the positions and proper motions of the principal stars in the cluster of coma berenices
TRANSCRIPT
[ . ~ Y A I S K.Y. ACAD. &I., Vol. XII, No. 10, pp. 341 to 478, April 3, 1902.1
THE POSITIONS AND PROPER MOTIONS
OF TIiE
l'RINCIP.4L STARS IN THE
CII-STER OF COMA BEKENICES
CONTENTS .
PART ~.-CATALOCULT. P.AGl
I . CATALOGUES AND WEIGHTS . Introduction ........................................................................... -343 List of Cataloguer .................................................................... -444
................................................................................ Weights 350
11 . METHOD OF REDUCTION . ................................................................................ preceshn 352 Proper Motion ........................................................................... 354 Systematic Corrections ................................................................. 357 Formulr for Adjustment .............................................................. 361
StnpTnbles ................................................................................ 367 Catalogut of Result ..................................................................... 394
111 . TABLES AND RESULTS .
PART I I . -PIIOTM:RArHS . 1 . THE PLATES : DESCRIPTION AND MEASUREMENT .
.............................................................................. Description 398 Measurement ............................................................. .....- ..... -400
Division Emn ........................................................................ 421 Corrections for Runs and Screw E m ........................................... 4 2 2
Measured Coardinntcs and Rotntion Errors ....................................... 427 Scale-mlue Corrections, Projection E m , and Deviation of the Cylinder
from Straightness ................................................................... 429
Transfornution Corrections ............................................................ 438 Kefrnction Corrections .................................................................. 4 4
Constants of the Plates ................................................................. 4 9
I f . INSTKUMENTAI . CORRECTIONS
I I I . METHOD OF REDUCTION .
Precession, Nutation and Aberration ................................................ 4 8
1V . RESULTS . Constants ............................................................................... 456 True Scale-.Value ....................................................................... 459 Separate Results ....................................................................... 461 Gtaloguc of Results .................................................................... 476
PART I.
CATALOGUE POSITIONS OF THE STANDARD STARS.
1. Catalogues and Weights.
FOR the reduction of stellar photographs it is necessary that the positions of certain stars on the‘ plate be known as accu- rately as possible. Such stars are designated in the following as standards. When I undertook the measurement and reduction of the Rutherfird Photographs of the Cluster in Coma Herenices, the problem arose to determine such standards,
There was no sufficiently accurate set of meridian observa- tions available. Chase’s triangulation of the cluster, made at the Yale Observatory, 18g1--18gz,’~includes a number of my stars, and these I might have used as standards. But results obtained by the heliometer are not always reliable ; that is to say, although the relative positions are in general very accurate, the group as a whole may show a large systematic error. This was to be feared in the present case, as the absolute positions of the stars of the cluster were made to depend ultimately on but two points, determined by meridian observations. Aside from this consideration, Chase gives a very good authority from which to obtain the proper motions of those stars common both to his work and to the Rutherfurd photographs. Motion of the group PS a whole would, however, be eliminated, were his star places
“Trinngulation of the Principal Stan of the Cluster in, Coma I3creniccs,” by Transactions of the Astronomical Observatory of Yale Univer- Frcderic L Chue.
sity. Referred to PI C/W.
( 3 )
341’ KRETZ
employed (in the reduction of the plate-measurements. I de- cided, therefore, to obtain the positions of as many stars as POS-
sible from all the catalogues available to mc, and to use these as standards, that being the method commonly regarded as leading to the most accurate results. How this assumption was borne out in the progress of the work will be shown later (Part 11, Sect. IV). The list of catalogues examined includes all that may claim any confidence mentioned in Knobel’s memoir,’ besides all important modem ones, and I have attempted to make it practically complete. Twelve stars were thus found sufficiently well determined to warrant their reduction. One of these was subsequently rejected as standard, the remaining eleven being finally retained. I shall give, however, a record of all observations of stars in my zone which I found in the catalogues.
List of Oatalogues Used.-Of *the catalogues examined, the following contained observations of stars present on the plates :
(I) BRADLEY, 1755. Neue Reduction des Brad- ley’schen Beobachtungen aus den Jahren 1750 bis 1762 von Arthur Auwers.
(2) PIAZZI, I 800. Pmcipuarum Stellarum inerran- tium Positiones Mediz * * * ex observationibus habitis * * * abanno 1792adannum 1813.
The dates wcre obtained from the original observations in the Storia Celeste ; they are however very doubtful, as in almost every case more observations were found than agreed with the number given in the catalogue, with no way to determine which were ex- cluded from the final reduction. The mean date of all observations was thereforc taken ; but in assigning weights the argument used was the number of observations as given in the catalogue.
St. Petcrsburg, I 888.
Panormi, 1814.
(3) LALANDE, 1800. Histoire CCleste Frangaise, Tome I. Paris, 1801.
Baily’s Lalande,” published by the British Association in 1847, was used only as an index to the zone observations, which were re-
’ Knobel, ‘‘ The Chronology of Star Gtologues,” in Memoirs of the Royal Ast. SX., VOl. 43, p. I .
( 4 )
STARS IN COMA BERENICES. 346
duced to 1600 by Von Asten's Neue Htilfstafeln zur Reduction der in der Histoire CCleste enthaltenen Beobachtungen," Viertcljahnschrift der Astronomischen Gesellschaft, appendix to Vol. 4. Account was taken of the ernta published in the introduction to the Pans cata- logues, by Peten, and by others.
(4) D'AGELET, 1800. * Reduction of the Observations of Fixed Stars made by Joseph Lepaute d'Agelet * * * with a catalogue * * * by B. A. Gould. Washington, 1866.
The mean of the separate observations given in the catalogue was used.
( 5 ) BESSEL, I 825. Astronomische Beobachtungen auf der Keniglichen Universitits-Sternwarte zu Kenigsberg, . for the years 1821 to 1833.
Weisse's Catalogue of Bcssel's Northern Zones was used only as index to the original observations, which were reduced anew by theaid of Luther's tables in " Astronomishe Beobachtungen auf der Konig- lichen Universitits-Sternwarte zu Konigsberg," Abt., 37, 2"' Ted. An explanation of the necessary formula there given, which are similar to those in use with Von Asten's tables, will be foundin Arge- lander's Bonner Beobachtungen, Vol. I , p. xxxvi. Account was taken of the errata to the zones recorded in Part I of the volume containing Luther's paper. The star numbers in the Tables, Sect. 111 of the present paper, are those of Weisse's catalogue.
46) STRUVE, 1830. Stellarum Fixarum * * * Positiones Medire pro epocha 1830 * * * ex observationibus * * * anni's 1822 ad 1843. Petropoli, 1852.
Positions were taken from the ' I Catalogus Generalis" beginning on page 235, and the mean date was used as there given in column nine, unless a B was found in that column. This means that a certain proper motion, deduced from comparisons with Bradley, was included in the reduction, but as its value is not given, i t was deemed best, in such cases, to take the star's position directly from a 11 Catalogus Specialis " in theprecedingpart of thc volume. Refer- ence to the page will in general be found in column eleven of the
Catalogus Gcncralis." The Correctioncs Ultimz " given on pp. 360ff. were not applied in such cases. (7) POND, 1830. A Catalogue of 1 1 1 2 Stars * * *
from Observations made at * * * Greenwich from the years 1816 to 1833. London, 1833.
ANNAIS S. Y. ACAD. SCI., I I I , Feb. 12, 1900-22. ( 6 )
346 KKETZ.
The mean date of observation is not given in the Catalogue. It was obtained from the original records, published in the " Annual Results of Observations at Greenwich." All observations of small stafs were made in the years 1830 to 1833 incl. ; those of principal stan in right ascension from 1816 to 1833, and in north polar dis- tance from 1826 to 1833. There are, in general, two observations in N. P. D. for each day, one with each of the two mural circles. For one star (No. 501, decl.), more observations were found'in the annual results than are counted in the catalogue ; the same rule with regard to the weight and the mean date was followed in this case as in that of Piazzi.
A General Catalogue of the Principal Fixed Stars from Observations made * * * at Madras in the years 1830 to 1843. Madras, 1844.
It was obtained from the original records in Vol's 1 to 5 of the Madras observations in a manner simi- lar to that explained by Argelander on pp. 18 and 19 of Vol. VII, Bonner Beobachtungen ; remembering however, that according to the introduction to Vol. 3, the transit instrument was down from 1834 March 6th to 1835 Jan. 31st, and that Taylor was absent in England in the years '1840 and 1841. Account was also taken of the fact that the constellation Coma Berenices comes to the meridian before midnight in the early part of the ytar. The star numbers as printed in this paper were corrected according to the errata, pp. bs, of the catalogue. (9) ROMKER, 1836. Mittlere Oerter von I 2,Odo Fix-
sternen * * * aus den Beobachtungen auf der Hamburger Sternwarte * * * Hamburg, 1852.
The mean date was taken as 1841, in accordance with the note given by Schorr in his Bemerkungen zu Carl Riimken Sterncata- logen," Mitteilungcn der Hamburger Sternwarte, No. 3, p. 6.
(10) ROBINSON, 1840. Places of 5,345 Stars observed from 1828 to 1854 at the Armagh Observatory. Dublin,
Thc mean date was obtained from the record of the separate ob- servations printed in the first part of the volume.
( 1 1 ) GILLISS, 1840. CataIogue of 1248 Stars ob- served at Washington between October, 1838 and July, 1842 * * * Washington, 1846.
The mean date was obtained from the annual results given in the same volume.
(8) TAYLOR, 1835.
The mean date is not dven.
1859.
(6)
STARS IN COMA BERENICES. 347
(12) PARIS,, 1845. Catalogue de I’Observatoire de Paris. Etoiles observkes aux Instruments Mkridiens de 1837 A 1853. Vol. 3, Pans, 1896.
A Subsidiary Catalogue of 1440 Stars * * * from observations made at Madras in the years 1849-1853. Madras, 1854.
Positions from this catalogue were kindly furnished in manuscript by Prof. Pickering. (14) WROTTESLEY, 1850. A Catalogue of the
Right Ascensions of xoog Stars ; in Mem. Roy. Astr. So- ciety, Vol. XXIII, p. x .
(15) SIX-YEAR, 1850. Catalogue of 1576 Stars formed from the observations made during Six Years, from 1848 to I853 at * * * Greenwich.. London, 1856.
(16) POULKOVA, I 8 5 5. Positions Moyennes dC- duites des observations faites * * * ;84+1869. Obser- vations de Poulkova, Vol. VIII.
!t was obtained from the Vols. VI and VII of the ‘ I Observations de Poul- kova.“ (I 7) ARGELANDER, I 85 5. Mittlere Oerter von
33,81 I Sternen, abgeleited aus den * * * in den Jahren I 845-1 862 angestellten Beobachtungen.
Seven-Year Catalogue of 2,022 Stan deduced from Observations extending from 1854 to 1860 at * * * Greenwich.
Catalogue de I’Observatoire de Pans. Etoiles observkes aux Instruments Mkridiens de 1854 A 1867.
Catalogue of Stars observed at the United States Naval Observatory during the years 1845 to 1877. Third edition, revised * * * by Professor Edward Frisby. Washington, 1889. (21) BRUXELLES, 1865. Catalogue de 10,792
htoiles observkes * * * de 1857 a 1878 * * * par Ernest Quetelet. Bruxelles, 1887.
The catalogue itself does not include positions of the fundamental
(13) JACOB, 1850.
London, 1854.
St. Pktersbourg, 1889. The number of observations is not given in the catalogue.
Bonn, 1867. (18) SEVEN-YEAR, 1860.
London, 1864. (19) PARIS,, 1860.
Vol. 3, Paris, 1896. (20) YARNALL, 1860.
( 7 )
348 KKETZ.
stars determined at this observatory. They are given in a *parate list on pp. xv ff. of the same volume. h'one of my stars was found among them.
(22) SAFFORD, 1865. Observations in Right As- cension of 505 Stars, being Vol. IV, Pt. I1 of the Annals of Har,vard College Observatory.' Cambridge, I 878.
The positionsas used were taken from pp. 30-108, where they are given uncorrected for proper motion, and, in the case of ephemeris stars, with certain periodic terms neglected (cf. lntrod ; p. ix). They are repeated, with these corrections applied, i n the General Catalogue on pp. I - I Z O . I n each case, however, the amount of the conec- tion, with its proper sign, is set down in column 9, tinder the head JR (Introd. p. sv).
(23) NINI<-YEAR, 1872. Nine-Year Catalogue of 2,263 Stars deduced from observations extending from I 868 to 1876, made at * * * Greenwich. (No date, Appendix to Obscrvations for 1876.) (24) DREYER, 1875. Second Armagh Catalogue of
3,300 stars * * * from observations * * * during the years 1859 to 1883 * * * Dublin, 1886.
Catalog von 5,634 Sternen aus den Reobachtungen am Pulkowaer Meridiankreise wahrendder Jahre 1874-1880 * * * St. Petersburg, 1891.
Catalogue de 1'0bservatoire de Paris. ktoiles observCes aux Instruments MCridiens de 1868 i 1881.
Catalogues no. (IZ), (19), and (26) appcar as one work of four volumes, each volume crnbraciiig six hours of right ascension for all of the three epochs, 1845, '60, and ' 7 j . The three corresponding quantities for each star will always hc found together on the same line. ,
(27) KOGKRS, 1875. Catalogue of 1213 Stars ob- served during the years 1870 to 1879, being Vol. XV, Part I of thc Annals of the Astronomical Observatory of Harvard College., Cambridge, I 886. (29) RESPIGHI, 1875. Catalog0 delle Declinazioni
di 1463 Stellc comprese fra i paralleli zoo e 64' nard * * * in Vol. VIII, Ser. 3, Reale Academia dci Ihcci, 1879-80. Roma, 1880.
(25) ROMRERG, 1875.
(26) PARIS,, 1875.
Vol. 3, Paris, 1896.
medie * 8 C
( 8 )
STARS IN COMA BERENICES. 349
(29) CATALOG DER ASTRONOMISCHEN GE- SELLSCHAFT, Zone IX. Catalogue of 14,464 Stars be- tween 24O I 5’ and 30~57’ North Declination, I 85 5 * * * by A. Graham. Leipzig, 1897. (30) TEN-YEAR, 1880. Ten-Year Catalogue of 4,059
Stars deduced from observations extending from 1877 to 1886 at * * * Greenwich. London, 1889.
Annual results reduced to the beginning of the year of ob- servation, but as yet uncombined to form larger catalogues, were used in exactly the same manner as were the preceding works. The following series were found to contain observations of my stars.
(31) CAMBRIDGE YEARLY RESULTS, 1836- I 869. Astronomical observations made at the Observatory of Cambridge in the- years I 836 to I 869.
The stars in these lists are not numbered. The mean date was obtained fro6 the separate results preceding the Catalogue. The same remarks apply to no. (32).
(32) EDINBURGH YEARLY RESULTS, 1840- 1886. Astronomical Observations made at the Royal Ob- servatory, Edinburgh, from I 840 to I 886.
Observations were taken at Edinburgh previous to 1840 by Hen- derson. They were reduced under his direction, while those taken after 1840 were reduced by C. P. Smyth. The earlier set being en- titled to higher weight than the latter, I have not grouped them both under one heading. None of my stars was found in the earlier se- ries. The Catalogue compiled from all. of these observations by Srnyth, under the title “Star Catalogue, Discussion, and Ephemeris from 1830 to 1890 ” was used only as index to the yearly records.
(331 RADCLIFFE YEARLY RESULTS, 1862-1879. Results of Astronomical Observations made at the Rad- cliffe Observatory in the years 1862 to 1879.
No observations of stars were made in 1877, ’78, and ‘79.
(34) MADRAS YEARLY RESULTS, 1862-1882. Results of Observations of the fixed stars made at Madras in the years 1862 to 1882 inclusive, under the direction of N. R. Pogson.
( 9 )
360 KRETZ
(35) GREENWICH YEARLY RESULTS, 1887 to 1894. Results of the Astronomical Observations made at the Royal Observatory, Greenwich, in the years 1887 to 1894.
The Greenwich Five-Year Catalogue includes some of these obser- vations ; but the greater part of them are not as yet combined. Such of my stars as were found in this series were of the latter number.
Weights : On the preceding pages I have detailed the cata- logues used in the present paper. The observations are, of course, not all of the same standard of excellence. Weights were assigned depending approximately on the probable error of a position as given in a catalogue, the probable error of an observation of unit weight being taken arbitrarily as o’I.4 of arc of a great circle. A table of weights was constructed on this basis by Dr. Davis when engaged in a research similar to the present one, and is printed in his memoir on the subject.’ To it I refer. It must be remembered, however, in regard to the An- nual Results, that I have regarded the observations of each year as forming a separate catalogue, and have weighted them as such, whereas Dr. Davis first reduced them all to 1875, and then assigned a weight to the mean depending on the total number of observations taken at the observatory in question. In all other respects the table was used exactly as there explained.
A. few of the catalogues used by me are not included in this list. They follow, together with the number of the star or stars, the corresponding number of observations, ,and the assigned weight. The figures in brackets refer to the preceding list of catalogues.
( I I ) GILLISS, 1840. Star no. 6 0 5 , I oh. , wt. = 0. I .
Star no. 608, I 3 obs., wt. = 1.0. (14) WROTTESLEY, 1850. Star no. 447, 5 obs., w t = 0.5. (22) SAFFORD, 1865. Star no. 1 9 4 ~ 7 obs., wt. = 2.0.
Star no. r g ~ , 6 obs., wt. = 2.0.
1 ‘‘ Declinntions and F’rdper Motions of Fifty-Six Stars,” by Human S. Ihrir, Ph.D. Memoir I, of the N. Y. Academy of Sciences. Referred to BS D a b . Th table of weiRhts will be found on pp. 14 to 18.
(10)
STARS IN COMA BERENICES. 361
For (17) ARGELANDER, 1855, the same weights were used as are given for Oeltzen-Argelander in Davis.
The same table was assumed to apply to both n'ght ascensions and declinations. This has been the generally accepted method: but my results indicate that it is not always correct. On the whole, the residuals are larger in right ascension than in declination. Especially is this the case with the older catalogues. I have compared the prob- able errors in the two cGrdinates obtained from the eight published zones of the A. G. C. (that being my standard of weight) and find a difference, which, though slight, is in the direction mentioned. A separate table of weights to be used for right ascensions would therefore be desirable. For my purpose, I have not deemed the additional accuracy obtained thereby sufficient to compensate for the labor involved.
11. Method of Reduction.
Precession.-The epoch selected was 1875, that being very near the mean of the dates at which the plates were @ken. The precession factors were computed ,by Professoi Hill's for- mulae as given in the "Star Tables ofthe Ainericati EphemeniJJJ Wash., 1869, pp. xviii, xix. The constants used were those of Peters and Struve, being, for 1800
tn= 3' .07082+ D.oa,o~8ggr n Z= 20".0607 -'/.ax, 0 8 6 ~ .
Introducing these values in Hill's formula, we obtain for 1875, the numbers in brackets denoting logarithms :
cia d, = 3'.07za5 + [o.126115) sin n tan A + p
dd = [1.302206] cos a + p'
+ [4.9866 - 101 pp' Inn d
$- O.'ooo 032 210
f [6.7367.- 101 p* sin id.
The third term, both in right ascension and in 'ileclination, was taken from Kloock's If Tufeh der Pmccessioii," that being
(12)
STARS IN COMA BERENICES. 353
sufficiently accurate on account of the small value of the propcr motion for all of my stars.
In the above formulae, a, p, B and p’ denote respectively the right ascension and corresponding proper motion and the dec- lination and corresponding proper motion for 1875. In calcu- lating the constants, the right ascensions and declinations were taken uniformly from the Astronomische Gesellschaft Catalog, Zone IX ; the proper motions either from Auwers’ “Nciic Rcdnc- tion dcr Brdty’schrrr Bcobachtungcr ” or from Saford’s I d Cnia- loguc of Mean Dtclination of 2,028 Stars,’’
If now we put
and let T= the epoch of any catalogue, and ah b, = the right ascension and declination as there given,
then will
d,“,=dl + L ( ~ 8 7 5 - T ) + M l - 1 8 7 5 - T ) ’ + ~ ( - 1875-T)’ 200 rm
as is evident at once when we remember that the above expres- sions are the first few terms of the expansion by Taylor’s for- mula of a and d, thus
and similarly for 6. Here a,, is the right ascension at the epoch for which the precession is to be computed, 1875 in the present case, and t is the interval from this epoch to the epoch of a. For dates later than 1875, t is plus ; for those earlier, it is min- us. Hence, transposing a. to the first, and n to the second member, changing the signs and introducing the previous nota- tion, we obtain the series in the form given above.
(13)
364 KRETZ.
The coefficients of f, K and P, denoted respectively by U, P, and W, depend only on the time, and may be tabulated. This is here done for the epochs used by me, Signs at the, top are for the dates at the left of the table ; signs at the bottom are for dates at the right.
40 39 3s 33 32
31 30 28 25 lo
19 17 16
- .-
8 . m 7.605 6.115 5.445 5.120
4.805 4.500 3.920 3.115 1 .Ooo
1.&5 1.445 1.280
- W
+ 1.718 0.41a 0. '33 o.11g 0.091
0.064 0.059 0.043 0.036 0.033
0.030 0.017
- -- - - .-
0 . 4 7
1.115
0.720 0.605
0.500 0.405 0.320 0.145 0.180
0.125 0.080 0.045
0.035
".P 0. 45
0.010
O.OO0
- . - -
- W
t
0.003 0.003 0.002 0.002 R00l
0.001 0.001 0.001 O.Oo0
- ... - - Roper Motion.-Some catalogues take account of the proper
motion in reducing from apparent to mean place. As its value, however, in general differs from that assumed in the present paper, a correction to eliminate its effect must be introdued. ,u being the proper motion as assumed by me, p' that used in the catalogue under consideration, and Tand t, as usual, the epoch of reduction and the epoch of the catalogue respectively, we have
which becomes, for / I / = o Correction for ermncouspm= ( T - t ) ( p - p f ) ,
( T--rh.; It is not always plain whether a certain catalogue uses pro-
per motion in the reduction to mean place or not. I subjoin (14)
STARS IN COMA DERENICES. 366
the conclusion at which I arrived in each special case, and in ac- cordance with which the correction was applied in the succeed- ing calculations. The numbcrs refer to the catalogues detailed in Sec. I.
( I ) The proper motion given is used in the reduction. See pp. 18 and 20 of the introduction.
(2), (3) (4) ( 5 ) These do not take account of proper mo- tion. In (3) and ( 5 ) it is not mentioned ; in the case of (4) see Introd., p. 26, 5 I I ; and for (2) see Argelander’s Bonner Beobachtungcn, Vol. VII, p. 10.
(6) No proper motion is applied unless a B is found in the column headed ‘ I Epocha Media.” Its value, although not given, may be obtained from the value for Str.-Bradley, given pp. 299 H. (7) Pond uses the A. S. C. constants and no proper mo-
tion unless therein included. Such cases are marked by an asterisk in the column of precessions,‘ttie same as in the volumes from which the c‘onstants are copied.
(8) Proper motions greater than d’. 5 are always, and those greater than o’I.25 are sometimes included in the reduction. Smaller values arc always neglected.
(9) No statement. Proper motion is probably not taken into account.
(10) According to Introd., p. xxviii, proper motion is not used in the reductions.
( I I ) Proper motion is neglected in reducing the observa- tions to the beginning of the year, except where included in the A. S. C. constants (Introd., p. XXIV); but in combin- ing the separate annual results into a general catalogue, it is takcn into account (p. 595, “ Column 6 ”) whenever its value is given.
See Introd., p. LXXX.
Introd., p. 2.
( I 2) See (26). (13) This catalogue does not take account of proper mo-
tion. As it was not accessible to me, I could not personally verify the above statement, which is made in accordance with Davis, p. 28, no. 6g.
(14) I could not find any definite statement bearing on (15)
366 KRETZ.
the point in question. It seems, however, that proper mo- tion is not used. Cf. Introd., pp. 15-17.
:, (15) The same notes apply to this catalogue as to no, ( I I), except in the case of N. A. stars, when the proper mo- tion is taken into account. See Introd., p. iv; also Twelve- Year Catalogue, pp. vii and ix, and Seven-Year Catalogue for 1860, pp. {v i j and {XI, and Appendix.
(16) No statement is made in the introduction to Vol. VIII of the I t Observations de Poulkova," which contains the catalogue, Backlund, however, in an article designed ongin- ally to form the preface to the catalogue, but afterwards pub- lished in the Memoirs of the St. Petersburg Imperial Acad- emy, states, that proper motion was used when given either by Auwers in his " Bradfty " or by Argelander in his I' 250 Stars with Proper Motiotis." Backlund superintended most of the computations.
No mention of this matter is made in the introduction.
See Intro- duction, pp. jv'l and {XI.
LOC. cit., Vol. 34, no. 7; p. 4. (17) Proper motion seems to be neglected.
(18) Proper motion is used in the reductions.
(19) See (26). (zo), (21) Both catalogues neglect proper motion. See
(22) See the remarks on this catalogue in Sec. I of the
(23) Proper motion is used. See Introd., p. 4. (24) This catalogue does not take acFount of proper mo-
tion. Cf. Introd., p. ix. (25) The proper motion as given is included in the reduc-
tions. See Introd., p. (12).
(4, ( I 2), and (19) According to p. [2) of Vol. I, proper motion is always neglected.
(27) Account is taken of the proper motion whenever given. Introd., p. vi.
(28) Proper motion is included in the annual variation for each star given in this catalogue. Its value, although not set down, may be obtained by subtracting the corresponding
(20) Introd., p. XXIV ; (21) Introd., p. XII.
present paper.
(10)
STARS IN COMA BERENICES. 367
geometric precession from that quantity. The original author- ity for the proper motions of all others than fundamental stars is the B. A. C. See p. 134. (29) Proper motion is not used. (30) As in the other Greenwich catalogues, proper motion
is employed in the reductions, In the case of the Annual Results, proper motion has a very
slight effect as it is always used for a fraction of a year only, and is therefore mther unimportant. I found, however, the following :
Proper motion is not ta- ken into account, except for Nautical Almanac Stars when included in the annual variations there given.
