Ex Libris C. K. OGDEN CASTLE COMBE. i)W it rl i / f *~^-r-1 . 4 / L * (/ ' V '^ - "^-r^-*- VI s HOW TO KEEP THE CLOCK RIGHT BY OBSERVATIONS OF THE FIXED STARS WITH A SMALL FIXED TELESCOPE. TOGETHER WITH TABLES OF STARS AKKANGED TO SHOW, BY THE USE OF A LITTLE ARITHMETIC, THE MEAN SOLAR TIME OF THEIR APPARENT TRANSITS, TO THE END OF THE CENTURY. BY THOMAS WAENEE. 11 ontjou : WILLIAMS AND NOEGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON AND 20 SOUTH FREDERICK STREET, EDINBURGH. 1869. LONDON: PRINTED BY BPOTTtSWOODK AND CO., NKW-STI1EKT SQl ; AK8 iND PAltl.lAUKNT STltKKT fcnnex OC HOW TO KEEP THE CLOCK RIGHT. THE DIFFERENT METHODS usually adopted for keeping time with tolerable accuracy, by means of observations of the heavenly bodies, may, with some convenience, be divided into two great classes : First, observations of the altitudes of the objects observed. The advantages of this method are, that the instruments, sextants, &c., are portable, and can be used when other instru- ments would be unavailable, as on board ship : amongst the disadvantages may be mentioned the trouble of reducing the observations. The second class consists of observations on the meridian. This class must, however, be subdivided into two divisions ; the first, when the observations are made with good transit instruments, which are occasionally examined for errors, and of which the errors are known and allowed for. The observa- tions by such instruments are the most perfect of any but the instruments are costly; they require and deserve careful treatment, and trouble and skill are necessary in detecting the errors. The second subdivision comprises observations made with inferior transit instruments, or good ones which are not occa- sionally examined for errors. Fixed meridian lines, across which a bright spot of sunlight, from a small hole in the roof above, passes at apparent noon, and dipleidoscopes. The ad- vantages of these instruments are that if they have been once fixed nearly in the meridian (no very difficult matter in the case of the transit), they will continue to give fairly approxi- mate time as long as they keep their position. The disadvantages of these instruments are, that some of them (transits), are rather costly, and require considerable care ; and the others, meridian lines, and diplcidoscopes are with difficulty fixed in the meridian, and when not fixed in the meridian, will give instrumental errors, differing with the different declinations of the objects observed, and all are liable 5002115 4 HOW TO KEEP THE CLOCK RIGHT. to give erroneous results through the shifting or bending of what they are fixed to. This is the chief defect of the fixed telescope for observing the stars, which, night after night, and year after year, pass across its field. But when we consider that with an exposed pillar or build- ing, if the sky has been clear during the morning, the sun has had all that time to bend the pillar, c., to the west ; and that the observation (if of the sun), will be taken when the bending is nearly at its maximum ; and that if the morning has been dull, and the sun has come out only a short time before noon, the pillar, when the observation is taken, will be but little bent ; it must be clear that meridian solar observations with exposed pillars, and fixed and untested instruments, are likely to give discordant results, and can hardly be sufficiently de- pended upon. The case is different when fixed telescopes are used for observing the stars ; when these are used, even if the pillar has been exposed to the sun and has been bent during the day-time, the interval which would generally elapse before the stars became visible would allow the pillar to resume much of its proper form ; but for observations in the zone, 50 to 53 N. P. D., it would often be easy to build the pillar so that it should never be exposed to the action of the sun, and conse- quently one important source of instrumental error would be much diminished if not obviated altogether. If, however, the ground upon Avhich the pillar is built should be subject to much movement the case is more difficult ; sex- tants or examined transits could alone give fairly good results, and the examination of the transit must be unpleasantly fre- quent. In the Isle of Wight there is a considerable district where a fixed instrument would be useless ; on the other hand, the pil- lars of the Greenwich transit are known to have a very slow alternating movement, extending over many months, and affect- ing the time of the transit of a zenith star by less than a second. I am at present unable to describe the best form of telescope for fixing to a pillar ; I have tried a few experiments, but in consequence of not being perfectly satisfied with my designs, fc shall describe one, which, though not actually existing, may be considered a combination of what I have already tried and found to succeed, may be safely relied upon, and is unquestion- ably very simple. THE FIXED TELESCOPE. 5 The telescope is similar to that of a 14-inch dumpy level (of Messrs. Troughton & Simms' construction, who have made the telescopes I have experimented with) ; the object glass corrected for parallel rays is a cemented one of 1?? inch aperture ; the eyepiece end is of the usual form, and has a prism attached to the eyepiece for facilitating observations near the zenith ; the diaphragm plate, which is able to turn in the axis of the telescope through an angle of 10 to 20 degrees, has in the centre of the field a pair of parallel wires, each thick enough to obscure a star for about two seconds, and the distance between the wires is such that a star would take from 8 to 10 seconds in passing from the first wire to the second. There are two other wires, each thick enough to obscure a star for 8 seconds, one on each side of the pair and parallel to it, and perhaps a sixteenth of an inch from it ; these latter are of use when stars are occasionally rendered invisible by passing clouds. The reason for having a pair of parallel wires in the centre, instead of a single one, is that an observation would, with this construction, be made by looking for the reappearance of the star from behind the first wire, taking the time of the reappear- ance from the watch, then seeing the star disappear behind the second wire and taking the time of the disappearance, and adopting the mean as the time of the instrumental transit. The eye has no difficulty in keeping itself fixed for two seconds while waiting for the reappearance of the star from behind the first wire, nor in finding the star between the two wires after it has been withdrawn to look at the watch. The case is not so with the single wire ; the star is invisible when the watch is first looked at, and the eye has to be directed on returning to the telescope, not to the star, but to that part of the wire where the star is to reappear ; and when the star is small, it is frequently not caught at the right instant. The telescope should be fastened to the pillar by screw bolts and brackets fixed as near as may be to the two ends of the telescope. The above is the simplest form of telescope that I can recommend. With a telescope optically similar and with a field of more than 1 in declination, I have observed with ease Vega in mid-day and 7th magnitude stars at night. The telescope should be thus fixed : 1st, the optician should mark on the inner tube the distance it should be drawn out, so 6 HOW TO KEEP THE CLOCK RIGHT. that the image of the star and the wires should be the same distance from the object glass. 2nd, the telescope should be fixed against the pillar so as to show the zone of stars intended to be observed. 3rd, the wires should be placed at right angles to the path of the stars. This must be done by comparing the observed interval between the passage of a star at the north end of the field and of one at the south end, with the interval given in some good star catalogue, or such tables as the following, which are more convenient, and having ascertained the difference of the intervals and having calculated the proper correction turning the diaphragm round the requisite amount. Example: suppose the observed interval between the transit across the wires of (in hour 2) 1 Gr. 250 and 3 Gr. 199 be 6 m. 14 s. and the interval shown by the tables be G m. 22'75 sec., the difference between the intervals will be 8 '7 5 sec, which will have been caused by the wires not being at right angles to the path of the stars. Now the difference in the NP Distances of the stars is 48' and the space passed over by the stars in -this list in one second of time is about equal to 12" or one-fifth of a minute of arc ; consequently, the wires diverge from the line at right angles to the path of the stars by an inclination of 8'75-r-(48 x 5), and consequently the southern end of the diaphragm must be turned to the west by that amount. When the wires have been*placed nearly at right angles to the path of the stars it would be better not to alter the position till the error had been estimated by the average of several double observations, shown to have been sufficiently well taken by their tolerable agreement with each other. It is well to remember that errors may be so small that it would be better to allow for them than to attempt to correct them. Having adjusted the wires at right angles to the path of the stars or parallel to a meridian, the fourth and last step is to ascertain the error of the instrument ; that must be done by comparing the time, according to a watch or chronometer the error of which is known, at which a star is observed to pass the wires, with the time the star should cross the meridian according to the tables ; thus, supposing on some night a star is observed to pass the wires at 8 h. 10 m. 20 sec., and accord- ing to the tables it should pass the meridian at 8 h. 9m. 10 sec., the error of the instrument will be -f 1 m. 10 sec., and this will be the same for all stars and for all time till the telescope from any cause becomes moved. THE FIXED TELESCOPE. 7 This instrumental ci'ror, when combined with the mean solar time of the apparent transit, on any day, of any of the stars in the following list, which may be easily found from the tables, will give the mean solar time of the star's pnssinff the telescope ; and from that the error of the clock or chronometer may be discovered .and corrected. The 14-inch telescope I have described, though scarcely admitting of any greater simplicity, may be improved by using a sliding eyepiece so as to increase the range of declination. I have one, shown in the vignette in the title page, which gives more than 3 degrees of declination ; the stars certainly have tails at the extremity of the field, but that is not of much consequence since the stars disappear instantaneously enough. A more serious objection is, however, the want of a slow motion for adjusting the wires at right angles to the path of the stars, an error in their position amounting to an inclina- tion of 1 in 900, making a difference of 1 second in the passage of an extreme northern and an extreme southern star. I have in trial a 2-inch glass, 30-inch focus, with more than 3 range in declination, and have found it answer optically very well indeed ; it would show the companion to the pole star nearly to the extreme end of the field. The tube is sloped off near the eye-piece, so as to enable the eye to reach the prism with greater ease ; it has also a slow motion for fixing the wires at right angles to the path of the stars, and I find the adjustment easy up to my powers of observing: eighth-magnitude stars are quite large enough for it (very many, however, of these small stars have not been accurately catalogued, and are con- sequently of little use for keeping time by). The telescope is now attached to a pillar by two cast-iron cradles one at each end. A single cradle would have been better, and then perhaps the instrument might have been worthy of a fuller description. An objection may be reasonably urged against the use of such telescopes that it is impossible to depend upon the per- fect rigidity of the pillars or upon the stability of the ground they stand upon ; no doubt it is so. At the same time, there is reason to think that generally the movements are very small, and the most important of them, that of level, can be to a certain extent detected and allowed for. The tubular part of a spirit level, sufficiently sensitive to indicate a change of one minute of arc by the movement of the bubble over an inch in the length of the tube, might be 8 HOW TO KEEP THE CLOCK RIGHT. attached by means of a horizontal iron bar and vertical adjusting- screws to the pillar at about the height of the middle of the telescope ; and then in these latitudes and with the stars in the tables, the movement of one inch in the bubble would represent an alteration in time of five seconds. The level would not of course show any change in azimuth, but in these latitudes, and with stars so near the zenith as those in the list, the change in time produced by azimuthal move- ment is very much less than that produced by an equal change in level ; and it is not probable that in a detached pillar there would be any azimuthal change, unaccompanied by a much greater change in level a change which would be detected by the spirit level, and would indicate that the pillar, or the ground it stood upon, was unsuitable for a fixed instrument of any sort, at least without frequent testing. Perhaps the best arrangement for the instrument would be a cast-iron cradle to carry a 2-inch telescope, 24 to 30 inch focus, with a sliding eye-piece, and also to carry the spirit level, the cradle, &c., to be fastened to corbels projecting from the north side of the pillar. The instrument to be protected from the weather by a box hung as a door to the pillar. The pillar should have a thoroughly good foundation, and should certainly not be less than eighteen inches square the bricks and corbels should be set in Portland cement. Such is the Fixed Telescope, at present admitting of many improvements, but very simple ; it has no working parts affect- ing the accuracy of the observations taken with it, and is not likely to be disarranged by unskilful usage. It will not find the time, but the time having been once found I believe it will keep it in a very satisfactory manner, and though it may take something from Astronomy and give little in return, it is cal- culated to be of no small service to Horology. The tables of stars to be observed with it, have been carefully prepared from the highest authorities, and have been arranged so as to be readily used by those who are not astronomers, and whose acquaintance with mathematics is limited to the knowledge of a little arithmetic. With these facilities for reducing the ob- servations of the fixed stars to mean solar time, is it too much to hope that others may improve upon the instrument ? 