 verging to a point. 13 Group (1) Apparitions (1), (3) __\_\\ determine a line which does not 3 pass through or near the conver- gence point. Group (2) Apparitions (2), (8), __,._ (13) fall quite accurately on a FIGURE 1 straight line, which passes between Relations of reduced apparition dates and the points of apparitions (10), years of apparitions.