(32) The Edinburgh Annuals, up to the publication of the B. A. C. in the year 1845, were reduced by means of the A. S. C. add Nautical Almanac constants, using proper motion only if therein included. After that, however, the B. A. C. values, both of precession and proper motion, were always used, if possible, for stars not given in the N. A.
(33) The Radcliffe Annuals do not use proper motion. For Nautical Almanac Stars it is, however, generally included in the precessions ; these are markcd with an asterisk in such cases.
See Introd., p. 4.
(31) The Cambridge Annuals.
(34) The Madras Annuals do not use proper motion. (35) The Greenwich Annuals employ propcr motion in
the reduction to mean place.
Systematic 0orrectione.-The system used throughout was that of thc ‘‘ Fiindarrirntd- Catalog der Astrofzowischeri Gcsell- schafl.” Corrections to reduce the catalogue positions to this standard are given by Auwers in the. Astronomische Nach- richten nos. 3 195-96, and 341 3-14. A number of lists of stars, notably annual results, are not mentioned in these papers, how- ever. For such cases it was generally possible to obtain values of the corrections to the declinations from Boss, “Report 011 t h Dtc/inatiori of Stars, etc.,” pp. 579 K They were reduced from his I‘ mean system ” to the A. G . C. system by the aid of the
(17)
368 KRETZ.
formulae and table following, which I reproduce from Dr. Da- vis' memoir :
To Boss' value add the quantity
mf X ( T-1883) when T< 1866
m + K'( T- 1883) when T> 1866.
hy = A. G. C.- Bou (good for 1883)
or
Here
and is obtained from the Berlin Jahrbuch, 1884, Appendix. Kand K' are the annual variations of M computed as shown in the table, p. 359, in which we assume Ada = 0.
There still remained a number of cases to be treated, how- ever, chiefly right ascensions, for Boss gives correct;ons to the declinations only. For all of these I deduced corrections by direct comparison with some suitable catalogue whose system was well known. The labor was greatly simplified by the fact, that no account had to be taken of change in right ascension or in declination, as my stars are all situated within a few degrees of each other. The rule laid down was to compare as many stars as possible (usually about 1 z ) within not more than one hour in right ascension, and five degrees in declination on either side of the center of my plate. Systematic corrections were thus deduced for the following catalogues :
Bcssrl((5) of Sect. I), Zoiirs 464 and -qo.j.-Auwers. in his zone of the A. G. C., gives corrections to all those of Bessel's zones which fall within thc limits of his catalogue. He shows that they consist of two parts, a systematic one, depending on the constants used in the reductions, and one due purely to ac- cidental causes. Luther's tables fail to eliminate the latter class. Without attempting to distinguish between them, I deduced the total amount by direct comparison with the A. G. C., correcting for proper motion whenever that was possible. I find thus :
A. G . C.-ner4, Zone 464 ( i n n ) = + 0 . ~ 9 0 ' '* " '1 ( i n d = - 3 n . b
A. G. C.--lles~cl. Zone so! ( i n n ) = + os.122 I " " " ( i n i l l = + 3/'.:5
( 1 8 )
STARS IN COMA BERENICES.
i T I + ++ + ++ +++
6 4
+ 9 r" - -
."a 9
T I + ++ + ++ +t+ __ . . . . . . .- __ . - - - - m e - - m Y) ta
+t+ ++ + +-t- + I I -. _-
360 KRETZ.
Cnttibringc Airriunls (3 I).-Observations in right ascension of my stars were taken in the years 1842, '44, '45 and '47. Corrections to the years 1842 and 1845 were obtained by di- rect comparison with Struve's (' Positiones Mediae." During 1844 and 1847 not enoygll stars were observed in the zone selected by me to warrant a comparison with Struve. For ISM I accordingly assumed the same corrections as for 1845, and for 1847, zero was used, as no other value was procurable. Corrections to the declinations are given by Boss. My inves-
. tigations give, for the right ascensions :
A. G. C.--CPmbridge I@ = - om.07s A. G. C.-Cambridge 1845 = + om.lq7
Editibiirglr Atititids (3 2).-Boss, who gives corrections to the declinations, divides this series into several groups, of which the following include the dates of observation of my stars: 1854-1860, 1861-1864, 1865-1869. Corrections were com- puted by comparison with the A. G. C. for the yean 1856, I 864, and I 868, being one year in each group. Two stars were observed in 1842, and for this year a correction was deduced by comparison with the new Seven-Year Catalogue. The re- ductions were always made including proper motion if possible. The vWes found were as follows :
A. C. C.-Edinb. 1842 =. - e.012 A. G. C.-Edinb. 1856 = -@,o87 A. G. C.-Edinb. 1864 = - om.070 A. G. C.-Edinb. 1868 = - @.qs
Ka&IiJit Atiiritals (33).-Corrections to the dec inations c 3-
served before 1874 are given by Boss. One of my stars was found in the volumc for 1874. The correction in this case was calculated by extrapolation from .1872 and 1873. For the right ascensions the usual 'method was followed, comparisons being made both with the A. G. C. and with the Paris 1875. Corrections to the observations of the years 1868, 1870 and 1871 were thus obtained. In the year 1873 not sufficient stars were observed to make a satisfactory comparison possible. For
(20)
STARS IN COMA BERENICES. 361
this case, zero was therefore assumed. The results reached were as follows :
A. G. C.-Ridcliffe 1868 = + cP.033 A. G. C.-Ridcliffe 1870 = - fl.071
A. G. C.-Radcliffe 1871 - - - cP.020
Crctnwih Atmrm& (3 S).-The same systematic corrections were used as are given by Auwers for the Ten-Year Catalogue. See Davis, p. 24, no. 40.
A few of the catalogues deserve special notice in this connec- tion. They are: (I) ~ltwcrs-B~udcy.-No systematic corrections to this cat-
alogue have been published by the author, which indicates that their value is zero. I have so assumed it for the two stars found in this list. (4) d'Agclrt-Auwers gives systematic corrections to this
catalogue on p. 60 of his zone of the A. G. C., but applying only within the Iimits'of that zone. On page 30 of the intro- duction, Gould himself gives the result of a comparison with Piazzi He gives cor- rections for what he calls the first and second group, without stating where the dividing line between the groups is situated. I have assumed it to be at 1 2 ~ in accordance with a statement at the bottom of page 29, and find thus
His terms are not quite clear, however.
Piuzi-d'Agelet in a = + 0'.079 Piazzi4'Agelet in J = + xU.ra,
whence (A. G. C.-d'Agelet) is easily obtained. (6) Sfntvc.-The same correction was assumed to apply to
the " Catalogus Specialis " for I 824 as to the " Catalogus Gen- eralis " for I 830. (17) Argchtdtr.-In accordance with pp. vi and ix of the
introduction, the corrections of the Abo Catalogue reduced to 1855,'as given by Auwers, were applied to my stars found in this catalogue.
(121, (IS), and (26) Pun*s.-The corrections given by Au- wers for the first twelve hours of right ascension were assumed to apply equally to the third quadrant.
ANNALS N. Y. ACAI,. %I., XII, Februuy 14. 1900-23
(21)
362 KRETZ.
(20) Yumnll.-Corrections to this catalogue will be found in both of Auwers' papers. The second set was used by me.
Formalee for Acljustment.-The usual methods of least-square solution with artifices of computation analogous to those pub- lished in Da&, pages I I and 12, were employed. I shall de- duce the formulae for right ascension only; the discussion for the other cocirdinate is entirely similar.
Bd= the seconds of an observed right ascension reduced to 1875, using an assumed value for the proper motion, and cor- rected for systematic errors ;
If we let
ti= the date of observing Bi ; a. = the seconds of the right ascension to be obtained from the
observations, corresponding to some fixed epoch T, ; d p p t h e correction to be subtracted from' the assumed proper
motion ; then evidently we should have
~ - ~ & + A p ~ [ h - ~ ) f = o ; (1)
diq,-/&Ap, [ h - 7 J - / S B c = o . (-1
or, if the weight of Bi be pi,
Writing, then, m equations of condition of the above form, one for each observed Bi, and solving by least squares, we get the following normals, where the square brackets as usual denote summation :
} ('1 [PI "0 - [ P ( t - To)] 4% - [pal = 0
-[A'- 7-Jl a0 t CP(r-70l'I bi- "(~-T0)]=0.
By suitably selecting the epoch To we can greatly facilitate the succeeding work-an artifice first employed for this kind of work by Professor Safford.' For let us take as the mean of all the dates t, that is, let
I Sce Safford, "C~talague of 1018 Stan," Introd., p. 12.
(22)
STARS IN COMA BERENICES. 363
then will [At- To)] = 01
and equations ( 2 ) become
(3 ) [ti Q . - [ P ~ I = o [PP- 72'1Ah + r p w - 7-4 =ot
whence at once
If now we write ( t - G ) = C , p ( t - T , ) = D ,
% - B = E , and remember that
since.
we get finally the formulae
[PC(%--B)I =4rm -rp=4 = - [ P ( t - T.14
"=o,
The probable error of an observation B whose weight is unity is, by the usual formula
the v's being the residuals obtained by substituting the final values of a. and dr, in equation (I). Hence the probable error of
364 KRETZ.
As dpoSind a. are not independently determined the correcl- It is, how- ness of the last formula is not immediately evident.
ever, easily proved. For we have
nlnl=n,S (1875- T,,)APo
and since the 8 s are independent, and the probable error of Bi is Y, / JA, we get for the' probable error of
.................. I +
= rlJ + (1875 - G)* rr' remembering that
[ j ) q - = o and [ p C f i J = [ C D ] .
In applying the above formula to a special case, I invariably proceeded as follows (the explanation is again confined to right ascension ; it applies equally to declination, however) :
(24)
STARS IN COMA BERENICES. 365
Calculate the sums
Then
and $' being the remainders. Now form for each catalogue position the qu'antities
( I - T,) = C, ?(I- TO) = D, ( 0 0 - B ) = E.
The computations up to this point will all checked,' when Zj(a0- B ) =-p, Z) ( t - - q) = + /9'.
From the expressions last obtained we easily get Z(DE) and X( CD)
which we check' by the equations
Z ( D E ) = Z ( p E . C) 2( CD) = Z(PC*).
Then
and Po = c- A/+
ti being the previously assumed proper motion. Also
%l= a0 - 4% (1875 - 5).
To obtain the probable errors, I did not, however, employ formulz (6) as they stand. For thereby the weight of each star is placed on an independent basis, and the probable errors form no means whereby to judge of the relative accuracy of the final positions. is not the same for all the stars, depending, as it does, on the accidental error in each cat- alogue as shown by the residual. We must seek a value for Y,,
which will satisfy all the observations taken of all the stars, not of one star only. Such a value is furnished by the statement in Sec. I, WEIGHTS," which reads, that the probable error of an observation of unit weight was arbitrarily assumed as 0".4
( 2 6 )
For the factor
1 As suggested in DaVir, page I1.
of arc of a great arcle. read
If then we change forrnuk (6) to
and, as before
rnrr = Jrf + I(I875 - Gk,, I'* we obtain probable errors which make a direct comparison pos- sible, and which enable us to assign relative weights to the re- sulting positions for 1875. This is what I have done through- out, and all probable errors are computed by the above expres- sions. It should be mentioned here, however, that, for right ascensions, the values obtained by the above formula: must be multiplied by sec d, in order to make them applicable to the position of the star ; for evidently the formula: give the probable error in equatorial seconds for both coordinates. This I have done for all of my stars, and the probable errors in right ascen- sion found in the succeeding tables are therefore in terms of seconds of arc of a small circle of declination passing through the star in question.
111. Tables and Results.
Star-Tables.-On the following pages are recorded the data from which the final position; were obtained, together with the most important part of the calculations. The tables, when taken in connection with the preceding sections, require little com- ment. A few points may be mentioned, however.
The caption gives the Bonn Durchmusterung number, the usual designation of a star, and Chase's number ; also the pre- cession constants, together with the right ascension and declin- ation for 1875, and the respective assumed proper motions used in calculating the same.
Columns I, 2, 3, 4, 5 , 6 and 12 require no explanation. They refer to matters treated in Sect. I of this paper.
Columns 7 to I I are discussed in Sect. 11; column 7 under the head ' I PROPER MOTION "; column 8 under that of I s PRECES- SION "; and 10 under that of I' SYSTEMATIC CORRECTIONS." Col- umn g is the sum of 6, 7, and 8. 1 1 is explained by the heading.
Column r 5 shows the residual of each observation, and 23 and 14 exhibit the computation by which these are derived. This matter has not been treated in detail before, as I deem it rather unimportant for the present purpose. The probable er- ror is not made to depend on the residuals, and they are here recorded merely to give an idea of the interagreement of the observations ; they are nowise used in the work. The method is sufficiently explained by the headings ; and it is plain that, if car- ried through as shown, the desired quantities will be obtained, remembering the form of the observation equations,(equation ( I ) of FORMULR FOR ADJUSTMENT," Sect. 11).
(27)
368 KRETZ.
h U l t 8 : At the end of each table the results are shown. They are as follows: Column 3 contains To; 5 the total num- ber of observatibns ; 6 the coordinate a,, or do at the time T, ; 7 the correction for L!K, to reduce these to 1875 ; g the cocirdi-
'UIb 11'
d,,, 2 6 O - Con. for Emne'r
Motion. proper
-__ a
0. Qx)
.ooo
.ax)
.ooo
.ax)
- S h .
# 0.00 .W .a,
STARS IN COMA BERENICES 369
nates for I 875 ; 10 the probable error at the time q, and I I that at 1875 ; 1 2 the weight of a, or (r, at the time T,, that is [ p ] ; 13 the final proper motion ; 14 the probable error of the proper motion ; and I 5 its weight, [ CD] , at T,.
f = + 3'.03565 K = - 0.01215 P= 0.014 L = - 2cf.0250 Iu= t 0.0315 N= + 0.16
~ ~~
jRightAxen. I I
1875. , a + A. a , System- H.
Declination j d + A . 1875. B&
6 A I_._ I-- ( h m s .- I I S
I 12 12 22.911 $0.254 23.165 I 12 22.666 $ 0 zp I 22.856 I 12 21.890' $0.043 I
370 KRETZ.
9 B. D. So.9$%-4S Coma Bcrcnltes ( 8 CHASE),
Autborlty. of
BAgelet 2893 Ldande 23065 Raui 39
Taylor 56qq
Kadcl. An. 632 1870.32 Pnris, 15077 1872.8 18;s A. ti. C. 6061 1878.0 1875 Rombcrg 2711 I 1879.4 1875
Keiults 1 1663.01 I875 I
d‘bgclet 2893 I 1785.25 ]So0 kluldez3065 , 1194.31
kxl (W,.) 231
BWXCllCS 5031
- -
P h i 3 i 1 ~ s . 5 1 i ;E, I r1834.81 ’ 1835
&SYl (\I, .) 1381 1830.32 1825 raY.ylm 5644 Robinson 2639 lQ9.30 I 1840 Radcl. An.743 1868.24 1868 Bruxeller5031 1 1868.33 186s Radcl. An. 632 I 1870.29 f 1870 k i s , r 5 q 7 1871.8 I 1875 A. G. C. 6061 I 1878.0 I 1875 Ramberg 2711 I 1879.4 1875
Beiult8 I 1883.17 I 1875
I #
-25 4.86 -25 4.86 -15 4.86
-13 22.40
- ?,20.38 - 3 =55 - I 40.27
-16 43.05
-1 I 42.07
I
L - L
STARS IN COMA BERENICES.
- Right Ascen
1875. a
Declination 1875.
6
12 12 44.161 12 43.791 12 43.661 12 43.637 I2 44.092 12 43.735 12 43.716 12 43.710 12 43.810 11 43.640
-- h m i
h m i ia IY 43.m
- System-
atic Corr.
A
- a + A. B.
J + A. Bd
--__
K= - 0.01 X X )
M= + aoui N=+o.16 P= + a013
S
44.493 44.044 43.914 43.%3 44.033 43.778 43.645 43.813 43.810
-.a33 ; 43.637 9
*0.0120
N
I.. .. *I I.---&- 4' ,..., I --..">
41 10.10 1 4 . 2 2 42 11.80 ! -2.63
42 10.40 I 4 8 2 41 11.41 1 -0.Q
42 9.54 t0.03 42 10.53 ' 4 . 0 1 42 11.56 14.68 42 10.83 4 2 2
41 10.59 I .oo 41 10.93 I .M
d45i iarai I kojlr52
rn zt 0.0136
371
0.5 I -a136 1.0 +0.018 1.0 1 +0.036 1.0 I +0.048 1.0 S0.073 1.0 +o.&
e.4 I --ohm - _ _ I
' 43.897 ' 43.796 : 43.681
I 43.883
* 0 . q
, 43.861
; 43;717
. ___ X
9159 0.1 I +;164 11.23
9.17 0.3 , +I.N , 1038 -9.88 4 0.2 , to.+ I 10.57 9.58 I 0.5 $0.60 10.18
10.57 I 0.2 , $0.29 10.86
8.54 0.1 I +r.45 999
4 . 1 0 7 4.006 -10. '09 4 . 0 7 1 4 . 0 9 3 +0.073 8308
4f83 +0.41 50.02 4 . 1 7 $0.22 4 . 4 6
9.57 1 0.5 4 . 1 i I 9.46 so.*
I 10.61 I 1.0 I 4.20 , 10.41 j 4 . 0 1 I 10.59 1 1.0 I 4 . 3 1 10.28 f0.12
10.52 I 1.0 , 4 I 1 10.41 I 4 . 0 1 I 10.88 ' I 0 , 4 . 1 5 ~ 1073 4 . 3 3
1 10.93 1.0 I 4 . 3 4 10.59 I 4 . 1 9
312
4 3 2
KRETZ.
d'Agelet 2909 I 1785.25 I 1800 Lnlnnde2~118 , 1794.31 I 1800 Piuri52 I 1 8 q . o ~ I 1900
5 BCSKI~W,. ) 27c 8 T a y b 5659
21 Bnuelles 5045 33 Radcl. An. 636 33 Rndcl. An. 624 26 Paris, 15mo 29 A. G. C. 6070 25 Romhrg 2725
Results - -. . -. - .
1870.35 1873.21 1875.6 1876.3 1879.9 1881.89
.
I ' I2 1014.1
16 i 10 14.24 I X I 29.76
3 1330.84 2 1346.25 I ' 13.55.03 3 14 1.09 6 : 14 I 05 2 : 14 1.02
I 1 ' 10 14.30
2 1 I2 0.53
h m s na ' l a 1 1 1.w
. . . . .
I 2606d4412 I ' 6647.2 10 : . 66 44.6
55 3.11 1 ~ 53 26.22 I 44 2.01 4 ' 45 3.01
I 58 18.9
.- 8 ' I U S
a m /+3 47.677 .OOO i+3 47.677 .- :+3 47.677 .ooO +231.708
.OCOlf 30.318
.OOO !f 15.157
.om
.om
.om
.ml+2 1.341
.ooo + 6.063 - - - -
.- ..
-444 -is494
-0.12 -24 59.94 -a. 19 -16 39.76
00 -13 19.74 -0.28 -11 39.75
-10% 17 -24 59.94
4.01 '- 2 19.92 4.10 ,- 3 19.88, -0.01 - 139.94 I
STARS IN COMA BERENICES.
f = + 3'.03116 K = - 0.01188 P = +a013 L = - 1g.9867 M= + 0.0356 N= t0.16
! Pa _?..-I
a I S
f0.331 I 2 . 1 9 $0.153 ! 2.230
4.071 .om'
to.043
- .w3
*0.0113
-1.41 -2.63 -2.63 +3. 15 4 . 8 1 -0.82 fo.03 -0.01 --o. 68
.ooo I
Y
1.336 1-93 1.133 I .050 1.017
s k0.0134
&9 44.80 41.91 42.10 42.56 45.37 42. I I 43.02
- - .. -_
44.92 4 11 42.63
P __ 0. I 0. I
0. I
I .o
0.3
0.3
0.5 0.5 I .O I .o 1.0
5.8 I_
0. I 0. I
0. I
0. 2
1.0
0.3
0.5
0.5
0.5
313
. . 4 . 4 7 0 ' , 1.120 4 .414 , 1.398 +0.025 1.216 +0.g6 S0.117 $0.150 t o . 160 +O.lIO
--o:ot(b Y
0.00 .m .w .a, .w .W .OO .a, .oo
1.412
I. 183
1.227
f O . o o o 5
1.210
1.210
a
Y
43.29 44.80 41.91 42.10 42.56 45.37 42.11 43.02 44.91
0.5 ! .oo , 42.63 -0.21 42.26 1.0 ~ .m 42. 26
42.56
4 r 3 5
+0.38
-1.86 + I . O j to.& -2.43 $0.83 4 . 0 8 -1.98 f a 3 1 +0.68
* N t m : See Sect. 11, Systematic Corrections to Radcliffe Annuals.
374 KRETZ.
Wmde 23120
RUmker 3916 Poulkora 1852 Gmbr. An.
Paris, 15101
Jacd [ 4 w I Wrottcsley 447 Edinb. An.
1' , ' . . I , $1 I 1
(1 I '
Yamall5240 Edinb. An. Radcl. An. 637 Paris, 15101 A. G. C. 6071 Rombcrg 2726 Ten-Year 1927
( t I L T
1794.31 1841.2 :1841.31 1841.31 18q7.3t 1850.27 1851.1 1856.22 1858.21 1864.26 1865.16 1866.0 1868.26 I 870.24 1875.3 1877.3 1879.4 Isso.02
,< 'I
I1 "
I ' '* 'I "
" ,. , d 'L
Radcl. An. 413 Edinb. An.
'I I'
.' , I
I
I Llnnde 23120 I 1794.31 I&X I I !27"44'1618 Rlmker 3916 1 [1841.3] 1836 \ I 32 10.01 Poulkova 1852 I 1841.32, 1855 ~ 4 25 46.2 Paris, 15101 1845.3 I 1845 1 I 29 7.5 Cimb. An. 1847.35 1847 ' I 28 27.98 Jacob [4153] 1850.17 1850 , 27 26.19 YWlYdl 5240 1854.4 I I860 24 3.7 Edinb. An. 1855.31 I 1855 25 454
1858.21 I I858 1859.25 i 1859 1860.23 I I&
1864.26! rw 1865.26' 1865
1866.27 I 1866
1868.27 I 1868
Fdinh. An. rS6g.31 1% Radcl. An. 637 1870.24 I 1870
' I *' 594 1871.28 \ 1871 '' '' 625 1873.36 I 1873
Paris, 15roi I 1875.3 1 1875
Romberg 2726 ! 18794 \ 1875 Ten-Year 1927 ' r88o.o~ 1880
1863.191 l%3
1865.27 1 1865
1867.23 I I 8 6 7
1868.27 I I868 Ridcl. An. 748
A. G. C. 6071 I 1877.3 1 1875
I I
4 3
7
6 3 7 3
I
2
2
24 44.3 24 23.8 24 4.7 23 2.6 Z2 43.8 22 22.9 22 23.63
3 I 22 4.0 2 ! 21 44.7 5 21 24.0 3 I 21 21.96 4 1 21 5.4 I 2042.88
- - . I .I .a: I I,.-; I 1
7
3 2
STARS IN COMA BERENICES. 376
Right Awen. I8jS.
0
Declination 1875- s
h m i I2 24 2.648
14 2.714 14 2.743 14 2.704 14 1.707 14 2.448 14 2 648 14 2.712 14 2.687 14 2.757 14 2.666 14 2.523 14 2.583 14 1.491 14 2.490 14 2.520 14 1.450 14 2.511
h m i l¶ 14 4530
O ' *
27 J9 4.13 19 4.72 19 1.42 19 2.98 19 3.79 19 2.45 19 0.73 19 2.54 19 1.79 19 1.44 '9 2.49 19 0.w 19 2.19 19 1.45 19 2.18 19 2.71 I9 3.55 19 3.00 19 0 4 19 4.55 19 2.17 19 2.19 19 0.32 19 2.14 19 1.80 19 3.27 I9 3.71
s73@ O l i w -
system- atic Con.
A
'taw +a047 $0.039 t0.058
.oool to .310 $0. 163 4.d7 4 . 0 8 7 4 . 0 7 0 4.042 $0.033 +.%a 4.q1 to.043
4 . 0 0 3 +O.OlO
k0.W
-2.58
-_ S
.ooo
¶
_ _ _ _ _ 4 . 3 2 4.02 4 . 4 5 -1.62 4. I3
4 . 7 0 4 . 6 6 -0.64 -J 61 40.26 $0.18
-0.40 I 4 . 0 7 1 4 . 0 6 I
-0.05 4.68 -030 I 4 . 1 1 I 4 . 2 2 I
4 . 1 0
4 . 0 7 i
$0.02 ;
t0 .03 I , +0.08 ,
- a+ A.
Be
d+A. Ba
S
2.903 2.761 1.782 2.762 2.707 2.758 2 811 a 625 1.600 2.687 2.624 2.556 2.541 2.420 2 533 2.520 2.447 2.522
ko.ol2g S
-
1:55 4 40 1.40 2.53 2. 17 1.32 0.63 1.84 1.13 0.80 1.87
2.47
1.7 2.64 3.48 1-94 0. gs 4.50 1.49 1.89
1.92 I .@a 3.30 3 79
1.10
0.21
+~)(oA !
- Veight
p (xi 0.7 0.1 2.0
0.3 0.5 0. S
0.6
0.6 0.3 0.5 0.5
0. I
0. I 0. I
1.0 1.0 1.0
ie.0
0.1 0. I 2.0 0.3 n.,
w- G: P.