47 SUSSEX SQUA.EE, BRIGHTON. CORRECTION. Since these Tables were printed a small error in them has been pointed out to me, which, though of no practical importance, requires notice. The formula a + Aa + El> &c. p. [6 1 ], which has been used in the construction of Tables II. III. and the L.N.E. of Table V., contains the quantities C"m and -02519 sin 20m. These quantities refer the right ascensions of the stars to the true equinox instead of to the mean equinox, which Table IV. relates to. This introduces an error, affecting all the stars alike, which might gradually increase from nothing to 2*3 seconds in the space of 9-3 years, after which it would gradually diminish, till, at the end of a like period, the error would vanish, and would begin again a similar fluctuation. Auxiliary Tables of C"m and +-02519 sin 2 m would of course enable this error to be corrected, and they are here subjoined, Tables Ha. and Ilia. They ought, when combined with Tables I. II. III. and IV., to bring the mean times of the transits of the stars to a close agreement with that derived from the Nautical Almanac. See the examples which follow. An inspection, however, of the two Auxiliary Tables will show that, while the Table Ilia contains only quantities so small that they may be here safely neglected altogether in practice, the values in Table Ila change so slowly that they might, if it were worth while to take any notice of them, be conveniently combined with the instrumental correction, which might be changed accordingly every year or two. But, perhaps, the best way to deal with this variation would be to take notice of it only when fixing the instrumental error, p. 6, and afterwards when comparing the time given by the fixed telescope and Tables with that derived from other accurate sources. Thus, suppose that on Jan. i, 1870, a star is observed to pass the telescope at 50. 17m. 285. P.M., and that according to the original tables it should pass the meridian at 5h. 1 6m. i6'73s. then correcting this latter time by the Auxiliary Table Ila, 1870 + 0-93, Ilia Jan. l, 0*03, the exact time of the star's passing the meridian will be 5h. l6m. 17-633., and the mean instrumental correction will be 5h. 17m. 285. 5h. i6m. 17-635., or im. 10-373., which may be used on all occasions, excepting when comparing the time by the fixed telescope, and that derived from other accurate sources, on which occasions the Auxiliary Tables should be referred to. 2a J AUXILIARY CORRECTIONS. TABLE Ha. TABLE Ilia. Jan. I J ul y 3 sec. sec. sec. 1868 + 0-40 + 0-56 Jan. i o'O3 1869 + 071 + 0-83 li 0-05 1870 + 0-93 + roo 21 O-07 JL. I8 7 I 1872 + 1-04 + I '03 + i '05 + 0-99 31 Feb. 10 0'08 0'08 1873 + 0-91 + 0-8 1 20 0-06 I8 74 + 0-69 + -55 March 2 O'O4 I8 75 + 0-40 + 0-23 12 T O'O2 1876 + o - o6 O'll 22 + O'OI I8 77 1878 0-28 o - 6o - '45 073 April I + 0-03 I8 79 0-85 - '94 II 21 + 0-05 + 0-07 1880 I'OO 1-04 1881 1-05 T May i + 0'08 1882 0-98 ii + 0'08 1883 - 079 21 + 0-07 1884 - 0-51 3i + 0-05 1885 - 0-17 June 10 + 0-03 1886 + 0-19 20 + O'OO 1887 + 'S3 3 O'O2 1888 1889 -t- 0-80 + 0-99 July i o 20 0*05 0-06 1890 + i '05 30 0-07 1891 1892 1893 1894 -h i 'oo + 0-84 + 0-58 + 0-27 Aug. 9 '9 29 O O 0-08 0-07 o'o6 1895 0-08 Sept. 8 0-04 1896 1897 0*41 070 18 28 O'OI + O'02 1898 0*92 Oct. 8 + 0-04 1899 1-04 18 + o - o6 1900 i '04 28 + 0-07 Nov. 7 + 0-08 17 + 0-07 27 + 0-06 Dec. 7 + 0-04 17 + O'O I 27 0'02 37 o'O4 [ 3* J Examples of the Tables compared with the Nautical Almanac. Jan. 1 1, 1871. Jan. n, 1872. Mean Time of the Transit of Vega. P [60] Tables I. and II 18 32 13-31 18 33 12-45 Table III. 8-41 8-41 P [50] Table IV. P.M. 438 4-81 438 4-81 Table Ila. ... ... ... 1-04+ 1-03 Table Ilia. '05 -05- A.M. ii 10 27-52 II ii 26-65 The same by Nautical Almanac. Apparent Place... ... 18 32 31*99 18 32 34-00 Retardation of Mean Time ... ... 3 2-26 3 2-27 18 29 29-73 18 29 31-73 P 20 M.T. ofT. of P.P. of A P.M. 44057-79 441 54-92 A.M. ii 10 27-52 ii ii 26-65 Mean Time of the Transit of 3 G 1019=0 Canum Venaticorum. P [26-7] Table I. 12 47 44-84 12 47 44-84 3 and 4 Years' Variation ... ... 8-42 11-23 Table II. interpolating 2 40-95 3 38-26 Table III. interpolating ... ... ''35 IO '35 P [50] Table IV. P.M. 438 4-81 438 4-81 Table Ha. ... 1x34+ 1-03 Table Ilia. '05 -05 A.M. I 5 28 50-36 5 29 50-47 The same by Nautical Almanac. Apparent Place of a Can. Ven 12 49 58-71 12 50 1-69 Retardation of Mean Time ... ... 2 6-14 2 6-15- 12 47 52-57 12 47 55-54 P 20 M.T. of T. of P.P. of A P.M. 44057-79 441 54-92 A.M. 5 28 50-36 5 29 50-46 Mean Time of Transit of 3 Gr 1742 = 61' Cygni. P [42-3] Table I. 20 57 32*24 20 57 32-24 3 and 4 Years' Variation ... ... 8 - oo 10-66 Table II. 2 41-26 3 38-29 Table IIL 8-56 8-56 P [50] Table IV. P.M. 438 4-81 438 4-81 Table Ila. 1-04+ 1-03 + Tablellla. '05- -05- P.M. i 38 35-86 i 39 35-54 The same by Nautical Almanac. Apparent Place of 6 1' Cygni 21 I 4-68 21 i 7-25 Retardation of Mean Time 3 26-60 3 26-60 20 57 38-08 20 57 40-65 P 20 M.T. of T. of P.P. of A P.M. 44057-79 441 54-92 P.M. i 38 35^7 i 39 35'57 47 SUSSEX SQUARE, BRIGHTON : 1869. [ 4* j CORRECTIONS. Also ') - ' T '"'") 7 Ust line,' instead of AM. riad P.M. / [i] RULE. To find, for a given day, the mean solar time of the apparent transit of one of the stars included in the following list. Add together From Table I. the Star's mean place given in column 3, with its annual variation in column 4 multiplied into the number of years since 1 868 ; from Tables II. and III. the corrections nearest to it in date and right ascension ; and from Table IV. the time for the day or the day before as the case may be; and the sum will be the mean solar time of the Star's apparent transit, true to a second without interpolation. EXAMPLE I. Required the mean time of the apparent transit of 3 Green 66=^ Andromedae for Oct. 20, 1871. Table I. col. 3 . . . o 49 17-92 3 x 3*291 col. 4 ... 9-87 Table II. i h Dec. 32 . . 24078 Table III. i h Oct. 1 8 . . 14-18 Table IV. Oct. 20 . . 10 i 26-53 P.M. Apparent transit . . . 10 53 49-28 P.M. EXAMPLE II. Required the mean time of the apparent transit of Vega for the same date. Vega, Table I. and II. Dec. 32 . 18 32 13-29 Table III. Oct. 1 8 . . . 11-03 Table IV. Oct. 19 . . 10 5 22-44?^. Apparent transit Oct. 20 . . 4 37 46-76 J?.M. ' TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [ 2 ] Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. + O 1 II _ " + " Ra 6316 G 7'3 o o 48-69 3-065 023 50 39 21-0 20-05 oo R 6317 G 6-8 o o 4973 3-065 023 50 35 9-8 20-05 oo 2 Gr 17 R=Andr 5'4 o 10 10-40 3-107 024 52 3 5'3 20-00 02 Ra 62 G 6-7 12 43-51 3-124 O26 50 o 10-5 20*03 02 BAG 67 =Andr p 5'5 o 14 8-2i 3-133 024 52 45 42-8 19-99 03 WB 561 L 7-8 22 47-31 3-166 027 S 2 24 9-5 19-96 05 Ra 1 80 G 6-3 o 33 52-70 3-220 029 51 15 58-4 19-84 06 Ra 185 G 6-7 o 34 45-22 3-231 "029 50 2 I- 4 19-82 07 R 1986 T o 37 18-60 3-243 029 50 2 34-4 19-79 07 Ra 234 r o 45 28-35 3 -2 79 029 50 28 28-5 19-66 9 3 Green 66 = Andr p 4* o 49 17-92 3-291 030 52 13 2-26 19-64 11 R284G 77 o 51 56-25 3'3 10 032 50 33 26-3 19-53 II i Gr 69 R 6- o 57 1-91 3-335 031 50 42 59-8 19-42 12 [3] TABLE II. TABLE III. year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 ch R.A. m sec 3 46-5S 3 46-35 3 46'i5 ih R.A. m sec 3 46-49 3 46-28 3 46-08 Jan. i 1 1 21 oh R.A. sec 975 9-58 9-42 ih R.A. sec IO'2I IO'C3 9-85 1869 Jan. I C July 3 Dec. 32 o 47-38 o 47*20 o 47-03 o 47-30 o 47-11 o 46*94 3 1 Feb. 10 20 9-27 9-15 9-06 9*68 9*51 9'37 1870 Jan. I B July 3 Dec. 32 i 44- 1 6 i 44*02 i 43-90 i 44-07 i 43-92 i 43-80 Mar. 2 12 22 9-01 9-01 9-0; 9*26 9*18 0*15 1871 Jan. I A fulv 3 2 41-03 2 4.0*04. 2 40*94 2 4.0*84. April I 9-14 9*17 Dec. 32 2 40*87 2 40*78 II 9-29 9*25 1872 Jan. i G July 2 Dec. 32 3 38-01 3 37*98 3 37-98 3 37-92 3 37-89 3 37-9 21 May i 1 1 9*49 974 10*03 9-38 9'57 9*81 1873 Jan. I July 3 Dec. 32 o 39*21 o 39-24 o 39-30 o 39'-3 o 39*18 o 39-25 21 3 1 June 10 I0 '35 10*71 11*07 10*09 10*41 10*76 1874 Jan. 1 D July 3 Dec. 32 i 36-44 i 36-53 i 36*65 1 36-39 1 36-49 I 36-63 20 3 July 10 11-45 11-83 12-ig 11*13 11*51 n-8g 1875 Jan. I C July 3 Dec. 32 2 33*79 2 33*93 2 34-09 2 3377 2 33-92 2 34-10 20 30 AIIP n 12-53 12-84 1 1' 1 1 2 12*26 12'6l 1 876 Jan. I B July 2 Dec. 32 3 31*22 3 3^40 3 3'"59 3 31-23 3 3I-43 3 3 '"63 raug. y '9 29 Q<*r-,f C 1 5 l ' I3-34 I3-53 -,-.Q i i yq. I.V23 J3-49 1877 Jan. I G July 3 Dec. 32 o 32-81 o 33*00 33''9 o 32-85 o 33*06 o 33-26 18 28 I 3 Do 1378 I3-83 J371 -3-89 H3 1878 Jan. I F July 3 Dec. 32 i 30'33 i 30-52 i 30-69 i 30-40 i 30-60 i 30-78 Oct. 8 18 28 I3-85 I3-82 13-76 14-12 14*18 14*20 1879 Jan. i E July 3 Dec. 32 2 27-83 2 27-99 2 28-14 2 27-92 2 28-09 2 28-23 i Nov. 7 ! 7 27 I3-6 7 '3'55 3'4' 14*18 H'13 14*05 1880 Jan. i D July 2 Dec. 31 3 25-27 3 25-39 3 25-48 3 25-37 3 25-49 3 25-58 Dec. 7 17 27 37 13-26 13-09 12*92 12-74 3'94 13-80 '3-65 13.48 hour 1 TABLE I. [4] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in MEAN SOLAR TIME Authority and Mag. North Polar Dicf- Variation Star's Name Right Ascension Variation Ulo\, t Annual Secular Annual Secular h m s sec. + sec. + o ' /; _ // + " i Gr 71 7-8 i o 24-57 3'343 030 51 27 II-2 9'34 12 R* 39 8 * 7-2 I 11 8-86 3'395 031 50 43 52-0 19-10 *H BAG 409 6- 1 15 55-65 3-401 030 52 58 26-9 18-98 16 R 434 G 6-9 I I 9 55-01 3*44' 034 50 20 58-3 18-84 17 Ra 497 G =Andr r S'S I 32 3277 3'5'3 *34 50 5 32-5 i8-43 20 Ra 508 G 7-1 i 34 34'3 6 3-506 032 50 17 24-8 18-36 20 BAG 544 W.B. 6- i 40 35'43 3-506 031 52 42 1 8-0 18-15 21 WB 1218 L 8- i 52 5-84 3*554 34 52 2 51-9 17-69 25 * By Groombridge R.A. i II 8-19 [5] TABLE II. TABLE III. hour 1 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 3 2 ih R.A. m sec 3 46-49 3 46-28 3 46-08 ah R.A. m sec 3 4 6 '42 3 46-19 3 45^8 Jan. i 1 1 21 ih R.A. sec IO'2I 10-03 9-85 ah R.A. sec 10-65 10-49 10-31 1869 Jan. i C July 3 Dec. 3 2 o 47-30 .0 47-11 o 46-94 o 47-21 o 47-0 1 o 46-83 3' Feb. 10 20 9-68 9-5I 9'37 IO-I3 9*93 975 1870 Jan. I B July 3 Dec. 3 2 I 44-07 i 43'9 2 I 43-80 i 43-97 i 43-82 i 4370 Mar. 2 12 22 9-26 9'l8 9-15 9-58 9*45 9-35 1871 Jan. i Afnlv 1 2 40-94 2 40-84 April I 9-17 9*30 J u v 3 Dec. 3 2 2 40-78 * T 7i 2 40-70 II 9-25 9-3i 1872 Jan. i G July 2 Dec. 32 3 3" V 9 2 3 37-89 3 37*9 3 37-84 3 37*83 3 37-85 21 May I II 9-38 9*57 9-81 9-37 9*49 966 1873 Jan. i E July 3 Dec. 3 2 o 39-13 o 39-18 o 39-25 o 39-08 39 H o 39-23 21 31 June 10 10-09 10-41 10-76 9-89 10-17 10-48 1874 J an - l D July 3 Dec. 3 2 i 36-39 i 36-49 i 36-63 ' 36-37 1 36-49 i 36-64 20 3 July 10 11-13 11-51 11-89 10-83 II-20 II-58 1875 Jan. I C July 3 Dec. 32 2 3377 2 33-92 2 34-10 2 3378 2 33-95 2 34*14 20 3 Augr. Q 12-26 12-61 I Z'QA. 11-96 12*34 1 2*70 1876 Jan. i B July 2 Dec. 3 2 3 3i'23 3 31-43 3 31-63 3 31*28 3 3 T *48 3 3i-7 19 29 C--.* Q 13-23 13*49 13-04 13*35 1877 Jan. i G July 3 Dec 32 o 32-85 o 33*06 O 7V26 o 32-92 o 33*14 O 1 2*3 C 18 28 13 7 1 13*89 14*03 13 04 13-89 14-10 ** 3J '""' '' 3J J> 1878 Jan. i F July 3 Dec. 32 I 30-40 I 30-60 I 30-78 1 30-49 I 30-69 I 30-88 Oct. 8 18 28 14-12 14-18 14-20 14 20 H-42 14-52 1879 ' an - ' E July 3 Dec. 3 2 2 27-92 2 28'O9 2 28-23 2 28-O2 2 28*19 2 28-33 Nov. 7 7 27 14-18 H*i3 14-05 I4-58 14-60 *4'59 1880 Jan. i D July 2 Dec. 32 3 25*37 3 25-49 3 25-S8 3 25*47 3 25-58 3 25*66 Dec. 7 '7 27 37 13*94 13-80 i3'65 13-48 H*54 4-45 I4-33 J4*i9 hour TABLE I. [6] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in MEAN SOLAR TIME Authority and Star's Name Mag. North Polar Dist. Variation Right Ascension Variation > Annual Secular Annual Secular h m s I sec. + sec. -- O 1 II _ " + " BAG 649 5'5 2 o 12-34 3'5 88 032 52 46 3-9 I7-3I 26 R628 G 7'I 2 2 32-82 i 3-603 '34 5* 35 5'3 17-23 2 7 R 629 G 7'3 2 2 33-67 3-603 -034 51 34 52-0 17-23 27 R 682 WB 6-8 2 ii 8-68 3-652 031 50 46 28-8 I6-82 30 i G 213 Ra 6- 2 21 22-65 3-680 33 51 27 11-5 16-32 31 Ra 725 7-6 2 21 39-64 3 <6 75 033 51 38 8-7 16-32 '3 2 R 742 WB 6-8 2 26 49*07 3-711 33 50 54 52-9 i6'o6 '3' i G 229 Rad 5' 2 33 30'44 375 2 *34 50 21 57-6 15-52 '34 3 G 1 88 Ra 5'4 2 41 49-08 3756 33 5 2 U 337 15-15 36 BAG 888 6-5 2 44 56-04 3749 032 52 12 8-2 14-98 36 Ra 840 A 6- 2 49 12-95 3-766 031 5 1 55 3' 14-80 36 i Gr 25oRa = Per TT 5' 2 49 51-92 3-804 *33 5 5 2 3' 6 1471 '37 Ra 855 G 6-9 2 53 0-72 3787 032 5' 38 47'5 14-58 '37 3 Gr 199 Ra=Pers p 4' 2 56 14-67 3-812 033 51 40 24-8 14-24 "39 TABLE II. TABLE III. hour 2 Year and Dominical Letter 1868 Jan. l E July ^ Dec. 32 zh R.A. m sec 3 46-42 3 4 6-1 9 3 45-98 3h R.A. m. sec 3 4 6 *3i 3 4 6 ' 8 3 45-87 Jan. i 11 21 zh R.A. sec 10-65 10-49 10-31 3h R.A. sec 11 -06 IO- 93 10*77 1869 Jan. I C July 3 Dee. 32 o 47-21 o 47*01 o 46*83 o 47-10 o 46-90 o 46-73 31 Feb. 10 20 10-13 9 - 93 9*75 10-59 10-39 10-18 1870 Jan. I B July 3 Dec. 32 i 43-97 i 43-82 i 43-70 1 43*87 1 43-72 I 43-62 Mar. 2 12 22 9-58 9*45 9-35 9-98 9-80 9-65 1871 Jan. I A Tulv 3 2 40-84 2 4.O'7C 2 4*75 2 40*68 Apr. i 9-30 9'54 Dec. 3 2 2 40-70 2 40-64 II 9*31 9-47 . . . 1872 Jan. I G July 2 Dec. 32 3 37*84 3 37*83 3 37-85 3 37*78 3 37*78 3 37*82 21 May i II 9'37 9 '% 9-66 946 9-51 9 62 1873 Jan. I E July 3 Dec. 32 o 39-08 o 39-14 o 39-23 o 39-05 o 39-13 o 39-24 21 3 1 June 10 9*89 10-17 10-48 9-78 lO'OO 10-26 1874 J an< l D July 3 Dec. 32 i 36-37 1 3 6> 49 i 36-64 i 36*37 i 36-51 i 36-68 20 30 July 10 10-83 1I'20 1I-58 10-57 10-91 11-27 1875 Jan. I C July 3 Dec. 32 2 3378 2 33*95 2 34*i4 2 33*82 2 34-01 2 34*21 ! 20 3 AUP o 11-96 12*34 I 2"7O 11-64 12-03 1 2 'A I 1876 Jan. i B July 2 Dec. 32 3 31-28 3 3i*48 3 31*7 3 3i*35 3 3^*57 3 31*79 nug. y '9 29 Cf> n t- fi 13-04 13*35 12-78 13-I3 1877 Jan. I G July 3 Dec. 32 o 32-92 33*14 33*35 o 33-02 o 33-24 33*46 18 28 13 4 13-89 14-10 ! 3 47 13*77 14-05 1878 Jan. I F July 3 Dec. 3 2 i 30-49 i 30-69 i 30-88 i 30-60 i 30-80 i 30-99 Oct. 8 18 28 14-28 14-42 14-52 14-30 14-52 14-70 1879 Jan. i E July 3 Dec. 32 2 28-O2 2 28-19 2 28-33 2 28-12 2 28-29 2 28*42 Nov. 7 17 27 14-58 14-60 14*59 H-84 H'95 15*01 1880 Jan. . i D July 2 Dec. 32 3 25*47 3 25*58 3 25-66 3 25*56 3 *5'67 3 2574 Dec. 7 17 27 37 H'54 H'45 14*33 14-19 15"3 15-00 14*94 14*83 hour TABLE I. [8] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and Mag. MEAN SOLAR TIME North Polar Oist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. -H O 1 >l _ ;/ + " Ra 890 BAC=Per w 4'9 3 2 1671 3'837 032 50 53 31-7 14-00 4 Ra 917 G 6-5 3 8 41-81 3-850 031 51 12 147 13-60 '4 1 WB 392 L 7- 3 19 16-92 3-912 033 50 17 23-5 12-90 "44 Ra 1004 G 6-4 3 2 4 i9' 8 4 3'9'9 033 50 32 51-5 12-55 45 BAG 1123 6- 3 3i 59*29 3-896 027 52 50 48-8 I2'09 '45 Ra 1054 G 7" 3 36 21 '06 3'9'5 027 51 44 32-8 II-JO 48 I Gr 336 Ra 3'4 3 48 22-55 3^93 027 50 22 28-9 10-79 '49 Ra 1108 WB 6-5 3 49 5-oi 3-955 -027 51 32 28-6 1079 48 R 11146 6-6 3 So I5-94 3'957 026 5 1 33 34'9 10-69 "5 BAG 1264 7'5 3 58 7'8o 3-970 024 5 2 16 34'5 9-86 5 BAG 1268 6-5 3 5 8 53-15 3-939 024 52 37 16-5 9-91 50 BAG 1269 5'5 3 59 9-97 3-974 "024 52 18 31-5 9-83 50 [9] TABLE II. TABLE III. hour 3 Year and Dominical Letter 1868 Jan. i E July 2 Dee. 32 3h R.A. m sec 3 4 6 -3i 3 46-08 3 45-87 4h R.A. : m sec 3 46-20 3 45-97 ; 3 4575 Jan. i 1 1 21 3h R.A. sec I I -06 10-93 1077 4h R.A. tec 11-39 II-32 II-I9 1 869 Jan. I C July 3 Dec. 3 2 o 47*10 o 46-90 o 4673 o 46-98 o 46-79 o 46-63 i 3 1 Feb. 10 20 10-59 10-39 IO-I8 I 1-04 10-84 10*64 1 870 Jan. I B July 3 Dec. 3 2 i 43-87 i 4372 i 43-62 I 4376 1 43* 6 4 i i 43-54 i Mar. 2 12 22 9- 9 8 9-80 9-65 10-42 IO'2I 10*01 1871 Jan. I A July i 2 4075 2 40*68 2 40-68 2 40*62 Apr. i 9'54 9^5 Dec. 32 2 40-64 2 40*60 ii 9'47 972 1872 Jan. I G July 2 i Dec. 3 2 3 377 8 3 37-78 3 37-82 3 3774 ! 