Po'( /-To; Fd
4 . 4 6 9 -0.136 --o.lJs 4 . 1 3 5 -0 0 9 2 -0.071 -0.065 4 "9
+O 02n
_-
-_ ¶
4 . 0 1 5
$0.035
-t 0.057 +o.qo
So.071 $0.106 + O . l 2 1 $0.136 $0.140
4 b 7 1
y;
_ _ + i.k +033 -+ 0.53
-.= , 0.5 j to .31 0.6 $0.22 (1.1 ! ~ 0 . 1 9 0 6 , $o.ii 0.1 , $0.10 0.6 I $0.08 0.3 I -00 0.6 I -coz 0.3 I -005 0.5 I -0.0.5 o. j
0.6
0.3 0.5
0.5 0.5
0. I
I .o
1.0
Corrected R. A. 1875. I.'=Be+ I!( Cometcd
Dec!. 1975. k'-l B6+ F,
2.434 2.625 2.647 2.627 2.615 2.687 2.746 2.596 2.585 2.715 2.659 2.596 2.5# 2.491 2.639 2.641 2 583 2.662
* O . d
a
I
4 oj -0.~9 -0.12 I
4 I 2 ' -i-o.r4 1 4 . 1 6 I -0.19 -0.24 - -03 -0.29 1.63
1.0 \ 4 3 3 1 1.47 1.0 1 4 . 3 8 a.92 1 0 I -0.40 I 3.39
I
3.21 4.93 1.93 2.96 2 4 5 1.63 0 85 2.03
090 J.95
2.45 1.18 1.73 2.57 3.39 2.82 0.86 4.36 1.33 1.70
I. ' 5
J. 10
- ao- B,
T.
I!, - Bd V8
-
I_
5
$0.19
-0.02! -0.0: t 0 . q -0 063 4. I 2 2 +0.028 $0.035 - - O . q 1 -0.03 S0.028 +0.026 $0.13 -.erg -0.017 I .O.oql -0 038
4849
-1.23 -2.95 $0.05 -04 4. s7 w.65 f1.13 4 05
0.73 + 1.08 I 40.03 1 $0.88 ' 4 . 4 1
, $0.15 I 4 . 5 9
-1.41 4 84 f 1. I2 -2.38 10.65 $0.18
' $2.01 : fo.35 1 fo .51
4.001
-- ,
; $0.80
4 . 9 4 I -1.41
~~
I Note : See Sect. 11, Systcmitic Corrections to Cambridge Annunlr.
(35)
378 KKETZ.
Resalts , 1881.01
Lknde 13134 ' 1794.32
Argclnnder 2332 1858.29 Puis, ISIIJ I 1873.3 A. C. C. 6078 j 1875.1 I
&uel (WI.)2ag 1831.31
I NOTE: According to Pariq, p. [99] this should be corrected - xd' ; I have not
WARS IN COMA BERENICES. 377
j = + 3'.02942 K= -0.01164 P = +- 0.013 L = -2cP.0125 hf= -fa0371 N= + 0.16
a - 1 s - ' I ' a
47 650 , 0.1 I 4.048 47.601 4 . 1 3 47.342 I 0.3 -0.021 41.321 +O.&
47.189 0.2 4 . 0 0 4 , 47.185 $0.224 47.430 1.0 S0.023 47.453 I-0.044
47.59 0.1 4 . 1 0 7 47.485 ; 4 . 0 7 6
8 I S
C 0.0273, 1.2 -0.0016 , f 0.0011 764
~~
done so, however, for obvious reasons.
ANNAIS N. Y. ACAD. SCI.. XII, Februw 17, rgocrz4
(W)
378 KRETZ.
Anthorlty.
-- LPlandc 23136 Cunbr. An. Dreycr 141 7
A. G. C. 6079
PtruIt8
PdS, 15114
~ iEpod Dateof I of
Obi. Cat.
STARS IN COMA BERENICES. 379
/= + jm.o3o71 x= - 0.01121 P .- + 0.013 L = - Icr*.orq hf= + 0.0371 N= +- 0.16
1875. I ! A -___-
h m I I--; :a 14 48.624 I $0.253
? - - - - - ~- 1 0 , ! 2543 6.b 1 -2.29 I 43 11.70 -1.28
1 I _ - j 1 . . -
48877 48.099 47.4eg 47.652
, 3.40
1O.AZ
0.1 , - 1.179
1.0 ' + 0:250
8.1 - e.0166
0.1 +I;&
1.0 - 0.334 0.6 I + 0.121 1.0 . + 0.129
1
- . - . . --
0.3 + 3.74 0.3 ' + 3.45 43 10.37 1-1.59 I 8.78
43 14.90 4 . 2 2 X4.68 ; 2.0 - 0.54 43 13.70 I $0.28 13.98 0.6 I - 0.93
~ 43 14.90 I .m I 14.9 , 1.0 - 1.59
47.781 47.770
a * 0 . d
14.20 14.16 12.23 14.14 13.05
4 . 0 2 1 t 0. '34 4 037 --a&
15e1
-0.54 -0.9 +1.43 4 . 4 8 50.61
._
11.11 +o. 1 c
KRETZ
Lalande 23x32 Cambr. An.
,I 'I
" I'
Pnris, 151m A. G. C. 6 d l r
Resalts
Lalrndc 23x32 Gmbr. An.
.-.
,' a '
*' I S
'I I ,
Pa* rg12o A. G. C. 6081
Results
STARS IN COMA BERENICES.
f = + 3'.m976 K= -0.011 16 P= + a013 L = - d t . 0 l q M= + 0.0378 N= f 0.16
381
' a , , , 1 25 41 31.22 -2I(@ I 41 27.91 -1.19
i 4 I 29.71 -1.26 ' 41 29.99 -1.28
41 30.11 -1.59
1 41 2 7 . 9 .a 41 2840 -9.22
a
9. I34 9.328 9.153 9.100 9.142 9 . h
0.3 4 . 0 5 0 0.3 4 .046 1.0 +o.a48 1.0 to.058
9.190 9.118
*O.O008 I
d 7 8 26.68
2853 0.1 +d.;g
28.71 , 0.3 $0.05 28 76 -0.83 28.45 , 0.7 sO.0.j 1 28.50 I -0 .57 28.52 0.7 +o.q 98.56 4 . 6 3 28.18 1.0 4 . 0 7 28.11 i 4 . , 8 27.90 1.0 4 . 0 9 27.81 , $0.12
26.62 I 1.0 $0.06 +-1.25
+o. 11:
+o.oqs
1410
4: 85
4 , 0 2 2
382
7 8 '
12 I I 9
% 10 18
19 12
20
21
KRETZ.
Pond 50; '
Taylor 5673 Paris, 15141 Gilliss 6 q Rilmker 3932 Edinb. An. Poulkova 1859 Robinson 2658 Seven-Yeu 976
Paris, 15141 SplTord 1% Bmxellcs co62
Y m d l 5253
8 B. D. 98°.p387 - 1% Coma Berenlca (d CEA8Eh-R. A.
15 23 34
5 29 35 35
I /Epoch ' Dateof I of Autborlty: cat.
I
Rot&< &I , Nine-Year 1140 Madror An. 466, Ten-Year 1933 I Midrm An. 539 A. C. C. 6osg , Green. An. 777 " " I552 '
Z I : t . T
1873.8r I&& 4 I 1628.3091 .ooo 1879.28 1 1879 3 162507 .w> 1880.0 1875 I 3 16 13.22 +a& 1888.12 I I888 3 1652.493 .ooo 1894.45 1894 1 3 I7 105601 .oQ)
_- - I Undlcy 1658 1755.4 I 1755 4 d'Agelet 2925 , 1794.38 1800 3 I.nLndc2316g 179.31 , I800 2 Piazzi 59 1800.68 I 1800 6 Z. Gt. Soec. 412 1821.74 , 1826
- r5.115 - i a o g i ,
- 39.294 1 - 57.422 1
-
13 IZ z6.q s 1338.83
. .__ . - r n #
orcoo 1+6 3.656
--u.oIo It3 47.08i 4 . 0 2 7 t 3 47.081
4-0.001 If3 47.081 4 . 0 0 1 +234.341
183i.07 ' 1830 13 57.06 I +o.oOI 14-2 16.168 [1832.7] 1835 I 15 14 12.19 -0.004 f 2 1.026
1840.29 1840 I 1427.0391 .ax, +I 45.888 , [1841 3 1836 i 3 14 15.1og: + o . d +I 57.598 1842.28 1842 I 3 1433.37 ' .a tI39.833 1842.32 1846.64 1859.3 1863.3 1863.7
10 I
1840.0 1845 I 7 1442.43 1-0.008 I t 1 30.751
1865.41 1871.17
1855 I 4 15 1 z 6 j I .oco 1840 I 4 14 27.25 ' to.011 1860 6 1527.86 1 4 . 0 0 3 1860 3 ' 15 27.83 +0.006
1865 7 I 15 43.016 to .001
1875 16 16 13.2338 .ooo 1875 4 16 13.21 I 4.001 1875 8 16 13.20 I ,000
I860 I 21 , I5 27.79 I s0.d I865 I 3 , 15 42.91 I *0.011
t ' + 1 0.490
'+ 45.363 + 45.363
t 30.239 , j+ 30.239
I t 1 45.888
I+ 45.363
- 1 , i z
STARS IN COMA BERENICES. 383
/= + 3'.02333 K= - a01158 P= + a013 L = - rq.* M = + 0.0398 N= + 0.16
Right A x .
b m s. 12 16 13.216
16 12.921 16 13.122
16 13.212
16 13.254
16 13.171
16 13.174 16 12.927
' 16 13.111 16 13.203 16 13.130
16 11.210 16 13 149
16 1i.199 $0.03; I6 13.159 I t O . 0 5 1 16 13.256 ! + o . d 16 13.160 $0.044
16 13.209 i +0.042 16 13.233 t0.w
16 IXXU I -0.m.3
. .. -..-, I ~ _ , - _ I a I
13.216 0.5 13.586 0.2 13.174 0.1 I 13.375 0.3 I
13.215 2.0 I 13.212 1.0 13.154 0.5 13.221 I 2.0 12.878 , 0.1 I 13.148 I 0.3 13.191 0.3 I 13.217 0.3 13.207 2.0 I 11.231 I 0.6 I
13.189 I 2.0 I
13.210 3.0 13.262 2.0
13.237 3.0
13.197 4.0 ,
13 204 ' 1.0 ' 13.251 ' 2.0
I3 220 1.0
s i 4 . 0 5 2 I 4 . 0 3 8 I 4.033 I
4 . 0 1 8 1 4.014 '
4.010 4.010
4 030
4 or4
16 1j.214 ! So.& 1613.261 +o.o18 , 1j.279 ' 0.7 , + o . q i6 13.194 1 +o.orci I 13.204 1.0 + o . q 16 12.978 +a018 12.996 1.0 $o.oro
16 13.199 $0010 13.209 ' 1.0 $0.014 16 13.138 I + O ~ O I 1 13;148 , 1.0 j to;or7 / 16 13.228, I .OQ, 1 13.228 , 1.0 I So.oro j
h m n 418 18.40% I fooos2 1 C 0.0062 8¶.@ ; 4.00$$ 1 f 0&02 I 1Ol191
13.198 , +o.ora
13.211 -0.001
13.182 +0.018 13.180 +0.030 13.210 .cca
13.212 I +.a12 13.265
13,140 s O . 0 7 0
12.868 +0.341 13.139 + O * g I
13.207 +O.OoS 13.233 4 . 0 2 3
13.210 I":%
13.213 4 . 0 0 3
13.238 4.028 13.223 4 . 0 1 3
13.006 +0.204
'3.165 I + O . W
3R4 KRE'I'Z.
8 B. D. 96@.$951- 1% Coma Berealces (d OBAEP).--Decl. alffl 12 16. 13'.22 p,-0~.0017 *Iff b a60 33' 2 9 . 7 R W.d -
i w-
j d I"
I 4 3
6 7 8 I2 9 P 16 t o I8 21 20
2
27 23 26 25 98 34 34 30 99 35 35 -
" 539 Tea-Yenr 1933 A. G. C. 6.ag Green. An. 777 " " 1552
5
5
3 5 4 3 6
13
2
kcl I nrtlon at Epoch of Cnt.
-_ 2 6 O 7 i 261s
57 256.2 57 27.1 57 25.5 49 24.6 47 35.9 45 44.34 42 25 9 45 24.34 43 25.1 39 4.6 44 4.37 37 24.40 35 44.46 37 25 9 32 24.01 33 24.18
32 24.3 32 2 3 4 31 13.5 31 4.4 30 44.14 31 12.7 28 3.56 26 3.60
32 23.8
-I----- I # oloo -40 2 . 3
t 0 . q -35 0 . 9 S 0 . 0 3 -25 0.9
.OO -25 0.9
4 . 0 1 -15 a30 f0.W -13 20.23 t 0 . q -10 0.12 4 . 0 3 -13 o n
.m -11 0.1s
.03 - 6 4 0 0 4 -0.08 -XI 40.17
.m - 5 0.02 4 . 0 2 - 3 10.00 4.q - 5 0.01
4 . 0 1 - I am
.OO -17 0.39
- .oo
.m
.m
.m
- - -
STARS IN COMA BERENICES.
.
f = f 3 '-02333 K= - 0.01158 P = + a013 L = - If..9980 N= + 0.0398 N= + 0.16
2 1 . 9
23.17 23.69 23.29
I
32 15-39 32 26.23 32 24.60 32 24.21 32 25.59 32 24. '3 32 25.82 32 24.09 32 24% 32 24.56 32 24.12 32 24.38 32 2444 32 25.81 32 24.01 32 24-17 32 23.80 32 24.30 3' 23% 32 23.49 32 24.39 32 4-12 32 22.67 33 93.50 32 23.49
Y 0.00
-1.41 -2.63 -2.63 -1.04 -1.90 4 . 8 4
- d + R .
Ila
- Weight
P 0.4
0-3
__
0.2 0. I
2.0 1.0
386
0.5 t 0 . 0 3 0.7 +0.03 0.3 ! S O O I 0.3 t o m 1.0 to.02 0.3 * I +o.oI 2.0 so01 0.3 .a 0.6 4 . 0 1
3.0 I -0.01 3.0 4 . 0 1
4.0 4 . 0 1 I 0 4 . 0 1
1.5 j 4 . 0 1 0.7 4 . 0 1
4 . 2 9 I 24.10 1.0 4 0 1 SO.08 24.20 I 3.0 1 -0.01 .a 1 2267 1 . 0 4 . 0 1
+0.09 ' 23.59 ~ 2.0 4 . 0 1
$0.09 , 23.58 I 2.0 1 4 . 0 3
i 24[;6 4 . 5 9 24.06 4.09 23.67 +0.30
I 22 03 S1 .94 23.21 1 +0.76
I 23.31 $0.65
238r 10.16 I 23.85 40.12
23.72 4-0.25
25.40 -1.43
24.56 4 . 5 9 23.31 kC.66 24.30 4 . 3 3 24.41 4 . 4 4 25 6 -1.72 24.26 -0.29 23.70 +0.27 23.57 -1-0.40 24.29 4 . 3 2 24.14 4 . 2 7 23.19 I -1078
I 24.09 -0.12 24.19 -0.22 22.66 +1.31 23 57 -k"J40 23 55 , +0.42
386 KRETZ.
~ e l a n d e r 1338 Tixelles 5063 . G. c. 6 o y omberg 2742
B~sollr . _ _ Dbinson 2659 1853.68 I 1830 rgclandcr 2338 1858.12 11155 vxellcs 5063 1868.31 1865
Dmberg 1742 1877.6 1875
R*Oltlt8 1814.43 1 1635
. G. c. 6090 1877.3 1875
I ! I1 15 13.77 1s 43.96
4 1 16 14.27
11 ,19 1U l4.!B3 h m a
-
: i I
11 7
0.mO ' + I 0,513 .030 + 30.156
.mO I 0:oOe - ~-~ , It d.'m -11 4038 .oo - 640.16
.oo - 1
.oo -320.06
- - i .oo +d&
STARS IN COMA BERENICES. 887
f = + 3'.02501 K= - 0.01157 P = -1 0.013 L = - 2d/.CO39 M= + 0.0398 N= + 0.16
388
.ooo
.ooo
.ax
.ooO
.m
.Qx,
KRETZ.
+346.861
+130.666 +l o.gr1 fI45.787 + 21.146
t Z 3 1 . 1 6 9
10 B. D. W.W3 (18 CEASE).
.oo
.oO
.w
.GO
.aJ
I
u
3- 03 - 0 6
4 -
3 1 5
11 8
10
33 1 1
3.3 16
29 25
20
3
5 8
33 33
13 33 16 33
'9 25
1
10
? I
20
I
-1320.09
- 339.95
- 3 19.95
-11 40.05
- 119.97
-7 -.-- I._.__ Piorri @-a--# I - I 7-v a- ---- I _- 1804.461 I B ~ 8 I 13 59.90
Besxl (W,.) 348i 1831.31 I 1815 I 15 15.38 Paris, 15178 , 1838.9 I 1&5 3 16 16.30 Tnylor 5688 183 .8], 1835 6 1.5 46.16 Robinson 2663 I 'I~,$.JJ, 1840 Radcl. An. 750 1868.36361 1868 DNXCIICS 5068 1869.87' 1865 Radcl. An. 595 I 1871.36/ 1871 Pnriss 15178 1871.7 I 1875 Ynrnill5i69 1876.0 , 1860 A. G. C. 61ai 1878.3 1875
I878.4 I875
Ialande 23207 Pirui 68
2 I I I7 IZ 25. . I% i 17 16.71 2 , 1734.88
3 17 1.60 5 17 46.97
I I
1794.31/ 1800 I 16°5i423 I 1800 9 . 5742.2
Beuel ( W , . ) M ~ 1831.311 1825 I I 49 16.6 Tnylor5688 $1838.8) 1835 1 8 ' 46 1 . q
Robinson 2663 1853.04 I&O 5 ! 4421.84 Rndcl. An. 6qi , 1864.31. 1864 I 2 36 21.81
$1 11 750 1868.30 1868 1 I 3458.53 I B ~ x e l l e i 5 0 6 8 1868.311 1865 : I 36 1.48 Rndcl. An. 571 I 1869.301 sag ~ 1 , 54 40.53 ~
' I 595 1871.36' 1S71 2 34 1.30 I ~arikr5178 ~ 1871.7 I 1875 i 5 j 31 41.5 Rndcl. An. 714 ' 1874.21 1874 z , 31 59.55 Yarnall 5168 1876.4 I 1860 2 37 41.1 ,
A. G. c. 6100 1 1878.3 j 1875 I 4 ' 32 40.6 '
Romberga751 1878.4 1875 , 4 I 3140.7 ,
Ran118 i 18tl7.70i 1875 i 49 I !M% rdhl I i
STARS IN COMA BERENICES.
I= 17 47.044 I7 46.764 17 46.549 17 46.966 17 47.071 17 47.617
389
$0.003 -0.156 -0.080 4 . 0 1 8
Right k e n , 1875.
0
1 - tO.253 47.297 0.1 , 4 . 1 4 2 $0.253 47.017 , 0.3 -0.121 S0.122 I 46.671 : 0.1 , 4 .068 $0.047 , 47013 1.0 -0 .052 -0.058 ; 47.013 . a5 -0.051 $0.068 47.155 I 0.1 4 . 0 3 4 -10.033 47.039 0 5 $0.006 -to.o44 46.974 0.7 +o.- 4 .010 . 46.943 , 0.5 $0.012 +O.Oql ' 47.012 2.0 +O.OIg -+-o.o31 I 46.951 0.6 +o.on .OM 46.970 1.0 4-0.026
-0.003 I 46.847 2.0 $0.026
3241.79 ' 4 . 8 2 I 40.97 3241.85 ! 4 . 8 2 41.03
' 3241.52 ~ 4 . 0 3 41.49 1 12 40.56 ! -0.40 40.16
: 32 38.56 S0.02 38.58
I 3241.32 I 4 . j ~ 41.01 ' 12 d1.W - 0 . 2 2 41.28
47155 46. W 46 603
' 46.961 ! 46.962 ' 47.121 ' 47.045
46.9(13 46.955 47.027 46.973 46.995 46 873
_ _ . ,I 1
0.1 , t l . 1 0 42.ro -1.49 4-0.95 $0.55 +0.43 S 0 . 2 2 $0.05 -0.01 -0.01 -0.02 -0 .05 -0.07
3240.60 .oo 40.60 1.0 ' -0.16
- . - 3239.56 4 . 0 3 , 39.53 -0. lo 3241.14 1 4 . 0 9 41.05 I 06 I 4 . 1 3
3240.70 , .M) , 40.70 2.0 -0.16 0 I l l Y '
! i 8B89 40.79 1 ko.127 1 & ii138 1 8.8 i +0:015
~ 39.85 $0.76 40.09 + 0 5 2
I 4060 I +O.OI 41.19 1-0.58 4 I d 4 . 4 7 38.57 $204
I 41.48 4 . 8 7
41.21 4.60
40.14 t0 .47 40.96 1 4 . 3 5
4054 I
I 3943 Sr.18 I 40.91 4 . 3 1
4044 '$0.17
f. 0'0075 1 $888
390 KRElZ.
11 B. D. BQ0.$s14--1af Coma Berenlcea (19 CEA8E).
- 2 3c; z ; 0 % L - I 4 3
5 7 8
2
10 I 2 I 1 9
16 32 18 19 21 22
a7 34 25 29 34 30
I 4 3 2
5 7 8
9 16 92 ' 5
I8 ' 9
'7 18 14 15 19 54 P
I2
10
21
-
Arthorlty. Date of
Obs.
t
1755.8 1783.37
DCKUCI ( IT,.) 3311 ioju.5r Pond 502 I 83 I .67 hylor 5 6 1 ,[1832.3] Robinson 2665 ; 1836.05 $sl 15182 1838.0 . ~ i l l i s s 60s 1840.79 RUmker 3950 ![IQI] 'odkovn 1862 1841.34 Edinb. An. 1842.28 kven-Year 977 I 1854.3 I'aris, 15182 1859.8
Xord 195 1865.41 i0ger.i 534 1872.6 h d n s An. 468 ' 1878.39 tomberg 2754 1878.4 4. ti. C. 6102 1878.6 Mndros An. 541 18j9 31 ren-Year 1935 1sS3.24
BIUXCIICS 5072 ' X861.96
Results llM5.01 - . ..
Imdley 1661 1754.2
alnnde 23211 1794.31 'iazri 70 1801.28
'ontl 502 1831.~6 'nylor 56qr [1831.5] 'ark, 15182 1838.0 lilmkcr 3950 [ i f411 'oulkovr 1862 1841.34 Idinh. An. 1842.30 lix-Year 802 1849.3 tobinson 2665 1849.67 leven-Year 977 1854.3 ;
: o ~ r r s 534 1872 6 Lespighi 686 1875.31 faritas An. 468 187S.39 :omberg 2754 187S.4 L. (;. C. 6102 187f1.6 I d r w An. 541 1879 31 'tn-Year 1935 1883.24
I'i\grlCt 2931 1183.37
kS5Cl (\v,.) 351 1830.32
)oris 1g182 1860.8 l f l lXCl lCS 5072 1862.77
Epoclii KO. of of
Cot. , Obi
T n -__ -
6 !El * 1- - .'+ .J.'J , -'-JJ ' I a*"."-" I&O I 14 15.25 i -0.011 1$3 46.620
1825 2 15 31.10 ' fO.011 1+2 31.005 1800 7 ; 14 15.18 1 +0.003 +346 .6~ ,
1830 6 15 46.49 I +0.003 '+2 15.891 1835 1 2 , 16 1.42 I 4 . 0 0 5 l+2 0.780 IQO 7 16 16.44 , --(r.d +I 45.672 1845 9 , 16 31.57 1-0.014 1i-I 30.567 I& 13 16 16.470 +0.002 .+I 45.672 1836 , 7 16 4.3591 $0.010 14-1 30.758 1855 I 4 17 1.82 .wo . + I 0.367 1842 3 16 22.55 i 4 0 . ~ 1 !-+-I 39.630 1860 i 3 ' 17 17.01 -0.017 ,+ 45.271 1860 2 17 16.80 I ,000 :+ 45.271 1865 ~ 3 1731.97 --o.c06 It 30.178 1865 6 17 32.035, + O . W ~ I+ 30.178 1875 12 18 2.181 ; So.001 - 1875 , 4 ' 18 2.16 .ax, - 1878 3 I 8 11.08 t O . 0 0 1 '-- 9.051
1875 4 18 2.16 $0.007 I - I8j9 2 18 14.24 t O . 0 0 1 .- 12.068 I,% 3 ~ 18 17.234 . W O .- 15.084
2 X
2 14 6 4 8 4 3
5 6
9 ,
2
2 1 2
12 lo 3 4 4
3 2
h m s 18'15 121 11318 9.183
-. -. . 0 , .I
f 2687 35.1 72 31.4 72 32.5 72 34.0 64 10.3 62 33.3
57 30.6 60 32.28
60 51.91
54 11.m
- . - _ -o:o!o
,I ' , 0.00 -40 4.42
-4.35 1-25 2.14 -0.12 -25 2.14 to .03 '-25 2.14 $0.11 ,-1641.18 4-0.02 '-15 1.02 -0.07 -1.3 20.86 *.I5 ,-I0 0.59 +O.IO -13 O Q .a - 640.35
.oo - 8 20.46 38324 I +O.oI -11 0.67
59 11.46 $0 .20 -11 40 73 5230.93 +O.O5 - 5 0.25 5230.9 I ~ 0 0 2 - 5 0.15
47 3091 -0.01
5 5 5 1 48 i
5051 47 1-005 - 3 20.15 - 47 30.i3 .oo -
47 30.3 , i-0.08
4632.2 , to.or f I 0 . q ' 4731.3 .a,
45 50.62 .M) 1. I 40.06
- - I 46 12.0 I .OO L I 20.05
STARS IN COMA BERENICES. 391
f = 4- 3 '.01718 K= - 0.01156 p = + 0.014 L = - m'/.0132 M= f 0.0432 N = + 0.16
Right Asc. I 1875. System-
d C COK.