3 3776 3 37-82 21 May i ii 9-46 9-51 9-62 9-65 9-63 9-67 1873 Jan. I E July 3 Dec. 3 2 o 39'5 o 39-13 o 39-24 o 39-05 o 39-15 o 39-27 21 3' June 10 9-78 IO OO 10-26 9-76 9-91 IO'I2 1 874 Jan. I D July 3 Dec. 32 i 36-37 i 36-51 i 36-68 i 36-41 i 36-57 i 3675 20 30 July i o 10-57 10-91 11-27 10-37 io'66 10-99 1875 Jan. I C July 3 Dec. 32 2 33-82 2 34-01 2 34-21 2 33-89 2 34-10 2 34-3I 20 30 A 112. Q 11-64 12-03 12*41 "34 11-70 12-08 i 1876 Jan. l B July 2 Dec. 32 3 3I-35 3 3I-57 3 3179 3 3^45 3 31-68 3 3I-9 1 .nug. y '9 29 Cr,t- 8 12-78 13 13 12-46 12-83 1 877 Jan. I G July 3 Dec. 3 2 o 33-02 o 33-24 o 33-46 o 33-I3 o 33*36 33'57 18 28 *3 47 1377 14-05 I3-55 13-88 1878 Jan. i F July 3 Dec. 32 I 30-60 I 30-80 I 30-99 i 3071 i 30-91 i 31-09 Oct. 8 18 28 14*30 14-52 1470 14-19 14-48 14-73 1879 Jan. I E July 3 Dec. 3 2 2 28-12 2 28-29 2 28-42 2 28-23 2 28-38 2 28-51 Nov. 7 17 27 14-84 H'95 15-01 I4-95 15-13 15-27 1880 Jan. I D July 2 Dec. 32 3 25-56 3 25-67 3 2574 3 25-65 3 2574 3 2579 Dec. 7 17 27 37 15-03 15-00 14-94 14-83 I5-37 15-41 15-41 15-36 TABLE I. [10] MEAN PLACES OF FIXED STARS FOR JAN. i, iS68. Expressed in Authority and Mag. MEAN SOLAR TIME North Polar nic Variation ottir s iSiJinc Right Ascension Variation WM Annual Secular Annual Secular h m s sec. + sec. + O / II _ // + " WB 188-9-10 8- 4 I0 i3'3 4-023 025 5i i 357 9'l8 5 2 WB 461-2 7-8 4 21 40-28 4'73 '024 50 16 48-0 8-2 7 "54 WB 693-4 6- 4 3 2 6 ' 8 9 4-032 'O2O 51 58 31-4 7'43 '55 BAG 1476 6- 4 40 i5*5 6 4-015 017 52 44 50-1 6-82 *55 BAG 1530 5' 4 49 3^8 4-050 OI 5 5z 18 43-3 5-91 5 6 Ra 1368 G 6-2 4 50 26-41 4-101 oi 6 50 48 31'! 5-92 '57 Ra 1369 G 6- 4 50 29-86 4-110 016 50 32 54-0 5-91 '57 TABLE II. TABLE III. hour Year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 4h R.A. m sec 3 46-20 3 45'97 3 4575 5 h R.A. m sec 3 4 6 '7 3 45-85 3 45^4 Jan. l II 21 4h R.A. sec H'39 II-32 II-I9 Sh R.A. sec 11-63 II-62 11-55 1869 Jan. I C July 3 Dec. 32 o 46-98 o 4679 o 46-63 o 46-87 o 46-69 o 46-54 3 1 Feb. 10 20 11-04 10-84 10-64 U'43 11-27 I I -08 1870 Jan. I B July 3 Dec. 32 I 43-76 1 43-64 I 43-54 I 43-68 I 43-56 1 43-49 Mar. 2 12 22 10-42 IO'2I 10-01 10-86 10-65 10-42 1871 Jan. I A Tulv 3 2 40-68 2 40*62 2 40-62 2 4.O" C 8 Apr. i 9-85 10-22 Dec. 32 2 40-60 2 40-59 ii ?'-6- IO-O5 1872 Jan. I G July 2 Dec. 32 3 3774 3 377 6 3 37-82 3 3772 3 3777 3 37-85 21 May i ii 9 6 S 9*63 9-67 992 9-84 9'8l 1873 Jan. I E July 3 Dee. 32 o 39-05 o 39-15 o 39-27 o 39-08 o 39-19 o 39'34 21 31 June 10 9-76 9-91 10-12 9-83 9-92 IO-05 1 874 Jan. I D July 3 Dec. 32 i 36-41 i 36-57 i 36-75 I 36-48 I 36-65 I 36-85 20 3 July 10 10-37 10-66 10-99 IO-24 10-48 10-75 1875 Jan. i C July 3 Dec. 32 2 33-89 2 34-10 2 34-3I 2 33-99 2 34-20 2 34-43 20 30 Aug. o *34 11-70 12-08 I I 'O6 JI'39 H'75 1876 Jan. I B July 2 Dec. 32 3 3^45 3 31-68 3 3I-9 1 3 31-56 3 3i-8o 3 32-03 '9 29 nr 8 12-46 12-83 I2'I2 12-49 12-86 1877 Jan. I G July 3 Dec. 32 o 33*13 o 33-36 o 33 57 o 33-26 33-48 o 33-69 18 28 I3-55 13-88 13-24 13-60 1878 Jan. I F July 3 Dec. 32 i 30-72 i 30-91 i 31-09 I 30-83 I 31-02 I 31-19 Oct. 8 18 28 14-19 14-48 H'73 13-95 14-29 14-60 1879 Jan. l E July 3 Dec. 32 2 28-23 2 28-38 2 28-51 2 28-33 2 28-47 2 28-58 Nov. 7 17 27 H'95 15-13 15-27 14-89 15-14 15-36 1880 Jan. I D July 2 Dec. 32 3 25-&5 3 25-74 3 25-79 3 2571 3 25-79 3 25-82 Dec. 7 17 27 37 I5-37 15-41 15-41 15-36 I5-53 15-65 15-72 I5-74 hour TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. + O ' (/ _ " I + " Ra 1426 G =Aur p. 5'4 5 3 34' 8 4-085 013 51 40 29-4 4'75 58 3Gr384Rad Aur X 5" 5 9 072 4-198 014 50 I 19-5 3-64 60 BAC 1663 =Aur a 5'5 5 H 49'4 4-063 oio 52 44 27-6 3-84 58 R 1491 G 6-9 5 20 41*19 4-I53 007 50 16 48-4 3-33 ;6 2 R 1493 G 77 5 20 58-06 4-162 008 50 4 29-9 3-3I 61 Ra 1496 * 7-1 5 21 30-67 4-097 007 5i 47 2-3 3-26 60 R 1515 G 7'4 5 26 55-97 4'IO2 006 51 44 40-7 2-79 61 R 1538 G 7'9 5 32 2075 4*101 006 51 52 22-5 2-32 60 R 1541 7'4 5 32 49'*7 4'IQI 006 51 52 15-9 2-28 60 Ra 1558 G 6-8 5 38 45-42 4' '59 005 50 30 557 176 61 Ra 1559 G 5' 5 39 6 'H 4-142 005 50 52 2-3 173 61 BAC 1844 =Aur v 5'5 4-080 004 52 44 8-6 59 Rad 1564 G = Aur v 4*5 5 4 1 24-50 4-I45 004 50 53 36-9 1-56 6 1 3 G 447 BAC = Aur 6 y 5 49 45-83 4-079 004 52 47 59'7 0-69 60 R 1609 WB 77 4-122 ooi 5 1 32 53-4 0-6 1 60 R 1611 WB 7-2 5 52 0-46 4-129 ooi 51 17 13-8 0-60 60 Ra 1622 WB 6-9 5 54 35-23 4-125 ooi 51 25 27-0 0-38 60 Ra 1624 WB 6-4 5 55 0-98 4-099 ooi 52 2 1-3 0-26 60 Ra 1625 G 5'9 5 56 30-53 4-122 ooi 51 30 30-3 0-21 60 R 1 634 BAC 6-8 5 57 28-96 4-111 ooi 51 54 27-4 0*06 60 * Ra 1496 RA. by G 30-185 by WB 30-16; by L 30-05 [13] TABLE II. TABLE III. hour Year and Dominical Letter i 868 Jan. I E July 2 Dec. 32 5h R.A. m sec 3 4 6> c7 3 45^5 3 45'64 6h R.A. m sec 3 45-95 3 4573 3 45-54 Jan. i II 21 Sh R.A. sec 11-63 II-62 11-55 6h R.A. sec U'77 11-82 11-82 1869 Jan. I C July 3 Dec. 32 o 46-87 o 46-69 o 46-54 o 46-76 o 46-60 o 46-47 3 1 Feb. 10 20 U'43 II-2 7 II-08 I 1-76 11-64 11-48 1870 Jan. i B July 3 Dec. 3 2 I 43-68 i 43-56 i 43-49 I 43-60 1 43-51 1 43'45 Mar. 2 12 22 10-86 10-65 10-42 I 1-29 I 1*07 IO-85 1871 Jan. i A July 3 2 40-62 2 4.o-c8 2 4'59 2 4O-?7 Apr. i 10-22 10*63 Dec. 32 2 40-59 2 40-60 1 1 IO-05 10-43 1872 Jan. I G July 2 Dec. 32 3 3772 3 37*77 3 37-85 3 3773 3 37-8o 3 37-9 21 May i n 9-92 9-84 9'8l IO-25 IO'I2 10-03 1873 Jan. i E July 3 Dec. 32 o 39*08 o 39-19 o 39*34 o 39-13 o 39-26 o 39-43 21 3* June 10 9-83 9-92 IO-05 9'99 10-01 10-08 1874 Jan. i D July 3 Dec. 32 i 36-48 i 36-65 i 36-85 i 36-56 i 36-75 i 36-96 20 30 July 10 IO-24 10-48 IO-75 10-19 10-36 10-58 1875 Jan. i C July 3 Dec. 32 2 33'99 2 34*20 2 34-43 2 34' 10 2 34-32 2 34*55 20 3 A UP o I I *O6 11-39 I I'7C 10-83 11*11 I I "4-2 1876 Jan. i B July 2 Dec. 32 3 3''5 6 3 3i'8o 3 3 2 -o3 3 31-69 3 31-92 3 32-15 "& y '9 29 C-_ t 1 / J 12*12 12-49 , -.Of. I 1-76 12'II , _. . o 1877 Jan. i G July 3 Dec. 32 o 33-26 o 33-48 o 33-69 o 33-38 o 33-60 o 33-80 18 28 n-H 13-60 124 I2-85 I3'23 1878 Jan. i F July 3 Dec. 3 2 I 30-83 I 31-02 I 31-19 I 30-94 I 31-12 1 31-28 Oct. 8 18 28 I3-95 14-29 14-60 13-60 13-97 I4 ! 33 1 879 Jan. i E July 3 Dec. 3 2 2 28-33 2 28-47 2 28-58 2 28-41 2 28-54 2 28-63 Nov. 7 '7 27 14-89 15-14 15-36 14-67 14-98 15-27 1880 Jan. i D July 2 Dec. 32 3 2571 3 25-79 3 25-82 3 25-76 3 25-81 3 25-83 Dec. 7 17 27 37 I5-53 15-65 1572 574 I5-5I 1571 15-85 I5-94 IM hour TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [14] Expressed in Authority and Mag. MEAN SOLAR TIME North Polar Diet Variation otur s PI s me Right Ascension Variation ISla Annual Secular Annual Secular h m s sec. + I sec. O ' /' + " + " R 1676 WB 77 6 4 8-65 4-168 003 50 17 37-6 0-46 6 1 R 1694 G 6-9 6 7 3379 4'l6l ooi 50 29 o-o 076 6 1 R 1698 7-6 6 8 34*20 4'II2 002 5i 43 4'3 0-85 60 R 1702 G 7-2 6 9 37-14 4-122 ooo 5i 30 537 0-94 60 R 1758 7-1 6 23 28 86 4' 1 54 009 50 27 31-5 2M5 60 R 1761 G 6-8 6 24 1 3-26 4 -I 3 006 51 49 40-4 2-22 60 Ra 1763 G 7-9 6 24 33-40 4-119 009 51 21 46-2 2-25 6 1 R 1768 G 57 6 26 24-68 4-115 009 51 27 3'I 2- 4 I 60 Ra 1777 G 5'9 6 28 26-84 4-152 006 50 29 42*6 2-59 62 Ra 1794 G 7-1 6 32 23-87 4-130 009 50 S 8 587 2'93 59 Ra 1827 G 6-4 6 42 50-43 4*133 01 1 50 58 367 3^3 58 Ra 1828 WB 6-4 6 43 3'87 4- 1 06 on 51 24 1-3 4-OO 58 Ra 1830 G 6-5 6 43 47-60 4-108 009 51 20 11*5 3'93 60 R i 840 G 6-9 6 45 25-63 4-084 on 51 55 13-6 4-06 '59 R 1852 G 7-9 6 48 16-27 4-085 on 51 50 21'2 4-29 *57 Rad 1856 G 6-2 6 48 55-97 4-087 on 51 46 9-6 4*45 58 [15] TABLE II. TABLE III. hour 6 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 6h R.A. m sec 3 45'95 3 4573 3 45"54 7h R.A. m sec 3 45-83 3 45- 6 3 3 45-45 Jan. i 1 1 21 6h R.A. sec 11-77 11-82 11-82 yh R.A. sec 11-78 Il-gi 11-98 1869 Jan. i C July 3 Dec. 32 o 46-76 o 46-60 o 46-47 o 46-68 o 46-53 o 46-42 31 Feb. 10 20 1 1-76 11-64 11-48 II- 99 II- 93 11-82 1870 Jan. I B July 3 Dec. 32 I 43-60 I 43-51 i 43'45 I 43-55 I 43-48 I 43-44 Mar. 2 12 22 1 1-29 11-07 10-85 11-66 11-48 11-27 1871 Jan. I A Tulv 3 2 40-59 2 4O-C7 2 40-58 2 4-O'CQ Apr. i 10-63 11-04 Dec. 32 2 40-60 2 40-63 ii 10-43 10-83 _ C - 1872 Jan. I G July 2 Dec. 32 3 3773 3 37-80 3 37'9 3 37*77 3 37-85 3 37-97 21 May i ii 10*25 10-12 IO '3 10-63 10-46 10-32 1873 Jan. I E July 3 Dec. 32 o 39-13 o 39-26 o 39'43 o 39-20 o 39'35 o 39-53 21 31 June 10 999 lO'OI 10-08 10-23 10-18 10-18 1874 Jan. I D July 3 Dec. 32 i 36-56 i 3675 i 36-96 i 36-67 i 36-86 i 37-08 20 30 July 10 10-19 10-36 10-58 10-24 10 '33 10-48 1875 Jan. I C July 3 Dec. 32 2 34'io 2 34*32 2 34-55 2 34-22 2 34^5 2 34'68 20 30 Aut? o 10-83 irn 1 1 -42 io-66 10-88 11*14 1876 Jan. I B July 2 Dec. 32 3 31-69 3 31-92 3 32-15 3 31-82 3 32-05 3 32-27 ""& y ^9 2 9 C or ,1. 8 11-76 I2'II U'43 11-74 1 877 Jan. I G July 3 Dec. 32 o 33-38 o 33-60 o 33-80 o 33-50 o 337i o 33-90 18 28 I2-85 I3-23 12*07 12-42 12*79 1878 Jan. I F July 3 Dec. 32 I 30-94 I 31-12 I 31-28 I 31-04 I 31-20 i 3i'34 Oct. 8 18 28 I3-60 I3-97 H'33 13-17 13'SS I3-93 1879 Jan. I E July 3 Dec. 32 2 28-41 2 28-54 2 28-63 2 28-48 2 28-58 2 28-65 Nov. 7 i? 27 14-67 14-98 15-27 H"3i 14-67 15-01 1880 Jan. I D July 2 Dec. 32 3'2576 3 25-81 3 25-83 3 2579 3 25-82 3 25-81 Dec. 7 '7 27 37 15-51 15-71 15-85 T94 15-31 15-58 15-80 15*96 hour TABLE I. [i 6] 7 MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and Mag. MEAN SOLAR TIME North Polar Diet Variation ottir s Wsmc Right Ascension Variation lot. Annual Secular Annual Secular h m s sec. + sec. ' // + " + " i Gr 637 Rad 5' 7 i 25-13 4-130 -014 50 28 2-6 5-45 58 R 1919 G r 7 7 3i'25 4-097 017 5 53 30'4 5*93 '57 R 1926 WE 7-1 7 8 42-18 4-088 017 5i 5 32-3 6*03 '57 R 1937 G 67 7 12 i'45 4-094 O2O 50 45 26-9 6-32 5 8 R 1938 G 5*' 7 12 2-40 4-015 017 S 2 59 37-9 6- 3 I 56 Ra 1958 WB 7-1 7 17 24-12 4-075 Q2O 51 4 18-4 675 "55 R 1969 7-8 7 19 49'52 4-063 C2O 51 17 28-0 6-96 57 R 1970 G 7-2 7 20 2-46 4^53 020 5' 33 33-8 6-97 '55 Ra 1973 G 6-9 7 21 45-22 4-077 *O2O 50 49 45-1 7-11 '55 R i 994 G 7*3 7 27 59' 8 2 4-044 02O 51 26 53-1 7-61 '53 Ra 1999 G 8- 7 28 38-33 4-045 O2O 51 22 I 97 7-68 '55 Ra 2006 G 6-2 7 30 7-35 4-044 O2O 51 21 23-3 7-80 '55 WB 1083 L 6- 7 36 35-4 4-006 019 52 9 59-0 8-32 '53 WB i2 9 7L 8- 7 45 9-98 3-979 020 S 2 27 44'3 9'oo 52 WB 1490 L T 7 53 26-69 3-961 021 S 2 29 52-4 9-64 51 TABLE II. TABLE III. hour 7 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 7h R.A. m sec 3 45-83 3 45-63 3 45-45 8h R.A. m. sec 3 4574 3 45-55 3 45-38 Jan. i II 21 7h R.A. sec 11-78 11-91 11-98 8h R.A. sec 1 1 -68 n-88 I2'02 1869 Jan. i C July 3 Dec. 32 o 46-68 o 46-53 o 46-42 o 46-61 o 46-48 o 46-39 31 Feb. 10 20 11-99 II- 9 3 11*82 I2'IO I2'I2 I2-07 1870 Jan. i B July 3 Dec. 32 * 43-55 i 43-4 8 1 43 '44 I 43-53 1 43-47 I 43-46 Mar. 2 12 22 1 1 -66 11-48 11-27 H'97 11-82 11-64 1871 Jan. I A lulv i 2 40-58 2 AO'CQ 2 40-60 2 40*62 1 Apr. i 11-04 H'44 Dec. 32 2 40*63 2 40*69 11 10-83 1I*23 1872 Jan. I G July 2 Dec. 32 3 3777 3 37-85 3 37-97 3 37-82 3 37-93 3 38-06 21 May i II 10-63 10-46 10-32 II-03 10-83 10-67 1873 Jan. I E July 3 Dec. 32 o 39-20 o 39-35 o 39-53 o 39-29 39*45 o 39-64 21 3 1 June 10 10-23 10-18 10-18 '0-53 I0 '43 10-37 1874 J an * l D July 3 Dec. 3 2 i 36-67 i 36-86 i 37-08 i 36-78 i 36-98 i 37-20 20 3 July 10 10-24 -0-33 10-48 10-36 10-39 10-46 1875 Jan. i C July 3 Dec. 32 2 34-22 2 34-45 2 34-68 2 34*34 2 34*57 2 34-80 20 3 AIIP o 10-66 10-88 1 1 -14. 10-57 1072 1 O'Q I 1876 Jan. i B July 2 Dec. 32 3 3'-82 3 32-05 3 32-27 3 3 J '93 3 32-16 3 32-37 *6 y 9 2 9 5-3i 15-58 15 80 15-96 H'95 15-27 '5'55 1578 hour 8 TABLE I. [18] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and Star's Name Mag. MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. O ' n + " + " Ra 2096 G 6-5 8 I 17-26 3-994 026 5 52 43-2 10-24 'SI WB 354 L 8- 8 15 26-25 3'9'9 025 52 II 87 11-28 '47 Ra 2164 G 6'3 8 22 57-31 3-9*7 029 51 31 56-9 II-8I '45 WB 688 L 7-8 8 28 23-79 3-875 O20 52 31 I7-2 12-20 '45 R 2206 G 7*3 8 39 3^3 3-882 031 51 10 14-1 12-93 '43 Ra 2248 G 6-4 8 50 39-66 3-826 031 Si 53 1-8 13-69 "4 1 Ra 2255 G 7'4 8 52 24-14 3-849 "034 50 49 36-2 *3'8o 40 R2258 G 7'4 8 53 3677 3-822 034 51 38 1-8 13-88 40 Ra 2260 WB & L 7- 8 53 52-86 3-848 032 50 44 1 6-6 13-89 '39 Ra 2269 WB 7'9 8 56 o-o 3-831 034 51 2 8'7 14-03 39 3 Gr 689 Rad S' 8 56 39*43 3-840 030 51 I 2O-5 I4'I3 39 [19] TABLE II. TABLE III. hour 8 Year and Dominical Letter 1 868 Jan. I E July 2 Dec. 32 8h R.A. m sec 3 4574 3 45*55 3 45-38 9h R.A. m sec 3 45-66 3 45*49 3 45'35 Jan. i ii 21 8h R.A. 1 sec n-68 n-88 I2-O2 gh R.A. sec 11-47 11-74 H'95 1 869 Jan. I C July 3 Dec. 32 o 46-61 o 46-48 o 46-39 o 46-57 o 46-47 o 46-39 31 Feb. 10 20 I2-IO I2'I2 I2-O7 12-10 I2-I9 12-21 1870 Jan. I B July 3 Dec. 3 2 1 43-53 1 43-47 i 43 '4 6 i 43*53 i 43-5 i 43-50 Mar. 2 12 22 II- 9 7 11-82 U-64 12-17 12-08 II-QC 1871 Jan. I A July 3 2 40-60 2 40-62 2 40*64 2 40-68 Apr. i 11-44 11-79 Dec. 32 2 40-69 2 40-76 ii 11-23 ir6o 1872 Jan. I G July 2 Dec. 32 3 37-82 3 37-93 3 38-06 3 37'9 3 38-02 3 38-16 21 May i ii II-03 10-83 10-67 11-41 11*21 11-03 1873 Jan. I E July 3 Dec. 32 o 39*29 o 39-45 o 39-64 o 39*39 o 39-56 o 39-75 21 31 June 10 10-53 IQ'43 10-37 10-87 10-73 10-63 1874 Jan. I D July 3 Dec. 32 I 3678 I 36-98 I 37-20 i 36-89 i 37-10 i 37-32 20 30 July i o 10-36 10-39 10-46 10-55 10-52 IO-C2 1875 Jan. I C July 3 Dec. 32 2 34-34 2 34-57 2 34-80 2 34^6 2 34'68 2 34-90 20 30 Anc' o 10-57 10-72 IO*QI 10-56 10-64 i n"7 r 1 876 Jan. i B July 2 Dec. 32 3 3I-93 3 32-16 3 32'37 3 32-04 3 3 2 -25 3 32'45 nug. y 9 2 9 Co-* O II-I3 11-39 ,./:,. 