1875. i s A -__ h m i I2 I8 2.268
18 1.737 18 1.859 18 1.803 18 2.116 18 2.384
I8 2. 104 18 2.123
18 2.127 18 2.187 18 2.181 18 2.164 18 2.071 18 2.142 18 2.214 18 2.181 18 2.030 18 2.1Q 18 2.167
18 2.195
18 2.144
' 4731.74 I 4731.02 I 4730.93
47 30.73 47 30.67 47 31.27
' 4730.90 47 30.23 47 31.25
' I 2.268 ' 0.6 -0.050 2 . q O 0.2 I -0.036 ' 2.113 I 0.1 I -0.030 2.057 0 3 I -0.027
2.367 0.6 -0.012
1 8
2.272 I 0.2 -0.012
2.138 0.5 -0.011 2.172 0.5 ' - 0 . q 2.170 , 2.0 -0.m - , 2.0gi 1.0 2.166 0.5 2.246 2.0 2.169 0.3 2.251 1.0 : 2.122 0.7 ! 2.186 1.0 I
2.185 3.0
2.167 1.0 2.191 0.7 2.160 1.0
2.220 2.0
2.048 i 1.0 2,157 '2.0 :
4 .007 4.0g -Og ~
- 0 . d '
4-0.002 S0.003 I to.005 ~
4-0.W)
.ooo
-'O.Ol2 ~ 0 . 0 1 2
+o.o12 4-0.012 I $0.014
-1.12 4 . 2 0 4 . 8 2 4 . 0 9 4 . 2 8
So. 26 4 . 0 2
+0.40 -0.29
-1.38 i7.53 0.2
! 473r.89 1 -2.60 I 29.29 0.3 : 47 29.23 -0.22 ~ 29.01 0.2
47 30.98 , 4 8 0 I 30.18 0.5 47 29.86 ' 4 . 4 5 , 2941 1.0
, 47 31.54 -0.30 ~ 31.24 0.5 4730.65 4 . 0 2 30.63 , 2.0 I
30.62 ' 0.3 30.82 I 0.7 30.11 0.5 30.64 2.0 i
30.39 0.7
31.16 3.0 30.63 1.5
I 47 30.38 1 .m , 30.38 I o ~ 47 32.05 -0.29 31.76 0.7
47 30.68 , $0.08 30.?6 . 1.0
47 30.24 -2.60 I 27.64 0.1
47 32.30 1 -1.p 30.40 * 1.0
51.25 0.7
32.96 1.0 , 4731.30 , +O.OI 31.31 2.0
' ,' i ~ 4 i 3 i . i ~ C;:d7 c 0.107 Si,a
i I . 2 6 ~ 1 . 0 7 I
+ 0.95 t 0.46 - 0 45
t 0.33 t o . 28 +o. 27 $0.26 ,
+o. I4 -to.13 -1-0.05 -0.06 -0.09 -0.26 -0.30 -0.36 -0.36 I
-0.36 -0.37 -0.44
S O 4 4
-oh
I
2.118 2.034 1.083 2.030 2.260
2.355 2.127 2.163 2.161 2.088 2.159 2.239 2.163 2.25 I 2.124 2.189 2.125 2. Igq 2.06a 2.169 2. I79 2.203 2. I74
CO.om2 #
32.k 28.79 28.71 30.24 29.47 30.85 30.62 29.74
- a0-B
do-B
la _- V8
1
4.031 +O. 14; t 0 . q 4-0.15 4.qr 4 . 1 7 , + 0.051 +O.OI( +0.02. + O . W so.02; 4.05; +O.OI! 4.+ +0.051 4.00; 4.04:
t o . 12: to.01: fO.COj
f 0 . d
lkml
-1.70 + 1 .9 12.02 -1-049 +1.26 -0. I 2 +o. I I t0.99 4 . 7 9 4 . 1 7
-0.01:
-0.021
. ,
30.24 -0.49 30.69 I +o .q 30.33 f o . 4 0 31.16 4 . 4 3 30.90 4 . 1 7
31.60 -0.87
30.02 j -to.71
* d.'0035 , 1W3
30.33 +0.40
30.95 , 4 . 2 2
31.39 4 . 6 6 30.32 t0 .41
392 KRETZ.
la B. D. $(l0."4+68 Coma Beredcea (49 OIIASE).
I I Epocl
bate of of Aufkorlti. obs,
d'Apdet 2933 Lnlnnde z p 1 4 LPos. hlcd. 1417 l'oulkova 1863 Ciinb. An.
Hrurelles 5073 Drcyer 1423 Paris, 15186 Rdmberg 2755 ' A. G. C. 6104
Paris, 15186
1785.25 is00
1818.5 1 1830 1841.32, 1855 1841.32 I 1842 1863.3 I 1860 1871.jo I 1865 187330 1875 1874.3 ' 1875 1875.3 1875
1794.31 I Is00
1876.4 ; 1875
I0'.24 p, o'.aa 33".3 p', cf.00
- I
0.000 .ooo .aa .aa .ooo .aa .am .aa .aa .ooo .aa
., . . -. . . _ '
STARS IN COMA IIEREZI'ICES.
18 9.860 18 10.394 18 10.351 18 10.42o 18 10.301' 18 10.205 18 10.1~0
$0152 10 1 1 2 ' 0.2 , -0.107 : 9.905 + o q $ 10.438' 2 . 0 : 4 . ~ 9 7 I rt8.34r $0.059 10411 1.0 4 . 0 5 6 I 10.355 - 0 . ~ 5 10.345 ~ 1.0 -0.053 10 292 $0.051 . 10.353 0.3 -1-11.014 10..467 S0.w , 10.249 I 1.0 + O . f y I I 0 190 + o q r 1o.1b1 1.5 -!-0.046 10.327
393
1631.77 1633.19
1633.06 1633.87
1633.30 I 1633.m I 1632.70
- %-E,
'j0 - d va
-0.19 +0.41
$O.Ol
$0.01
-0.04 -10.0 il $0 02
0 l l
-1.17 4 . 4 0 $0.68 4 6 6 t 0.04 $0.04 + 0.06 4 04 t 0 . m -0.13
0240
V.
I
--o.CIZ 4 . 0 3
4.(15'
-0.OII
.~ ,
-1.04 31.73 1 1.0 1 t o 4 8 32 21 4 . 0 2 33.17 ! 1.0 . t o 28 3345
-0.02 33.04 I 0.7 ' -0.19 32.85
4 . 0 1 33.r9 30 -0.16 iz-93
-1.18 32.59 I 1.0 I - t 0.16 32.85
-0.11 33.03 , 2.0 4 2 5 x.83
4 . 1 7 31.97 , 1.5 -0.28 32.69
394 KRETZ.
A few observations of other stars were found. I have re- corded them here for the sake of completeness. They were not reduced, however, as the resulting positions and proper motions would be entitled to but little confidence, and would be of no value whatever for my purpose.
ADDITIOHAL STARS. I No. I 1 ( B l g b t l ~ c . ~ No. in Authority. Epoch. at E ch
See. I. of G. ;
The above table is not intended to be exhaustive ; it includes only such stars as were found in more than one catalogue. A number of stars, the positions of which are given in the Astro- nomische Gesellschaft Catalog, and which fall within the limits of my zone, are not mentioned here for the reason stated.
Catalogue of Beenltn.-For convenience, I have collected into a table the final positions and:proper motions deduced from the data given on the foregoing pages. The quantities in this table all refer to the epoch 1875; the corresponding quantities for the date of observation &, will be found in the Star Tables under the heading " Results." The columns in the " Catalogue " require but little explanation. They are as
(54 )
STARS IN COXA BERENICES. 39b
follows : Col. I shows the Name or the B. A. C. or B. D. number of the star ; 2 and 3 the Right Ascension and Probable Error in Right Ascension for 1875, respectively; 4 and 5 the gcorrrttn’c Precessionmd Secular Variation respectively; 6 and 7 the Proper Motion in Right Ascension and its Probable Error; 8 the mean Date of Observation, T, ; and g the Number of Observations from which the results were obtained. Columns 10 to 17 have the same significance as 2 to 9, but refer to the declination. Column 18 contains Chase’s number, and rg the number as- signed by me to the star in question. It s’hould be mentioned, that the declination of B.A.C. 4 1 5 3 as here given does not in- clude Respighi’s observations of that star, which were acci- dentally overlooked, as the omission was not discovered until all the succeeding calculations had been made. The error in- troduced thereby is so trifling, however-being only 0“.03 in the position and o”.001 in the proper motion-that I have not deemed it necessary to carry through the correction. The con- stants of the plates, to compute which these positions are used, would not be changed by doing so. I have, therefore, left the quantities as they were used in the succeeding part of the work, although, of course, the corrected position including Respighi’s observations would otherwise have been preferable.
396
12 e. C o w B. B. D. 26°.r338
KRETZ.
16 11.893 +o.o146 j 3 0150 0.0116 I +O.oooL 17 (6.915 + O . O I ~ . -3.0205 0.01 1+-4,@3!M I--
Catnlogo of Twelve Stars of the Cluster in
&0.0032 ~ . o o o s
Mean eqalnox of 1A75.0.
h m s I 5 ' I a 1% 1% S.800 S~0.0146 3.0356 0.0112
12 4tTll fo.0136 j 3.0349 o.oIao 14 1.113, k0.0134 3.0312 0.0119
14 a.5~0 f o . o I ~ S I 3.0300 o .01~2
11 47.3117 Co.0~73 3.0294 0.0116
15 9.118 Co.oiy5, 3.0298, 0.0112
14 41.581 C0.0174 3.0307 0.0112
13 1. Comr B. '
is 18 9.11% i C - o . d t 3.0192 0.0116 1 -0,0045 ' &0.-2
H. I 18 10.38R ' &o.oior , 3 m ~ 0.0112 1 -0.0039 I ~t0.0004 I
Dott I No. of of Ob. I Obs.
1878.63 16
._
1883.61 , 49 1BR1.8BI 88 1880.80 I 48 11181.01 ' 0 1865.34 16 1858.;. I 19 18.i9.8f I 161 i~rs.ia i 11 1&15 49 1855.01 1 191 1833.95 I 41
STARS IN COMA BERENICES. 391
Comn Bercniccs froiii Mcridiun Observrrtiom. Epoch 1875.0.
PART 11.
MEASUREMENT AND REDUCTION OF THE PLATES.
I. The Plates : Description and Measurement.
Description.-The photographs of Coma Berenices were taken with Rutherfurd’s large telescope in the years 1870, 1875 and 1876. They differ in no particular from his other star plates. There are always two images of each star, obtained by stopping the driving clock a few seconds after the first expo- sure had been made, and then starting it again, leaving, mean- while, thc platc in position so that another impression could be made. A third image (or trail”) of the brightest stars is USU- ally found at the distance of about 35 mm. from the second image, obtained in a similar manner, except that the clock was stopped for a longer time than in the previous case. These trails were intended to give an independent means of orienting the plate. I have not used them otherwise than to place the photograph correctly in the measuring machine; for Dr. Schlesinger’ has shown that no reliance can be placed on the trails for other purposes.
The plates arc by no means uniform in quality, some of them giving a much sharper picture than others. Especially notice- able, and at thc same time rather annoying, is the elongation of thc imagcs on some of the photographs due to irregularities in the dock, which failed to keep pace exactly with the diurnal mo-
t ‘I ’The P m ~ p e Group. hlensurement and Reduction of the Rutherfwd Pkoto- Fnpha ” by Frank Schlesingcr. Annals of the N. Y. Academy of Scicncea, Vd. X. The page referred to is 282.
( 5 8 )
STARS IN COMA BERENICES. 399
tion of the stars. Then, again, the number of stars visible on the different plates varies greatly. This is the case even when the exposures were taken on the same night, although these were always of the same length, namely six minutes. The larg- est number of stars is found on the plates,taken in 1875. In spite of their variable quality, however, I decided not to omit any of them, but to measure or. each one all the stars that could be plainly seen. This was necessitated by the fact that I had but three plates of the early date; and again but five taken in 1875 and showing a fairly large number of stars. None of these could well be rejected without seriously injur- ing either the proper motions in the one case, or the positions in the other. But thereby the standard of excellence was placed so low, that none of the others could legitimately be omitted. The result is, that some of the stars show quite large residuals, due to the difficulty of measuring hazy images. Es- pecially is this the case for stars just on the limits of visibility, and for those lying near the edge of the plate, where radidl dis- tortion becomes very marked. On the whole, the cluster is not well adapted to photographic measurement, as it is very scattered, and the range of brightness is large.
The origin of co6rdinate.s was taken to coincide with star 14 ( I ze Coma: Berenices). For the reduction it is necessary that the point be known approximately where a line from the optical center of the lens strikes the plate perpendicularly. Ruther- furd always so adjusted his instrument, that this line should pass through the image of some bright star, no. 14, in my case.
I subjoin TABLE I, giving all necessary data regarding the plates. The column I ‘ Date ” shows the date, and that headed
Sidereal Time,” the time of exposure. This latter is the’mean of four instants, namely the beginning and end of the first, and the beginning and end of the second exposure. Next follow the reading of the barometer, together with the attached and external thermometers. The 7th and 8th columns refer to the telescope, the former showing the readings of a thermo- meter in contact with the tube, and the latter the reading of a micrometer head at the eye end. ‘This latter quantity depends
(69)
400 KRETZ.
on the distance of the plateholder from the object glass, and may bear some relation to the scale value ; a question which cannot be settled, however, until many more of the Rutherfiird photographs have been independently reduced. In the last column will be found remarks regarding the quality of the plate, and the number of stars measured.
VII VIII'
I X X XI
XI1 (111 XIV
TABLE I.-THE PLATES. O b w v n t o ~ ol I.ewis hl. Rulherfurd, h'ew York City.
I&. = 40' 43' 4W.5 . Img. = 4' 55~.56%1 W.
18;s. June 4.1 1 1 4 3 I Z 3"' o 187s. June 4.1 15 1302 jo.25fi 1876. Way 24.l I I 27 13 ,y1 136 rY76. May 26.; 13 55 $3 30 136 1876. hIay %.' 14 J I 5 2 . 30'1.36 1376. alny 26.! 14 53 32 , 3) 136 1876. May 77.' 1 3 20.38 3n.oY6 rS7h. May 27.; 1351 52 30.086
Expures . , Atmosphere. ! 'I'elescope. . -
No. 1 Date. 'Sid. Time.' Uar. ,A::r, jl'her. IT ~Pocus
6 ) 56 60 ~ 7 7 60 56 60 6Y 66 70 6 i , 66 70 59 55 59 55 60. 59 55 60 59 55 60 66 61 65 66 ~ 63 65
7.7 7.6 7.6 7.7 7.7 7 7 7 7 7.65 7.65
Good Poor; 16 s t m .
V . G d ; 14stus. G d : 16st.n.. (hod; 16stan. Fair; 1 6 1 ~ 1 ~ Poor: 15 SIM. Fnir ; I n run.
ti& ; 23 stun.
_ _ .- . 13 stus. , 17 stan. Is shn. 20 rtm. 18 Jtm. 22 stm.
Measnrement.-The fourteen plates were measured during the winters I 8+1 897 and j 897- I 898. and one of them in the fall o f 1898. During the first year. three observers were en: gaged in the work : Mr. Wi!liam I I. Hays, then graduate stu- dent in astronomy, Dr. Schlcs'~i:er. and myself; after the spring of 1897 only the latter two remained. I n 'this conncction, I wish to thank the two gentlemcn, Me.;srs. Hays and Schlesinger, for their interested and arduous services rendered in my behalf.
The older Repsold mwuring machine of the observatory was used throughout. A full description of one of these ex-
( H O )
STARS IN COMA UERENICKS. 401
cellent instruments will be found in Dr. Scheiner’s recent work “Die Photographie der Gestirne,” p. 148. I shall say only a few words on the subject : The essential features of the machine are a strong iron frame, to which are attached a circular inov- able plate-holder, and two parallel fixed bridges, one bearing three microscopes and the other a straight scale. The holder is capable of rotation about its centre, and of motion in a direc- tion perpendicular to the bridges. In this motion it is guided by an accurately straight steel cylinder, which is long enough to permit the entire plate to pass underneath the microscope. bridge. This latter bears, as already stated, three microscopes. Two of them are permanently fixed to either end, and point at a graduated circle on the circumference of the holder. They contain comb-micrometers, and read to Seconds of arc. The third, or measuring microscope, is mounted on a straight guid- ing-way, and has motion entirely across the plate, in a direction perpendicular to the cylinder. It is evident that any point on the plate may be brought into the field of view. At the left hand end of the bridge is attached a lever arm, by means of which the guiding-way together with the microscope niay be raised through a small angle. When in this position, the microscope points at the scale. Readings are made by means of a filar micrometer. This is so arranged, that two revolu- tions of the screw carry the wires over one division of the scale, i. c., over one millimeter. The head is divided into one hun- dred parts, so that twothousandths of a millimeter can be read by estimation. As the machine was originally designed for the measurement of rkseau plates, the microscope has two screws at right angles to each other; they are designated as the hori- zontal and the vertical screw respectively.
From the above description of the machine, the method ot measuring follows immediately. The microscope being pointed at a star, the niicrometer is read ; then by means of the lever arm, it is made to point at the scale, and, without moving the microscope itself, the screw is turiied until the threads cover the next lower division, and the head is again read. The dif- ference of the two readings, nddcd to the number of the line,
( 6 1 )
402 KRETZ.
will give the position of the star with respect to the scale, since the micrometer is so arranged, that the head will show increas- ing numbers, when the threads are made to move in a direction opposite to increasing numbers on the scale. To measure the plate, then, the following operations were always performed :
Set the plate correctly in the holder, i. c., so, that the meas- ured coordinates will coincide approximately with right ascen- sion and with declination. This is done by first making the line joining the central star with its trail (or third image) parallel to the cylinder, and then turning the plate through goo, in such a way that the trail shall be to the tight.’ Then will the hour angle in- crease toward the left on the plate, and the direction of a circle of declination will be perpendicular to the scale. Read the gradu- ated circle on both microscopes, observe for runs,’ and take the temperature. Now measure the position of each star as fol- lows : Point the microscope on the East Image of the star and read the micrometer ; point at the scale and read twice on the next lower line ; point again on the star and read. Move the microscope so that, the micrometer standing approxihately at the same point as before, the wires bisect the West Image. Re-
’ NOTE.--It will be seen that this method of orientation involves an e m due to the curvature of the path of the central stnr on the plate, which, for high declina- tions, kcumes Inrge. For n star which daaiber a small circle in the sky will trace an nrc on the pliopgraph, and if the plate is oriented by the method described above, the cylinder will be made prallel to a tangent to this c u m at the micldlepoinl be- tween the central star and iw trail, and not, u should be the case, at the st.~ itself. It is easily seen that the vnlue of this error in smnds of arc, x , / / is
r”= 4 d/’ tun J
where d” is the distonce in seconds between the cenjral star and its tmil (obtained b multiplying the disinnce in mm. by an approsim?te scale vnlue) and d is the declination of that star. If tlim we move the holder thmdgh an ~ g l e .d/, the plnte will be much more accurately oriented nnd the least quare solution for the mn- shntrof reduction will be greatly simplified. The sign of this correction will depend on the psition of the plate (whether in the northern or in the southern hemir- phne), and also on the gnduition of the plate-holder. In general it can he de. termined from the consideration thnt tlie tme Enst and West line parses through a p i n t which has an rrithmeticnlly smaller declination thrn the trail. In orienting my plates, 1 always applied the above correction. The method is due to Dr. Schle. singer.
*See.Sect. JI, RUNS AND SCREW ERRORS.”
(62)
STARS IN COMA BERENICES. 403
peat the operation as for the East Image. Take the mean of the readings on the scale, and subtract from it the mean of the readings on both images. The difference, dividtd 6y 2, is the distance in millimeters of the M U J ~ position of the star beyond the given line on the scale. I t is designated in the following by $ m. Measure in this way all the stars, beginning with the central. Read the temperature. Remeasure all the stars in the inverse order, with the rtiicrometer head set now at half a revolution from its previous position, in order to eliminate peri- odic errors of the screw. Read the runs, circles, and temper- ature.
In this way, on one day, all the stars were measured in one position of the plate. Two observers were always engaged on the work, each one reading all the stars, the runs, and the circles. After completing the measures in one position, the plate is rotated through goo, and the process is repeated, It is then evident, that if the first position gave differences in right as- cension, the second would give differences in declination. Since the two images are separated on the plate by about a millimeter in right ascension, it was in general necessary to use two lines on the scale when measuring that coordinate, while for the other only one was required. In all other respects the measures in both positions are entirely similar. To reduce personality, observa- tions were made with the plate respectively I 80' and 270' from its original position, care being taken that the same pair of ob- servers should always read one coordinate in both directions. The greater part of the systematic error, due to the difficulty of judging the center in hazy images, cannot be eliminated by this method, however.' The only way to obviate its effect, is to multiply the numkr of the plates, if that is possible.
In TABLE^ I1 and 111 are recorded all the observational data from which the succeeding reductions are made. TADLE I1 gives the daily record : It shows the date of measuring the plate, the runs in millimeters on 10 mm. spaces, the circle readings, the mean temperature of the morning, the position of the plate, and the initials of the observers, Schlesinger, Hays or Kretz. The runs as here given are the mean of the two
(63 )
404 KKETZ.
observations taken before and after measuring the stars. The circle readings as recorded show the degrees and minutes of the right hand microscope, while the seconds are the mean of all the reidings for the morning. The terms in the fifth column require a little explanation : It has been stated that the normal position for the plate is trnil nght. Measures taken in this position are designated as x d r d . Counter-clockwise rota- tidn of the holder, which is the direction of increasing numbers on the circle, brings the trails up. Measures in this position are denoted as 'y dird. The meaning of the other terms follows at once. It should be mentioned, that for trail right, right ascension, and for trail up, north polar distance, increase to- wards the left on the plate, and that the numbers on the scale increase towards the right.
TABLE I11 gives the uncorrected measured coordinates in terms of the scale-divisions and of $ ill, obtained as previously explained. As has been stated, the micrometer could be read by estimation to twothousandths of a millimeter. The mean being taken to one decimal further, unity in the last place of $ 111 will be a tenth of a micron. This corresponds approxi- mately to 0".005. The same statement applies to the quantities given in the fifth and ninth columns of the tables. In general it will be found that two lines are given for the x's and one for the y's, agreeing with what has previously been said on this subject. In a few cases a negative sign is attached to m: this means that the next higher line on the scale was used. The numbers of the stars in the tables were assigned by me, and increase with the right ascension.
STARS IN COMA BERENICES. 406
1897: i inmm. -_-. ........
TADLE II.-DAILY RECORDS.
Jan. ;: i -0.0028
Fcb. I ; -o.oozo ( 1 4.0030
" 2 I 4 . u ) I O
April 17 " 19 " 20 " 21
. . . . - . . . . . . .
Feb. 20 1 $0.0028 5"s; dji 65.2 I xdircct. '' 23 So.& I 95 49 59% ~ 65.0 , y direct.. " 24 i +0.0018 1 2754959 4 . 6 yrcversed. '' rrcversed. 15 1 fo.0055 ; 185 50 0% , 63.4 I . . . . . . . . . .
me vr. . . . . . .
March 9 $0.0065 27r02j ijf ; 62.7 rdirect. " 10 ! +o.a%5 , 91 25 I) , 63.6 , xrcveihed. " 11 j +0.0070 I I 25 10% I 62.1 : y direct. " 12 +o.m15 1111 25 9% I 62.1 yrcversed.
I - . _. - . . - . . . . . . . . . . . . . .
Male IV. . . . . . . . - - .
+o.o168 1 9<4; 4& ' 65.7 I xdirect. +o.or~z 181 42 40% I 6 4 8 ' ydircct. +o.o170 I 4238% j 68.1 I yrcverxd. +-O.OZ~O I 271 4241 I 64.8 ! rreversed.
. . . . . . . . . -. -. .
Plate VII. . ._ . - -. . - .- __ . -. .
M ~ Y 10 i +o.o34o j 18,"~; I& j 71.1
I 22 20% ' 72 5
y direct. " 11 +O.OJ~O 91 22 21% ' 72.5 ; rdircct.
y reversed. 271 22 18% 72.5 ' rreversed. . .- - - . -_ . - . .- .
Plate IX. . .- .. . . . . .
8 i o ; 4 2 ~ 66.9 I xdirect. 17701 4% ' 64.7 1 y direct. 267 or 5% I 66 7 xreversed. 357 01 8% j 67.0 I J reversed.
_. - .
Plate X. .. . - .
kc. 11 j - - O . O I Z ~ I i66"~; zik I 69.1 I* 16 ! 4 . 0 1 2 8 I 356 57 zH$, h6.4 I
rdirect.
J' direct. 14 4.0138 : 86 57 30% 1 6q.i rreversed.
r8 i -0.or45 , 17657 29k- I 65.7 , yreversed.
" IZ I + o . o j n
" I8 !
.... .. Plate V.
18I"2d5& / 64.6 ' y direct. 91 29 2% 64.6 I xdircct. I 2856% I 68.5 I y reversed.
271 28 58% I 58 9 I reversed
Plate I. - . . - - -.
406 KRETZ.
TAULE II . - (Cot i fhd . )
! I Circle j Thcr. i Position of PInte. Obs. inmm. I I
Plntc VIII. ' I - _ _ _ _ _ _ ~
I Plate XI. - - - ~ _ - ______
I 0 ' 6 '
1 Jan. 22 i -0.0115 I 267 2345% 1 67.8 i yreversed. 25 1 -a0110 177 2341% I 65.8 , xreversed. 27 - O . O I I O 1 87 23 4 0 g 65.8 I y direct.
rdircct. 16. 29 1 -o.oIr~ I 357 2344% 1 65.5 ;
I Feb. I --a0125 '' 2 1 4 . 0 1 3 5
4 .0105 - U O I 2 0
. - - - __ - - .- . .
Feb. 5 --O.OIIZ 'I 8 , -0.0115 " 9 , 4 . 0 1 0 2 '' I 1 I 4 . 0 1 0 8
x direct. y direct. I reversed. y reversed. K, S
~-_I--
r direct. I K , S y direct. K, S s reversed. K, s y revmed. 1 K,S
- - - - . . - . - . - . . -- - - - -__ I
Plate XIV.
Feb. 16 I -0.0115 1 267 52 37% I 61.4 , rdirect. I K,S - __ __ -
! I o , , , ' I I
17 I -~.mBs 1 87 52 36% 1 59.5 \ rreverxd. 19 4 . 0 1 1 8 i 357 52 38 1 65.3 j y direct.
I '* 22 ; 4 . 0 1 1 2 1 177 52 35% 1 66.0 I JJ re~ened. I K, S
- . . .-. - -- .. .- . ._.- __ __ Plate 11.
- __ -
K, s K, S K, s
y reversed. K, S
( 6 6 )
STARS IN COMA BERENICES.
TABLE I11 : MEASUREMENTS.-PLATE I.
407
$ IN. ! ;tar. Lines. ~ _ _ - . S-H 1 ' I Scbles. I Hays. I
1 5 111. Lines. ___ . _ _ _ _ ' Kretz. I Hays.
I direct.
0.8579 0.859 0.3450 0.3432
0.2339 0.2298
o.[bor 0.8021 0.4092 0.4072
0.6348 0.6360 0.8319 0.8341 0.6396 0.6378
x reversed.
0.1529 0.1504 0.1874 0.1838
0.2649 I 0.1621
0.1330 0.1316
0.5546 0.5.514 __ ___-
y direct.
73 o.gqg8 0.9482 +0.0016
68 57 I 0. O,i234t09231 50s 10.846 I If -t- 3 116 0.3085 03049 + 36
54 7 I 0.5781 0.84q 0.83$ 0.5762 + 3E + 19 5 0.5728 0.5715 + 13
63 o.jy,z 0.3158 - 6 62 0.1146 O.IIJI 5 -
3
43 (0.9442 0.9442 _. _.I___
' 0.6980 I 0.2171
0.3184 0.1926 0.7578 - 26
0.1459 3 0.4179 I -t- 41
0.4044 0.3701
a4195 1 + 5 0.7246 - 5
52
y reversed.
-0.0011 45 ; 0.6011 10.6052
- 36 61 I 06308 0.6295 - 25 50 0.7036 10.7046 f 34 0.7136 0.7126
_ _ _ - . - - __ 45 3 '0.2530 IO.2545 -
- 4 1:: ! 0.9161 10.9775 0.w 0.2399 0.4339 0.8768 0.0371 0. I449 0.6104
408 KRETZ.
' $ 111. ,tar. I Lines. - x-s
Kretz. 1 Schles. 1 .r direct.
7 8 9
14 '5 I Y '9
z a 23 24
10
2 1
- .. I 1 4 5 6 7 A 9
14 15 18
'9
10
I1 2 1
i3,73 i 03951 0.3971 67,8 0.4.510 ! 0.4318 51,52 , 0 0468 ' 0.0149 5 0 , ~ r 0.7680 I 0.7676 41,qi ' 0.3261 ' 0.3265 3 6 ~ 6 1 0 4 ; I 8 ' 0 4311
13.14 I 0.4726 I 04713 i1,ii I 0.1770 10.2750 11,13 , 0.1865 0.1866
1 7 ~ 8 , 0.17115 0.2699
- -- .r reversed.
- - 10,9 Io.1916 0.1865 15,14 I 0.399s I 0.4012 34934 ! 0.5149 0.5111
0.7263 O.6H61
0 6374 0.6115 ".U749
0.5318
0.4w 68 67 0.4611 -I- I3 68 67 0.7396 0.i410 - 14 78,77 0 1881 : 0.1Ml 83.61 I 0.5Sm 0 . 5 8 q - 92,gr o 1399 0.140.5 - 6
' -
37 50 50 8
66 56 70
117 1 '9 61 61 61
61 44
1 2
6
y direct. . . -. . . . 0.5651 0.1781 0.6494 -.a374 0.6159 0.5474 0.5369 0 1606 0.2676 0.0136 0:8186 0,3715 -.0388
0.2166 0.1061 0.6466
0.3766
__.
0.5598
0.6434 -.0030 0.6155 0.5496 0.5378 0.2796 0.2674 O.OlJ9 0.8160 0.3715 -a0448 a3758 0.2164
0.6449
0.1772
0.1054
- y reversed.
a9501 0.1196 0.8618
0.8845 -.03ge - . o h
0.5119
0.1348 0.1450 0 4900 0 6924 0.1391 0.5583 0.1346 0.2911 0.4069 0. %5
0.w66 t0.0035 0.2% + 7 0.8615 f 3
0.8831 -f 14 -.0384 14 -.0265 f 5 0.2296 f 51 0.1431 -k 19 0.49'4 14 0.6916 - 2
0.1389 t 2 0.5581 t I 0.1312 t 3 0.1916 5 0.4035 t 34 0.8689 t 6
0.5148 f- 81
-
-
-
STARS IN COMA BERENICES.
TAD= 111. ( C O ~ I J ~ ~ . ) - - P L A T E 111.
409
;tar. I Link. I
WJ. i Krcb. 1 Schles. I
' K-s
I revel -
0.5656 0.7625 a3736 0.3989 0.0826 0.5492
:d . 0.5621 0.7560 0.3711 0.3935 0.0760 0.5460 0.49% 0.4766
-
i- 42 + I9 4- I0 + 27 + 38 + 54
3 -- - .- 4.0033 + 5 + a
6
0 - 1 - - 1
0.9208 0.9200, -t 8 0.9326 0.9296 + 40
0.3782 o 768 ' + 14
-.OZIO -.oqo -+ 40 0.0886 I 0.0876 ' + 10 0.5479 0.5479 i 0
0.1814 0.1792' -?- 22
22 ' 0.8181 1 0.8159, f
ANNALS N. Y. ACAD. Scr., XII, April z, 19m-26
(69)
410
48 I 0.5614'
KRETZ.
0.5630
I direct. - I 2
4 5 6 7 8 9 I 0 I1 I 2
13 14 15 17 18 2 1 Z2 '3 24 _.
4 5 6 7 8 9 10 11 12
0.4700 I 0.4716 0.1735 I 0.2761 0.6708 z' 0.6728 0 . I A S I 0 . 1 ~ 6 0.4535 0.4828 a5298 0,0775 0.5935 0.8395 0.6171 0.5621 0.21~9 0.9259 (53502 a4&6 0.4294 0.6365
0.4565 0.482U 0.5262 a0768 a5918 0.8460 0.6318 0.5626 0.2148
0.4821
0.9291 0.3498
0.4329
0.0846 ' 0.0895 --0.-9 0.2852 0.2871 - '9 0.8882 0.8919 - 0.6021 ' a6022 0.5734 I 0.5752
0.4154 0.4218 - 0.5251 I o.gngg 0,4779 0.4831 0.4641 0.4698 0.7145 i 0.1108
_- 0.2781
0.3578 a7045 0.3285 0.2506 0. 24m -.o080 0.9744
0.5810 0.8111 a 7249 c.5258 0.0291
0.0790 0. osqq 0.9259 0.8183 a3479
-.OIOI
0.6095
__
y direct.
v reversed.
48 65 54 68 'IS [ I7
7 2 , I I 70 59 61 62 59 59 42 77 79 -
0. '934 0.8602 0.2199 0.2955 0.3081 0.5664 0.5829 a9441 0.4719 0,7345 0.8314 o.ol32 0.5225 0.4738 0.4699 0.6320 0.7371 0.20% -
0.2210 0.2970 0.3115 0.5635 0.585 I
0.4751 0.7340 0.8289 0.0146
0.4741 0.466) 0.6295 0.7379 0.2044
0.9511
0.5241
-
-0.0025 - 16 2
I1
- 4- 13 - - 15 - 34 t 29
- 71 - 32 t 5 t 35 - 14 - 16 - 3 f- 35 I- 25 - 8 - 18
22 -
-
STARS IN COMA BERENICES. 411
ill. 3tu. Lines. - ' s - H I ' I-.-- Schlcs. 1 Hays. 1 - I 2 4 5 6 1 8 9
I3 14 15 18 19
23 14
10
21 22
- I 1 4 5 6 7 8 9
13 74
I0
0,3593 0.825 I
y direct. - . _ _ _ _ _ _ ~
85 10.7S95 0 . h 73 jO.SI35 0.5142 72 0.8872 I 0.8888
115 10.2165 1 0.1236 5b 10.8581 i 0.8618 67 10.7849 ] 0.7885 53 0.7720 0.7732 6 10.5171 ' 0.5360 4 Io.soSa ! 0.5076
62 I a1589 I 0.2630 61 I 0.0624 1 0.6528 61 0.6159; 0.6186
62 10.6270 1 0.6274
51 0.3511 I 0.3536
111 0.206g' 0 . q
79 44 42
JJ ".,gn , ". I"*_ , ".-I-
46 ' 0.0390 46 0.6656 4 ' 0.3330
62 , 0.w 51 ' 0.7635 65 , 0.7811
113 : 0.0280 115 10.0494 68 IO.Is68
O.oq341- 44 o * ~ l - 4
0.69491- 50 0.3359'- 19
0.7660 1 - 15 0.7830 I - 8 0.0308 I - 28 0.0528 i - 34 0.:010! - 42
57 ' 0.1891 0.2915 I - 24 58 0.4870 1 04908 I - 38 56 ' 0.9359 1 0.9369 - 10 8 0 . ~ 5 ~ 1 0.3486 14- 16
56 0.9740 I 0.9111 1 f 19 40 I 00851 0.e~ - 44 7.5 1 o 1881 1 0.1884 1 - 3 76 :064591 0.64961- 3
412
- I 1
3 4 5 6 7 8 9
10 I1 I1
13 14 ' 5 16 I6 19
13 14
21 2 1
..
- I 2
3 4 5 6 7 8 9 10 I1 '2
'3 r4
Kretz. 1 Hnys. 1 x direct.
44
16 '3 33 5 9
41 37 41
'7 33
1 1
I1
2 1 20
13 14
4 30
I
1 1
y direct. __ L
83 71 6
70
54 65 51 4
107 48 59 58
60 108 60 77 41 40
I11
1 I11
I12
0.4614 0.7955 0.4332 0.3599 0.3445 O'IOq5 0.0802 0.6935 0.6819
0.8166 0.9115
0.8012 0.4195 0.3596 0.3444 0.0914 0.07qS 0.6916 0.6781 0.9231 0.8149
0.6145 . 0.6~45 0.6254 I 0.615:
0.1838 0.181:
0.1758 IO.175( 0.7605 0.759
o.oiii i 0.024: 0.9145 ' 0.9141 D.4502 0.4441 -
y reversed.
48 I 0.4- 0.461~
_- . - - - 36 0.1738 0.174e
112
469 65 54 6n ,I5 :17 7
70 59 60
11
-0.M)IC
"- - - I - -
0.8765 ~ 0.8738 0.6330 0.6349 0.7334 10.7321 0.92Yq 0.9309
59 10.3771 0,3775 10 0.7975 , 0.7gOl
77 0.6411 0.6422 I - 79 0 1% o.rq2 -
6 0.9312 10.9189
59 1 a3694 0.1740 4 1 0 5330 I 0 4 3 5 1 -
STARS IN COMA BERENICES.
I 2 4 5 6 7 8 9
14 15 I8
I 0
21 22
23 24 -
0.3405 0.5376
7 ~ 34,33 I O.jZ40
8 37936 ,01735 .. .
15 59.58 i 0.3750 I0.3762 ' - I 2
9 ! j?,36 I 0.2244 0.1209 10 1 42$41 0.7056 0.7065 i - 9 14 58,58 ! 0.6011 0.6032 - 21
18 i 68.67 , 0.8122 10.8138 i - 16 2 1 I 82,82 '0.3702 I 0.3689 I + 13 22 ! 86,85 10.6841 I 0.6814 I + 27 23 I 88,88 0.3674 0.3689 1 - 15 id I ~ 7 . ~ 7 o . m s I 0 . 4 5 ~ I i 11
0.6395 0.1718 0.3458 0.3'90 0.2774
4 . 0 0 1 I - 9
39
+ 50 39 + 35
-. -
12 - -
413
i X m . 1 Lines. I___---- I K-S
, Kretz. 1 Schlea. ,
y direct.
85 73 73
115 57 67 53 6 4
62 61
0.9712 0.6816 0.0458 0.3884 0.0156 0.9426 o.gjo5 0.6915 0.6578 0.655& 0.4055 10.4084 o.ao<o, 0.2od2
0.9705 0.6838 0 0469 a 3870 0.0158
0.9306 0.6828
0.9434
62 I 0.75;s 0.75b I - 5 62 0.7646 I 0.7655 1 - g 79 0.6116 ~ 0.6063 + 48 44 0.4916 0.4905 ' + 21 43 0.0265 0.0281 I - 16 - . ._
y revencd.
33 I 0. 938'' o 5942
46 ' 0.5026 ! 0.5050
62 I 0.5366 10.5362 51 I 0.6095, 0.6111 65 0.6254 ' 0.6261 112 I0.8749 ' 0.8729 114 10.9016 ! 0.9016 57 I 0.1438 I 0.1438
56 I 0.7929~0.7918
._ . . -_ .. .. . .- .
45 I0.8719 018749
4 I 0.1749 10.i741
58 0.3458 I 0.3449 56 0.7996 10.7960 39 I 0.9502 ! 0.9508 75 0.0615 ' 0 & 9 76 ' 0.5'214 I 0:5212
. -
- o.cKlo4 30 24
f 8 + 4 - ' 16
7 + 20
+ 9 + J + 11 - 6 + 6 + 2
- -
- 0 0
414
Stnr. Liner.
- I 2 4 5 6 7 8 9
I 0 I1 I2
:a 15 16 I7 18 I9 2 0
23 24
21 22
- - r
4 5 6 7 6 9
2
I 0 I1 I2 '3 14 15 16 17 I8 19 10 t I
I direct.
a563c 0.3661 0.263$ 0.72% 0.5436 0.5731
0.1859 0.4171 a2a14 0. Iggn
0.3009 0.5 '49 0.636
0.6832 0.6116
%i:
0.4411 0.5712
D.5281 2.2274 3.5291 3.4498 __
0.5622 I +o.ooo 03639 + 2 0.2630 1 -!- 0.7179 0,5419 0.5700 0.6205 0.6710 0.1860 04305 0.2188 0.1571 0.3008
r reveacd.
0.5130 0.6616, + zi
- 83 71 70
113 54 65 51 4 2
I12 107 49 60 58
57 60 log
60 77 41 40
I12
I11
__
- 3s 48
64 53 67 : 15 .I7
7
7 0 59 60 6
62 59
8 59
4:
I1
I 0
42 77 78
y direct. _- 0.6561
0.0761 0.7049 0.6281 0.6125 0.3662 0.3440
0.9535 Q.1891 O.Ogl1 0.8935 0.9059 0.401 I a4465 0.0374 0.5058 0.4538 0. ago2 0.1601
0.36qq a7318
-.0295
0.7191 ._ -
- 0.659 0.3656 0.73- avo5 0.7035 0.6262 0.6106 0.3719 0.3434 -.0312 0.9536
0. ogo5 0.8932 0.9022 0 . 4 w 0.4464 0.03.55 0. soas 0.2&) 0.1801 0.7%
0. I875
0.4511
- y reversed. __--
0.9135 10.9139 0.202 I 0.1012 0.8341 0.5039 0.86j1 0.9394 0.9548 0.0330 0.2318 0.- 0.6195 0.3818
0.6766 0.4785
0.6698 0.16yJ
0.5375 0.0681
0.1202
0.8334 a5012 0.8629 0.9391 o.955r
0.6036 0.6176 0.3824 0.4756 0.6748 0.6732 0.1682
0.2039 0.2305
0.1214 0.5334 0.0655
0.1171 0.n91 0.2818 10.2816
tO.001 - + + + + + + + + + + + f + f
+
+ -
-
- + -
9 7
27
3 3 9
13 53 19 6
29 18 34 8
41 26
16 27
2
12
20 12
STARS IN COMA BERENICES. 416
TABLE 111. ( C O ~ ~ ~ ~ ~ U ~ . ) - P L A T E IX.
a I /
I' : i
y direct.
0.q19 0.7826 a1442 0.4836 0.0;86 0.0261 0.7881 0.7564 0.5016 0.3018
0.5 0.1199
0.8532 O.%
-
0.0366 0.0150 0.7878 0.7569 0.5olI 0.2999 0.8526 0.69Yi 0.583 6 0 . 1 ~ ___
416
Star.
KRETZ.
Liner.
I direct.
0.3208 0.1304 0.5255 0.4861 0.8068 0.8365 0.8885 0.606 0.4591
7 1 39,38 8 Al.41
x revcrud.
0.1449~0.2476 -0.0027 0.4430 0.4445 - 15 0.0441 0.0449 - 1
0.7638 10.7629 f 9 0.7318 0.7312 - 4 0.6811 0.6792 + 19 0.6245 0.6168 + 77
- _ - _ -
0.5838'0.5861 - 13
9 42941 10 I 48,47 1 0 . ~ ~ 4 2 , 0.1102 + 40 14 I 64,63 I 0.5031 0.5031 0
18 I 74,73 I 0.1335 0.2320 -!- 15
t i , 9i,91 ,0.0872 0.p886 - 14 r3 I 94,93 0.2758' 0.2776 I - 18
15 64963 "3.794 I 0.7795 f 49
11 U,87 0.2800 0.2806 - 6
14 103,101 0.3649 0.3592 -1- 57
86 14 73
11.5 57 68 54 7 5
62 61 63 63 79 44 43
y direct. -_ . 0 4 7 9 0.0085 0.3750 0.7070 0.3482 0.2682 0.1530 0.0102 -0132 0.7330 0.5306 0.0811 0.0885
0.8208 0.9178
03959 0.0106 0.3754 0.7061 0,3414 a 6 7 5 0.2508 0.0132 -.or14 0.7338
33 0 0886 0.9188
STARS IN COMA BERENICES. 417
I ' 1. ;[a. 1 Liner. .i-L j K-s
: Kretz. 1 Schles. I
x direct. I 0.1op. 0.0976
0.9070 I O.go62 0.3016 1 o.3ora 0.7635 i 0.7664
0.6135 Io.6128 0.6629
0.2374 0.2331
0.5631 10.5659 0.1131 I 0.1212 0.0709 I 0.- 0.16sg 10.2655 no744 ; 0.0746 -.mi6 -.-
. . ~ - -
0.5946 u.590~
::% 10.7264
0.8416 1 0.&00
-.I . ... -. . . - -. . -. - x reversed.
- - _ _
tO.0074 f 8 + 16
29 + 41 f 7 + 65 t 25 + 43 + 26
17 + 19 + 11 + 34
t 4 4
-
-
- 1
-. . .
-0.0031 + 43 . + 21
3 17 15 35 59 19 55 63 22
I 36
111. Lines. I --K __ 1 K-s
, Kretz. I Schles.
_-_ 85 73 71
115 56 67 53 6 4
61 60 62 62 19
y direct..
0.6549 i 0.651~ 0.3641 i 0.3659
0.0649 ; 0.0631
0.6280 ~ 0.6298 0.6142 10.6096 0.3716 I 0 3706 0.3458 0.3455 0.Ogog ~ o.*
0.4459 ~ 0.4438
0.7310 1 0.719
0.706, 0.7035
0.8961 10.8946
0.2870 ~ 0.2869 0.4491 10.4464
__ . . . -.
y reversed.
46 4
61
33 a9111 0.9220 46 ' 0.2062 0.2078
0.8368 0.5128 0.8656 0.94i6
0.11~6
0.9599 0.1010
0.&5 0.5100 0 8646 0.gqOl
0.9572 0.2010 0.12A8 1 x 5
57 IO.1218 ~ 0 . f 2 1 1 1 - 57 0.4795 0.4734 . 58 0.6739 0.6721 ; + 57 ' 0.1156 i 0.1146 1 +
I 0.3880 0.345 j - 40 0.2834 10 .2808 , f
76 , 0.8542 I 0.8540 1 f 75
I8 I 0 4
a6 15 2
418 KRETZ.
y direct. - I 2 4 5 6 7 8 9
14 15
I0
In 11 12
'3 t4 - - I 2 4 5 6 7 8 :0 9 .
4 5 8 'I !Z 3 '4
I direct.
0.3558 0.3553
0.5559 0.5545 0.5270 0 . 5 2 9
0.6516 0.6536
a1406 0.3415 0.3695 0.3665 0.4196 0.4185 0.4741 0.46&6 0.4812 0.4772
0.6570 0.3662 0.7385 0.0692 0.7066 0.6330 0.6179 0 3818 0.3498
0.4556 a4604 0.2939
0.7256
3gg
0.1931 --
0.6552
0.7341 0.0678 0.7070 0.6314 0.6179 a3781 0.3501 0.~946 0.8996 0.4504 a4576
0.36!
D. 2960 D. 1894 ~.7376
y reversed.
: 0.863
0.2014 0.2055
a6709 o.117a 0.1140 0.2756 . 0.3841
I :;$ 0.4702
j O . 8 4 4 4
- 0.921 I 0.205 I
0.5026 0.8622 0.9370
0.1956
0.4686 0. w 0.1170 o.11rg
0.3831 03439
0.8351
0.9520
0.2134
0.2738
-
STARS IN COMA BERENICES.
- I a 4 5 6 I 8 9
I4 15
13 14
10
11 11
- - I 2 4 5 6 7 8 9
4 5
0
" 2
3 4 I
x direct.
o.rg11 o.15a 0.4571 0.4561
0.8075 0.8118 0.6416 0.639~ 0.6654 a663
o.a& o.a& a8888 0.8861 0.6og8 0.6134 0.11% 0.1189 0.3111 0.311 3.1150 o.1J 3.0474 10.0486
0.3555 0.35IE
0.7216 0.721i
0.7885 0.7866
x reversed.
419
y direct. - 0.4056 a1191 0.4819 0.8171 0.4538 0.3712 0.3614 0.1211 o.og34 0.8355 0.6378 D.Is9s 0.0312
0.9195 0.4536
0.4031 a i r61 0,4791 0.8115 0.4540
o.361a 0.1236
0.8332 0.6356 3.1888
3.4536
0.~71a
D.Io00
D.0274 0.9172 -
y reversed.
0. 1695
0.0898 0.7630
0.4578
0. I200 0. Po00 0.2120
0.4490 0.4312 0.7315 0.9350 0.3815 0.5430 0.6502 0.1174 -
- 0.1682 0.4562 0.w 0.7619
0.1028
0.4478 0,4779 0.73d a9342 0.3799 0.5421
0.1222
0.2121
O.%l 0.1174 -
+0.0013 + 16
+ 11 I
- 21
I
-
- 2a
'L I2 + 33 + 7 + a -1- 16 4 - 9 f 3
-
0 -
420 KRETZ
_ _ 1 2
4 5 6 7 8 9 (0
.-
o.nzq 10.2214 0.5280 0.5168
0.8855 i 0.8874 0.4256 I 0.4272
0.7135 ! 0.7152 0.7.394 I 0.74r)O 0.7885 10.7918 0.8565 0.8554 0.3648 0.3628 0.4655 , 0.4644 o.&z I 0.6925 0.2465 I0.2452 0.1939 ' 0,JglO 0.3870 0.3869 0.1961 Io.1980 0.1186 I 0 . 1 2 q .__ - r reversed.
695 0.3469 0.3476 II,IO 0.5& , 0.5428 3140 ~ 0.1449 1 0.1476 31.30 0.6825 0.6811 37,36 , o 8592 ' 0.8519 39,38 0.82go ! o 8301 42AI ' 0.7812 I 0.78139
y direct.
0.9181 0.6308 -. w 3 I 0.3174 -.0285 0.8921
O.QO8 0.8751
3 o.& 61 ! 0.3536
61 ,0.7102
60 ~ 0.1579 61 I 0.7085
78 1 0.5519 \ 0
43 1 0.4438 1 04404 42 :-.om2 /-.orgo
- - . . - - . y reversed.
0.9144 0.6332 -.0052
-.0284 0. WS 0.8766 0.6402 0.6088 0.3556 0.1568 0.7068
0.3272
0.7105
34 46 47
5 63 52 66
113 116
0.6596 ! --0.0030 0.9405 - 6 0.5765 I + 0.5984 + 57 0.6811 I + 17 0.6958 I + 8
0.2472 1 + 14
11. Instrumental Corrections,
Divinion Errom-The measured co6rdinates of any star are the difference in the readings on the scale corresponding to the central star, and those corresponding to the star in question. Hence they depend directly on the distance between two given lines 011 the scale. If this wek perfect, an equal number of divisions would represent exactly the same length, no matter. what part of the scale were used. That is not the case how- ever, and corrections must therefore be applied to the different lines, so as to reduce all measured distances to a common unit. The unit selected was 1/13oth of the total length, that being the number of spaces into which the scale is divided. Each space equals approximately one millimeter.
In the winter of 1896-1837, the scale used for all the Coma measurements was carefully investigated for division errors, Pro- fessor Jacoby’s method, described by him in the Aittericaii /o:tmal of Scicitce, Vol. I, 1896, p. 3 33, being followed throughout. The details of the investigation are to be pub- lished at a later date by the observatory; I shall give here merely a table of results. A determination of the errors had been made previous to shipping the scale to America, by the . Kabrrliche N o r i d Auhittrgs Kotiititbsioii, at Berlin. Their results are publisheij in the At1ttnls o/ t h Ney YorR Acndefiy af Sciewes, Vol. IX, p. 206. I decided to exclude. them, however, as it was deemed most accurate to use only those results which had been obtained under the same conditions and with the same instrument as all the other observations em- ployed in the reductions. Nor were the quantitiei as used greatly affected thereby, for the two determinations agree quite well, differing in no case by more than O”.I I . As each star was made to depend on a number of lines, the error introduced
( 8 1 )
422 KRETZ.
by using an inaccurate value of the: division errors was still further reduced.
In the table on p. 423 the corrections, which must be added to the measured m. with the sign shown, are givenjn milli- meters. The argument is the number of the line. When two lines,were used, the mean of the corresponding corrections was applied to m.
Oomectiona for Bpna and lcrew Errola.-As has already been stated, observations were made for runs twice a day, once by each observer, A complete observation always consisted of two determinations, made as follows : The screw being set at about 5 R (the R representing revolutions), the spider-threads were set on the line 70, and the micrometer head was read. Then, without moving the microscope, the screw was turned until the threads bisected line 65, and a reading was taken. Then once more on 65, and back to 70, and the observation was completed, The lines 65 and 70 were selected as they have nearly the same division errors. Since the screw makes two complete revolutions while the threads cover the distance of one millimeter on the scale, and since the screw readings in- crease when the threads are moved in a direction opposite to that of increasing numbers on the scale, it is evident, that, if it were not for runs, the readings on line 70 would be less than those on line 65 by exactly 10 R. If that is not the case, then the correction to be added to any observed vt in order to reduce it to the case of no runs of the screw, is
r . - ( X W I ) -- millimeters, 5
2r = Reid. on line 65 - R u d . on line 70 - xoR.