1U /I, 10-90 1 1 -08 1877 Jan. I G July 3 Dec. 3 2 o 33-60 o 33-80 33-97 o 33-68 o 33-86 o 34-02 ocpt. o 18 28 1 1 07 11-98 12-32 I I'3O 11-56 11-84 1878 Jan. I F July 3 Dec. 32 I 31*11 I 31-26 I 31-38 i 31-16 i 31*29 i 31-39 Oct. 8 18 28 12-67 13-05 I 3'43 12-16 12-50 12-87 1879 Jan. I E July 3 Dec. 32 2 28-52 2 28-60 2 28-65 2 28-53 2 28-59 2 28-62 Nov. 7 17 27 13-82 14-21 H'59 13-25 13-65 14-04 1880 Jan. I D July 2 Dec. 32 3 25-78 3 2579 3 25-76 3 25-76 3 2575 3 2 57o Dec. 7 17 27 37 H'95 15-27 I5-55 15-78 H'43 14-80 15-14 i_5_-4J 9 TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [20] Expressed in Authority and Mag. MEAN SOLAR TJME North Polar Diet Variation Right Ascension Variation 13L Annual Secular Annual Secular h m s sec. + sec. O / II + " + " Ra 2294 6-8 9 5 871 3-806 34 50 51 i-o 14-60 39 2 Gre 664 BAG 4* 9 9 7-10 3747 031 52 38 25-4 I4-8 7 37 Ra 2311 G 6-4 9 II I2'22 3774 *34 51 15 17-4 H'95 3 6 3 G 732 BAG 6- 9 23 51*22 3-696 030 52 55 50-0 15-71 *33 R 2379 G 7-1 9 3' 37'35 37^9 *34 50 26 49-6 1 6- 10 '34 Ra 2405 WB 6-6 9 42 45-56 3' 6 54 034 51 28 3-3 1 6-66 31 Ra 2434 7-0 9 54 2I 74 3-611 034 51 20 16-0 17-20 28 [21] TABLE II. TABLE III. hour 9 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 9h R.A. m sec 3 45-66 3 45-49 3 45-35 ioh R.A. m sec 3 45-62 3 45-46 3 45-34 Jan. i n 21 9 h R.A. sec H'47 11-74 11-95 ioh R.A. sec i ri6 11-48 11-75 i 869 Jan. I C July 3 Dec. 32 o 46-57 o 46-47 o 46-39 o 46-57 o 46-48 o 46-42 31 Feb. 10 20 I2'IO I2M9 12-21 11-97 12-13 12-23 1870 Jan. I B July 3 Dec. 32 * 43-53 i 43'5 i 43'5o i 43-56 i 43-54 i 43-56 Mar. 2 12 22 I2-I7 I 2-08 II-95 12-27 12-25 12-18 1871 Jan. I A July 3 2 40-64 2 40-68 2 40-70 2 4.0*76 Apr. i H'79 12-06 Dec. 32 2 40-76 2 40-85 n 1 1 -60 n 92 1872 Jan. I G July 2 Dec. 32 3 37'9 3 38-02 3 38-16 3 37'99 : 3 38-11 i 3 38-26 ; 21 May i II II-4I IT2I irO3 11-75 11-58 11-40 1873 Jan. I E July 3 Dec. 32 o 39^9 o 39-56 o 3975 o 39-49 o 39-67 o 39-86 ; 21 31 June 10 10-87 10-73 10-63 IT22 II-07 10-93 1874 Jan. I D July 3 Dec. 3 2 i 36-89 i 37-10 i 37'32 i 37-00 i 37-20 i i 37-42 20 30 July 10 10-55 10-52 IO'C2 10-81 10-72 io'66 1875 Jan. I C July 3 Dec. 32 2 34-46 2 34- 6 8 2 34'9 2 34-5 6 2 34-77 i 2 34-98 20 3 10-56 10-64 10-63 10-63 1876 Jan. I B July 2 Dec. 32 3 32-04 3 32-25 3 32-45 3 32-12 3 32-32 3 32-51 /iug. 9 19 29 Cn., Q 10 75 10-90 1 1 -08 10-74 10-85 1 877 Jan. I G July 3 Dec. 3 2 o 33-68 o 33-86 o 34-02 o 33-74 o 33-90 o 34-04 oept. o 18 28 1 1*30 1 1-56 11-84 10-99 11-18 II-39 1878 Jan. I F July 3 Dec. 32 I 31-16 I 31-29 I 31-39 I 31-18 I 31-29 I 31-38 Oct. 8 18 28 I2'l6 12-50 12-87 11-65 11-95 12-27 1879 Jan. I E July 3 Dec. 32 2 28-53 2 28-59 2 28-62 2 28-51 2 28-56 2 28-57 Nov. 7 17 27 13-25 13-65 14-04 12-63 13-01 13-4 1 1880 Jan. I D July 2 Dec. 32 3 2576 3 2575 3 2570 3 2571 3 25-68 3 25-62 Dec. 7 '7 27 37 H'43 14-80 15-14 I5-43 13-81 14-20 14-58 14-92 m hour TABLE I. J_U MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [22] Expressed in Authority and otiir s ^(3 me Mag. MEAN SOLAR TIME North Polar TVcf Variation Right Ascension Variation UlSl. Annual Secular Annual Secular h m s sec. + sec. 1 1' + " + " Ra 2456 WB 6-1 i o i 44' i o 3-568 037 51 56 55-3 I7-53 27 WB 197 L /8 8- 10 ' 8 56-44 3'545 031 51 49 58-0 17-82 23 3Gr8o6BAC = LeMi 4'5 10 18 32-95 3-482 030 52 37 2'3 18-29 21 Rad 2503 G 57 10 20 4179 3-5I9 037 50 24 ro 18-30 23 R 2505 G 7'4 10 21 38*04 S'S^ -037 50 18 7-8 18-30 21 3 G 825 Rad 6- 10 29 50-77 3-443 031 51 24 9-5 I8-62 18 WB 894-5 L 7-8 10 43 20-75 3-410 031 50 57 46-3 19-00 15 Ra 2614* 7'9 10 54 42-58 3'3 6 3 034 50 19 42-3 19-29 13 R 2 6i5 WB 7-2 10 55 8-47 3-360 034 50 25 15-1 19-30 13 Ra 2616 WB 6-1 10 55 22-95 3-353 031 51 2 53-9 19-31 "H Ra26i7 WB 7'6 10 55 35-69 3-352 "031 51 2 34-0 19-31 3 -t- *Ra 1614. RA. by G to 54 43^x0 TABLE II. TABLE III. hour 10 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 ioh R.A. m sec 3 45-62 3 45^6 3 45-34 iih R.A. m sec 3 45-6i 3 45-47 3 45-36 Jan. i ii 21 3 Feb. 10 20 Mar. 2 12 22 April i ioh R.A. sec 11-16 11-48 1175 11-97 12-13 12-23 12-27 12-25 12-18 12-06 Iih R.A. sec 10-77 11-13 11*46 II74 11-97 12-14 12-25 12-30 12-30 12-25 1 869 Jan. I C July 3 Dec. 32 o 46-57 o 46-48 o 46-42 o 46-59 o 46-51 o 46-48 1870 Jan. I B July 3 Dec. 3 2 1 43-56 I 43-54 I 43-56 i 43-6i i 43-61 i 43-64 1871 Jan. i A July 3 Dec. 3 2 2 4070 2 40*76 2 40-85 2 40-78 2 40-85 2 40-95 n 21 May i ii 21 3 June 10 20 3 July 10 20 30 Aug. 9 '9 29 Sept. 8 18 28 11-92 1175 11-58 11-40 11-22 ir07 10-93 I0'8l IO-72 10-66 10-63 10-63 10-67 10-74 10-85 10-99 11-18 11-39 12-16 12-04 11-90 1174 11-57 11-41 11-25 ii-n 10-98 10-87 10-78 10-71 10-68 10-67 10-70 10-76 10-86 11-01 1872 Jan. I G July 2 Dec. 32 3 37-99 3 38-ii 3 38-26 3 38-08 3 38*21 3 38-36 1873 J an - l E July 3 Dec. 3 2 o 39-49 o 39-67 o 39*86 o 39-59 o 39 77 o 39-96 1874 Jan. I D July 3 Dec. 3 2 i 37-00 I 37-20 i 37-42 i 37-09 i 37-29 37'5 1875 Jan. I C July 3 Dec. 3 2 2 34-56 2 34-77 2 34-98 2 34-64 2 34-84 2 35-04 1876 Jan. I B July 2 Dec. 3 2 3 32-12 3 32-32 3 3 2 -5i 3 32-17 3 32-36 3 32-53 1877 Jan. I G July 3 Dec. 3 2 o 3374 o 33-90 o 34-04 o 3376 o 33-91 o 34-03 1878 Jan. I F July 3 Dec. 3 2 i 31-18 i 31-29 i 3i'38 i 31-17 i 31-27 i 3I-33 Oct. 8 18 28 Nov. 7 7 27 Dec. 7 7 27 37 11-65 11-95 12-27 12-63 13-01 13-41 13-81 14-20 14-58 14-92 11-19 11-42 11-69 I2'OI I2'35 1273 13-12 13-52 I3'92 14-30 1879 J an - * E July 3 Dec. 3 2 2 28-51 2 28-56 2 28- 5 7 2 28-47 2 28-50 2 28-50 1880 Jan. i D July 2 Dec. 3 2 3 2571 3 25-68 3 25-62 3 25-64 3 25-60 3 25-53 hour 11 TABLE I. [ 24 ] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in MEAN SOLAR TIME Authority and Mag. North Polar Dist- Variation Star s N arne Right Ascension Variation I*rl5l. Annual Secular Annual Secular h m s sec. + sec. O ' // + " + " BAG 3811 WB 6- ii o 15*24 3-322 029 52 58 28-4 19-44 12 Ra 2643 WB 77 ii 5 59-17 3-299 -029 51 42 8-4 9'53 9 3 Gr 883 Rad 5' ii 10 5*69 3-2B3 028 51 5 27-1 19-71 9 Ra 2675 WB 6-9 11 I 4 54-19 3-256 029 52 2 25'2 19-70 9 R 26856 7'3 ii 18 47-16 3 <2 43 029 51 I 9 54-4 974 5 Ra 2696 7-1 ii 21 17-96 3-232 '028 5 I I 9 5 -I 19-80 08 WB 596-7 L 8- ii 29 49-97 3-198 027 50 37 9-6 19-90 5 3 Gree 934 Radc 67 ii 43 26-24 3'47S 024 51 20 3-1 25-71 'O2 3 Gre 941 WB 8- ii 50 0-23 3-101 023 51 23 20-6 20^04 01 TABLE II. TABLE III. hour 11 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 3 2 nh R.A. m sec 3 45'6i 3 45-47 3 45*36 izh R.A. m sec 3 45-63 3 45'5 ! 3 45'4" Jan. i 1 1 21 3 1 Feb. 10 20 Mar. 2 12 22 April i jiih R.A. sec 1077 II-I 3 11-46 11-74 11-97 12-14 12-25 12-30 12-30 I2-25 nh R.A. sec 10-33 10-72 11-08 I 1-41 11-69 11-93 12-11 I2-24 I2-3I 12-33 1869 Jan. I C July 3 Dec. 32 o 46-59 o 46-51 o 46-48 o 46-64 o 46-58 o 46-55 1870 Jan. I B July 3 Dec. 32 I 43-61 I 43-61 1 43*64 I 43-69 I 43-69 i 4373 1871 Jan. I A July 3 Dec. 32 2 40-78 2 40-85 2 40-95 2 40-87 2 40-94 2 41*04 II 21 May i II 21 31 June i o 20 3 July 10 20 3 Aug. 9 '9 29 Sept. 8 18 28 12-16 12 04 II-90 11-74 11-57 II'4I 11-25 II-II 10-98 10-87 10-78 10-71 10-68 10-67 10-70 10-76 io'86 iroi 12-31 I2-25 12-I5 I2-03 11-89 11-74 11-59 11 '43 11-28 II-I3 10-99 IO-87 10-77 10-69 IO-&4 10-62 10-64 1O70 1872 Jan. I G July 2 Dec. 3 2 3 38-08 3 38*21 3 38-36 3 38-18 3 38-31 3 38-46 1873 Jan. I July 3 Dec. 32 o 39"59 o 3977 o 39-96 o 39-68 o 39-85 o 40-03 1874 Jan. I D July 3 Dec. 32 i 37-09 i 37-29 i 37-50 i 37"!7 i 37-36 i 37-55 1875 Jan. l C July 3 Dec. 32 2 34-64 2 34-84 2 35'4 2 34-69 2 34-88 2 35-06 1876 Jan. i B July 2 Dec. 32 3 32-17 3 32-36 3 32-53 3 32-20 3 32'37 3 32-52 1877 Jan. I G July 3 Dec. 32 o 3376 o 33-9 1 o 34-03 o 3375 o 33-88 33'99 1878 Jan. I F July 3 Dec. 32 i 31-17 i 31-27 i 31-33 i 31*13 i 31-21 i 31-27 Oct. 8 18 28 Nov. 7 17 27 Dec. 7 17 27 37 11-19 11-42 11-69 12-01 12-35 12-73 13-12 !3-5' 13-92 1 4' 30 IO-8I 10-96 11-17 11-42 II7I 12*05 12-41 12-80 13-20 '3-59 1879 Jan. I E July 3 Dec. 32 2 28-47 2 28-50 2 28-50 2 28-40 2 28-42 2 28-41 1880 Jan. I D July 2 Dec. 32 3 25-64 3 25*60 3 25-53 3 25-55 3 25-51 3 25-43 hour 12 TABLE I. [26] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in MEAN SOLAR TIME Authority and Mag. North Polar Dicr Variation Star's Name Right Ascension Variation L/lst. Annual , Secular Annual Secular h m s sec. + ; sec. II + " _ // Ra 2801 7'4 12 O 48-08 3'47 026 50 37 50-0 20*05 o R 2806 G 7-6 12 2 30-43 3-040 023 50 8 10-2 20-05 o 2 G 799 R T 12 II 38-58 2-999 022 51 21 52-8 2O'O2 02 R 2843 G 7-8 12 12 29*29 2-993 023 5' H 35'5 20-OI 04 I G 1009 Rad 5-6 12 17 I9'52 2-964 022 50 14 56-4 20-O7 3 Ra 2880 G 6-4 12 25 1-31 2 '935 *O20 51 12 6-4 I9- 9 2 5 Ra 2909 B.A.C. 6- 12 36 40*15 2-840 O20 50 o 1 1-7 19-60 9 i G 1028 Ra 6- 12 41 49- 1 2-861 oi 8 51 45 51-6 19-68 08 3 Gre 1018 R r 12 47 43-63 2-810 015 50 58 19-0 *9'54 10 3Greioi9R=CaVea 3* 12 47 44-84 2-808 015 5 58 S'3 19-52 10 f>7] TABLE II. TABLE III. hour 12 Year and Dominical Letter 1 868 Jan. i E July 2 Dec. 32 izh R.A. m sec 3 45-63 3 45'5' 3 45*4' I3h R.A. m sec 3 45*68 3 45'57 3 45*49 Jan. i ii 21 izh R.A. sec I0> 33 10-72 1 1 -08 I3h R.A. sec 9-88 10-27 10-65 1869 Jan. I C July 3 Dec. 32 o 46-64 o 46-58 o 46-55 o 46-72 o 46-66 o 46-64 31 Feb. 10 20 11-41 11-69 11-93 II'OI "'34 11-62 1870 Jan. i B July 3 Dec. 32 I 43-69 I 43-69 i 4373 1 4378 i 4379 i 43-83 Mar. 2 12 22 12-11 I2-24 I2"ll 11-87 12-07 12*21 1871 Jan. i A July 3 2 40-87 2 40-94 2 40-97 2 41*04 Apr. i 12-33 12*31 Dec. 32 2 4I-C4 2 4 I *'3 II I2-3I 12-35 1872 Jan. i G July 2 Dec. 32 3 38'i8 3 38-31 3 38-46 3 38-27 3 3 8 -39 3 38-53 21 May i ii I2-25 12-15 I2-O3 12-36 12-32 12-26 1873 Jan. i E July 3 Dec. 3 2 o 39*68 o 39-85 o 40-03 o 3976 o 39-91 o 40-08 21 31 June 10 11-89 M'74 U'59 12-16 12-04 11-90 1874 Jan. i D July 3 Dec. 32 i 37-17 i 37-36 i 37*55 i 37-22 I 37-39 I 37-57 20 30 July i o "'43 11-28 I I"I3 11-75 11-59 I IM.3 1875 Jan. I C July 3 Dec. 32 2 34-69 2 34-88 2 35'06 2 347 2 34-88 2 35'05 20 3 A no r\ 10-99 IO-87 ICi'TI I I-26 irio 1876 Jan. I B July 2 Dec. 32 3 32-20 3 32-37 3 32-52 3 32-18 3 32-34 3 32-48 f\ug. y '9 29 Qr>t Q 1U ff IO-69 IO-64 ,_./:_ 10 94 10-80 10-68 1877 Jan. i G July 3 Dec. 32 o 3375 o 33-88 o 33-99 o 33-71 o 33-83 33-93 18 28 IO 02 10-64 IO-70 10*59 10*53 10-51 1878 Jan. i F July 3 Dec. 3 2 i 31-13 i 31-21 i 31-27 i 31-06 i 31-14 i 31-18 Oct. 8 18 28 icrSi 10-96 11-17 iQ'53 1 0*60 10-73 1 879 Jan. i E July 3 Dec. 3 2 2 28-40 2 28*42 2 28'4I 2 28-32 2 28-33 2 28-32 Nov. 7 I? 27 ii -42 1*1-71 12-05 10-91 1 1-14 1 1-41 1880 Jan. i D July 2 Dec. 32 3 25-55 3 25-51 3 25'43 3 25-46 3 25-41 3 25-34 Dec. 7 17 27 37 12-41 12-80 13-20 '3'59 11-74 12-09 12-47 12-86 hour 13 f* TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [28] Expressed in MEAN SOLAR TIME Authority and Mag. North Polar p\!.b Variation Star's Name Right Ascension Variation IJlSt. Annual Secular Annual Secular h m s sec. + sec. O / II + " _ " i G 1051 R 6- 13 I 25-28 2-775 015 51 52 21-8 I9'28 -II R 2969 BAG 5'9 13 I 29-05 2-762 '017 50 45 42-9 19-28 12 R 2970 G 7-1 13 I 48-99 2759 017 50 34 20-0 19-27 '3 R 2971 G 5'9 13 I 50*96 2-761 017 5 47 55'9 19-27 '3 R 2999 G 7-2 13 13 1'22 2719 014 51 27 0-8 18-97 '5 Ra 3007 WB 6-4 13 15 44-07 2717 014 52 16 317 18-90 'H R 5048 G 6-9 13 26 19-23 2-647 014 50 32 3-5 l8- 57 16 3 G 1085 Ra 5' 13 26 41*67 2-683 009 52 8 27-0 18-65 15 Ra 3060 S 7'8 '3 30 4'84 2*624 014 50 8 34-7 18-44 17 R 3090 G 6-3 13 38 21-63 2*600 on 50 50 2'0 18-15 17 R 3092 G 6- 13 39 378 2-596 on 50 47 45-2 18-13 16 WB 929-30 L T 13 41 45-03 2-618 007 52 4 2 35'4 I8-Q2 17 WB 976-7 8- 13 43 29-85 2-594 007 51 37 36-1 17-95 17 WB 1281-2 8- 13 56 17-07 2-548 006 5 1 59 37'3 *7'43 19 09] [TABLE II. TABLE III. hour 13 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 3 2 I3h R.A. m sec 3 45-68 3 45'57 3 45-49 I4h R.A. m sec 3 45-76 3 45-66 3 45-59 ! Jan. i II 21 I3h R.A. sec 9-88 10-27 10-65 14)1 R.A. sec 9'43 9-80 10-18 1 869 Jan. I C July 3 Dec. 32 o 46-72 o 46-66 o 46-64 o 46-81 o 46-76 o 46-75 31 Feb. 10 20 I I -01 I-34 II-62 10-56 10-91 11-24 1870 Jan. I B July 3 Dec. 32 I 4378 i 4379 i 43-83 I 43-88 1 43-89 I 43-93 Mar. 2 12 22 II-87 I2-07 12*21 11-54 1 1 -80 I2'OI 1871 Jan. I A Tulv 3 2 40-97 2 4.1'OA 2 41-06 2 41*12 Apr. i I2-3I 12-17 Dec. 3 2 2 41-13 2 4I-2I II 12-35 12-29 1872 Jan. I G July 2 Dec. 32 3 38-27 3 38'39 3 38-53 3 38-35 3 38-46 3 38-58 21 May i II 12-36 12-32 I2-26 .12-37 12-40 12-40 1873 Jan. I E July 3 Dec. 32 o 39-76 o 39-91 o 40-08 o 39-81 o 39-95 o 40-10 21 3' June 10 I2'l6 I2-O4 11*90 12-36 12-28 12-18 1 874 Jan. I D July 3 Dec. 32 i 37-22 37-39 1 37-57 I 37-24 I 37-40 I 37-56 20 30 July 10 11-75 11-59 11 '43 12-05 11-90 11-74 1875 Jan. I C July 3 Dec. 32 2 3471 2 34-88 2 35-05 2 34-70 * 34-85 2 35"OO 20 30 Au? o 11*26 II'IO lO'QJ. 11-56 11-37 i i"i8 1876 Jan. I B July 2 Dec. 32 3 32-18 3 32-34 3 32-48 3 32-14 3 32-28 3 32-41 rxug. y 19 29 C Arif . O 10-80 10-68 11 '00 10-82 1877 Jan. I G July 3 Dec. 32 o 33-71 o 33-83 O 33 03 o 33-64 o 33-75 o 33*84. 18 28 10 59 JO'53 10-51 10-53 10-43 T8~7~8~Jan~ f~ F July 3 Dec. 32 131 -06 i 31-14 i 31-18 i 30-97 i 31-04 i 31-08 Oct. 8 18 28 10-53 10-60 10-73 10-38 10-37 10*41 1879 Jan. I E July 3 Dec. 32 2 28*32 2 28-33 2 28-32 2 28'22 2 28-23 2 28-22 Nov. 7 7 27 10-91 11-14 11-41 10-51 10-66 10-87 1880 Jan. i D July 2 Dec. 32 3 25-46 3 25-41 3 25-34 3 25-36 3 25-32 3 25-26 Dec. 7 17 27 37 11-74 12*09 12-47 12-86 11-13 11-44 11-78 12-14 <\ hour TABLE I. [30] J_4 MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and otar s Name Mag. MEAN SOLAR TIME North Polar Diof- Variation Right Ascension Variation l^ldt. Annual Secular Annual Secular h m 8 sec. + sec. o / /; + " _ // WB 77-8 8- 14 2 38-53 2-511 -005 51 22 36-3 17-14 20 Ra 3183 G 7-1 14 II 10*47 2-459 009 50 37 27-5 1674 21 Ra 3187 G 6-8 14 12 2'55 2"455 009 50 35 52-5 16-70 21 Ra 3196 G 7*4 I 4 15 40-38 2-476 006 52 ii 40-1 16-53 20 Ra 3201 G 6-2 14 17 45-10 2-443 006 5i o 34-3 16-42 21 2G9O3Rad=Bootisy 3* 14 24 23'88 2-421 005 51 6 47-6 '5*94 21 Ra 3219 G 6-3 H 2 5 34'54 2-445 006 52 27 22-6 I 6-02 -22 BAC 4825 L 6- 14 26 52-84 2-459 -005 52 47 32-0 16-00 22 Ra 3242 G 7-6 14 32 19-61 2'39S 003 51 19 16-5 15-64 24 R 3244 G 7'4 H 33 *9"55 2-390 006 51 17 24-6 I5-59 2 3 Ra 3265 WB 6-2 14 41 31-50 2-370 003 Si 38 38-9 15-13 24 Ra 3269 WB 6- 14 42 52-41 2-379 003 52 ii 4-6 15-05 25 R 3276 G 7'5 14 44 4-62 2-327 006 50 21 6-6 14-98 24 3 G 1190 Ra 5' 14 52 6-78 2-295 ooo 50 12 35-4 14-48 2 4 [30 TABLE II. TABLE III. hour 14 Year and Dominical Ltter 1 868 Jan. i E July 2 Dec. 32 14-h R.A. m sec 3 4576 3 45-66 3 45'59 I5h R.A. m sec 3 45-86 3 4577 3 45^9 Jan. i ii 21 31 Feb. 10 20 Mar. 2 12 22 April i I4h R A. sec 9'43 9-80 I0-l8 10-56 10-91 11-24 11*54 1 1 -80 12-01 I2-I7 I5h R.A. sec 9-03 9'37 9'73 10-10 10-46 10-81 11-14 11-44 11-71 11-94 1 869 Jan. I C July 3 Dec. 32 o 46-81 o 4676 o 4675 o 46-92 o 46-87 o 46-85 1870 Jan. I B July 3 Dec. 32 1 43-88 1 43-89 43^3 1 43-99 1 43-99 I 44-0 1 1871 Jan. I A July 3 Dec. 32 2 41-06 2 4I-I2 2 4I--2I 2 41-15 2 4I-20 2 41-27 ii 21 May i ii 21 31 June i o 20 30 July 10 20 30 Aug. i 19 29 Sept. 8 18 28 I2-29 12-37 12-40 12-40 12-36 12-28 I2-I8 I2-05 II'90 1174 11-56 11-37 II-I8 u-oo 10-82 10-66 10-53 10-43 12-13 12-27 12-38 12-44 12-47 12-45 12-40 12-31 12-19 12-05 11-87 n-68 11-48 11-26 1 1-05 10-84 10-65 10-48 1872 Jan. i G July 2 Dec. 3 2 3 38-35 3 38-46 3 38'58 3 38-4 3 38-50 3 38-61 1873 Jan. i E July 3 Dec. 3 2 o 39*81 o 39-95 o 40-10 o 39-84 o 39-96 o 40-09 1 874 Jan. i D July 3 Dec. 32 i 37-24 I 37-40 i 37-56 i 37*23 I 37-37 i 37-51 1875 Jan. i C July 3 Dec. 32 2 34.70 * 34-85 2 35-00 2 34-65 2 3479 * 34-93 1876 Jan. i B July 2 Dec. 3 2 3 32-14 3 32' 2 8 3 32-4 1 3 32-07 3 32-20 3 32-31 1877 J an - ! G July 3 Dec. 3 2 o 33-64 o 3375 o 33-84 o 33-54 33-64 o 3373 1878 Jan. i F July 3 Dec. 32 i 30-97 i 31-04 i 31-08 i 30-87 i 30-93 i 30-97 Oct. 8 18 28 Nov. 7 17 27 Dec. 7 17 27 37 10-38 10-37 10-41 10-51 10-66 10-87 11-13 11-44 11-78 12-14 io-35 10-26 10-23 10-24 10*32 10-45 10-64 10-89 11-18 11-50 1879 J an - l E July 3 Dec. 32 2 28-22 2 28-23 2 28-22 2 28-11 2 28-13 2 28*13 1880 Jan. i D July 2 Dec. 32 3 25-36 3 25-32 3 25-26 3 25-26 3 25-23 3 25-18 hour 15 TABLE I. [32] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and Mag. MEAN SOLAR TIME North Polar nicf Variation otiir s r^srnc Right Ascension Variation 1^/loC. Annual Secular Annual Secular h m s sec. + sec. O 1 II + '' _ " i G 1226 L 7i 15 4 23-86 2-324 52 44 53'5 373 2 5 Rad 3336 G 6-2 15 6 5-21 2-276 51 14 21-2 13-64 24 R 3346 G 6-9 15 7 27-09 2*271 51 12 36-9 I3-55 25 2 Gree 972 S=Boo // 4'3 15 16 59'6i 2-261 52 9 307 12-84 25 2Gr973RSBootis/i2 8- 15 17 I '02 2*261 52 II 19-0 12-92 2 5 i G 1259 ^ a 6-7 15 21 5-49 2-219 50 49 7-4 12-63 25 3 G 1 240 R = CorBor p. 5' 15 27 51-94 2-193 50 33 0-6 12-16 26 3G 1 244-5 s CorBor 4* 15 31 51-14 2-253 52 56 1-8 11-99 27 WB 862-3 T 15 32 58-21 2-224 52 3 22-2 11-82 27 WB 892-3 7-8 IS 34 2-57 2-189 51 i 3-6 II74 26 Ra3472G=CorBor\ 5'i 15 48 23-75 2-174 51 40 I2'O IO-62 2 9 Ra 3482 67 i5 53 37^4 2-II7 50 2 7 4-5 10-31 26 [33] TABLE II. TABLE III. hour 15 Year and Dominical Letter 1868 Jan. i E July 2 Dec. 3 2 ifh R.A. m sec 3 45-86 3 4577 3 45-69 i6h R.A. m. sec 3 45-98 3 45-89 3 45-8i Jan. i 1 1 21 3' . Feb. 10 20 Mar. 2 12 22 Apr. i Ifh R.A. sec 9'3 9'37 9-73 lO'IO 10-46 10-8 1 11-14 11-44 11-71 11-94 i6h R.A. sec 8-69 8-98 9-3I 9-65 10-00 10-36 10-71 11-04 u'35 11-63 1 869 Jan. I C July 3 Dec. 32 o 46*92 o 46-87 o 46-85 o 47-04 o 46-98 o 46-95 1870 Jan. i B July 3 Dec. 32 1 43-99 1 43 '99 i 44*01 I 44-09 I 44-08 I 44-09 1871 Jan. i A July 3 Dec. 3 2 2 41-15 2 4I-20 2 41-27 2 4I-22 2 41-26 2 41-31 II 21 May i 1 1 21 3 1 June 10 20 30 July i o 20 3 Aug. 9 '9 29 Sept. 8 18 28 12-13 12-27 12-38 12-44 12-47 12-45 12-40 12-31 12-19 12-05 11-87 u-68 11-48 11-26 11-05 10-84 10-65 10-48 u-88 12-09 12-26 12*40 12-49 12-54 12-55 12-51 12-44 12-33 12-18 I2'OO n-8o 11-58 "34 I I'lO 10-87 10-65 1872 Jan. i G July 2 Dec. 32 3 38-41 3 38-50 3 38-6i 3 38-45 3 38-52 3 38-61 1873 Jan. i E July 3 Dec. 32 o 39-84 o 39-96 o 40-09 o 39-84 o 39-94 o 40-06 1874 J an - l D July 3 Dec. 32 i 37-23 i 37*37 i 37'5 i i 37-I9 * 37-32 1 37-44 1875 J an ' * C July 3 Dec. 32 2 34- 6 5 2 3479 2 34-96 2 34-58 2 3471 2 34-83 1876 Jan. i B July 2 Dec. 3 2 3 32-07 3 32-20 3 32-31 3 3I-97 3 32-09 3 32-20 1877 J an - * G July 3 Dec. 32 o 33*54 o 33-64 3373 33-43 o 33-53 o 33-61 1878 Jan. i F July 3 Dec. 32 i 30-87 i 3^93 i 30-97 i 30-75 i 30-82 i 30-87 Oct. 8 18 28 Nov. 7 17 27 Dec 7 17 27 37 10-35 10-26 Io ' 2 3 10-24 10*32 10-45 10-64 10-89 iri8 1 1-50 10-46 10-31 10-20 10-14 10-13 10-19 10-31 10-48 10-70 10-97 1879 J an ' ! E July 3 Dec. 32 2 28-11 2 28'13 2 28-13 2 28-OI 2 28-03 2 28-04 1870 Jan. i D July 2 Dec. 32 3 25-26 3 25'23 3 25-18 3 25-18 3 25-16 3 25-13 hour 16 TABLE I. [ 34 ] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and Mag. MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. + / II + " _ " R 3516 WB " 6-4 16 4 49-88 2-097 003 5 36 12-3 9*45 27 R 3520 G 7- 1 6 5 52-40 2-128 003 51 35 30-1 9'37 28 3 G 1329 BAG 6'5 16 18 1-41 2-129 003 52 18 13-9 8-41 29 R 3546 WB 77 16 18 5-27 2-109 OO2 51 47 13-0 8-42 26 Ra 3574 G 6-8 16 26 23-27 2-088 -OO2 51 38 6-6 774 30 Ra 3585 G 6-9 16 30 52-771 2-027 003 50 9 22-5 7-38 27 iG i396Radc=Her7j t 16 35 38-72 2-049 ooi 50 49 29-8 7-04 28 WB 1457-8 8- 16 44 17-32 2-048 004 5i 15 35-o 6-28 29 Ra 3637 G 7-1 16 52 52-70 2-OI2 ooo 50 42 27-7 5'55 29 [35] TABLE II. TABLE III. hour 16 Year and Dominical Letter 1868 Jan. i E July 2 Dec. 32 i6h R.A. m sec 3 45-98 3 45^9 3 45'8i I i?h R.A. m sec 3 4 6 ' 10 3 4 6 ' 01 3 45'9 2 , Jan. i ii 21 i6h R.A. sec 8-69 8-98 9 'K iyh R.A. sec 8-45 8-68 8-95 1 869 Jan. I C July 3 Dec. 32 o 47-04 o 46-98 o 46-95 o 47' 1 5 j o 47-09 : o 47-04 | 3i Feb. 10 20 9-65 10-00 10-36 9-25 9-57 9-91 1 870 Jan. I B July 3 Dec. 32 I 44-09 I 44-08 I 44-09 i 44- 1 8 i 44-15 i 44-14 j Mar. 2 12 22 10-71 1 1-04 n'35 10-26 1 0-60 10-94 1871 Jan. I 2 41-22 2 41-28 Apr. i 11-63 11-26 A July 3 Dec. 3 2 2 41-31 4 1 *? j 2 4 r 33 ii n-88 11-55 1 1*82 1872 Jan. I G July 2 Dec. 32 3 38'45 3 38-52 3 38-6i 3 38-46 1 3 38-52 3 38-59 ! May i ii 12-26 12-40 12-05 12-25 1873 Jan. I E July 3 Dec. 3 2 o 39-84 o 39-94 o 40-06 o 39-81 o 39-90 39'99 ! 21 31 June 10 12-49 12-54 12-55 1 2*41 12-53 I2'6l 1 874 Jan. I D July 3 Dec. 32 i 37-19 i 37-32 i 37'44 i 37-I3 i i 37-23 i 37'35 20 30 July 10 12-51 12-44 12-33 12-64 12-62 12-56 1875 Jan. i C July 3 Dec. 32 2 34-58 2 3471 2 34-83 2 34-49 2 34*60 2 34-72 20 3 Aug. 9 12-18 I2'OO 11-80 12-46 12-31 12-13 1 876 Jan. i B July 2 Dec. 32 3 3''97 3 32-09 3 32-20 3 3I-85 3 3i-97 3 32-08 19 29 Sept 8 II-58 "'34 I I'lO 11-92 11-69 1 1-44 1877 Jan. i G July 3 o 33-43 o 33-53 o 33-3 1 o 33*4* n ii' en 18 28 10-87 10-65 11-18 10-94 33 OI u 33 3 U rw s 1878 Jan. i F July 3 Dec. 3 2 i 3075 i 30-82 i 3 -87 I 30-63 I 3071 I 30-77 18 28 10-31 IO'2O 10-49 10-32 1 879 Jan. i E July 3 Dec. 32 2 28-01 2 28-03 2 28-04 2 27-91 2 27-95 2 27-97 Nov. 7 17 27 IO-I4 IO-I3 lO-ig IO-I2 10-10 1880 Jan. i D July 2 Dec. 3 2 3 25-18 3 25-16 3 25-13 3 25-11 3 25-11 3 25-10 Dec. 7 17 27 37 IO-3I 10*48 10-70 10-97 10-14 10-24. 10-39 10-59 -X hour 17 TABLE I. [36] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Expressed in Authority and Mag. MEAN SOLAR TIME North Polar Dist, Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. + or n -f '' _ // R 3682 G 6-9 17 6 1279 2*003 ooo 50 51 32-8 4-42 29 3 G 1402 BAG 5" 17 10 17-92 2-064 003 52 34 6-7 3-96 30 Ra 3693 G 6- 17 ii 8-04 2'Oo6 003 51 3 8-2 4-00 29 2 Gr 1 1 23~4S=Herp 4' 17 16 17-50 2'o6/ 001 52 43 50-6 3'53 3 o Ra 3705 G 6-8 17 16 45-50 2-O12 O06 51 17 49-5 3'5 '3 1 R 3707 WB 7-1 17 17 25-21 1-986 ooi 50 40 15-1 3'45 28 Rad 3717 G 6-6 17 23 24-29 1-995 003 5' i 37 2-94 29 Ra 3758 G 6-5 17 38 36-11 1-989 003 5i 3 53'8 1-61 30 Ra 3759 G 67 17 38 43-02 I-97I 003 50 37 32-8 i -60 30 2G n6iS=Herc0 4' 17 48 47-98 2-049 ooo 52 43 49-4 0-67 30 Ra 3839 7-9 17 58 29-96 1-983 ooo 51 o 46-8 0-13 29 [37] TABLE II. TABLE III. hour 17 Year and Dominical Letter 1 868 Jan. i E July 2 Dec. 3 2 iyh R.A. m sec 3 46.10 3 46-01 3 45"92 i8h R.A. m sec 3 46-23 3 46-12 3 4 6 -o3 Jan. i ii 21 3i Feb. 10 20 Mar. 2 12 22 Apr. i jyh R.A. sec 8-45 8-68 8-95 9-25 9'57 9-91 10-26 10-60 10-94 1 1-26 i8h R.A. sec 8-32 8-47 8-68 8'93 9-20 9-51 9-83 10-17 10-51 10-85 1 869 Jan. I C July 3 Dec. 32 o 47-15 o 47-09 o 47-04 o 47-26 ] o 47-18 o 47-11 j 1870 Jan. I B July 3 Dec. 32 i 44*18 i 44-15 i 44-14 I 44-25 1 i 44*20 ] i 44*18 1871 Jan. I A July 3 Dec. 3 2 2 41-28 2 41*29 2 4^33 2 41-31 2 41-31 2 41-32 ii 21 May i ii 21 31 June 10 20 30 July 10 20 30 Aug. 9 19 29 Sept. 8 18 28 ii-55 11-82 12-05 12-25 12-41 12-53 I2'6l 12-64 12-62 12-56 12-46 12-31 12-13 11-92 11-69 11-44 11-18 10-94 11-17 11-48 n-77 12*03 12-26 12-44 12-58 12-69 1274 12-74 12-69 12*59 12-45 12-27 12-06 11-82 11-57 11-31 1872 Jan. I G July 2 Dec. 32 3 38-46 3 38-52 3 38-59 3 38-45 3 38-49 3 38-53 1873 Jan. I E July 3 Dec. 32 o 39-81 o 39-90 o 39-99 o 39-76 o 39' 8 3 o 39-91 1874 Jan. I D July 3 Dec. 32 I 37-13 1 37-23 I 37-35 i 37-04 i 37-I3 i 37-24 1875 Jan. I C July 3 Dec. 32 2 34-49 2 34-60 2 3472 2 34*37 2 34-48 2 34-59 1 876 Jan. I B July 2 Dec. 32 3 31-85 3 3i'97 3 32-08 3 373 3 31-84 3 31-95 1877 Jan. I G July 3 Dec. 32 o 33-31 o 33-41 o 33 50 o 33-18 o 33-29 33-39 1878 Jan. I F July 3 Dec. 3 2 i 30-63 i 3071 i 30-77 I 30-52 I 30-61 I 30-69 Oct. 8 18 28 Nov. 7 17 27 Dec. 7 17 27 37 10-70 10-49 10-32 IO'2O I 0'12 lO'IO 10-I4 IO-24 10-39 10-59 1 1-05 10-81 io'6o 10-42 10-28 10-19 10-16 10-18 10-26 10-39 i 879 Jan. I E July 3 Dec. 32 2 27-91 2 27-95 2 27-97 2 27-82 2 27-88 2 27-93 1880 Jan. i D July 2 Dec. 32 3 25-11 3 25-11 3 25-10 3 25-06 3 25-09 3 25-09 TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [38] Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation 3.ight Ascension Variation Annual Secular Annual Secular h m s sec. + sec. O ' ii " _ " Ra 3856 G 7'6 1 8 3 33-26 1-985 51 4 0-6 0-57 28 Ra 3859 WB 7-1 18 3 52-49 1-980 50 55 43'i 0-60 28 Ra 3867 G 6-3 1 8 5 42-30 ''993 51 15 42-4 0-76 29 R 3913 G=Lyrae/u 5'i 18 16 52-68 1-967 50 33 4 6 7 1-74 28 R 3959 WB 77 18 25 16-62 2-OOO 51 13 59-0 2-47 28 Ra 3960 G 7'3 1 8 25 24-83 2-OO6 51 15 41-1 2-48 27 i G 1630 Ra T 18 27 54-23 I- 994 51 12 41-0 2-65 29 3 Green w 1501 Vega I- 18 29 25-91 2-O25 51 20 15-9 3-11 29 R 3999 G 6'2 1 8 30 42-49 1-974 50 26 48-2 2-95 2 9 Ra 4006 G 6-6 18 32 41*24 2-038 51 45 13-6 3-12 30 Ra 4031 G 6-5 1 8 35 49-30 1-992 50 49 5i'3 3-39 29 Ra 4036 G 6-4 18 36 33-96 2-021 51 36 2-9 3'4S 28 36 i5O4-52Lyras 4 4* 1 8 36 54-57 1-982 50 27 57-9 3'53 28 3 G 1 506-72 Lyras 5 4' 18 36 56-87 1-985 50 31 26-2 3'55 28 3 G 1509 S Lyras j 4'5 18 37 lo-ii 2-059 52 31 53' 1 3'55 29 3Gi5ioBACLyras 2 5' 18 37 11-93 2-060 52 32 30-4 3'57 2 9 R 4047 G 7'5 18 37 38-30 2-029 51 49 9-9 3-54 27 Ra 4083 G 7-6 1 8 42 4-52 2 030 51 43 25-8 3'93 2 9 Ra 4093 WB 7-2 18 43 10-72 1-997 50 48 50-5 4-02 27 Ra 4099 G T3 1 8 43 5-24 1-999 50 50 11-9 4-09 28 Ra 4140 G 7'4 1 8 50 49-83 1-994 5 32 77 4-68 28 Ra 4141 7'3 18 50 57-78 1-989 50 24 0-6 4-69 28 Ra 4145 G 6-4 18 51 39-83 2-011 5 57 49'5 475 28 R 4152 G 7-6 18 52 53-04 2*009 50 50 57-9 4-85 2 7 R 4 i 57 G 77 18 53 4'35 1-989 50 20 25-0 4-87 28 R4I58 G 7'4 18 53 5'95 1-988 50 19 8-4 4-87 27 Ra 4173 G 7-9 18 55 35-67 1-988 50 14 21-5; 5-09 29 R4i8o WB 77 18 56 32-22 1-983 50 4 42-9 5-16 2 9 [39] TABLE n. TABLE III. hour 18 Year and )ominical Letter 1868 Jan. I E July 2 Dec. 32 i8h R.A. m sec 3 46-23 3 46-12 3 46-03 I 9 h R.A. m sec 3 4 6 '34 3 46-23 3 46-12 Jan. i 11 21 i8h R.A. sec 8* 3 2 8-47 8-68 igh R.A. sec 8*30 8-38 8- 5 2 1869 Jan. i C July 3 Dec. 32 o 47*26 o 47-18 o 47-11 o 47-34 o 47-25 o 47-16 3* Feb. 10 20 8-93 9-20 9-51 8*70 8-92 9*17 1870 Jan. I B July 3 Dec. 32 i 44-25 i 44-20 i 44- 18 i 44-30 i 44 >2 3 i 44-19 Mar. 2 12 22 9'83 10-17 10-51 9-46 9-78 10-09 1871 Jan. I 2 4'3 ? A I'll 2 41-32 2 4.I'2Q April i 10-85 10-43 t\ jmy 3 Dec. 3 2 * 4* 3* 2 41-32 2 41*28 II 11-17 10-77 1872 Jan. I G July 2 Dec. 3 2 3 38-45 3 38-49 3 38-53 3 3 8 -42 3 38-43 3 38-46 21 May i II 1 1 "48 11-77 12-03 Il'IO " '43 11-73 1873 J an - l E July 3 Dec. 3 2 o 39-76 o 39' 8 3 o 39-91 o 39-69 o 3974 o 39-80 21 31 June 10 12*26 12-44 12-58 I2-O2 I2-26 12-48 1874 J an - ' D July 3 Dec. 32 i 37-04 i 37-13 i 37-24 i 36-94 i 37-02 i 37'n 20 3 July 10 12-69 12*74 12-74 12-65 12-77 12-84 1875 Jan. I C July 3 Dec. 32 2 34-37 2 34^8 2 34'59 2 34' 2 5 2 34*36 2 34'47 20 3 Aue. o 11-69 12-59 12'4-C 12-85 12-82 I 2'7-t. 1876 Jan. I B July 2 Dec. 3 2 3 3'73 3 3*'84 3 3"95 3 3i'6o 3 372 3 3 1- 84 '9 29 0/>nt 8 I2*27 I 2*o6 1 1-9.-T I2'6l 12-44 1877 J an - * G July 3 Dec. 3 2 o 33-18 o 33-29 33'39 o 33*06 o 33-18 o 33-29 18 28 11-57 11-31 12 23 I2-OO H'75 1878 Jan. i F July 3 Dec. 32 i 30-52 i 30*62 i 30-69 I 30-43 i 3'53 i 30-62 Oct. 8 18 28 11*05 10*81 1 0-60 U'49 11-23 10-99 1879 J an - ! E July 3 Dec. 32 2 27-82 2 27-88 2 27-93 2 2776 2 27-84 2 27-90 Nov. 7 7 27 10-42 10-28 10-19 10-78 io - 6o 10-45 1880 Jan. i D July 2 Dec. 3 2 3 25-06 3 25-09 3 25-09 3 25-04 3 25-08 3 25'" Dec. 7 17 27 37 10-16 10-18 10-26 10*39 10-35 10-31 10-32 10-37 h u >- TABLE I. 19 MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [40] Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. O t II _ " _ " Ra 4202 G 7'3 19 o 1073 2-034 51 16 45-9 5'47 27 Ra 4203 T '9 o 37'35 2-025 51 3 14-0 5'S 1 28 Ra 4213 G 7-9 19 3 13-66 2-029 51 2 467 573 2 9 3 Gr 1552 R Lyrae 77 4*5 19 6 7'66 2-037 51 4 46-8 6-03 28 361560 BAG Lyra; 4'5 19 8 38-47 2*071 52 6 ro 6-12 2 9 Ra 4284 G 67 19 12 50-36 2'0l6 50 19 io'9 6-53 27 Ra 4306 G 7-1 19 16 29-05 2-048 51 2 377 6-84 2 9 Ra 4322 7'4 19 19 5-46 2-025 50 18 1 1 -o 7-05 27 Ra433i G 6-9 19 20 5879 2-029 50 19 46-2 7-21 2 9 Ra 4361 WB 6-6 19 25 49-00 2-081 51 31 26-9 7-60 28 R 4390 G 6-6 19 29 6*14 2'IOO 51 54 38-8 7-85 26 R 4394 G 67 19 29 27-89 2-094 51 42 6-3 7-88 26 Ra 4414 WB 7*4 1 9 33 3 I>2 9 2-106 51 50 58-8 8-22 28 Ra 4418 G 6-8 19 33 54-68 2-052 50 17 13-7 8-24 26 Ra 4420 G 6-4 '9 34 '3'85 2-044 50 3 24-6 8-28 27 R442 9 6-5 19 35 18-98 2*102 51 38 28-1 8-35 26 Ra 443 1 G T 19 35 18-93 2-056 50 1 8 59-0 8-37 28 Ra 4434 WB 7-1 19 35 57-10 2-067 5 34 2 5'3 8-42 27 3 G 1599 BAG ^ 5-6 19 36 17-80 2-161 52 57 477 8-53 28 R 4450 G 7-2 19 38 7-96 2-066 50 25 55-5 8-59 2 7 Ra 4457 G r 19 40 5470 2-071 50 24 48-2 8-81 2 7 Rad 4462 G 6-3 1 9 4i 33'S 2-117 5 1 37 i3'8 8-86 28 Ra 4468 G 5' 2 19 42 39*00 2'I l6 5 1 36 55'5 9-07 2 9 R447 5 G 7-8 '9 43 44'3 2-091 5 48 5'9 9-02 26 Ra 4485 G 77 1 9 45 6 '34 2'I2O 5i 34 5 6 '9 9-14 28 R 4 507 6-4 ! 9 47 49-9 2-078 50 10 34-3 9'35 27 R 4508 BAG 5' 1 '9 47 53'43 2-138 5i 5i 45'i 9'35 28 Ra 4519 6-9 19 49 30-03 2-I50 5 1 53 44' 9'43 28 R 4 522 7 '4 19 49 39-98 2 'H3 51 57 8-6 9'49 28 Ra4558 G 7'9 19 53 35'47 2-087 50 3 59-0 978 26 Ra 4571 G 77 19 55 8-13 2-096 50 1 1 45-8 9-90 25 Ra 4590 7-i 19 58 24-13 2-140 51 1 6 52-7 10-15 26 TABLE II. TABLE III. hour 19 Year and Dominical Letter 1868 Jan. I E July 2 Dec. 3 2 igh R.A. m sec 3 46-34 3 46-23 3 46-12 ioh R.A. m sec 3 4 6 -44 3 46-31 3 46-18 Jan. i ii 21 igh R.A. sec 8*30 8*38 8*52 zoh R.A. sec 8*40 8*42 8-48 1 869 Jan. I C July 3 Dec. 3 2 47*34 o 47-25 o 47*16 o 47-41 o 47-29 o 47-19 3 1 Feb. 10 20 8*70 8*92 9-17 8*58 873 8'93 i 870 Jan. I B July 3 Dec. 3 2 i 44-30 i 44-23 i 44-19 i 44-33 i 44-24 i 44-17 Mar. 2 12 22 9-46 978 lO'OQ 9-16 9*42 9'72 1871 Jan. I A July i 2 41-32 2 4-1-20 2 41-31 2 4.1*26 Apr. i 10-43 10-03 Dec. 32 2 41*28 2 41-23 11 10*77 10-37 1872 Jan. I G July 2 Dec. 32 3 38-42 3 38-43 3 38-46 3 38-36 3 38-36 3 38-37 21 May i ii 11*10 ii-43 11-73 10-71 i i*o6 1 1*40 1873 Jan. I E July 3 Dec. 32 o 39-69 o 39-74 o 39*80 o 39-60 o 39*64 o 39*69 21 3 1 June 10 I2'02 I2-26 12-48 11-72 I2-O2 12-29 1 874 Jan. I D July 3 Dec. 32 i 36-94 i 37-02 i 37-11 i 36*83 i 36-90 i 36-99 20 3 July 10 12-65 12-77 I2'84 I2-52 12-71 12-86 1875 Jan. I C July 3 Dec. 3 2 2 34-25 2 34-36 2 34-47 2 34-I3 2 34-23 2 34-35 20 30 12*85 12-82 12*95 12-99 i ? "r>7 1876 Jan. i B July 2 Dec. 32 3 31-60 3 3i-7 2 3 3f84 3 31-48 3 31*61 3 3^73 /iug. 9 '9 29 li /^ I2'6l 12*44 1 A y/ 12-90 12-79 1877 Jan. I G July 3 Dec. 32 o 33-06 o 33-18 o 33-29 o 32-96 o 33*09 o 33*21 oept. o 18 28 12*23 I2'00 11*75 1 2*63 12-44 I2'22 1878 Jan. I F July 3 Dec. 32 I 30-43 I 30-53 I 30-62 i 30-35 i 30*47 i 30*58 Oct. 8 18 28 11*49 11-23 10*99 1I*98 11*74 11*49 1879 Jan. I E July 3 Dec. 32 2 27-76 2 27-84 2 27-90 2 27-72 2 27-82 2 27-90 Nov. 7 17 27 10-78 10-60 10-45 1 1-26 1 1-05 10-87 1880 Jan. I D July 2 Dec. 32 3 25 04 3 25-08 3 25-11 3 25-04 3 25-11 3 25*15 Dec. 7 1 7 27 37 10-35 10-31 10-32 10-37 10*73 io - 6z 10-56 10-55 hour 20 TABLE I. [42] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. o n _ // _ " Ra 4607 WB 7*3 20 o 4976 2'123 5 35 '3'2 10-35 27 Ra 4628 G 77 20 3 21-40 2-161 51 34 27-1 10-54 28 R 4632 G 7-6 20 3 33-69 2' 1 60 51 30 46-7 10-54 26 R 4650 G 7-1 20 5 17-12 2-168 5 1 37 53'6 10-68 2 7 R465I G 7-6 20 5 18-04 2-169 51 40 6-3 10-67 26 R 4662 7-8 20 6 26-97 2-120 50 4 1 6- 1 10-75 "4 R 4684 G 6-8 20 7 57-30 2-I7I 51 30 19-2 10-88 27 R 4694 5-3 20 8 54-86 2*125 50 2 30-6 10-94 26 R 4702 G 6-6 20 9 21-15 2*152 50 48 54-7 10-97 26 R 4 7i7 77 20 10 37^98 2-132 50 II 4-9 1 1 -06 26 R47I9 G 6- 20 10 50-37 2-175 51 24 28-7 1 1 -08 26 R 4722 G 7 '4 20 II 2-33 2-167 51 8 22-9 11*11 28 R 4726 G 77 20 II 23-80 2-185 5i 40 55'3 11-12 26 Ra 4735 S 6-4 2O 12 9'IO 2-166 51 o 42-7 II-I9 27 R 4741 G 7'9 20 12 59-35 2- 1 80 51 23 10-4 II-25 27 2Grei3i5BACCygy 3-2 2O 14 10-02 2-147 50 9 51-9 "35 26 R 4752 G 6-9 2O 14 49- 1 2 2-179 51 12 42-8 H'37 26 Rad 4771 G T 20 16 43*20 2-154 50 16 28-4 II-5I 26 R 4777 A rs 20 17 2I-05 2-167 50 38 10-7 11-55 26 R 4778 G 7-8 20 17 23-88 2-158 50 19 55-4 11-55 26 Ra 4781 6-9 20 17 58-70 2-150 50 i 46-4 II-59 25 R 4787 G 77 20 18 37-88 2-153 50 5 8-7 II-64 24 R 4793 WB 7'4 20 19 14-88 2-175 50 42 6-9 n-68 26 BAG 7061 6- 20 19 20-43 2-215 5 1 59 33'o n-66 26 R 4836 WB 7'4 2O 23 1 6'O8 2-180 50 30 24-8 11-97 26 Ra 4914 G 6-5 20 32 41-43 2-234 51 23 n-i 12-63 26 R 4970 G 7*5 2O 40 36-28 2-265 51 37 21-4 13-16 25 R 5025 WB 77 20 47 13-42 2-264 50 52 51.1 '3'59 24 Ra 5037 G 7-2 20 49 9-24 2-270 5 50 45'3 13-72 24 R 5041 G 7-6 20 49 31-70 2-253 50 14 11-3 *375 24 R 5061 6-8 2O 51 I2'2I 2-300 51 41 24-9 13-85 24 Ra 5076 S 7'4 20 53 19-87 2-294 51 15 24-7 13-98 25 Radc 5085 BAG 6-4 20 54 31-48 2-315 51 51 46-8 14-06 24 3 Green 1742 R 5-6 20 57 32-24 2-666 5' 53 53'9 17-46 23 3 Green 1743 R 5-6 20 57 33'8o 2-672 51 54 1-6 17-24 23 Radc 5118 77 20 59 29-41 2*334 52 o 1 0-9 H'37 24 [43] TABLE II. TABLE III. hour 20 Year and Dominical Letter 1 868 Jan. i E July ^ Dec. 32 zoh R.A. m sec 3 4 6 '44 3 46-3 1 3 46-18 2ih R.A. m sec 3 46-51 3 46-36 3 46-22 Jan. i n 21 aoh R.A. sec 8-40 8-42 8-48 2ih R.A. sec 8-62 8*56 8*55 1869 Jan. I C July 3 Dec. 32 o 47-41 o 47-29 o 47-19 o 47-45 o 47*31 o 47*19 31 Feb. 10 20 8-58 8-73 8-93 8-58 8-66 8-79 1 870 Jan. i B July 3 Dec. 32 1 44-33 I 44-24 I 44-17 1 44-32 i 44*22 i 44-13 Mar. 2 12 22 9- 1 6 9-42 9-72 8*95 9-16 Q'4-I 1871 Jan. i A July 3 2 41-31 2 41*26 2 41*26 2 41*20 Apr. i 10-03 9^9 Dec. 32 2 41-23 2 4 I>I 5 II 10-37 10-00 1872 Jan. i G July 2 Dec. 32 3 38-36 3 38-36 3 38-37 3.38-29 3 38-27 3 38*27 21 May i II 10-71 1 1 -06 11-40 10-33 10-67 1 1-03 1873 Jan. i July 3 Dec. 32 o 39-60 o 39-64 o 39-69 o 39*50 o 39-53 o 39-58 21 3' June i o 11-72 12-02 I2-29 11*38 1 1*72 12*04 1874 Jan. i D July 3 Dec. 32 i 36-83 i 36-90 i 36-99 i 36-71 i 36-79 i 36-88 20 30 July 10 12-52 1271 12-86 12-33 12-58 12*79 1875 Jan. I C July 3 Dec. 32 2 34 -I 3 2 34-23 2 34'35 2 34'oi 2 34*12 2 34-24 20 30 Aus o 12-95 12*99 I2"Q7 12-96 13*07 i i'i i 1876 Jan. i B July 2 Dec. 32 3 3i'48 3 3i-6i 3 3173 3 3^38 3 3i-5i 3 3'-65 niug. y '9 29 C- nf 12*90 12*79 1 3 * J I3-H 13-09 1 877 Jan. i G July 3 Dec. 32 o 32-96 o 33-09 o 33-21 o 32*88 o 33*02 o 33*16 18 28 12-44 I2'22 12-86 12-69 1878 Jan. I F July 3 Dec. 32 i 30-35 i 30-47 i 30-58 i 30*30 1 3'44 i 30*57 Oct. 8 18 28 11*98 11*74 11*49 12-50 12*28 1 2-06 1 879 Jan. i E July 3 Dec. 3 2 2 27-72 2 27*82 2 27-90 2 27*71 2 27*83 2 27-93 Nov. 7 '7 27 11*26 1 1-05 10*87 83 62 42 1880 Jan. i D July 2 Dec. 32 3 25-04 3 25-11 3 25-15 3 25*07 3 25-15 3 25-22 Dec. 7 17 27 37 10-73 10-62 10-56 10*55 24 09 10-98 10-90 \o hour 21 TABLE L [44] MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. + o / // _ " _ " 3Grei756BACCygr 4' 21 6 3-39 2 '385 005 S 2 3 1 o'99 15-23 -23 3 G 1760 R Cyg a 4'5 21 8 45-60 2-349 005 51 9 27-19 14-91 22 Rasi73 77 21 8 58-04 2'335 003 50 48 24 -3 14-94 ' 2 3 R 5181 WB T 21 1O 2O'4? 