Thus 3r is the total error of runs on ten revolutions ; for each day of observation it is evidently equal numerically to the “Runs in mm.” of TABLE 11. For one millimeter the error will evi- dently be J4- 2r/5, the factor y reducing the quotient to mm. And since the correction to each $ wt must be proportional to
(82 )
where
I
5 6
- 7 8 9 I 0 XI I2 13 14
Line.
0 I a 3 4
I :5 17 : 18 19 20 21 22
23 24 1 : 28
STARS IN COMA BERENICES.
TABLE IV.-DIVISION ERRORS OF THE SCALE. - Cnncction in
mrn.
f O . W l 1 4 . m 7 -0.m1 $0.- 4.m4 + O . r n I 4 .W13 -0.boos 4 . o o o g
+o.m14 +O.m06 $0.0014 $0.0016 +o.w15
+o.oorz +o.0012 S0.W +o.oorg Co.0016 +o.m14 ' -~0.0012 +O.m7 $0.0016 +0.0033 +0.0026 + 0.0020
0. moo
4 . M o I
$,43
Comction in Line. mm.
57 58 59 60 61
+0.0032 +o.w28 $0.0030 s0.0034 $0.0038 $0.0034 s0.0034 +0.0018
425
Comction in Line. 1 -.
+o.w25 + a m 6 +o.w18 +0.m7 +0.0015 +o.0026 $0.0016
. $0.0016
+o.u114 + 0.w $0.0019 -f-o.oooq 4.0005 +0.m2 +0.0014 $0.- +C.OulZ $0.0002 +O.o0l2
to.ooo2
:::3
.moo -0.ooO2
I 1 2 -0 om6
114 to.0005 I15 1 4.0303 116 i .moo 117 . +-o.mo 118 I + 0 . 0 0 ~ 2 119 -+0.0026
I21 , +o.w14 122 +0.0024 123 +o.0015 124 I $0.0024 125 S O . 0 0 1 2 126 to.0018 127 i +o.w14 128 I +0.0005 129 lo.00rg
I I J 1 -0.Wl3
120 j +o.oozr
.ocm
424 KRETZ
that quantity, the above formula follows at once. Tables with the argument $ in may evidently be constructed giving the cor- rections corresponding to any value of 27.
Before proceeding to do so, however, let us consider the errors of the screw, These are of two kinds, periodic and non-peri- odic. The former were eliminated during the measurement by always setting the screw to a certain reading (usually gR) when pointing at a star during the first half of the day's work, and then, upon reversing the operation, setting it always at a reading differing from the former by o.5R. Thus each star was read with the screw in both positions. In order to obviate the effects of non-uniformity of pitch, certain corrections must be applied, however. Investigation showed these to be :
Corrections in Millimeters.
Radinp of Micrometer Head. 5R 6 7 8 9
10
I1 x2
13 '4 IS
T
Gerticai Screw. Horizontal Snew. O.oo00
i - 0 . ~ 4 i-o.ooo4
4.0007 4 . o o r 4
4 . 0 0 0 2
4.0020
O.oo00 + o.Oo05 +0.0002 -0.0003
-0.0017 4 . 0 0 1 2
4 . 0 0 2 2
4 . 0 0 2 4 4 . 0 0 2 1 -0.0023 4 . 0 0 1 3
0.0000
-O.Q)22
4.0014 O.oo00
The above quantities are in mm. and must bc added to the readings. The vertical screw was used for one plate only, No. I1 ; the following discussion applies to it as well as to the hori- zontal screw, mutotis irrritotidis.
It will be seen that between gR and r rR the increase in the correction is proportionate to the' distance from gR. Hence if we start our measures of any star with the original setting of the micrometer head at gR, then the increase in the correction will be proportionate to sit!, remembering that the Maximum value $ i n can have is 1.0, which corresponds to 2R. This was always done except in certain cases to be mentioned later. As the co6rdinates are the difference between the readings on the
( 8 4 )
STARS IN COMA BERENICES. 426
stars and the readings on the central taken on the same day, we may, yithout affecting the final results, subtract a constant from the screw.correction. Taking, then, the zero point at 'gR, and as our argument tenths of millimeters (or fifths of a revolu- tion) beyond gR, we get the following table for correcting the readings of the horizontal screw :
Reading of Head.
9.0 9.2
9.4 9.6 9.8
10,o
10.2 10.4 10.6 10.8 11.0
Corresp. snt. 0.0
0. I 0.2
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Corrcip. Comction. O.axx,
4 . 0 0 0 1
a . 0 0 0 2
-0.0003
4 . 0 0 0 4 4 . 0 0 0 5
4.0006 4 . 0 0 0 7
4.d 4.0009 4 . 0 0 1 0
During the second half of a day's work, the initial setting on the star uhs usually 9.5R. As a result, the readings on the scale sometimes fell beyond I I R. For such cases the above table will no longer apply as it stands, for the correction beyond I I R does not bear the same proportion to $ I J ~ as holds below that point. We may, however, construct a table similar to the preceding, but differing in the last figures. For, all the stars being again measured beginning always at the same point on the screw, we may, as before, subtract a constant from the screw correctioirs. We obtain thus the table :
Reading of Head. Corresponding m. Corresponding Correction. 9.5 0.0 4 . 0 0 0 0
! 9.7 0. I 4 . 0 0 0 1
9.9 10.1 0.3 -0.0003
10.3 0.4 4 . 0 0 3 4
10.5 0.5 -0.0005
10.7 0 6 4 .0006 10.9 0.1 4 . o m 7 11.1 0.8 4.00074
0.2 - 0.0002
11.3 0.9 4 .00072
11.5 I .o 4 . 0 0 0 7 0
ANNALS N. Y. ACAD. Scr., XII , April 3, 1900-27.
(86)
426 KRETZ.
One platc was measured, beginning with 8.7R during the first half, and 9.2R during the second half of each morning’s work. This required the construction of a third table. The method was cntirely similar to the above, so that I need not enter on it here.
In the foregoing it has been shown that the screw cor- rection may be put in a form to be directly proportionate to $vz. But we have seen previously, that, from the nature of things, the correction for runs is proportionate to the same quantity. We can therefore construct a table with the argu- ment % f ~ , which will give at once the combined effect of both corrections. For example, let us consider the case of Dec. rqth, 1897. From Table I1 we find that 2r on that date was - 0.0069 mm., i. e., the means of the four differences
Read. on 65-Rend. on ~ O - I O R
was - 0.0069 mm. The screw therefore registerr less than the true‘distance, and a certain quantity must be added to each $iu. By the general formula this quantity is
(sm) x0.0138/10 millimeters.
Giving 5 4 ~ the values 0.1, 0.2 . . . 1.0, and combining with the corresponding screw corrections, we get the table
X I . 0.0
0. I 0.2
0.3 0.4 0.5 0.6 0 7 0.8
0.9 1.0
Beginning at 9.0 + O.oa330
.-4
.oood)
.OO015
.om19 ,00023 . W o Z T .00030 .&34 .00038
.OO011
Beginning at 9.5 f 0.00000
.cQJo4 ,00008 .ooo11 .wr5 .am19 .ooo2j .00027 .am36 .am52 .ooo68
Tables like the specimen were constructed for each observed value of the runs. The columns headed Beginning at 9.0’’ and I‘ Beginning at 9.5 ” give the corrections in mm., to be applied
(86)
STARS IN COMA BERENICES. 427
to the measured $ d s . They refer respectively to the first and to the second half of the morning's work. One point regarding the use of these tables deserves mention : It some- times happens that the reading on the scale corresponding to one image of a star is less, and that corresponding to the other image is greater than I IR . In such cases the correction must be found from the table separately for each reading, and then the mean of the two taken. This is evident if we remember the way in which $ t ~ t is obtained.
Measured Ooordinatea and Rotation Errom-Having applied the corrections described above, we are in position to obtain the measured cGrdinatcs. These are the differences of the readings on a star and the readings on the central star, i. e., star No. 14. As the n is to be positive when the star has a greater right ascension, and the y is to be positive when it has a greater declination (algebraically) than the central, we must apply the following rule : Subtract the position of the star from that of the central for x direct, and subtract the central from the star for y dirccf, For the opposite positions. of the plate these operations must, of course, be reversed. The reasons for this rule are plain, when we remember that the numbers on the scale increase towards the right.
The coordinates thus obtained are not yet free from error, however. For it is evident that, unless the plate were always rotated exactly goo from its previous position, the axes of ref- erence would not be rectangular. This was, however, found to be impossible of accomplishment. The best that could be done was to turn the plate approximately go", and then to measure exactly the angle through which it had been rotated. In order to obtain formula to reduce the measured coordinates to what they should have been, let us call
a', y' the coordinates referred to the central star as measured; x, y the same coordinates as they should be ; OX OY' the position the axes actually had on the plate; OX, OYthe position they should have had;
(87)
428 KRElZ.
B the angle A'OX', positive if the plate must be turned counter- clockwise in order to make OX and OX' coincide. Then the positive OX' will fall between positive OX and OY, for, on the plotel positive coordinates correspond to the usual position of the axes, i. e., positive x to the right, and positive y up, when the trail is left (corresponding to x rhrrsed).
Let also xd, yo'; x,,, yo be the co6rdinates of the central star referred to the center of rotation, 0, corresponding to the actual and to the corrected position of the plate respectively.
Then by the usual formulz for the transformation of coijrdi- nates, we have
Z, + I = (z,' + d ) c05 4- +f ) sin B 8 Yo t Y = (ref +4 Jn e+ Lvc'+Y')
or expanding and remembering that
xo=-x,'cosB--y,'sinB
yo = .rot sin 4 +y,' cor 0
and that B is very small, we find
x = d - f . H" sin I"
y =yt + d . 8" sin I"
i. e., from the measured x' we must subtract y'. &'sin I" and to the measuredy' we must add x'. 6" sin I" in order to obtain the correct co6rdinates.' It will be seen that these formulae take account of the fact that the center of rotation of the plate does not coincide in position with the origin of coordinates.
To determine what sign- to give B" in any special case, we need but remember that in the Repsold measuring machine an increase in angle corresponds to positive (counter-clockwise) rotation of the plate. Q = the seconds of the circle reading to which all the psi-
tions are to be reduced ;
Hence if we let
1 See in this connection Harold Jamby, I' Permanence of the Ruthcrfurd Photo- graphic Hates," Annals New York Academy of Sciences, VolI IX, p. 167, where the same formulx are given.
( 8 8 )
STARS IN COMA BERENICES. 429
Q' = the seconds actually read on the circles at any given date, then will the equation
Q-Q'=V
give 8" with the sign with which it is to be used in the formulle. Tables can,, of course, be constructed for any value of P,
having as argument .distances in .millimeters. This has been done and by their aid the measured coerdinates have been re- duced to the position of rectangular axes. The values of Q' used were as follotvs (Q need not, of course, be any one of the readings; it is best taken so as to make the corrections as small as possible).
Rate I ........................................................ Q = 6c# ................................................................ I1 43"
11 I... 23# I \'. 4Mfi v S8"%
VI 9°K VI I 2O"x
IX ............................................................... S"X x 2gnK XI ................................................................ 44"X
............................................................. .............................................................. ................................................................ ................................................................ ................................................................
VIII ................................................................ 26"
................................................................
XI1 ............................................................. 8" XI11 ............................................................... XIV 36"X ................................................................
Scale-Value Oorrectiona, Projection Errors, and Devie- tion of the Oylinder from Straightnees.-None of these have any appreciable effect. The first is due to the fact that the scale is made of German silver, while the plate is glass. Changes in temperature might, therefore, give rise to unequal expansion, and hence to a change in the scale-value. Dr. Schlesinger ' in 1897 investigated this question, and his results show that in no cas? could this change affect my results by as much as 0".04. I have therefore felt justified in neglecting this error altogether.
1 See his I' Pmsepe " pp. 22~223.
( 8 9 )
430 KRETZ.
The second category, projection errors, have been eliminated entirely in the case of the .Repsold machine in use for the pres- ent research by an improved guiding way with,which it was equipped in 1896.
As regards the deviation. of the cylinder from straightness, an investigation made under Professor Jacoby's' direction shows- that. no appreciable error is introduced thereby, the greatest range of variation not exceeding 0".04. I have therefore ne- glected. this correction.
In TABLE V are recorded the final corrected coijrdinates ob- tained from the measures of TABLE 111. The process of com- puting them is very simple : To the number of the line add the mean of the two corresponding svi's corrected for runs and division errors. In case two lines are used, substitute for the line of above the mean of the lines. The resuit is the mean position of the star with respect to the scale for each of thc four positions of the plate. Then calculate the measured co6rdi- nates, as previously explained, by comparison of these four quantities with the corresponding quantities for the central star, obtained in the same manner: Apply thereto the rotation cor- rections, having care for the sign, and the result will be the quan- tities set down in TABLE V. No further explanation of the terms there wed is necessary ; it may be mentioned, however, that, as before, unity in the fourth place of decimals corresponds to about o".oo~.
I " Permanence of the Kutherfurd FhoCogmphic Plates," Annals New York Acndemy of Sciences, Vol. XX, p. 207.
STARS IN COMA BERENICES.
TABLE V : CORRECTED CO~RDINATES-PLATG I.
431
Direct
-33.4486 -32.9343
-24.7756 -21.8240 -21.8558 -16.3918
O.oo00 + 0.2751 +23.7752
+29.7712
-26.7422
+27.57&3
+38.8579 -
MeUl.
-33.4504 -32.9340 -26.7431 -24.7772 -2 1.8255 -21.8552 -16.3922
+ 03743 + 23.7746 f27.5773 +49.7707 i-38.8569
O.oo00
-
PLATE 11.
itar. I Direct. -I
x - Rev'd - .2778
Direct
+ 10.6314 +52.9854
+ 5.531 - 8.4788 -55.7458 -57.7503
- 1.2018 + 0.3586 t 17.1978 -17.9134 -19.3756
- 5 .39y
0.omO
-
Mean.
-58.2748 --
-53.0658 -33.4516 -32.9302 -26.7434 -24-77k -2 I. 8238 -21.8518 -I 6.3882
0.- + 0.2797 + 9.7232 +15.116a. +23.77Q +27.5764 $29.7713 t38.8588 -
Y Rev'd -
Mean.
t la6330 +52.9856 - 5.3948 3- 5.53 6
-55.7412 -57.7494
- 1.1995 + 0.3594 4-17.1982 -17.9120 -19.3746
- 8.47i-4
0 . m
-
Y Direct. Rev'd ' Mean.
t 23.5483 +I I 2654 +10.6330
- 5.3878 + 5.5358 - 8.4796 -55.7386 -57.7504
- 1.1936 + 0.3576 S48.9410 + 0.3618 +1?.2022 -17.9071 -19.3713
t52.9774
O'ooOO
$23.5462 + x u 6 4
t52.9770 - 5.3912 + 5.5330 - 8.4814 --55.1392 -57.7514
- 1.2004
4 0.3545 f48.9384 4 0.3596 +17.a&
+10.632!
0.Oay)
432 KRETZ.
TABLE V. (Continrimd.)-PmrE 111. - stu
- I 2
4 5 6 7 8 9 I0
Ilirect.
-58.2620
-33.4544 -32.9304
__-
-53.0662
_I -_. -
X
Rcv'd
,2648 .07m
.9296 a7469
4530
-7782
. lo34
.go81
PLATE IV. ~~
I itsr. I .
I Direct. , Rev'd.: Mean. - - - . .- .. .- . . .- -. .-
I 1 -58.2560 ; 2624
4 ! -3334568 ' .4609 5 I -32.9293 . 9 3 q 6 j -26.7400 .7466 7 I -24.1681 .7752 8 -21.8154 .8214
1 0 1 -16.379 ' .J819
2 ! -53.0578 . a 7
9 I -21.8650 ! .a683
11 - 1 1 . 6 3 ~ .6375
Y ____ Direct.
. -- +25.5445 + I 1.2665 tro.6342 t 52.9755 - 5.39rr + 5.5359 - 8.4786 -55.7366 -57.7463
0 . 0 - 1.1972 + 0.3642 + 17. m67 -17.9065 -19.3675 , .j69s
-58.2592 -53.0612 -33.451 -32.93a3 -26.7433 -24.771 6 -21.8184 -11 8666 -16.38~9 -11.6338 -10.4232 - 8.3516
0.- + 0.1832 t 2.8606
MCUl.
+23.5412 + I I . Z U + i 0 . 6 3 ~ 9 $.52.9750 - 5.3937 + 5.5341 - 8.4804 -55.1365
--
-57.7470 0. OOQ)
- 1.1974 + 0.3639
47.9073 4 9 . 3 6 8 5
+l 7.1050
STARS IN COMA BERENICES.
TABLE V. (cuniitirird.)-PuTE V.
433
Mean. __- -58.1678 --53.*4 -33 46.33 -32 9483 -6.7413
Y Mean.
Ei -5303 1 d-23.5330 A497 , f I 1 . 2 J I I ,6258 I +10.6162 . 9 5 4 I $52 9590
PLATE VI.
I X I V . -. . -_ . _ _
Direct. Rev'd.' Mean. -I- ----- - - ;tar. - - ____ . . -
Direct I Kcv'd. Mean _I-._.._ - .
I ' -58.2580 2 I -53.o611 3 ' -50.~673
5 ' -32.9312 6 -26.7438
4 I -33.4%
9 I 41 .8743
7 1 -14.7752 8 I -11.8109
10 , -16.3890 11 11.6369
13 . - 8.3571 I1 -10.4297
.a618 -58.1599
n719 -5o.qoi . d l3 -53.06'7
4633 I -33.4619 ,9349 -31.9536 .74 3 26.7466 .77& , z14,7766 . 8qg , -11.8117 .a745 -11.8744 .388o -16.3885 .6410 -11.6394
.3636 ' - 8.3604 .4314 -10.4310
+23.5561 + I 1.2721 -53.1676 +10.6@
'-51.97Q4 - 5.3929 i 5.5377 - 8.q8r I -55.7257 -57.747s -51.864
- I 0.9046 4- 47.851!
O.oOu0
4 5 8 8 ' i13.5514 .1736 ~ 1 1 . 2 7 1 8 .la50 -53.2663 .a10 +I06411
-55.7237 .7452 -57.7464
3597 t47.8562 .W33 , -1o.goqo
I .oooo ; 0 . m
.w ; t51.8672
434
Direct. -- -58.2601 -53.0655 -33.4650 -32.9299 -26.7556 -24.7795 -2 1.82 I8 -21.8783 -16.3971
a m + 0.2794 + 9.7144 t23.7738
t29.7699 $38.8525
+27.5792
Mean. Direct. .
--58.2616 $23.5588 -~3.0671 $11.2748 -33.4656 +10.bq10 -32.9316 $52.9760 -26.7563 - 5.3908 -24.7806 + 5.5342 -21.8241 - 8.4861 -21.8786 -55.729 -16.3974 -57.7537
0. uxx) a m 4- 0.2768 - I . ~ O + 9.7128 t 0.3494 $23.7706 $ 0.3568 +27.5786 t17.2016 +2 7678 -17.9171 +38:85m -19.3797
PLATE VIII.
Y Rev'd __ -5526 .2747 .Q28 .9726 *39m 4370 .4818 -7232 .7s9 .oom .2012 .349
.3778
4545 * 1974 .9181 -
-- Man.
443.5557 +I 1.2748 +10&19 $52.9743 - 5.3914 + 5.5356 - 8.4813 -55.7241 -57.7528
- 1.2016 4- 0.3495 t 0.3556 3-17. I995 -17.9176 49.3788
O.oo00
-
itar - I 2 4 5 6 7 8 9 I0 I1
.? .
Direct, -58.2581 -53.0606 -33461 2 -31.9260 -26.7405 -24.7710 -21.8209 -21.872~ -16.3856 -11.6298
I6 ! + 1.1388 17 + 2.8614 18 + 9.7342 19 +1~.rt91 20 1 $18.1893 21 22
23 24
Mean.
-58.2578 _ _ _ _
-53.o6ro -33.4603 -32.9253 -26.7390 -24.7706 -21.82CO -2 I. 8706 -16.3852 -11.6278 - 10.4 I 88 - 8.3544
+ I.14oq + 9.7334 +IS. 1214
a m + 0.2871 4- 2.8634
+18.1919 + 23.7749 +23.7?54 $27.5738 4757 +27.5748 449.7734 a7743 f29.7738 f38.85.18 .854l , +1Y.8540
Y
+ 23.5670 +I 1.2769 +10.6A26
.WSI +51.4121 .4146
STARS IN COMA BERENICES.
TABLE v. (ChfhMfCd.>-PLATE Ix.
436
Y
PUTE X.
I I ' 2
4 !
7 1
9 '
5 ' 6 '
8 ,
'I0
21 I
21 ,
24 , 23 I
436 KRETZ.
TABLE V. ( C O ~ ~ ~ ~ U ~ ~ . ) - P L A T E XI. I I
Y
Inr. I--- ---
I I -58.2.564
4 I -33.4591
Direct. ---
2 -530611
5 -32,9126 6 I -A 7522 7 I -147722 8 1 -21.8256 9 -21.81170
10 i -163752 Id O.oo00
Rev'd
* 2591 .& .4597 .9154 .7479 .7697 3179 .mi6 .3914 .oom ,2814 .7126
- 1.1956 f 0.3549
1-17.1969
-10.2726
+ 0.35So -17.9136
PLATE XII.
Y Direct Rev'd. I. .-
itnr. 1. .. . '--. _______ Direct Rev'd Mean, --! '-1- Mean.
$23.5537 f II .2680 + 10.6381 +51.9683 - 5.39'9 + 5 5358 - 8.4810
m
SW.
- I 2
4 5 6 7
' 8 9
14 15
23 14
I0
21 22
- Star, -
I 2
4 5 6 7 8 9
14 15 I 8 21 22
2 3 24
10
-
STARS IN COMA BERENICES.
TABLE V. (Corrrilrrtrd.)-Pu~~ XIII.
Direct. -__ -58.2619 -53.0649 33 .4649 -32.9213 -26.7510 -24.7777 -21.8344 -2I.gml -16.4105
0. am t 9.2760 +23.i697 +a74772 -+297630 $38.8422
I
Rw'd Mean.
-58.2601 -53.Cw -33.4630 -31.9194 -26.7454 -14 7734 -21.8314 -21.8966 -16.4054
t 0.2781 +23.77& t 2 7 5789 +19.7634 +38.8456
--
0.m
-
-58.1545 -53.0607 -33.4612
-26.7501 -24.7776 -11.8272 -21.8933 -16.4015
O.oo00 + 0.2740
-32.9211
--L Direct. Rev'd
431
+23.5697
+ 52.9749 - 5.3814 -t- 5.5398 - 8.4738 -55.7161 -57.7415
- 1.1978 + 0.3552 + 17.1957 -17.9165 -19.3818
+ 1 I. 2839 +10.6485
0.OoQ)
- PUTE XIV.
.2616 I -58.2580
. 06sI 1 -53.0619
.4611 I -33.4612 ,9137 ! -32.9224 .75q -26.7504 .777r I -14.7774 .8154 -21.8263 .w I - 2 1 . ~
. 3 ~ -16.4~07
.OW0 I o.ocoo
.1768 i +- 0.2754
Mean.
+23.566.5 +11.2808 t 10.6463 +52,9740 - 5.3862 t 5.5356 - 8.4778 -55.7150 -57.7430
0.omO - 1.2005 + 0.3528 +I7.1930 -17.9184 -1 9.3841
I f23.5619 + I 1.1787
10.6423 +5?&96 - 5.3838 + 5.5392 - 8.4791
-57,7497 -55.7 I81
0. cax, - 1.1978
t23.5586
+ 10.6398 + 5?@4 - 5.3& + 5.5346 - 8.4832 -55.7209
+ I 1.2754
-57.7438 O.oo00
- 1.2010
111. Method of Reduction.
Having obtained in the manner explained in the preceding section the measured co6rdinates of the stars on the plates, we are in position to deduce from them the differences in right ascen- sion and in declination to which they correspond. I t is plain that certain corrections must be applied before this can be accom- plished. In the first place, a photograph is a plane picture of the sky ; hence we must introduce the “ Transformation Cor- rections.” Then the stars’ positions are affected by refraFtion, precession, nutation and aberration, and the nieasures must be freed therefrom. We shall find, however, in the progress of the work, that before we can apply these corrections to the measured coordinates, we must reduce the latter into differences of right ascension and of declination (except for the corrections mentioned above) by means of certain constants to be dis- cussed later. These are found by comparing the positions with respect to a given origin of certain well known stars on the plates with their measured coijrdinates, corrected for refraction, etc. Thcse constants being known, we shall find that by means of simple foxmulx the measured coiirdinates can be trans- formed into angular distances and at the same time freed from the effects of refraction and eriors of orientation. Adding these distances to the known coordinates of the origin of measures on the plate, we obtain the celestial co6rdinates of the starsex- cept for the transformation corrections. The latter are then ap- plied to the means of all the observations on each star, and we have the final right ascensions and declinations.
Let us proceed to discuss these several steps.
Transformation Oorrectiona.-An astronomical photograph may be regarded as a central projection on a plane of part of
(98)
STARS IN COMA BERENICES. 439
the heavens. A certain quantity, known as the “.Transforma- tion Correction,” must therefore be added to reduce any meas- ured distance on the plate into the distance on the sky to which it corresponds. To find an expression for this correctiqn, let us consider the spherical triangle whose vertices are the pole, the center of the plate, and any star on the plate. By center is meant the point at which a perpendicular on to its plane from the object glass cuts the plate. It is the point of tangency of the plate with the spherical image of the sky formed-at the focus of the object glass. Now let
a. = the right ascension of the center, and a = the right ascension of any star; p,, = the north polar distance of the center, and p = that of the star ; 7 = the parallactic angle at the center, and x = the angular distance from center to star ;
then, by the usual formulz [Chauvenet, Sph. Trig., Equ.’s
sin (go-q) cot ( 0 - 0 ) - .-’- sin q ( 2 )
( 3 )
Now consider a central projection of the figure onto a tangent plane at the center of the plate, 0. Let OX, OY be the axes, 0 Y being the projection of the hour circle through the center 0, and OX being perpendicular to OY; Let also S be the pro- jected position of the star, and X and Y its rectangular co- ordinates on the plate expressed in seconds of arc of a great circle, the positive directions being the same as those of the ‘I Measured Coordinates ” (cf. p. 427). Then we shall have, taking the radius of the sphere as unity,
cot 7 = - - . - _. .
where tm q = tang COI (a - 00) .