2-340 -003 50 48 23 ] 15-02 2 3 WB 564 L 8- 21 2O 2O'O3 2-366 006 50 16 24 -o I5-58 21 BAG 7505 WB 5'5 21 25 51-90 2-440 004 S 2 3 23 -5 i6'oo 12 R 5292 * 7-6 21 26 6-86 2-406 004 51 9 5 -8 15-89 20 Ra 5309 G 6- 21 28 7-93 2-392 005 50 10 41 -i 16-00 20 R 5316 G 6-8 21 28 55'8l 2-437 005 51 16 32 7 16-05 21 R5537G 7-2 21 30 59-31 2-424 006 5' 4 5 6 '3 16-15 21 R5353G 7-9 21 32 23-97 2-430 005 5i 7 3^ 7 16-22 21 Ras35 9 G 7-2 21 33 19-02 2 '433 005 51 4 32 -9 16-27 21 I Gr 1936 5-6 21 34 25-50 2-469 005 52 19 10 'o 16-35 21 i G 1937 WB 7* 21 34 36-54 2-465 005 52 17 52 -4 16-36 21 Ra 5398 G 7-2 21 39 17-32 2-468 006 51 39 20 -6 16-57 "2O R 5413. 7'4 21 41 25-54 2-466 006 51 10 24 -6 16-68 '2O Ra 5426 G 6-2 21 42 3-48 2-466 006 51 4 50 -i 16-71 20 R 5503 WB 7'4 21 51 4472 2-505 008 51 6 25 -8 17-17 I 9 R 5507 WB 7-1 21 51 57-47 2-512 008 51 23 15 -i 17-18 2O R5520 7'9 21 53 45-07 2-513 008 51 4 25 -4 17-26 I 9 * R 5291 RA by G ^\ 26 6-34 hou 45] TABLE II. TABLE III. OH Year and Dominical Letter 1868 Jan. I E July 2 Dec. 32 2ih R.A. m sec 3 46-51 3 46-36 3 46*22 aah R.A. m sec 3 46-55 3 46-39 | 3 46-23 j Jan. i II 21 31 Feb. 10 20 Mar. 2 12 22 April i zih R.A. sec 8-62 8-56 8-55 8-58 8-66 8-79 8-95 9-16 9-41 9-69 zzh R.A. sec 8-93 8-82 875 871 871 8-76 8-86 9*00 9-18 9-41 1869 Jan. I C July 3 Dec. 32 o 47-45 o 47-31 o 47-19 o 47*45 o 47-30 o 47*16 1870 Jan. i B July 3 Dec. 32 i 44*32 i 44-22 ' 44 !I 3 i 44-29 i 44-17 i 44-07 1871 Jan. I A July 3 Dec. 32 2 41*26 2 41*20 2 4IM5 2 4I-2O 2 4IM2 2 41*06 ii 21 May i ii 21 3i June i o 20 30 July 10 20 30 Aug. 9 '9 29 Sept. 8 18 28 lo-co 10-33 10-67 11-03 11-38 11-72 12-04 12-33 12-58 1279 12-96 13-07 13-13 !3*H 13-09 13-00 12-86 12-69 9-68 9*98 10-31 10-66 1 1 -02 11-38 1174 12-07 12-38 12-66 12-89 13-08 13-21 13-29 '3'33 13-31 13-25 13-14 1872 Jan. I G July 2 Dec. 32 3 38-29 3 38-27 3 38'27 3 38-20 3 38-I7 3 38'i7 1873 J an - l E July 3 Dec. 32 o 39-50 o 39"53 o 39*58 o 39*4 o 39-42 o 39-47 1874 Jan. I D July 3 Dec. 32 i 36-71 i 36-79 i 36-88 i 36-61 i 36-68 i 3678 1875 J an * ! C July 3 Dec. 32 2 34-01 2 34*12 2 34'24 2 33*9 2 2 34-03 2 34*l6 1876 Jan. i B July 2 Dec. 32 3 3i*38 3 3i*5i 3 31*65 3 31-30 3 3i-44 3 31*60 1877 Jan. i G July 3 Dec. 32 o 32-88 o 33-02 o 33-16 o 32-82 o 32-98 33-14 1878 Jan. i F July 3 Dec. 3 2 i 30-30 i 30*44 i 30*57 i 30-28 1 30-44 i 30-59 Oct. 8 18 28 Nov. 7 i? 27 Dec. 7 17 27 37 12-50 12-28 1 2-06 i -83 i -62 i -42 i -24 i -09 10-98 10-90 13*00 12-84 12-65 12-45 12-25 12-05 n-86 1 1-69 11-54 11-41 i 879 Jan. i E July 3 Dec. 3 2 2 2771 2 27-83 2 27-93 2 27-72 2 27-86 2 27-98 1880 Jan. i D July 2 Dec. 32 3 25-07 3 25-15 3 25-22 3 25*'2 3 25-22 3 25-30 \v hour TABLE I. 22 MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [46] Authority and Star's Name Mag. Expressed in MEAN SOLAR TIME North Polar Dist. Variation Right Ascension Variation Annual Secular Annual Secular h m s sec. + sec. + O 1 H _ n _ " JRa 5589 A 77 22 2 I'47 2 '535 008 50 28 50-8 17-61 18 3 Gr 1859 R 5' 22 4 35-41 2-570 on 50 56 22'3I 17-56 17 3 G 1861 BAG 5'4 22 6 35-14 2-601 on 52 54 28-30 17-82 17 WB 467 L T 22 17 59*88 2-613 013 50 51 43-1 18-24 ''5 R573I T9 22 22 52-87 2-619 on So 3 43'4 18-42 *5 R 5732 WB 6'2 22 22 5579 2-633 on 50 53 547 18-42 ' 1 5 Ra 5752 rs 22 25 54*28 2-648 on 5 5 487 18-52 *'5 Ra 5755 S S 6-6 22 26 18-80 2-648 on 51 3 21-3 I8-26 15 R 5756 S 6-1 22 26 18-85 2-649 on 51 2 53-7 I8'53 '5 R5757 7-2 22 26 38-28 2-656 012 51 20 41-8 18-54 i5 R 5780 G 5-8 22 29 38*79 2-672 012 5 I 3 8 9 -8 18-65 5 R 5793 G 57 22 31 52-18 2-666 OI2 50 27 477 1870 '4 Ra 5808 G 6-1 22 34 '25-37 2-688 013 5 1 n 3 J '9 1878 *4 R 5813 G 6-4 22 35 11-85 2-694 013 51 29 27-8 1 8-8 1 *4 R 5863 G 7-6 22 42 35-74 2-714 014 50 26 4-5 19-03 13 Ra 5869 G; 6- 4 22 43 25-73 2-719 014 50 31 59-6 19-05 13 Ra 5894 G 7'4 22 47 46-17 2-747 014 51 1 8 59-0 19-17 12 R 5895 WB 7-1 22 47 50-45 2-749 014 51 23 46-4 19-17 12 R 5970 WB 7-5 22 58 47*39 2-799 016 51 32 45-2 19-42 io R 5973 WB 7-4 22 58 57-70 2-802 015 51 47 57-0 19-44 I I R 5977 G r 22 59 53-12 2-801 016 51 14 44-4 i9'45 "9 [47] TABLE II. TABLE III. hour 22 Year and Dominical Letter i 868 Jan. I E July z Dec. 3 2 22h R.A. m sec 3 46-55 3 46-39 3 46-23 23h R.A. m sec 3 46-57 3 46-38 3 46-20 Jan. i 11 21 22h R.A. sec 8-93 8-82 8-75 23h R.A. sec 9-31 9-17 9-04 1869 Jan. I C July 3 Dec. 3 2 o 47H5 o 47-30 o 47* 1 6 o 47-43 o 47-26 o 47-10 31 Feb. 10 20 871 8-71 8-76 8-94 8-88 8-86 1870 Jan. i B July 3 Dec. 3 2 i 44-29 i 44-17 i 44-07 I 44-24 i 44- 1 o 1 43'99 Mar. 2 12 22 8-86 9*00 9-18 8-88 8-94 9-06 1871 Jan. i A Tulv t 2 41*20 2 4I'I2 2 4I-I2 2 4.1*0? April i 9-41 9*23 Dec. 3 2 2 41*06 2 40-97 ii 9-68 9'44 1872 Jan. i G July 2 Dec. 32 3 38-20 3 38-7 3 38-I7 3 38-11 3 38*07 3 38-07 21 May i ii 9-98 10-31 10-66 9*70 9-99 10-32 1873 Jan. i E July 3 Dec. 3 2 o 39-40 o 39-42 o 39-47 o 39-30 o 39-32 o 39*37 21 3 June 10 11-02 11-38 11-74 10-67 11-04 11*41 i 874 Jan. i D July 3 Dec. 32 i 36-61 i 36-68 i 36-78 i 36-51 i 36-59 i 36-70 20 30 July 10 12*07 12*38 12-66 11-77 12-12 12*45 1875 Jan. i C July 3 Dec. 3 2 2 33-92 2 34-03 2 34-16 2 33-84 2 33-96 2 34-11 20 30 A IIP n 12*89 13*08 I 3*2 I 12-74 12-99 i 3*20 1 876 Jan. i B July 2 Dec. 3 2 3 3i-3 3 3I-44 3 31-60 3 31-24 3 3I-4 1 3 3^57 nug. y '9 29 C or . f Q 13*29 13-33 13-36 I3-48 1877 J an - * G July 3 Dec. 3 2 o 32-82 o 32-98 o 33-14 o 32-80 o 32-98 33''5 18 28 1 3'3 I -3-25 iHH *3"54 13-56 '3-53 1878 Jan. i F July 3 Dec. 32 I 30-28 I 30-44 I 30-59 i 30-29 i 30-46 i 30-63 Oct. 8 18 28 13-00 12-84 12 65 13*46 13-36 i3- 2 3 1 879 Jan. i E July 3 Dec. 32 2 2772 2 27-86 2 27-98 2 27-76 2 27-92 2 28*05 Nov. 7 7 27 12*45 12-25 12*05 13-08 12-91 12*73 1880 Jan. i D July 2 Dec. 32 3 25-12 3 25-22 3 25-30 3 25-19 3 25-30 3 25-39 Dec. 7 17 27 37 n-86 1 1*69 11-54 1 1*41 12-55 12-37 I2'2O I2-O4 hour 23 10 TABLE I. MEAN PLACES OF FIXED STARS FOR JAN. i, 1868. [48] Expressed in MEAN SOLAR TIME Authority and Mag. North Polar T~\: ... Variation Star's Name flight Ascension Variation JJlSt. Annual Secular Annual Secular h m s sec. + sec. + O / It _ a // Ra 5998 WB 7'5 2 3 3 4'H 2-812 Ol8 50 42 54-0 I 9 -5I "fO R 6034 WB 7-6 23 9 37'33 2-847 017 51 25 547 19-64 08 BAG 8136 6- 23 I0 43* I 9 2-876 OI 7 52 32 15-4 19-62 08 Ra 6096 G 5-8 23 20 58*04 2-926 019 51 29 177 1977 07 i G 2111 R 6- 23 24 19-80 2-913 O20 50 29 27-9 I9-83 06 WB 689-90 8- 23 28 18-85 2-937 O22 51 41 8-2 19-91 05 WB 805-6 8-9 23 33 20-45 2-964 021 S 2 49 5'5 19-95 04 Ra 6211 6-8 23 43 29-56 3-003 'O22 51 27 10-6 2O'O2 02 R 6233 WB 7-6 23 47 45'5 6 3-024 023 51 46 13-0 20-04 02 R 6242 G 7'3 23 48 i5'4 3-026 023 51 37 20-5 20-O4 O2 R6252 G 6-6 23 49 22-61 3-031 023 51 52 30-8 20^04 ci Ra63i6 G 7'3 23 56 5278 3-065 .023 50 39 21-0 20-05 oo R 6317 G 6-8 23 56 53-82 3-065 023 50 35 9-8 20^05 oo [49] TABLE II. TABLE III. hour 23 Year and Dominical Letter 1868 E J an. I uly 2 Dec. 3 2 23h R.A. m sec 3 46-57 3 46-38 3 46-20 24h R.A. m sec 3 46-55 , 3 46-35 i 3 46-15 Jan. i 1 1 21 23h R.A. sec 9'3 9-17 9-04 24-h R.A. sec 975 9-58 9-42 1869 J C i an. i uly 3 Dec. 32 o 47^3 o 47-26 o 47-10 o 47-38 o 47-20 o 47-03 31 Feb. 10 20 8-94 8-88 8-86 9-27 9-15 9-06 1870 j B ; an. i ul 7 3 Dec. 3 z I 44-24 i 44- 10 1 43-99 i 44* 1 6 i 44-02 i 43-90 Mar. 2 12 22 8-88 8-94 9-06 9-01 9-01 9-05 1871 j A an. l 2 41*12 2 41-03 April i 9-23 9-14 ** J . my 3 Dec. 32 * 4 1 3 2 40-97 z 40 94 2 40-87 II 944 9-29 1872 J G . an. i uly 2 Dec. 32 3 38-11 3 38'07 3 38-07 3 3 8 -oi 3 37-98 3 37-98 21 May i ii 9'7 9'99 10-32 9H9 9'74 10-03 1873 J E . an. i uly 3 Dec. 3 2 o 39-30 o 39-32 o 39-37 o 39-21 o 39-24 o 39-30 21 3 1 June 10 10-67 11-04 11-41 io*3S 10-71 11-07 1874 . r> . an. i uly 3 Dec. 3 2 i 36-51 i 36-59 i 3670 ' 36-44 i 36-53 i 36-65 20 3 July 10 11-77 12-12 12-45 11-45 11-83 12-19 i8 75 c J an. i uly 3 Dec. 32 2 33^4 2 33-96 2 34-11 2 3379 2 33'93 2 34-09 20 3 A IIP o 12-74 12 99 1 V2O 12-53 12-84 i ? 1 1 1876 . B J , an. i uly 2 Dec. 3 2 3 3 I<2 4 3 3i-4i 3 3^57 3 31-22 3 3!-4 3 3i 59 ! nug. y '9 29 C^-. Q 3'3 6 '3-48 1 5 l L 3'34 I3-53 i ->-A8 1877 G an. i u iy 5 Dec. 32 o 32-80 o 32-98 33"*5 o 32-81 o 33-00 o 33-19 18 28 1 3 54 13-56 U-53 13-78 I3-83 1878 F ; an. i uly 3 Dec. 32 i 30-29 i 30-46 i 30-63 I 30-33 ! 1 30-52 I 30-69 Oct. 8 18 28 13-46 13-36 13-23 I3-85 13-82 13-76 1879 E J an. i uly 3 Dec. 32 2 27-77 2 27-92 2 28-05 2 27-83 2 27-99 2 28'14 Nov. 7 17 27 13-08 12-91 12-73 13-67 13-55 13-41 1880 D ] Ian. i uly 2 Dec. 3 2 2 25-19 2 25-30 2 25-39 3 2 5' 2 7 3 2 5'39 3 25>8 Dec. 7 17 27 37 12-55 12-37 I2'2O I 2*04 13-26 13-09 I 2-92 12-74 DAY TABLE TABLE IV. [50] JANUARY FEBRUARY MARCH J fe P.M. *i >> n P.M. J >-. rt P.M. Q Q h m s Q Q h m s d Q h m s A I 5 13 28*00 D I 3 " 34-87 D I 21 29-34 B 2 5 9 32-09 E 2 3 7 38-9 E 2 7 33-43 C 3 5 5 36-18 F 3 3 3 42-99 F 3 13 37-52 D 4 5 i 4 '27 G 4 2 59 47-08 G 4 9 41-61 E 5 4 57 44' 3 6 A 5 2 55 51-17 A 5 5 45-/0 iF 6 4 53 48-45 B 6 2 51 55-26 B 6 i 49-80 G 7 4 49 5 2 '54 C 7 2 47 59-35 C 7 o 57 53-89 A 8 4 45 5 6>6 3 D 8 2 44 3-44 D 8 o 53 57-98 B 9 4 42 0-72 E 9 2 40 7-53 E 9 o 50 2-07 C 10 4 38 4'8i F 10 2 36 U-62 F 10 o 46 6 i 6 D ii 4 34 8-91 G ii 2 32 15-7I G ii o 42 ,10-25 E 12 4 30 13-00 A 12 2 28 19 80 A 12 o j8 '14-34 F '3 4 26 17*09 B 13 2 24 23 ' 89 B 13 o 34 18 43 |G 4 4 22 21 18 C H 2 2O 27 -98 C H O 30 22 52 A '5 4 18 25-27 D '5 2 l6 32 -07 D 15 o 26 26 61 B 16 4 14 29-36 E 16 2 12 36 ' 17 E 16 22 30 ' 70 C 7 4 I0 33-45 F '7 2 8 40 ' 26 F 17 o 18 34-79 D 18 4 6 37'54 G 18 2 4 44'35 G 18 o 14 38-88 E 19 4 2 41-63 A *9 2 o 48 44 A '9 o 10 42 -97 F 20 3 58 45-7 2 B 20 i 56 52-53 B 20 o 6 47 -06 C 21 2 51- I 5 G 21 3 54 49 '81 C 21 52 56-62 P.M. A 22 3 5 53'9 D 22 49 0-71 "A.M. B 2 3 3 46 57*99 E 2j 45 4*80 D 22 ii 5 8 55-24 C 2 4 3 43 2 08 F 2 4 41 8-89 E 23 11 54 59-33 D 25 3 39 6 ' i? G 25 37 12-98 F 24 5 l 3 ' 43 E 26 3 35 10-26 A 26 33 '7-07 G 25 47 7-52 F 27 3 3 1 H'35 [B 27 29 21-16 A 26 43 ii *6i G 28 3 27 18-44 |C 28 25 25-25 B 27 59 '5-70 A 2 9 3 23 22-54 I CJ 28 35 '9"79 ! B 30 3 19 26-63 1 PM. Dl 29 31 23-88 C 3 3 5 30-72 j E 3 27 27-97 F 3' 23 32-06 PM. I A.M. RULE. To find the Mean Time at Greenwich of the transit of the Mean Equinox on any day : Add the Equinox Correction for the Year from Table V. to the time for the day given in Table IV., and the sum will be the time required. TABLE IV. DAY TABLE APRIL MAY JUNE J >> o A.M. -i K rt A.M. J >, A.M. Q Q h m a i Q h m ( Q Q h m i G I II 19 36-15 B I 9 21 38-87 E I 7 19 45-67 A 2 II 15 40*24 C 2 9 17 42-96 F 2 7 15 49^6 B 3 II II 44-33 D 3 9 ! 3 47-05 G 3 7 ii 53'8s C 4 u 7 48-42 E 4 9 9 5i-H A 4 7 7 57'94 D 5 n 3 52-51 F 5 9 5 55-23 13 5 7 4 2-04 E 6 10 59 56-60 G 6 9 i 59-32 C 6 7 o 6-13 F 7 10 56 0-69 A 7 8 58 3-41 D 7 6 56 IO-22 G 8 10 52 4- 78 J] 8 8 54 7-50 E 8 6 52 14-31 A 9 10 48 8-87 C 9 8 50 i i 59 F 9 6 48 i 8 40 B 10 10 44 12-96 D 10 8 46 15-68 G 10 6 44 22-49 C ii 10 40 17*05 E u 8 42 19-77 A u 6 40 26-58 ID 12 10 36 21 ' 15 F 12 8 38 23-86 B 12 6 36 30-67 JE 13 10 32 25 -24 G 13 8 34 27-95 C 13 6 32 34-76 F H 10 28 29-33 A H 8 30 32-04 D 14 6 28 38- 85 G 15 10 24 33-42 B 15 8 26 36- 13 E >5 6 24 42-94 A 16 10 20 37-51 C 16 8 22 40-22 F 16 6 20 47 -03 B 17 10 16 41 -60 D 17 8 i 8 44-31 G 1 7 6 1651- 12 C 18 10 12 45 -69 E 18 8 14 48-41 A 18 6 12 55 21 D *9 10 8 49*78 F 9 8 10 52 50 B '9 6 8 59 30 E 20 10 4 53-87 G 20 8 6 56-59 C 20 6 5 3-39 F 21 10 o 57-96 A 21 8 3 0-68 D 21 6 i 7-48 G 22 9 57 2-05 E 22 7 59 4 77 E 22 5 57 ii-57 A 23 9 53 6-14 C 23 7 55 8 '86 F 23 5 53 15-67 B 24 9 49 10 ' 2 3 D 2V 7 5i 12-95 G 24 5 49 '9 -76 C 25 9 45 H'32 E 25 7 47 I7-04 A 25 5 45 23-85 ,D 26 9 41 18-41 F 26 7 43 21-13 IJ 26 5 4 1 27-94 IE 27 9 37 22-50 Q 27 7 39 25-22 C 27 5 37 32-03 F 28 9 33 26-59 A 28 7 35 29-31 J) 28 5 33 3 6< i2 G 2 9 9 29 30 68 B 2 9 7 3i 33-40 E 29 5 29 40-21 A 3 9 Z 5 34*78 C 30 7 27 37-49 F 3 5 2 5 44-3 D 31 7 23 41-58 A.M A.M. A.M. DAY TABLE [52] TABLE IV. JULY AUGUST SEPTEMBER 4 !! A.M. J 6- A.M. J x A.M. Q Q h m a Q Q h m s Q & h m G I 5 2I 48-39 C I 3 19 55' 20 F i 1 8 2-00 A 2 5 i? 5 2> 4 8 D 2 3 15 59-29 G 2 14 6-09 B 3 5 '3 5 6 '57 E 3 3 12 3-38 A 3 10 10-18 C 4 5 10 o 66 F 4 3 8 7-47 B 4 6 14-28 D 5 5 6 4'75 G 5 3 4 H'5 6 C 5 2 18-37 E 6 5 2 8-84 A 6 3 o 15-65 D 6 58 22 -46 F 7 4 5 8 I2 '93 B 7 2 56 19-74 E 7 o 54 26-55 G 8 4 54 17-02 C 8 2 52 23-83 F 8 o 50 30-64 A 9 4 50 21 1 1 D 9 2 48 27 -92 G 9 o 4 6 34-73 B 10 4 46 25 20 E 10 2 44 32-01 A 10 o 42 38 82 C ii 4 42 29-29 F ii 2 40 36- 10 B ii o 38 42-91 D 12 4 38 33-39 G 12 2 36 40-19 C 12 o 34 47-00 E '3 4 34 37-48 A 3 2 32 44-28 D 13 o 30 51-09 F H 4 3 4*57 B 14 2 28 48-37 E H o 26 55 18 G 15 4 26 45 -66 C 15 2 24 52-46 F 'I O 22 59-27 A 16 4 22 49 "75 D 16 2 20 56- 55 G 16 o 19 3-36 B 17 4 18 53'84 E 17 2 17 0*65 A 17 o 15 7-45 C 18 4 H 57*93 F 18 2 13 4'74 B 18 o ii 1 1 - 54 D 19 411 2-02 G '9 2 9 8-83 C 19 o 7 15-63 E 20 4 7 6-n A 20 2 5 12 -92 D 20 o 3 19-72 A.M. F 21 4 3 10-20 B 21 2 I 17-01 P.M. G 22 3 59 4'29 C 22 57 21 10 D 20 ii 59 23-81 A 23 3 55 1 8-3 8 D 23 53 25-19 E 21 ii 55 27-91 B 24 3 5' 22-47 E 24 49 29-28 F 22 ii 51 3 2 oo C 25 3 47 26-56 F 25 45 33 '37 G 23 ii 47 36-09 D 26 3 43 30-65 G 26 41 37-46 A 24 ii 43 40 i 8 E 27 3 39 34-74 A 27 37 4 I< 55 B 25 ii 39 44-27 F 28 3 35 38-83 B 28 33 45 '64 C 26 ii 35 48-36 G 29 3 3 1 42-92 C 2 9 29 49-73 D 27 ii 31 52-45 A 30 3 27 47-02 D 3 25 53-82 E 28 ii 27 56-54 B 3 1 3 23 51-11 E 3i 21 57-91 F 2 9 1124 0-63 G 3 1 I 20 4-72 AM. A.M. PM. [531 DAY TABLE TABLE IV. OCTOBER NOVEMBER DECEMBER J h. P.M. _j > P.M. 4 >-. Vt P.M. Q Q h m s Q Q h m s Q Q h m s A I II l6 8'8l D I 9 14 15-62 F I 7 16 18-33 B 2 II 12 12-90 E 2 9 10 19-71 G 2 7 12 22-42 C 3 ii 8 16-99 F 3 9 6 23 80 A 3 7 8 26- 52 D 4 ii 4 21 -08 G 4 9 2 27-89 B 4 7 4 3o-6i E 5 ii 025-17 A 5 8 58 31-98 C 5 7 o 34-70 F 6 10 56 29 26 B 6 8 54 3 6 '7 D 6 6 56 38-79 G 7 10 52 33-35 C 7 8 50 40-16 E 7 6 52 42-88 A 8 10 48 37-44 D 8 8 46 44-25 F 8 6 48 46-97 B 9 10 44 41-54 E 9 8 42 48-34 G 9 6 44 5 i 06 C 10 10 40 45 63 F IO 8 38 52-43 A 10 6 40 55-15 D ii 10 36 49 -72 G ii 8 34 5 6 '5 2 B ii 6 36 59-24 E 12 10 32 53 81 A 12 831 0-61 C 12 6 33 3-33 F '3 10 28 57 -90 B 13 8 27 4-70 D 13 6 29 7-42 G H 10 25 i -99 C H 8 23 8-79 E H 6 25 1 1 '.51 A 15 IO 21 6' 08 D 15 8 19 12-89 F 15 621 15-60 B 16 10 17 io' 17 E 16 8 15 16-98 G 16 6 17 19-69 C i? 10 13 14-26 F 17 8 ii 21-07 A 17 6 13 23-78 D 18 10 918- 35 G 18 8 7 25- 16 B 18 6 9 27-87 E '9 10 5 22-44 A 19 8 3 29-25 C '9 6 5 31 '9 6 F 20 10 i 26-53 B 20 7 59 33-34 D 20 6 i 36-05 G 21 9 57 3'62 C 21 7 55 37'43 E 21 5 57 40-15 A 22 9 53 34-7I D 22 7 5 1 41-52 F 22 5 53 44-24 B 2 3 9 49 38-80 E 2 3 7 47 45 ' 6l G 2 3 5 49 48-33 C 24 9 45 42*89 F 24 7 43 49 '7 A 2 4 5 45 52-42 D 25 9 41 46-98 G 25 7 39 53'79 B 2 5 5 4i S 6 ^ 1 E 26 9 37 5 J -o7 A 26 7 35 57-88 C 26 538 o 60 F 27 9 33 55-16 B 27 7 32 i'97 D 27 5 34 4-69 G 28 9 29 59-26 C 28 7 28 6 -06 E 28 5 30 8-78 A 2 9 9 26 3-35 D 2 9 7 24 10-15 F 29 5 26 12-87 B 30 9 22 7-44 E 3 7 20 14-24 G 30 5 22 16-96 C 31 9 18 11-53 A 3 1 5 18 21 -05 PM. P.M. P.M. DAY TABLE Leap Year. TABLE IV. [54] JANUARY LEAP YEAR FEBRUARY LEAP YEAR MARCH LEAP YEAR J $ P.M. J fr P.M. J fr P.M. Q Q h m 3 Q Q h m s D Q h m s A I 5 13 28-00 D I 3 ii 34-81 E I 17 33*43 B 2 5 9 32-09 E 2 3 7 38-90 F 2 13 37-52 C 3 5 5 36-18 F 3 3 3 42-99 G 3 9 41-61 D 4 5 1 40'27 G 4 2 59 47-o8 A 4 5 45-70 E 5 4 57 44-36 A 5 2 55 51-17 B 5 i 49-80 F 6 4 53 48-45 B 6 2 51 55-26 C 6 o 57 53-89 G 7 4 49 52-54 C 7 2 47 59-35 D 7 o 53 57-98 A 8 4 45 5 6 " 6 3 D 8 2 44 3-44 E 8 o 50 2-07 B 9 4 42 0-72 E 9 2 40 7-53 F 9 o 46 6 i 6 C 10 4 38 4-81 F 10 2 36 II-62 G 10 042 10-25 D ii 4 34 8-91 G ii 2 32 15-71 A ii o 38 H'34 E 12 4 30 13-00 A 12 2 28 19 ' 80 B 12 o 34 I8 '43 F 13 4 26 17 -09 B 13 z 24 23 89 C 13 O 30 22 52 G H 4 22 21 l8 C H 2 20 27 -98 D H o 26 26-61 A IS 4 18 25-27 D 15 2 16 32 -07 E 15 O 22 30-70 B 16 4 H 29-36 E 16 2 12 36 ' 17 F 16 o 18 34-79 C 17 4 I0 33*45 F 17 2 8 40 26 G 17 o 14 38-88 D 18 4 6 37'54 G 18 2 4 44-35 A 18 o 10 42-97 E '9 4 2 41-63 A 1 9 2 o 48 44 B 1 9 o 6 47 06 F 20 3 58 45-72 B 20 i 56 52-53 C 20 o 2 51-15 P.M. G 21 3 54 49 " 8l C 21 52 56-62 A.M. A 22 3 5 53'9 D 22 49 o'7' D 21 ii 58 55-24 B 2 3 3 4 6 57-99 E 23 45 4-8o E 22 11 54 59'33 C 24 3 43 2-08 F 2 4 41 8-89 F 23 11 5 1 3-43 D 2 5 3 39 6>I 7 G 25 37 12-98 G 24 ii 47 7-52 E 26 3 35 10-26 A 26 33 17-07 A 25 ii 43 n -61 F 27 3 3' 14-35 B 27 29 21 16 B 26 ii 39 15-70 G 28 3 27 18-44 C 28 25 25-25 C 27 ii 35 19-79 A 29 3 23 22-54 D 2 9 21 29-34 D '28 ii 31 23-88 B 30 3 19 26-63 P.M. E 29 11 27 27-97 C 3* 3 5 30-72 F 30 ii 23 32-06 G 31 ii 19 36-15 P.M. A.M. RULE. To find the Mean Time at Greenwich of the transit of the Mean Equinox on any day : Add the Equinox Correction for the Year from Table V. to the time for the day given in Table IV., and the sum will be the time required. C55l TABLE IV. DAY TABLE Leap Year. APRIL LEAP YEAR MAY LEAP YEAR JUNE LEAP YEAR _j >-. A.M. J >-, A.M. ' J >-. A.M. d Q h m s a a h m s Q Q h m s A I II I 5 40 24 C i 9 17 42-96 F I 7 15 49-76 B 2 11 II 44-33 D 2 9 13 47-05 G 2 7 ii 53-85 C 3 ii 7 48-42 E 3 9 9 Si'H A 3 7 7 57-94 D 4 11 3 52-51 F 4 9 5 55'23 B 4 7 4 2-04 E 5 ;io 59 56 -60 G 5 9 i 59-32 ,C s 7 o 6-13 F 6 ! io 56 0-69 A 6 8 58 3-41 1) 6 6 56 10- 22 G 7 1052 4 78 IS 7 8 54 7-50 E 7 6 52 14-31 A 8 10 48 8-87 C 8 8 50 i i 59 F 8 6 48 i 8 40 E 9 jo 44 12 '96 JJ> 9 8 46 15-68 G 9 6 44 22-49 C 10 10 40 17 '05 E 10 8 42 19-77 'A 10 6 40 26-58 D ii 10 36 21 15 F 1 1 8 38 23-86 E ii 6 36 30*67 E 12 10 32 25 24 Gj 12 8 34 27-95 C 12 6 32 34-76 F 13 10 28 29- 33 Al 13 8 30 32-04 D 1 3 6 28 38- 85 G H 10 24 33-42 B H 8 26 30- 13 E H 6 24 42-94 A '5 1O 20 37*51 C 15 8 22 40-22 F 5 6 20 47 03 B 16 10 i 6 41-60 D 16 8 1 8 44-31 G 16 6 16 51-12 : c 7 10 12 45 69 E 17 8 14 48-41 A 7 6 12 55 21 D 18 10 8 49*78 F 18 8 10 52 50 B 18 6 8 59 30 E *9 10 4 53-87 G *9 8' 6 56-59 C '9 6 5 3'39 F 20 10 o 57-96 A 20 8 3 0-68 D 20 6 i 7-48 G 21 9 57 2-05 B 21 7 59 4'77 E 21 5 57 n'57 A 22 9 53 6-14 C 22 7 55 8-8& F 22 5 53 15 ' b 7 B 23 9 49 I0 ' 2 3 D 23 7 51 12-95 G 23 5 49 i9"7 6 C 24 9 45 H'3 2 E 24 7 47 17-04 A 24 5 45 23-85 D 2 5 9 41 18 -41 F 25 7 43 21-13 B 25 5 4i 27-94 E 26 9 37 22-50 G 26 7 39 2 5'22 p 2O 5 37 3 2 '3 F 27 9 33 26-59 A 27 7 35 29-31 D 27 5 33 3^-i2 G 28 9 29 30-68 I] 28 7 3i 33-40 E 28 5 29 40-21 A 2 9 9 2 5 34'78 C 2 9 7 27 37-49 F 29 5 2 5 44 '3 B 30 9 21 38-87 D 30 7 23 41-56 G 3 5 21 4 rf> 39 A.M. E 3' 7 9 45- 6 7 A.M. A.ivl. DAY TABLE Leap Year. [56] TABLE IV. JULY LEAP YEAR AUGUST LEAP YEAR SEPTEMBER LEAP YEAR _j 6- A.M. _j fr A.M. J 6- A.M. Q Q h m s Q Q h m s d D h m s A I 5 i? 5 2- 48 D I 3 M 59-29 G I I 14 6-09 B 2 5 !3 56-57 E 2 3 12 3-38 A 2 I 10 io- 18 C 3 5 10 0-66 F 3 3 8 7-47 B 3 i 6 14-28 D 4 5 6 4'75 G 4 3 4 11 '5 6 C 4 i 2 18 37 E 5 5 2 8-84 A 5 3 o 15-65 D 5 o 58 22-46 F 6 4 58 12-93 E 6 2 56 19-74 E 6 o 54 26-55 G 7 4 54 7 '02 C 7 2 52 23 -83 F 7 o 50 30-64 A 8 4 50 21 ii D 8 2 48 27-92 G 8 o 46 34-73 B 9 4 46 25 20 E 9 2 44 32-01 A 9 o 42 38 82 C 10 4 42 29-29 F 10 2 40 36- 10 B 10 o 38 42-91 D ii 4 38 33-39 G n 2 36 40* 19 C ii o 34 47-00 E 12 4 34 37-48 A 12 2 32 44-28 D 12 o 30 51^09 F '3 4 3 4i'57 B 13 2 28 48-37 E 13 o 26 55 18 G H 4 26 45 66 C H 2 24 52 -46 F H 22 59- 27 A 15 4 22 49-75 D 15 2 20 56- 55 G '5 o 19 3-36 B 16 4 18 53-84 E 16 2 17 0-65 A 16 o 15 7-45 C '7 4 H 57-93 F 7 2 13 4'74 B 7 o ii 11-54 D 18 411 2 -O2 G 18 2 9 8-83 C 18 o 7 15-63 E 1 9 4 7 6-n A 1 9 2 5 12-92 D 1 9 o 3 19-72 F 20 4 3 10-20 B 20 2 I I7-OI A.M. P.M. G 21 3 59 H'29 C 21 57 21 10 D 1 9 ii 59 23-81 A 22 3 55 18-38 D 22 53 25-19 E 20 n 55 27-91 B 23 3 5 1 22-47 E 23 49 29 28 F 21 ii 51 32-00 C 24 3 47 26-56 F 24 45 33'37 G 22 47 36-09 D 25 3 43 30-65 G 25 41 37-46 A 23 43 40 1 8 E 26 3 39 34-74 A 26 37 4 r> 55 B 2 4 39 44-27 F 27 3 35 38-83 B 27 33 45-64 C 25 35 48-36 G 28 3 3i 42'9 2 C 28 2 9 49-73 D 26 3 1 52-45 A 29 3 27 47-02 D 2 9 25 53-82 E 27 2 7 56-54 'B 30 3 23 51-11 E 3 21 57-91 p 28 24. 0-63 c 3 1 3 9 55*20 F 3i I 8 2 OO G 29 20 4'72 A.M. A.M. A 3 i 16 8-81 P.M. : [57] TABLE IV. DAY TABLE Leap Year. OCTOBER LEAP YEAR NOVEMBER LEAP YEAR DECEMBER LEAP YEAR >4 > P.M. J * P.M. j ^ P.M. Q Q h m s ft Q h m s d Q h m s B I II 12 I2'90 E I 9 io 19 -71 G I 7 12 22*42 C 2 ii 8 16-99 F 2 9 6 23*80 A 2 7 8 26- 52 D 3 II 42I*08 G 3 9 2 27-89 B 3 7 4 30-61 4 ii o 25 17 A 4 8 58 31 -98 C 4 7 34-70 F 5 10 56 29-26 B 5 8 54 36-07 D 5 6 56 38-79 G 6 !o 5 2 33'35 C 6 8 50 40-16 E 6 6 52 42*88 A 7 10 48 37-44 D 7 8 46 44*25 F 7 6 48 46*97 B 8 10 44 41-54 E 8 8 42 48 34 G 8 6 44 5 i 06 C 9 10 40 45 63 F 9 8 38 52-43 A 9 6 40 55*15 D 10 10 36 49*72 G IO 8 34 56*52 B 10 6 36 59-24 E ii 10 32 53-81 A ii 8 31 0*61 C ii 6 33 3'33 F 12 10 28 57*90 B 12 8 27 4-70 D 12 6 29 7 -42 G 1 3 10 25 i -99 C 3 8 23 8-79 E 13 6 25 ii 51 A H 10 21 6-08 D H 8 19 12-89 F '4 621 15 - 60 B 15 10 17 io- 17 E 15 8 15 16*98 G '5 6 17 19-69 C 16 10 13 14*26 F 16 8 ii 21-07 A 16 6 13 23-78 D 17 io 9 18-35 G 17 8 7 25*16 B 17 6 9 27-87 E 18 io 5 22-44 A 18 8 3 29-25 C 18 6 5 31 -96 F 9 10 i 26-53 B *9 7 59 33 '34 D '9 6 i 36-05 G 20 9 57 30-62 C 20 7 55 37*43 20 5 57 40-15 A 21 9 53 34-7 1 D 21 7 51 41-52 F 21 5 53 44' 2 4 B 22 9 49 38-80 E 22 7 47 45-61 G 22 5 49 48-33 C 23 9 45 42 89 F 23 7 43 49-70 A 23 5 45 5 2 '4 2 D 24 9 41 46-98 G 2 4 7 39 53-79 B 2 4 5 4i S 6 ^ 1 E 25 9 37 5 1- 7 A 2 ! 7 35 57-88 C 2 5 5 38 0-60 F 26 9 33 55-i 6 B 26 7 32 i '97 D 26 5 34 4' 6 9 G 27 9 29 59 26 C 27 7 28 6-06 E 2 7 5 30 8-78 A 28 9 26 3-35 D 28 7 24 io- 15 F 28 5 26 12 87 B 29 9 22 7-44 E 2 9 7 20 14-24 G 2 9 5 22 16-96 C 3 9 18 11-53 F 3 7 16 18-33 A 3 5 18 21-05 D 3 1 9 14 15 -62 P.M. 1] 3i 5 H 2 5'H P.M. P.M. Equinox Correction. TABLE V. [58] Equinox Correction always -f E.G. and Lunar Nutation of Equinox L.N.E. COMMON YEARS LEAP YEARS Year D. L. E.G. -f L. N. E. Year D. L. E. C. + 1 L. N. E. Jan. I Dec. 32 Jan. I m sec sec Jan. I m sec sec sec 1869 C o 5772 - 071 1872 G 3 49"'3 1-03 0*91 1870 B I 54-85 - 0-93 1876 B 3 4'77 - 0-06 -f 0*28 1871 A 2 51-99 1-04 1880 D 3 34-4 i ; + I 'DO + I*05 1872 1-03 1884 F + 0-5I + 0*17 1873 E o 50-36 0-91 1888 A 3 19*69 0-80 0*99 1874 D I 47-50 0*69 1892 C 3 I2 '33 - 0-84 0-58 1875 C 2 44-63 0-40 1896 E 3 4-97 + 0*41 + 0*70 1876 0-06 1877 G o 43-00 f 0-28 1878 F I 40-13 + 0*60 RULE. 1879 E 2 37-27 + 0-85 To find, as a substitute for the quantities in 1880 + I -00 Table II. and the Instrumental Correction, I88l B o 35-64 + 1*05 ' The Year and Instrumental Correction,' 1882 A 1 3277 + 0-98 combine from Table V. the Equinox Cor- 1883 G 2 29-91 + 0-79 rection with the Lunar Nutation of the 1884 + 0-51 Equinox, add the combination to the Instru- 1885 D o 28-27 + 0-17 1 mental Correction and diminish the sum by 1886 C I 25-41 0-19 the 10 seconds given to Table III. (to make 1887 B 2 22-55 "53 it always additive), and the sum so dimi- 1888 0-80 nished will be the Year and Instrumental 1889 F o 20-91 - 0*99 Correction. 1890 E I 18-05 - 1-05 EXAMPLE. 1801 D 2 I5'I9 1*00 y 1892 1893 A o 13-55 0-84 0-58 To find the Year and Instrumental Correction for 1869 when the Instrumental Correction 1894 G I 10-69 0-27 is I m. 10 sec. -t- 1896 F 2 7-83 + 0*08 + 0-41 From Table V. E.G. L.N m sec . . o 57*72 + E. . 71 - 1898 1899 C B A 19 I 3-33 2 0-47 -f 0-70 + 0-92 + 1*04 Instrur 10 sec nental C in Tab orrection . le III. . . 1 , . I IO- -f- . IO* s s 1900 G I / 2 57*60 + 1-04 Year and Instrumental Correction I 57*01 -f- [59] TABLE VI. Interstellar Nutation TABLE VII. Right Ascension and Amount of Maximum Interstellar Mak ' l P^ 5 of M.I.L.N. corre- Lunar Nutation-M.I.L.N. T ^ ' Ce from R>A ' of Maximum. Jan I 1868 1869 1870 RA h m 22 52 21 46 2O 26 Diff. m 66 80 96 M.I.L.N. sec + 0-48 - + 0-44 - 4- 0*40 RA h m 10 52 9 46 8 26 Aug. 8 1886 1887 1888 Distance h m * 13 2 7 2 46 3 18 3 47 4 13 4 38 5 2 5 25 5 48 Multiple 0-95 0-85 075 0-65 0-55 0-45 '35 0-25 0-15 0-05 1871 1872 1873 1 8 50 17 7 M 32 103 95 79 + 0'37 - + 0-37 - 4- 0-40 6 50 5 7 3 32 1889 1890 1891 1874 1875 1876 H 3 13 8 12 IO 65 58 58 + 0-44 - + 0-47 - + 0-49 - 2 13 I 8 O IO 1892 1893 1894 1877 1878 1879 II 12 IO IO 8 56 62 74 89 + 0-48 - + 0-45 - + 0-41 23 12 22 IO 20 56 1895 1896 1897 1880 1881 1882 7 27 5 45 4 5 IO2 IOO 85 + 0-38 - + 0'37 - + 0-39 - 19 27 7 45 16 5 1898 1899 1900 1883 1884 1885 2 40 I 2 9 o 28 7 61 59 + 0-43 - + 0-47 - + 0-49 - 14 40 13 29 12 28 1886 1887 23 2 9 22 27 62 + 0-49 - + 0-47 - II 29 10 27 RULE. To find the Interstellar Lunar Nutation of a Star on a given date. From Table VI. take the R.A. of M.I.L.N. and the Amount, with the proper sign, of the Nutation. Multiply the amount by the decimal multiple corresponding, in Table VII. to the difference between the R.A. of the Star and the R.A. of M.I.L.N., and the product will be the Interstellar Lunar Nutation of the Star. EXAMPLE. Required the Interstellar Lunar Nutation of 3 Green 66 = /x Andromedae p. [2] for Aug. 8, 1888. h ni From Table VI. Aug. 8, 1888, RA. of M.I.L.N. 20 26 Amount + 0-40 R.A. of Star about o 50 Difference . 4 24 From Table VII. between 4 13 and 4 38 multiple = 0-4 Interstellar Lunar Nutation of Star = -f 0-40 x 0-4 = + 0-16 VEGA STAR VEGA TABLES I. and II. 1st Magnitude [60] TABLE III. Year and Dominical Letter 1 868 Jan. i E July 2 Dec. 32 h m sec 18 33 12-20 1 8 33 12-09 18 33 11-99 Jan. i ii 21 3 1 Feb. 10 20 Mar. 2 12 22 April i sec 8-29 8- 4 I 8-58 8-78 9-03 9'3 l 9' 6 3 9'94 10-28 10-62 1 869 Jan. I C July 3 Dec. 32 18 30 15-24 18 30 15-15 1 8 30 15-08 1870 Jan. I B July 3 Dec. 3 2 18 31 14*24 18 31 14-18 18 31 14*15 1871 fan. I A July 3 Dec. 3 2 18 32 13-31 18 32 13-29 18 32 13-29 ii 21 May i n 21 3^ Tune 10 20 3 July 10 20 3 Aug. 9 *9 29 Sept. 8 18 28 10-95 11-28 11-59 11-87 12-13 12-35 I2 '53 12-67 12-76 12-80 12-79 12-72 12-61 12-46 12-27 12-04 11-80 11-54 1872 Jan. I G July 2 Dec. 3 2 18 33 12-45 18 33 12-47 1 8 33 12-51 1873 Jan. i E July 3 Dec. 3 2 18 30 1576 18 30 15-82 18 30 15-89 1874 Jan. I D July 3 Dec. 3 2 18 31 15*05 18 31 15-13 18 31 15-23 1875 Jan. i C July 3 Dec. 3 2 18 32 14-39 18 32 14*49 1 8 32 14-60 1876 Jan. i B July 2 Dec. 32 18 33 1377 18 33 13-88 1 8 33 14-00 1877 J an - l G July 3 Dec. 3 2 18 30 17-25 18 30 17-36 1 8 30 17-46 1878 Jan. i F July 3 Dec. 3 2 18 31 16-63 18 31 16-72 18 31 16-80 Oct. 8 18 28 Nov. 7 '7 27 Dec. 7 '7 27 37 11-28 11-03 10-80 1 0-60 10-43 10-31 10-23 IO'22 IO-26 I0'35 1879 Jan. I E July 3 Dec. 32 1 8 32 15-97 18 32 16-04 18 32 16-09 1880 Jan. i D July 2 Dec-32 18 33 15-25 18 33 15-29 18 33 15-30 EXPLANATION AN imaginary point in the heavens, the mean equinox, may be said to revolve round the earth at an uniform rate, passing the meridian at intervals of 23 h. 56m. 4*090549806500. (Shortrede's tables, where the length of an equinoctial day is given in seconds.) The Fixed Stars also cross the meridian in the order of their " Right Ascensions," which express the time thay pass it after the equinox. This right ascension is not a fixed quantity ; each Star according to its position in the heavens is subject to noticeable variations in its right ascension, which may be conveniently arranged in three classes. 1st. With respect to the Stars included in this list there is a continual increase in their right ascensions, amounting to 2 to 4 seconds a year " Precession." 2nd. There is a slight fluctuation extending over a period of 18-6 years, the Star during that time gaining and losing upon its mean place " Lunar Nutation." 