L7-L YOS
X = OSsin YOS
Y = 0s COI YOS. (99)
440 KRETZ.
Also
so that
But from our spherical triangle '
sin I sin 11 = sin (a - ab) sin p. (5)
Dividing ( 5 ) by (I) , and remembering (4) we get
Similarly multiplying (2) by (6) we get
( 7 )
These expressions may be easily transformed by the aid of
cos (a-a.,) tanptan ( p o - q ) tan I
tan x cos I]= Y= -
(3). We obtain finally
Thc formulre (8) express rigorously the relation which holds between the true and the projected distances. They presuppose a knowledge of the scale-value, and of the position of the center, when the position of any other star may be found.
From these formulre very convenient expressions can be ob- tained in the form of series, giving the transformation correc- tions to any desired degree of accuracy. They may be used with advantage to within I 5' of the pole. Making thesame assump- tions as before with regard to the formuk (8) let us write them :
I Tlicse are Turner's lormuls for lrnnsfoming measured rectangular into celestial cocirddinates ; cl. Observatory, Yol. 16, pp. 373 ff.
(1c@)
STARS IN COMA BERENICES. 441
Substituting from (10) in (9) we get after slight reductions
or since X=tm (a-QO) cosp, [tnnpo- Y],
cos to = sin do, sin po = cos fro,
0-s =do,
Apply to this last expression the formula tan-1 = u - 4 148 + us - .
and expand each term by division. To terms of the fourth order the resulting series will be
(12)' t A a = X ~ c J ~ f A , ( . Y r c c A o ) Y A,=tan I!,,
+ A,( X rec 0, ) Yfi A, = tan't!,,,
+ A,( X KC 4,)' Y A, = - tan do, +- As( X s i x (lo) Ya A, =tan%&.
f A,( x uc fro)' A, = - 4,
The process may easily be continued to any number of ttmis ; but for most cases even terms of the third order are almost in- appreciable, and no accuracy is added by carrying the compu- tations further.' Higher terms will be necessary only when do becomes large, or when the plate covers more than 2' square.
The method is entirely analogous to the prcceding, but the algebraic work is much more intricate. For we cannot now eliminate 6' and thus get rid of that quantity once for all. We must keep it in the reductions until the end, and then eliminate it by the relation
J > do + Ad.
Let us*consider again the expression for .Y in the form (9). Remembering the last of equations (8) we can transform this as follows :
Let us now seek to find a similar series for d3.
From (8) and (9)
From (8) and (10) tan po- Y
O -. ). m p o + I tnnp cos ( a - n ) -
1 SCC rdnotc, p. 443. ANNALS N. Y. ACAD. %I., XII, April 4, 1 p . - 2 8 .
( 101 1
442 KRETZ.
1 U Z ( . \ ‘ r c c ‘ ~ o ) ~ Y n, - d ,
-.. D,(J’sec ‘ ‘ , , ) 2 Y’ D, - - rinfil, tan do, ; Y’ Dl p - 1 .
- U,( S s e r ‘lo ) I D, - i ( 3 siii ‘1, cnsa ‘To
Hence, after slight reductions, from ( I 3) and ( 14)
SO that X = s i n ( n - o o ) tan) [ Ytnnp, -+ 11 C O S ) ~ ,
s sin (u-%) [ Y sinj, + CMP,,]
Inn p = -.
’ ( ‘ 7 ) ’
or
and
X cold= :
sin da [ Y cos do + sin do]
sin dn [ Y+ tan J,, J .Y scc do t a n ( d , + . I d ) =
Expanding and reducing IVC obtain finally :
(‘6) sin An [ J v + tan ‘I,,] - X sec 11, tan do x aec ‘I, + i n ~n [ Y + tnn d , ~ tan (I,, ‘
ran Jd ?-
This may be written, substituting for the sine,
STARS IS COMA I(I.:RI<KICES. 44 3
is'not the case with the measured .Y and r! The formula, ar- ranged for calculation to terms of the third order, are as follows :
The simplicity and elegance of the above -expressions are ;ti once evident when we remember that Jo is tlic declination of the center of the plate, and is thercforc constant for any group, or, in fact, for an cntirc zone. I t is, Iiowcver, necessary, that the position of thc ccnter should be known. As has prcviously been mentioned, liuthcrfurd was careful to havc this point coincide with sonie bright star ; in the casc of the Coma Platcs the star selccted was I 2 c (my no. 14). Taking thus tlic values of -la and lri' from tlic Ccitnlog tk.r A S I ~ O I I O I I I ~ J C ~ ~ I ~ Cid/schizft (c f. the '' Lisr oi; CATALVCCES" in Part I of the present paper), ant1 applying forniulrc (18) and (19) to cadi star, tlic quatititics (JU-~Y) sec I;, and Jd - )'are obtained. I llnvc collected thcni in' TAIILE VI. Since the rectangulx coOrdinatcs, .Y and J', ~ w r c measured from the same star as origin, it i s evident that the tablc will give at oticc the corrections which havc to bc added to .\- sec Jo and k-, i. r. . to tlic niensurcd coiirdinates multiplied by tlic scalc-value for the ccntcr oftlie plate, it1 order to changc them to Ju atitl S. It i s also plain that tlic table will be constant for all the platcs. and that tlic corrcctions may thcrcforc be applied cqtially well to the mean of all tlic detcrnlitiations, as to each one sepnmtely. 'I'liis I havc done.
I Siw - - F : ~ I I ' s ( IZ), ( 1 7 ) , ( I S ) nntl ( 1 9 ) were first dcducrd by this mctliid hy I'rofcssor Jarnby. See his review of " I)onncr, 1)clcrminnlion des (~onslnnts, etc.," in the Vierteljahntchrift for 1895, p. 114, where these scries, to terms of the fifth order are given, Init without demonstrntion. I'reviously. 1i:d nnd I<nmhi t In Trans: Roy. Irish Acad. , XSX. 1"t. IV, had deduced the lirst two of the nhove P S -
pnnsinns to ttrms of the third order, hut they were obtninctl by n ]wocess entirely different from that shown here.
(105)
414 P RE'I'Z.
A few words more on this subject may not bc amiss. In the first paragraph of this section it is stated that the transformation correction is applied in order to change a measured distance 011 tlir plntc into the corrcsponding actual distnncc on the sky. 'Iliat is, Iiowcvcr, not all : it docs something iiiorc than that, whcn the formulx ( I 21, ( I 7 ) or ( I S ) , ( 19) arc used. For t h y prcsup- pose that all tlic iiieasurcd J, 'S are niultipliccl by p , and all the measured .r's byj, scc $,,, \vlicrcp is tlic equatorial scalc-valuc, atid (I,, is die dcclinntion of tlic center of tlic plate. Hut by this pro- ccss RII error is iiitroduccd, ;is all the distances in right ascen- sion diose declination is grcatcr tlinii d,, become too small, and i i cc x r m . 'I'lii. grcat ;idv;iiit;igc in using tlic formulx men- tioned, is, tlint they take accoiint of this fact, ant1 pcrniit a con- stant scale-valuc t o be used for all tlic stars. Tlicy include still nilother corrcction, iiamcly tlint duc to tlic curvature of the projcctioiis on tlir' platc of tlic p:irallels of declination, whicli are riot str;iiglit lilies, but arcs taiigcnt to the dircctioii of tlic axis of -1; nt their iiiterscction d i tlic axis of I: Miese con- sidcriitioiis u i l l cspl;rin \vIiy tlic quaiititics in tlic table arc not 4ymiiictric;il \\it11 respect to tlic center.
1 .\ ui.1: \' I .--TI<.\ s . ~ HOIAT 10s Cc JIW:C IIUXS.
SLlr.
I S
9 I0
I 1 11
-0.233 .m .m
-0. ~6 --0.029 4 . 3 2 1 -0.938 -1 323 -1.916 - 2 . 0 1 0
- - < . O d h - 2 . (JgY
Refraction Corrections.--JI ucli has been written on tlic hiibjcct of pliotogrnpliic rcfractioii, niid several formulx put)- lislicrl tlchigiictl to cliniinntc its cffcct from tlic mcnsurcd rcctan-
(1n.I)
gular coiirdiirntcs. I have used those of Professor Jacoby’ which were dcdiicctl by him from Dr. Rnmbaut’s formulx publislicd in the Ashvlruiirischc~ iVachrichkit, ,No. 3 I 2 j.
p = the latitude of the plncc, + 40’ 43’ 50” in my case ; H - u0 = the hour iiliglc of the ccnter of the pliite, B being the
I‘ Sidercnl ‘I‘imc ” from TABLE I, atid y1 the riglit as- cension of star 14, roughly corrccted to tlrs date of ohscrvation ;
Let
t;“ = the declination of the ccntcr, Star 14‘; ,3 = tlic constiint of rcfraction computed for the centcr
with tlic argumcrit I ’ True Zenith Distance,” c0, and multiplied by to allow for the increascd refran- gibility of thc actinic rays’ ; SO thilt ,? = k‘. zt (Chnuvcnct, Astr.. Vol. I , $6 I 19, 120).
Now compute tlic quantities
A veiy simple way of verifying tlie above formulz is the fol- lowing I : Bessel gives correctioiis for clearing apparent differ- ences in right ascension arid declination, obtained by micromet- ric observations, from the effects of refraction in the form :
~ ( u ' - r i ) - I # [ t n n ~ ; , c o s ( p - y ) s i n y
- tan ;, sin 9 tnn J, em p + sin p ] scc Jo
A (rl' - , I ) ... JL [tan* (, cos ( p - q ) C O ~ y
+ tnn c,, bin g tan (Iu sin p + c o s p ]
where 5 and p are the measured distance and position angle, :,,and (I are tlie true zcnith distance and parallactic angle at the middle point between tlie two stars, whose coordinates are (a, d) and (a', G ' ) , and 2,) is the declination of that point. NOK (Chauvenet, Astronomy, Vol. 11, 1). 453)
L' tnn' :, 6 -
where, I' being tlie refraction,
sin :,, 1 I
sin (:".- r1 1 - r w t ; , , I--Y fl
Lo I I
'C , -- 'fl. dr dL.' KO Lo
placing cos r = I , sin I' = I' and rcmcmbering that I' = X.' tan c,, (Chauveiirt, Vol. I , p. 171), where r and k' are expressed i n parts of the radius. Expanding the expressions for n and b by division, we easily obtain
B I - I - I ? S C C I - tan i0
fiP b - u = tan' . kf tan ';,, + tan C, + ...,
KO
the succeeding tcrms being higher powers in XJ and "' which
can bc neglccted. For zenith distances less than 70' the term
in For irisidc that limit we have
4 0
CfA.'
fc, may also be neglected.
I Cf. St.lile,inpcr's ( ' Pr.rtrpc," SOW, 1). 285, wlierc the alwve lncthotl t v u first
* .\*tronmnisrhe L'ntersuclrunpxi, \'ol 1, p. 166 : or Chnovenet, Astronomy, p o i I l l C f l f,111
VIII I I , I\. J jR.
(106)
S'I'ARS IN COMA UERESICICS. 447
with sufficient accuracy, as both A' and i.' are practically con- stant, and ,4 and r do not 'vary with the zenith distance. But this is only 0.00002 at the limit sclccted; and since the
dk' tangent of 70' is 2.7, the term tail c0 will be inappreciable
when I, is less than 70". 4,
Hence \vc can write
or
with sufficient accuracy for photographic work, wherc J is not large.
1n.t US then substitute in thc original formulx for J ( d - a )
and A(;' - 13) from the following equations :
X Zi'
I >in) = .K
I to* p 7 Y
sin y - ff tan C, cos p -: G
and thcy become
A ( d - a ) 2: i~'.Yscc~l,,[ I + I / ' ) -L I.',.( G-1311 rl,,)ffsec '1,
A ( 11' - 1 1 ) x 4' X ( G ... la11 *lo) f / - 1 1.' 11 I -; G J )
where 4' is cxpresscd in parts of tlic radius. Thcsc formulz are evidently idciltical with Professor Jacoby's except for the fac- tor 66/65 by ~vhich Y must be multiplicd in order to obtain ,3. It should be observed that in the above equations terms in the sccond and highcr powers of s are ncglectcd ; for we take ac- count neither of transformation corrcctions, nor of thc fact that in llcssel's original formulx thc quantities c,, and I;, arc intended to apply to thc middle point betaecn tlic two stars, whereas RC
transfcr tlicni to tlic etid of tlic arc. 'This is, however, entirely Icgitimatc for most photographic platcs.
I subjoin 'r,\iii ,E VII which shows the values of thc four factors f i / r , L V ~ , .7{, N, for all of iny platcs.
(107)
448
1 l'lnte.
I I 1
I l l I Y V
\'I VI I
Y l l l IS S
s1 SII
SI\' siir
Precession, Nutation, and Aberration.-Yonc of thesc nced bc taken into account. For as regards the first two, they, bc- ing cluc to niotions of tlie earth, cannot affect thc configuration of the stars, nlthougli tlicy shift the axes of referciicc. The absnlutc tli.;tanccs bctwccn tlic stars will, thcrcfore, bc unaffected by thesc c;i~iscs, but tlic diferences in riglit nsccnsion and dec- liiiatioii will bc cli;inged. If, then, \vc cornputc thc constants by tlic nictliod to he detailcd later, i, c., by comparing ccrtain stars on the plate with their positions as obtaincd from meridian obscrvatiniis reduced to sonic coiivcniciit epoch, then it is evi- dciit that the resulting right asccnsions and declinations from thc platc will be rcferred to tlic sainc' cpocli, without the nced of applyiiig any corrcctioiis for prcccssioii or nutation. 1-or tlic clinngcs due to thcsc causcs consist partly in a motion of trans- lation, and partly in a iiiotion of rotation of the axes ; the former will be ciitirely cliniinatcd, wliilc tlic latter will he includcd in tlic oriciitatioii correction.
]:or I3csscl ' lias showli that i t c l ianps the position anglcs about a point equally, wliile it dfccts all tlic distances, in whatcver direction, by a const;int
\">I I I , 11. 4h6.
Ahc'rratinii rnny also be ncglectcd.
I :\-truiioiiii~chr ~n lcr .ur l iun~rn . I'd. J , 11. 207 ; o r Chnuvene!. Asimnomy,
( l ( J 8 )
STARS IN COMA 1~I:IIKSICES. 4.19
factor only. Its wliolc effect will thcrcfore be iqcluded i n the scrile-valuc and orientation corrcctiojis, when these arc obtained by the method now to be dcscribcd.
Constants of the Plates.-Four qunntitics, niust be known for c x h platc, in ortlcr that \vc' may dctcriiiinc thc absolutc po- sitions of the stars \vliosc coijrtlinatcs Iinvc been rneasurcd. 'They arc : the riglit ascension 11" and tlic tlccliiiation 4,) of tlic cmter, or origin ; tlic vnluc in seconds of arc of one division of the scale ; and tlic ;uiglc made by the nscs to ivliich the nicns- urcments arc referred, with tlic nst:s of rcfcrcncc i n the cclcstial sphere. To obtain tlicni, \vc milst coniparc tlic nicasurcd co;;r- dinates of certain stars ( 6 * stand;irds "1 with tlie corresponding distances of tlic snnic stars, from the same point as origin, ub- tained froni meridinn obscrvntions. llntters will bc greatly facilitated by n linoivlcdgc of approsinintc vnlucs for tlicsc con- stants. As rcxnrds my plates, such ii)form;itioii was avail;il)lc. The position of tlic ccntcr wliicli cniiicidcs \\it11 star 14 ( I Z ~ ' Conix), wns xcuratcly linowi ; tlic ;ipprosini;itc scnlc-vnluc \vns placed at
1111111. S Z f f . 1 ; 7 .
that being tlic result of a previous reduction of Ruthcrfurd's pliotogriq~lis of tlic I'lciatlcs ; wliilc tlic oricnt;itioii correction, due to tlic rotation of tlic nscs, \voultl be necessarily small, owing to tlic inniiiirr i n \vliicli tlic plnte \\;is ndjustetl i n tlic measuring nincliinc.
\Vc niust no\v ot)t.iin tlic distniiccs Ju = r i - ti,!, and Jt; = (1 - /ill, for certain st;irs on tlic pl;itcs. 1.c.t [IS return to 1):irt I , Scctioii 111 of tliis piper. \\'c h i d tlicrc Ip. 396) ;I c;itnloguc of twclve stnrs \uit;il)lc for this ixirpnsc. Of these, thc followiii~ clcvcn arc s~ifficiciitl!, \\.ell observed to scr\.c' ;I< st;ilitl;irtls " : 2 .
3, j, 6, 10, I I , (1. 14, IS, 19, 20. 'I'lic~c ;ire C'Ii;i.;c's iiunitxrs : they corrcsI)ontI t o ni!~iiunibcrs I , 2 , 4, j . 9, 10, 14 , I j, 2 1 , 2 2 ,
23, rcspcctivcly. 1 1 1 tlic fullo\viiiE I sli;ill t lcsipntc tlicni by thc Inttcr nunibcrs oiil).. ]hit t)cforc procwding tn obtxin Ju and J/; for tlicsc stnrs, \vc must apply n cnrrcction fi)r 1)rnpcr niotion.
( Ill9 )
. .
450 K I< El’%.
For, the photogrdphs being taken at three different dates, namely 1870.3 (Plates I-III), 187 j .4 (Platcs IV-VIII), and 1876.4 (Plates IX-XIV), tlie relative positions of the standards will not be thc same for them all, duc to the cause mentioned. As the epoch of reduction is to be.1875, wc must not apply any cor- rection for precession or nutation, otherwise what has been said above regarding this matter would not apply. We can, then, construct Thnu VIII. This table givcs the Right Ascensions and Proper Motions in Right Asccnsion, and the Declinations and Proper Motions in Declination, for 1575. Then follow six columns showing tlic seconds of the Right Ascensions and Ilcclinations with tlic proper motions applied to reduce them to the thee dates mentioned ; and in the last two columns whl be found the \\'tights in Right Ascension and in Declination, respec- tively, of cacli star for 1870 and 1875. Thc same weights were used for 187; and 1 8 7 6 They werc calculated by reversing the proccss for obtaining thc probable errors explained in Part I , Sect. 11, ‘I FORJICLE FOR A DJusT.vwr.’’ From tliese quantities we can then obtain J(I and JJ with their weights for each I ‘ staiidard ” on cvcry plate.
Now Ict u s coniputc for cacli standard on cach plate the quantitics 11’ and tiy as follo\vs : From TmLe V we obtain .rand
.I’ for cach star. = .tscc do . 5P.87 and I * = y . 52”.Y7. Correct tlicsc for refraction by nieans of TARLE VII aiid tlic corrcsponding forniulz, and apply the trans- formation corrections from T,iilw VI. Subtract from the sums thus obtained the corrcymnding Ju or JJ : tlie diffcrences will be lzl scc 6, ;und 11”. It is tlicn cvident that )I, and IJ” should be zero, i f it \rere riot for crrors of observation, and for errors in the assumed constants. \Vc arc to find the values of tlic latter. Lct 115 introduce tlic iiotntioii :
1:orm tlic products -1’ SCC
p = tlic correction to the nsrurned scale-valuc, so that the t ruc vnlue is 52”.87 ( I t p ) ;
I‘ = the oricntation corrcction, or small angle through which tlic axcs must be rotated in tlic direction of decreasing position angles ;
(110)
I 2 4 5 9 1
0
14
1.5
21
22
25
0
, d,
1s.;
5 43
.50
-<LO
39
10
55
96
-00
74
30
16.
70
--o
.iio
30 3
7 So
-0.1
06
41 5
3.76
- 249
47
16
17
-00
jS
ISJ
3 1
80
3
-0.0
53
5 54
40
-i 0.006
26 44.18 -
0.0
~0
50 ~
2.5
s -0 0.3s
3
2 3
3.99
-0
.048
2CP5
2'5~
';j
26 4
2 lo
.hj
26 .
ti 4
2.94
27
19
2.2
6 25
43
14.4
s
25 4
1 2
s.0
1
26 3
2 23
.93
26 3
1 20
.26
26 4
7 31
.0;
26 1
6 33
15
26 3
2 40
.72
43:'6
s 56
.51
17.6
9 3s
30
54.9
3 1
7 00
IS. 1
9
34.3
7 44
.32
32.7
6 3
4.2
2
57:b
4 10
.69
42
.b
2.76
'3 s
o 27
99
23.9
5 '9
85
40.6
5
31.0
5 33
.07
4 3:;
s 55
.93
16.6
2
37.7
6 53
.66
16 7
5 IS
.02
34.4
0 41
.17
32.5
6 33
97
5s:;7
I 0
.65
42.9
5 2
.22
14.5
4 2S
.01
23.9
5 20
.30
40.7
3 31
.03
43.4
5 55
.S6
16.4
1
37.6
5 53
.4'
I 6.7
0 17
.98
34.4
1 43.14
32.5
3
- r- 58
.';6
4 0
4.0
4.2
4.2
1
v,
10.6
4 5.
6 6.
3 4.
9 5.
4
42.9
5 5
.6
6.4
4.9
5.5
2.1
1
7.6
12.0
5.7
8.7
14
.a
3.5
4.3
2.9
3.8
28.0
2 2.
9 3.
1 2.
3 2.
3 23
.99
27.8
32
.3
23.5
28
.9
40.7
4 8.
9 9.
7 7.
5 8
4
20.3
s 1
.9
2.6
4.2
3.
7
31 o
z 16
.5 168
13.8
14
.1
33.1
7 1
0.9
10
.6
8.8
8.6
R = the correction in seconds of arc of a great circle to be added to the assunicd right ascension of tlic center ;
c = the correction in seconds of arc of a great circle to be added to the assumed dcclination of the center.
Tlicn tlie nicasurcd co~rdiuatcs in seconds of arc of a great circle, -Y and I', will require the following corrections :
Due to erroncous scnlc-value.
t)uc to orientation
Due to errors i n the assumed position of the center,
Correction 10 ,r k 4
( ' 1 rrcctirm to I ' -1. (.. b It is cvidciit that If wc add thc sum of thesc corrections to
A' and Y corrcctcd for rcfrxtioii and for trsnsformntioti crrors, ivc sIiouItI obtain Ju cos ;riid Jf; respectively. We Iiave, thereforc, from cncli star, tiyo cclirntioris of thc form
h . 1.V . r l ' i t , .;',
L PI ' - r.Y - v1 -7 ' :
wllerc tlic 7.'s, as usunl, arc thc rcsit1u;il crrors due to inaccuracy of the observations.
I x t [is JIOW form, for c;icli plate, cquntiotis like the above for cveryst;iritl;rrtl mc;tsurcd ; w e sliall get ;I sct of observation cqua- tious, from ivliich the constants cnii be tlctcrmincd by the method of lcnst squ;ircs. C.;unlly, wlicn :III the linve the same weight, or \\.lien tlic \+$its of corrcsponding cquntions in the two coor- tlitintcs arc cclual, it is possible to abridge tlic labor considerably by mcaris of ccrtin forrnuh deduced by I'rofessor Jacoby.' A s giveti by him. they apply to tltc cnsc of cqud wciglits only, but t h y miKlit casily bc gcticrnlizcd. I could not makc use of this
1 \)qmil i l r \ ~ ) I I I ~ . . , \I.IV, 1 h 1 ) 0 . 1, 4 2 4
( 110)
method, liowcver. For, owing to the nianncr i n which ur and /iy were obtained (narncly, by using -la and 2,; obtained from catalogbe positions), their wciglits arc quite irregular. 'The forrnulz of tlic general theory, tlicrcfore, had to bc used. . Each equation was first multiplicd by tlic square root of tlie \\+$it of tlic star 011 which tlic absolute term depended. 'Tliis, al- though not tlicorctically correct (sincc tlic wciglit sliould take account of tlic unccrtniiity in tlie position of the central star, and also of that of tlic I W ~ I S I I ~ C ~ photogrnpliic coc'~rtliiiatcs), was found to bc sufficiciitl~~ ;icctir;itc, owing to tlic niinutcncss of the unknowns. For tlic miic rc;isoii, 110 apprcci;tblc crror \v;is conimittctl by tiivitliiig thc cocffcicnts -Y and 1. by loo, and retaining only tlic first placc of tlccirnnls, \vhilc tlic ;iritIimctical work WIS greatly siiiiplifietl tlicrcby. Tlic follo\vin~ sct of ob- servation equations \vns tlitis obtaincd :
I fl c I fI .\./' I f l 1'!'f I f l J / , 0
......................................................
I f ... l f . . J f ' - - l f , . . \ , ' l,f.,'/, 0 .......................................................
464
[P, v, Y, . I l l / + [PI v,n.. I ] = 0
[pyY,vy’IlP’-!- [ r , ’ t - , y , ’ I l f l + [PyYz’J , . II=o [ fYX,XZ . l]Z -L [.p1Xl., . I] = o
Add’the first and third, and the second and fourth of the last equations, term to term, and from the resulting equations ob- tain p‘ and #. The values will be identically the same as if all the four unknowns had bcen eliminated from one se.t of normals by thc general method.
The weights of the unknowns could, in this case, at once be written do\vn, with sufficient accuracy. For owing to the fact that the weights in right ascension and in declination of the observation equations are nearly equal, we have
.
[Pl.\;T ~ l t . [ P Y ~ , v , . ~ l - ~ [ P l v , v , . I 1 t [ ? , G - * . I l
nearly and [PI XI VI. I ] + [ P Y 4 v, ’ I ]
small, so that \vc can place (cf. Chauvcnet, Astronomy, Vol. 11, 1’. 537)
KI c l r j / [p,xl.\; 11 -1- tp, v, v, I ]
\vt of z ’ [ p 1’Y 31
ivhcrc [pJ’Y. 31 dcnotcs the cocfficient of J in the last elimination equation. Siniil;irly, i n the invcrtcd elimination, the coefficients of p’ and I’ arc very large compared to those of k and r. so :hat at once
\\I. b -7 [ p , ] of the er1uation.r containing I. \\I, [ p , ] or the equations containing d .