3rd. There are two fluctuations apparent during the year, " Aberration and Solar Nutation." The laws which govern all these movements have been discovered by astronomers, and the movements can be calculated with the greatest certainty, and the positions also of a vast number of Stars have been accurately determined, so that for many years to come the times at which they would pass the meridian on any given day can be predicted to less than a second. These tables are intended to enable the observer to calculate with very little trouble, and with slight chance of error, the mean solar time of the apparent transits, across the meridian, of the Stars included in the list. It will be sufficient to show that the tables are founded upon and are in accordance with formulae adopted by the highest authorities. In the Nautical Almanac, on the page following the " Mean places of the Fixed Stars," it is stated that the apparent right ascension in arc of a Star for the time represented by / is a + Aa + Bt + Cc + Dtt+t^f where t denotes' the time reckoned from the moment when the Sun's mean longitude was 280, and expressed in fractional parts of a tropical year, and adopting the symbols for the Sun's, and ([ for the Moon's true longitude, $ f r tne mean longitude of the Moon's node, w for the obliquity of the Ecliptic, and a and the mean Right Ascension and Declination of the Star for the beginning of the year, we have the following values : N.A. for 1868 A = 2o"'445l cos w cos and a = cos a sec S B = 2o"'445i sin and b = sin a sec 3 C = t '02519 sin 2 and c = 46-0816 + 20-0549 sin n tan <5 34241 sin Si +-004 10 sin 2 $ which call 00405 sin 2 d m + sin o tan B D = '557 cos 2 an d ^ = cos a tan ^ 9-2237 cos SI + '0895 cos 2 & '0885 COS 2 ([ A c the annual proper motion in Right Ascension in arc. EXPLANATION. [62] In the following tables arc has been reduced to time by dividing by I 5. An inspection of the values of a, b, c and d will show that they refer to particular points in the heavens ; these have been calculated for declination 38 40 = NPD 51 20, and for every 15 of Right Ascension, or every sidereal hour. An inspection of the values of A,B,C,D will show that they are divisible into three classes: 1st. Those which depend upon the Sun's longitude and the time of the year, which may be called ABC 7 and D' ; 2nd. Those which .depend upon the longitude of the Moon's node, which call C" and D"; 3rd. Those which depend upon the Moon's longitude, and which are very small, and may be altogether neglected (see explanation of article Bessel's Day Numbers in Nautical Almanac), as may also / A c, which only applies to individual Stars. Class I have been thus computed; the Nautical Almanac for 1866 was taken as the authority, and the mean of the Sun's apparent longitude on noon Jan. i and Jan. 2, after adding the aberration, was adopted as the Sun's longitude for midnight Jan. I, and the longitude for every other tenth night was found in a similar manner. The value of / for midnight Jan. i, 1866, was taken as -00385, and the values of / for the following tenth nights were found by successive additions to it of -027379. With the Sun's longitude, and / thus obtained the values of ABC' and D' were calculated for every tenth night, and by usual methods C' was combined with m and D' with d. The values of A for every tenth night were marked on the blank side of a slide rule,* and with one fixing of the slide for each value of a, the 38 values of A a were read off, and in a similar manner the several 38 values B b and C'n sin a tan f were obtained. These five quantities, C'm, D'd, A a, B b, and C'n sin a tan c, together with 10 seconds to render the sum always additive, constitute Table III. The longitude of the Moon's node for midnight Jan. i, 1866, was calculated from the Nautical Almanac, and taken as 196 41''!, and its longitudes for the dates given in Table II. were found by allowing a half-yearly diminution in longitude of 9 40^25 (British Association Catalogue, p. 30). From the longitude thus found C" and D" were calculated, and C" combined with m in the usual manner, and C"# sin a tan S and D'V were taken from the slide rule. In this case with one fixing of the slide, the 26 values of C" sin a tan 5 were read off, and similarly those of D'V. These three quantities, C"m, C"# sin a tan 5, and D"J, when diminished by the 10 sec. included in Table III. and increased by the " Equinox Correction," constitute Table II. Thus all the correc- tions obtainable by the usual methods have been calculated for N.P.D. 51 20', and intervals of 15 = I sidereal hour, and together with the equinox corrections have been combined in Tables II. and III. Table IV. has been formed by the repeated addition of 23 56 4-09055, the assumed length of an equinoctial day, to 5 13 28, the time given for Jan. i. If then the transit of the equinox took place on that day at 5h 13' 28" P.M., the table would give the time of its transit on every other day in the year ; but it does not pass so soon as that on Jan. i in any year mentioned in Table II. The table will consequently require a correc- tion " Equinox Correction " for Jan. I, and for the remaining days in the same year it will require the same correction. * Since the slide rule here referred to is on an unusually large scale or " Radius," a description of it is given. The Radius is 33 to 34. inches in length, and is divided I ('005) 2 ( - oi) 5 ('05) 10 and the " modification invented by Mr. Silvanus Bevan," the divided radius was adopted (ee English Cyclopjedia, art Slide Rule) : an examination of the quantities to be calculated by it would show that the calculations could be made with quite sufficient accuracy. Messrs. Dring and Page, of London, have the brass pattern. [63] EXPLANATION. The amount of the correction has been obtained from Le Verrier's tables, one of which gives the Sun's mean longitude at Paris noon for Jan. I for every year in this century ; and 360 Sun's mean longitude at noon, when reduced from arc to mean solar time, and diminished by 1*527 sec. to adapt it to the meridian of Greenwich, has been taken as the mean solar time of the transit of the mean equinox, and this time less the 5,,i3,,28, given in Table IV. for Jan. I, constitutes the equinox correction which in each year forms part of the values found in Table II. The places of the Stars selected for this list hav been taken in order of preference from 1. The Greenwich y-year Catalogue for 1860, designated in column i as 3 G, 3 Gr, 3 Gre, &c., according as the Right Ascension depends upon less than 4, 8, 16, &c. observations. 2. The Greenwich 6-year Catalogue for 1850, similarly designated as 2 G, 2 Gr, 2 Gre. 3. The Greenwich 1 2-year Catalogue for 1840 and 1845, similarly designated i G, I Gr, I Gre. 4. The Radcliffe Catalogue for 1845, R, Ra, Rad, &c. 5. The British Association Catalogue for 1850, B.A.C. 6. Weisse's Bessel for 1825, W.B. In this list the plan adopted in forming the British Association Catalogue, of combining the places in different catalogues into a mean result, has not been followed ; here the Star's place depends entirely upon the catalogue first mentioned in column i , and the precession, secular variation, and proper motion adopted in that catalogue have been used in bringing up the Star's place to Jan. I, 1868. In the case, however, of Weisse's Bessel, which does not contain Secular Variations, and the epoch of which is as far back as 1825, the following treatment has been adopted : the Star's place has been brought up 40 years by the formula : precession, or p t = l842"78 + log - 1 2^90436 sin QJ tan ?, ; with the Star's place thus brought up, 40 years' precession has been calculated, changing the con- stants, according to Peters, by the formula p 2 = l843"'23 + log - 1 2*90428 sin u t tan f , : the mean of p t and p 2 -T- 15 or -* has been taken as the total precession from 1825 to 1865, expressed in sidereal time; p, -f- 600 has been taken as the annual precession 1865, in time, and p 2 p, -f- 240 has been taken as the Secular Variation. A similar process was applied to the North Polar Distance. From the Star's place thus found for 1865 the place was brought up by the usual methods to 1868. The sidereal time in which the Right Ascension and Precession of the Stars are expressed in the catalogues was reduced to mean solar time, the former by an extremely convenient Table to be found in Vega's Logarithms, by Dr. Bremiker (Berlin ; and Williams and Norgate, London) and the latter by a short manuscript table on the same principle. It may be noticed that often the Star's number in column I is followed by A, BAC, G, R, WB, S or S2. Those letters indicate an agreement to a quarter of a second between the Right Ascensions given in the catalogue from which the Star's place has been taken and the catalogues of Argelander, Epoch 1855, printed 1867; British Association Cata- logue, Epoch 1850; Grcombridge, 1810 ; Radcliffe, 1845 ; Weisse's Bessel, 1825 ; Struvc's Positiones Mediae, 1830, and in the case of some double stars, a combination of the EXPLANATION. [64] same with the Mensuras Micrometricae ; when WB is followed by L, it indicates an agreement to half a second between Weisse's Bessel and the British Association Lalande, Epoch 1800. In ascertaining these agreements, it was sufficient in the case of R and G to compare the Groombridge column in the Radcliffe Catalogue with that of the text ; Argelander, which has no Precessions, has been compared by the use of the Precessions &c. in the catalogue from which the Star's place has been taken : in the other cases the mean of the Precessions in the two catalogues has been adopted. A Star's Mean Right Ascension for Jan. i in any year up to 1880 will be found by adding to the Right Ascension for 1868 the seconds in column 4, multiplied by the number of years since 1868, and this will be the a in formula apparent Right Ascension = a 4- Aa + B^ + Cc + T)d ; and since the corrections Aa + Bt> + Ct + T)d for points sufficiently near to the Stars are contained in Tables II. III., which also contain the " equinox correction," working out the rule in page [i] will give the length of time the Star would appear to pass the meridian, after the equinox added to the mean solar time of the transit of the equinox, or in other words the mean solar time of the apparent transit of the Star, which will be true to a second without interpolation. An approximation to the time of the apparent transit of a Star, less accurate than that given on page [i], but yet possessing some practical advantages, may be obtained by sub- stituting for the quantities taken from Table II. a " year correction," formed by com- bining from Table V. the equinox correction and the Lunar Nutation of the equinox, and diminishing the amount by the 10 seconds given to Table III., and using this, when combined with the correction for instrumental error, for all Stars alike during the year. One of the advantages of this method is, that instead of having for each observation to combine with the quantities obtained from Tables I. III. and IV. the two quantities, viz. that obtained from Table II., and the correction for instrumental error, there is only one quantity, i.e. the year and instrumental correction which has been combined once for all, and for all Stars at the beginning of each year : thus the addition sum is reduced by one line. The disadvantage of this plan is, that besides increasing the insignificant error caused by neglecting the change which takes place in the amount of the Lunar Nutation of the equinox during the entire year, another small error is introduced by the omission of the quantity C"n sin a tan 3 + D"d, which represents the Interstellar Lunar Nutation of the Stars ; the amount however of the error is small, not exceeding on any night | sec. 4- or according to the Right Ascension of the Star observed. When, however, it is necessary, that error may be very much reduced with ease by means of Tables VI. and VII. Table VI. gives for Jan. I from 1868 to 1887, and for Aug. 8 from 1886 to the end of the century. The Right Ascension of the two parts of the zone, which on those days will be subject to the maximum 4- and Interstellar Lunar Nutation ; together with the amount of the Nutation I The Stars in the other parts of the zone will be affected to a less degree, varying with the cosine of the difference between the Right Ascension of the Star and the Right Ascension of the Maximum. Table VII. will readily give, corresponding to that difference, the decimal multiple for the amount of Maximum Interstellar Lunar Nutation, and the product will be the Interstellar Lunar Nutation of the Star. Perhaps the most ready way of using these tables would be by writing out on half a [65] EXPLANATION. note sheet, ist. The instrumental correction; 2nd. The combined year and instrumental correction; 3rd. The days of the week and the day letters which in that year correspond to them ; thus for 1 869 C Sun. D Mon. E Tues. F Wed. G Thurs. A F7i7~ B Sat. and keeping the half note sheet as a book-marker in the right place in Table IV. The day letters will, in a case of uncertainty, fix the day of the month, and the time opposite it should be at once combined with the instrumental correction, or the combined year and instrumental correction, as the case may be ; and this day's correction will be good for all Stars for the night. Certain small errors will arise from the use of these Tables, even when interpolation is resorted to : Taking them in the order of the columns ist. The description of time in Table I. columns 3 and 4, is mean solar time, and the hours in the headings, and also the tabular time of Tables II. and III., with the exception of the equinox correction, are all given in sidereal time : the neglect of this difference of time may from both causes produce an error not exceeding o - o8 sec. 2nd. The neglect of secular variation, which ought to count from 1872, since the precessions are those for 1870 rather than for 1868, will for several years to come produce no perceptible error: in the year 1900 the error will not exceed 0-15 sec. 3rd. In Tables II. and III. two sources of error are found : ist, the corrections there given are too small for Stars of 50 N.P.D., and too large for Stars of 53 N.P.D. ; this may introduce an error not exceeding 0*13 sec. in the southern Stars, and o'li in the northern ; 2nd. The distance between one hour and the next is too great for accurate interpolation, and might in the two tables combined introduce an error not exceeding 0-04 sec. The sum of the above errors, though insignificant for the ordinary purposes of time- keeping, maybe sufficient to condemn the indiscriminate use of the Tables for the purpose of regulating the highest class of mean-time clocks and chronometers. They will, how- ever, be found abundantly accurate for the purpose if the observer will for a considerable period use the same Star, and interpolate for days, if necessary, in Table III. A Star passes the meridian at the end of a month about 2 hours earlier than at the beginning. It would have been much better if the quantity represented by C'm had been intro- duced into Table IV. instead of Table III. ; the preponderating advantages were, how- ever, discovered too late. NOTES ON SOME OF THE STARS. Argelander assigns proper motions, which are not included in the Annual Variations of the following Stars: h 9. R. 2434 P.M. -0107 h 13. R. 3060 P.M. -0184 h 14. R. 3265 P.M. -0209 h. 14. R. 3269 -0198. h 15. 2 G. 973 After examining S. Mens Mic a proper motion of + o-oio has been included in the Annual Variation. h 15. 3 G. 1244-5 After comparing 3 G with S. Pos. Med. and B.A.C. a P.M. of + 0*013 has been rejected in the Annual Variation. h 18. 3 G. 1504-5 the P.M. of + 002 has been taken from B.A.C. LOITDON: PRINTED BY 8POTTISWOODR AND CO., HKW-STREET SQCAEB AND I'AKLIAMLM STREET 70 Astronomy. Warner (Thos ) How to Keep the Clock Right by Observations of the fixed Stars with a small fixed Telescope, with a Table of the Stars, &c., thin 8vo, cloth, as 6d i86 fl cr -< CD fri CO M CQ o a H w K * 3 5 sa ^ S t X n !O