Knowir g the weiglits, thc probable errors were then obtained in the usual maliner from the residuals.
(114)
It now reninins only to make use of the constants obtaine! by tlic methods dcscribed above. This is n simple matter, F o r we have to apply to tlic measured codrdinates the correc- tions
p Xxc I!, t r scc 11, . Y -:- 1. scc Ju (0 .\'w
f) 1' - r X , - c lo Y
due to errors in tlic assumed constants, and
f /I/, . .Y scc (1, f .\; Y 10 .Y sec (lo
:. hf, . X S C C + A', Y ICI Y
due to rcfraction. If then we add -Y scc du and 1; correctcd by the process cxplaincd abovc to tiu and I;, respectively, where u0
and 6,, are the assumed cocirdinntcs of tlic center, we will obtain for each star ccrtain quantities, ti1 and I ; , , \vhicli arc defined by the equations
11 -. Ill ~ 1;
I! I l l . 1i
wherc N ant1 6 arc the right ascciision and thc dccliiiation rc- spcctivcly of tlic given stitr, ;tnd Ta and & are tlic corrcsponding transformation corrections. 11, a i d d, may bc callcd the a ' pro- jcctcd " codrdiiintcs of tlie star. Collcctiii~ dl thesc operations togcthcr, it is cvident that n'c can writc thc follon.ing forniulx :
n1 . ( I i j I .l/,).i'.cc 11, -.. (.I., r scc ,lo) i ' -7 ( i t , 1. LCC ,to)
(Il = ( I + p f 'V,) }' . i ,I/,- ! C", tlu),Y >ec l!" lIu . I ),
and ,I . 11, L 7., , I I ! , . 7:
arid whcn takeii i i i conncction with the prccedi~ig discussioii, it is cvidcnt that tlicsc cquatioiis cxprcss in mntlicmatical lan- guage all the steps nccessnry to transform the measured rec- tangular cotirdin;~tcs 011 thc platcs, .rand J', into tlie corrcspond- ing riglit iisccnsions and dcclinations on tlic cclcstial sphere.
(11.5)
IV Results.
Constants.-~Iaking tlic least sqiinrc solution for each plate ;IS cxplaincd Sect. 111, w e get tlie constants sct down in TAIKE IS. They all tlcpcnd on clcvcn standards. except in the cilse of I’latc I , wlicrc two of tlicsc arc missing, owing to inaccurate 1)oiiitiiig of tlic telescope. ‘Thc probablc crrors conipiited for p aiid I‘ i n no casc differed by niorc t l i iui n unit in tlic last plncc ; I have tlicrcforc given only oilc vnluc, which applies to both tlicsc quaiititics.
T . \ i i u IS.--Cos~~r,\r.rs.
Plate.
I 1 1
I l l 1 \ ’
V V l
\ ! I \ I l l
I \ \
\ I \ I I
\ ! I ! \ I ‘.
F I’roLoLlc Er rur ofp or r.
- 0 . m 3 0 L: 2.y :I 26 t 26 ..I 2s
’ . 26 ’ - 24
24 t 2.4 7 2 5 .- 2 9
-- 2.4 -k 2J
,- -,
70.135 .- 0.131
4.073 0.003 0.166
-0.018
0.160 0.069
.. 0.148
, 0.739
0.089 - 0.093
- k O.OQ7
. 0.161
I I’rob. Er- ror of ,..
-0.119 ro.053
-0.174 -:o.qS
-0. I w z 0.052 .-0.161 -ro.o49
-0.176 .:n.oso -0.095 -0.a15 -0.060 -0.0.15 -0.089 ?0,1146 -0.108 t.o.o.53 -0.107 l 0 . 0 4 5 4.017 . 0.012
-0.083 ..O.O5J
4.178 ~0.0J;
4 . 0 8 4 :-V.OJ.j
I t will be sccn that tlic probnblc crrors ngrcc w r y well, so that the f i i u l positions from all tlie platcs arc ciititlctl to an ccltinl m o u n t of coiifitlcricc. A prohablc crror i n p or r of + 0.0000~ j corrcspoiids to m i uiiccrt;iiiity of about o”.oY of
~ r c uf ;I grcnt circle in the positioti of tlic most outlying star. Tlic grcat di\.crsity iii tlic vnlucs of I’ is tluc for the most part to tlic ;iccidciit;tl position i n wliicli tlic plate ivns sct in tile niensuring niacliinc.
( 1 1 6 )
The following arc' thc rcsiduals obtaincd by introducing tile values of the constants given above in the rcspcctivc obscr\a- tion equations (p. 452) :
From thc Riglit Ascensions :
Plate.
I
Star I. Star Z. Star 4. Star 5 . Star 9. Star 10. Star 11. Star 15. >tar 21. Star 22. Star 23.
t 0 . 1 4 4 . 2 5 -0.03 -1.03 +O.IJ j-0.16 - a 1 2 -;.lo , - O . Z ~
! - O . I j -0.J.l -3.0) -%Oj +0.24
IV -0.32 -10.19 - ;o .z8 -:-0.25 -0.10 +.81 -0.07 -t-o.24 -,-o.oJ -0.2s t o . 4 3
VI 4 . 4 6 -!O.IO - 0.16 . O . I I --O.JI --r.oS -;0.17 +o.z9 -0.30 -0.15 - : o . y \'I1 4 . 4 2 ., 0.06 -. 0.0s - . 0.10 -0.22 -1.16 .+0.14 c: 0 .12 -0.32 -: 0 0 2 .. u 25
V l 1 I 4 . 4 4 + 0.00 -: 0.15 .: 0.2s 4 . 1 2 - 0 . s ~ -0.02 - : - O . ~ I -0.16 -0.2~ -0.~6
IS -O.* -0.02 $0.26 -: 0.12 -n 21 -1.01 -:.0.16 .; 0 .27 -0.30 -0 IS +o.jr S -0.52 -! 0 . q +0.25 . 0.2s -0.37 -0.99 ---0.07 ~0.10 - 0 . 2 6 -0.07 -:-0.36
X I 4 . 5 2 -4.05 -i-0.34 - ' 0 . 3 j - 0 . j Y -0.9 - 0.0~) .o.rS -0.16 -0.15 :-o.32
XI1 -0.70 -:o.31 t-o.zY - : - o . I ~ -047 - 1 . q *-o.D() -0.06 - a 1 5 4 . 1 t i + 0 4 5 XI11 4 . 6 4 -LO.OJ -: 0.21 -0.16 +) . jg --0.91 - 0.16 - -O.IIJ -0 .27 -0.11 $0.30 XIV -0.50 $0.06 - 0 . 2 7 , 0 . 2 1 -042 -1.07 ;-o.og 40; - 0 . 2 2 -ov) -0.42
I1 -1lbz 0:'m :-O.dl i-0.15 -0.12 -1.09
111 4 . 3 9 4 . 1 7 -0.06 '0 .15 -0.0s -1.08 . O . I s - : -O.ZS -0.11 4 . 1 2 :-0.31
-0.48 -;-O.IZ -7 0.20 t0.21 4 . 2 8 -1.05 .OO -. 0.40 4 . 0 s -0.26 :-0 55
.. - . - - -. - . .. . . - . . . . - - . . . . . -. - .
Sfeans. --0:49 .; ~ I b s -: o I ' I ~ $0 16 -0'>5 -I;'OI $0.01) . : o.zj -0.17 -0.14 t 0 . 3 6
A consideration of thcsc rcsiduals brings out scvcral interest- ing fncts. In the first place it is evident that they arc almost entirely due to errors in the meridian places, as the residuals from thc different plates for any one star run very nearly alike. Ijut a niore important matter is their size. On the whole they art: fairly large, although perhaps not more so than miglit Ii;ivc been expected from the probable crrors of thc standard stars. At lcast is this the case with the dcclinations ; the right nscciisions show a much greater uncertainty. This is due partly to the fact t h t .r’s on the plates arc more difficult to mcasurs, owing to the elongation of the images ; but the chief C ~ U S C is the grc;itcr inaccuracy of tkr. catalogue riglit ascensions. The statenicnt regarding this matter i n Part I , Sect. I, I ‘ WI.:ir;irrs,’’ is thus fully borne out. It is important to notc, that the rcsi- duals scem to increase more rapidly tlinn tlic probablc crrors of the stars, so that the poorly detcrmiiicd standards show rela- tively larger residunls tliaii thc others. These considerations lead to tlic following conclusioiis : Cnlcss scvcr;il stars on tlic plates can bc found wcll clctcrnmincd in a considerable number of reliable catalogues, it will not p ~ y to go tlirough the laho- I-ious process of obt;iiiiiiig tlic positio:is of thc standards by tlic niettiod which I cniplo)wl. I f p o d modcrii observations are availablc. tlic constants determined froni tlicm will bc quitc siifficiei~tly ;iccur;itc ; provided, of coursc, that the date of ob- servation is not \.cry distillit from tlic date of exposure of the platc, or otlwrwisc, that the proper motion of tlic stars be accu- rately kiio\vn.
To siitisfy myself on this point. I dcduced thc constants nf Platc I l l , using v;ilucs of I ! , and M,, obtained by comparison nf nine of my stars with Konibcrg’s placcs. ‘The \veiglits assigned wcre tlic samc i ts lind bccn given to this catalogue tllrougliotlt the prescnt paper. I found thus :
STARS IN COJIA DEKI<NICI'S. 459
and the residuals : Slnr I . Star 2 Star 4 Star 5 . Star 14. Star 15. St.\r 21. SL.r 22. star 23.
In D -:6j $0.25 +'"I0 4 0y6g --3:47 --3:;1 -i.o.a7 - t i 5 5 $0.:6 I n rl t O . 0 ; ~ 0 . 1 s -2.23 +0.06 -3 2s 4-0.28 -: 0.37 t0.07 . 0.06
]loth tlic rcsitluals nntl tlic probable crrors. it is true, are rntlicr larger tliaii wlicii tlic constants \wrc obtained by thc more claborntc mctliotl. I h t considering tlic qunntitics tlicmsclvcs. it will be seen, that both p ant1 X. diifcr from tlic values previ- ously otitaiiictl by more than the sunis of the probablc crrors. 111 tlic lattcr casc, tlic rcnson for this tliscrcl)ancy is ;in uncs- plaincci systcniatic: tliifcrcncc bctwccn l<ombcr,o's plnccs, and tlic positions of my st:in(liIrcls. 'l'lic discordance i n p cannot be thus esplaiiicti. It is niucli tiiorc scrious, as it affects. not tlic group ;IS a \vholc, but cliniigcs thc rclati~e positions of tlic st;irs. It nplicars tlicn, that tlic constaiits arc by f i r the most tinrclinblc of all tlic quantitics iisctl i n tlic rccluctioii of tlic plates ; nritl i t \\roultl seem that an). labor spent on tlicm, out.s;itlc of \\.lint is absoliitcl~~ iicccss;iry. is but poorly repaid.
True Scale-Value.-It Ins 1)ecii st;itctl tha t the coniputctl sc;ile-vnluc, j _"'.8;( I + p), iiivolixs tlic effect of ;ibcrr;ition, I t may hc tiscf~il for fiiturc ~-cductioris of tlic I<utlicrfiircl plioto- graphs to set h v n tlic triic quantitic~. r\ltliougli for accuratc morli it \id1 i n gciicr;tI be neccssnry to pcrkirri~ tlic lcnst squ;m solution for c ; d plate, ;uid thus indcl)ciitlcritly to obt;iin thc scale-value. caws niiglit arise, ~vltcii ;i close ;ipprosiniation would bc sufficient, or wlicii the number of av;iil;tblc st;und;irils is so small, that no rc1i;uicc call be placctl on tltc rcsultiitg constants. *Tlicn, too. it is possible tha t ;I rclation niny csist bctwccn t l i c " focus " and t l l C sc;~lc-\,aluc.
To f i i i t l tlic forni of the corrcctioii to be atldctl to j2".S7(1 + 1) i n order to climi~i;ltc the effect of ;thcrratioii, \VC Ict
n = tlic / I - / / , distance i n sccontls of arc, from tlie ccntcr to
I / = tlic / ~ / ~ . m / ~ r d nuntbcr of ntillirnctcrs on thc plate, from ;my st;ir on ttic phtc ;
tllc center to tlic star \vliosc tlistancc is n.
( 11!l )
460 KRE'I'Z.
Then it is evidcnt, from thc method by which h e constants are derived (i. c., by compxison with catalogue positions) that, but for errors. of observation,
But evidcntly, I I is too great by the aniount of the aberration, being thc measured distance on thc platc. Hencc, if we let
y (I . . cos a. co5 I$ sin I",
- ( t a n P siii flu : sin (I,, cos 1 1 ~ ) . >in I 7
wlierc 5 is the obliquity of the ccliptic, and atid arc the coijrdinates of d i e central star, roughly corrcctcd to the time of exposure of tlic platc, then will (cf. Cliauvcnct, Astronomy, Vol.
u[ I .. c;. -t D I I ) 11, P. 467)
be the rncasiirctl distance on thc plate in seconds of arc. Cand D i n this formula rcprcsciit the llcssclinn clay numbers, and may be obtaincd from thc 1:;)licrnoris. NTc find, tlicn, evidently
or, rcrncrnbcring cquntioii ( I ) , and neglecting sninll tcrrns
A corrcctioti for tlic tcnipcratiirc at wliicli the platc \\as nimsurcd rni~lit also bc applied, usin:: for this piirposc tiic co- effiicimt of cqxinsioii tletcrtniiicd by I l r . Sclilcsingcr ( ' I I'rxscpc,'' p. 2 2 3 ) . Hut AS t h t quantity is not vcry roli;ihlc, and ;is tlic corrcctioris arc necessarilj. very small, bcing i n no cnzc ;is I a r ~ c as 0.0007 if \vc usc tlic \.nluc of 7' as given in tlic placc rcfcrrcd to. wliilc, oil t l ic otlicr Itarid, tlic tncaii uncc.rtninty of p is more t h n i i 0.0013. I Iinvc felt justified in ncglcctiiig the sanic.
CVc obtain thcn tlic fnllo\ving tablc : (12" 1
S'I';\KS IS COhI:\ IIII<ISIc'IS.
TAIILE X.-THUE SCALE VAI.CF-S.
4GI
Plate. I - - /'. C'orr. for Abcrr. G r r . Scale Vnlue. Tel. Thrr. Focus
The nican scale-value is : ,
5 ~ 1 . a a ~ 4 .
In forming tlic abovc table no account hns bccii tnkcn of tlic teniperaturc nt wliich the plntc was csposcd, nor of tlic rcatliiiK of the tclcscopic tlicrmonictcr " (\vliich arc copicd from 'r,\iim I ) . i\ tliscussion cf tlic effccts of tlicsc c;iuscs on the scale-value m u s t bc postponed unt i l a niucli larger numbcr of Rutlierfiird platcs havc bccii indcpciidentl~~ rcducctl.
focus " mid
Separate Results.-Employing tlic coilstants of T,\iirx IS as esplaincd in Sect. 111, \FC obtain thc ' I projcctctl " riglit asccii- sioiis and tlcclinatiolis. 11, and ( I , , ,ni\..cn on tlic succeeding p;igcs. From them IVC can firid the f i n d co;diri;itcs, 11 and 6, ant1 the proper motions. Tlie latter \wre tlcducctl from my rcsults. i n coiinection {vitli Chase's (cf. p. 343, foot-note, of tlic prcscnt pa- per) positions, for all those stars which he observed. Only t \ ro
others wcrc fuuiitl or1 a sufficient iiumbcr of plates to ivar- rant at1 invcstiption for proper motion. Tlic nictliod cm- plnyctl for all GISCS wlicn tlic observations were distributctl over morc tlian two distinct d.itcs, \\as that fully esplninctl i n Part I, Sect. 11, 1:oicwL.r. I ];OK i\i)ir..~.i.\ii.s.r." Tlic epoch bcing 1875, Clinsc's positions wcrc rcduccd from 1 8 9 2 to that datc, usinK liis gconictric prcccssioiis. A systematic cortcction
(121 1
463 KKE’I‘L.
of - o’I.44 i n K. A. and + o’I.72 in Decl.;iiidicated by direct comparison with niy standards, was then applied. As date of ob- servation I assumed uniforinly 1891.6. This differs in no case by more than . 3 of a ycar from the trut value, and the calcula- tions arc greatly simplified by using the same dates throughout, as then 2’; and 2’( CD) rcrnaiii constant. Unit weight was assigned to all the observations, includitig those of Chase. This was warranted by thc probable crrors, and the formulae of Part I , p. 36; wcre greatly simplified thereby. They become
X f / ) - ,<’ Y ( R ) - - . I , 7; 2 =- 111 IN
atid
where the notation is tltc same as bcfore and III denotes the number of observations. ‘l‘lie u,, and $u thus obtained iticlude Clinsc’s position, howevcr. A s I \r.ishcd to have an independent determination, deduced solely from the pliotogrnpliic obscrva- tions, these quantities were not uscd, but a value for 187 j was obtained dircctly by the following method : The proper mo- tion having bccii fouiicl as cxplaiticd abovc, the nieiisurcd posi- tion.; w r c corrcctcd to 18;s by applying to tlicni the quantity !i( I 87; - t ) . ?‘lie mean was then talicn of the currectcd placcs cxclutling Clinsc’s position, and this is tlic final ‘I projectccl ” cocIrditi;ite for IS^ j , i. i., 11, or I ; , , as the casc may bc, of tlic SIIC- cectliiig tables. The probable error of it single observation was obtaiiicd from 211 tlic rcsiduals by l’cters’ formula ;IS given by Roger5 in liis zone (Sort11 Dcci. so3 to 5 j ” ) of the f / i /a/oy d u :I.\f/,~//n//l/Si/lc.,r Ct~si//silr~I/~, 1’. ( I o), \r.liicli is
[ - - : I I )I [ !I - I / ’ )
c 0.8453
I I being tlic trJtal number of rcsiduals used, and d’ being tlic number of stars. \Ye find thus
STARS IN COMA UERENICES. 463
as thc probablc error of a single observation. The probable error of a catalogue position depcnding on fourtccn plates is thcrcforc
1.- : *0".025, ra . c0//.016,
tlic r,, k i n g in seconds of arc ,of a parallcl of declination through the ccnter of the platc. It sliould bc mentioncd, that the rcsiduals as uscd arc assumcd to bc all of equal weight. This, while not theoretically correct (since somc of thc positioiis include, besides errors of direct obscrvatioii, thc uncertainty of the proper motion) is sufficieiitly nccuratc, owing to tlic small value of the probablc errors of tlic propcr motions, and tlic fact that (1875- t ) is in no casc larger tliaii 4.7.
Tlic probable errors of tlic propcr niotioiis werc obt;iincd by tlic usual fornitkc (cf. I'nrt 1, Sect. 11. FowiLIr-.i,. i:oic A[)- JKSTJIEST ")
Thc iv's used licrc w r c the snnic ns bcforc, including, Iio~v- cver, the rcsiduills obtunctl froin Chase's position rctluccd to 1S7 j and corrcctcd for proper niotioii. Neglecting tlic fact that tlic niCill1 ti1 or r;, docs not includc Chase's observations, wliicli can hc tlonc witlioiit apprcciablc cffcct on tlic result, it is casy to sliow that the residuals obtaincd as csplaincd above have thc samc viduc as they \\auld Iiavc il computcd by tlic method dcscribcd in Part I, Scct. 111, " Si.\ic T.WLES." For by tlic Inttcr nictliod
f f l + ( I ? + .'' + ,I., A v o i l l -,- I: + . ' + 111
+ NI
- ( I , - All , , I,
for tlie case of c q w l weiglits of all thc t i ' s .
nic t h od l h t by the first
( 123 )
464 KRETZ.
so that the two results are identical. We can therefore use the formula for r,, given abovc, and, with thc cxception of the slight inaccuracy mentioned, tlie rcsults will bc thcorctically correct. All the probable errors of the proper motion in the succeed- ing tabss were obtained in this way.
On the followiiig pages arc recordcd tlic separatc positions of all the stars on thc platcs. Chase's place, reduccd to 1875, is printed in Italics at tlic end of cacti list. Thc headings are plain wlicn taken in connection with the prcccding discussion. At tlic ciid of each tablc arc given thc final means, 11, and d,, tlic date of obscrvation, and the propcr motion witli its probable error. t i , and d,, as Ins bccn stated, d o not include Chase's ob- servations. ]:or the stars iiumberctl I , 2 , 4, j, 6, 7;8, 9, 10, 1 4 ~ I j, 2 1 , 22, 2 3 , ;ind 24, ,u and ! f l wcrc computctl by thc method dctailcd abovc. The otlicr proper motions given in the tables wcre obtaiiied by subtrnctirig the mcnn of my determination\ from Chascb's position. and dividing tlic diffcrencc by the interval i n years. T h y arc iiicloscd in brackets, for tlie sake of dis- tinction. S o probable crror nas computcd for thcm. Tlie dntcs of obscrvntioti arc evidently tlic same in all cases, and are as follows: I'lates 1-111, 1970.3, Platcs IV-VIII, 1875.4, I'latcs lX-XI\-, 1876.4, and Chaw 1891.6. Tlicy i r e not rc- peatcd i n tlic tliblcs, but a t thc cnd of cacli is given thc mean datc of obscrvation (esclwhlg Chase) corrcsppnding to tlic star.
( 1 2 4 )
STARS IN COMA UERENICES.
STAK I.
465
Riglit Ascension.
2'. ' 'late At .Epoch of Curr. Elnch
I'lntc. for !I. 1875.
I1 I l l 1v v
V l 1'1 I
V I l l I X s XI
X I 1 XI11 XI\' 3 a . w
" 1 " 133 5 52.73 --0:33 52!41 d 6 3
5 53.36 -0.33 53.03 -1-n.ni
5 53.06 : 0.03 53 og -0 .05
5 53.:3 - '-o.q 53.16 - 0 . 1 2
5 53.23 - : - o o ~ 53.26 -0.22
5 53.09 10.U3 53.12 4.08
5 53.11 LO.O.J 53.14 -0.10 5 53 08 .0.10 5.1. IS -0.14 5 52.99 f 0.10 53x9 4 . o . j 5 52.98 +o.ro 53 08 -0.q 5 52.7% .-O.IO 52 SS -0.16 5 52.86 n 10 52.96 . 00s 5 52.99 : - O . I O 53.q 4 . 0 5 5 ; i . n h r . i h .i-..S-, : o 22
0 , 4 1 1 0 u 26 53 9.S1 t 0.34 10.15
53 9.75 i-0.34 1 0 . 9 53 10.0s -0.03 1005 53 1o.q -0.03 i0.01 53 10.05 -0.03 10.02 53 9.81 -0.03 9.79 53 10.19 -0.03 10.16 53 10.00 4 . 1 0 9.90 53 9.95 -0.10 9% 5.3 10.03 -0.10 9.93 53 10.05 -0.10 9.95 53 1o.n; -0.10 9.94 53 9.96 -0.10 9.X6 ;; i r , ; i --I.-,{ r t i . f ( i
, -0. I 7
-0.07 -0 03 -0.n.i -!-o. 19 -0. I8 . t 0.0s :-a 13 :-0.05 . 0.03 -; 0.04 -1 0. I 2 -,I. I- .
-+.I1
4GG KKETZ.
- ~
Right Ascension
A t Epic11 of Corr. Epoch _ ,
I'lntc. for 11. 1875. '.
I rS3 30 20.4s -0.85 19.63 -0 .07 1 I 30 20.43 -3.85 19.58 -0.02
r r f 3020.27 - 0 . ~ 5 1941 o 14 I\ ' 30 19.5s : 0.07 ry.65 --oog
1'1 j o 1945 ro.07 1952 . 0.04 \'I1 30 19.36 . ' o o 7 19.43 -0.13
IX 30 19.34 7 0.25 19.59 -0.03 S 30 19.33 t 0.25 1958 -0.02 SI 30 19.43 -:-0.15 1968 -0.12
SII 30 19.36 :-0.25 1961 +.oj SIII 30 19.30 + 0.25 19.55 t o 01 SIV 30 19.36 + 0 . 2 5 19.61 -0.05 &IJC ;,, I/l..<' -:-.;,,l'l '95' :u.,lJ
'11 i n i d ic~:je )ale of Ulivrvntioii. 1974.7
P --O:iAl =<.'m28
'late.
0 , Y ,, I ,
1 30 l9.48 t O . 0 ; 19.55 ' 0.01
v11I 30 19.43 -0.07 19.50 7-0.06
Declination. -
:At Epoch of Corr. I Ephj ,,. I'lnte. forp'. 1875. ,
0 I 8 , ,I I t,
25 45 25 94 4.01 25.93 1 - 45 26.23 +r.,;5JI 25.9.J I -
'1. 2 P 4 S 2 i ' ~ S Dnte of Observnhn, 1875.4
I' [ + ;.lo2 I I I
Dcclinntion.
,t l : p c h of Corr. Epoch I , ,
&4;46:42 -0y17 46159 .: ~ ' I O 41 4655 -: 0.1; 46.72 -0.03 41 46.51 -L0.17 46 68 -io.oi 41 46.69 - 3 . 0 1 46.6X -:O.OI
41 46.73 4 . 0 1 46.72 -0.03 j t 46.76 -0.01 46.75 -0.06 41 46.76 -0.01 46.75 -0.06 41 46.75 -0.m 46.74 -0.05 41 46.71 -0.05 46.66 1-003
41 46.68 -005 46.63 :-0.06 41 46.74 -005 46.69 0.00 41 46.77 -0.05 46.72 4 . ~ 3 41 46.66 -0.05 46.61 Lo.0l9
I'la~e. for)''. 1975.
4r 46.79 4 . 0 j 46.74 4 . n . 5
JI ~ 7 . - 4 - -<I.(%) 46.h6 . -CLOJ
4 29iida of Ub\cnntion, 1874.7
( 1 2 6 )
0 I I ,
27 1 9 6.84 19 6.52 19 6.62 19 6.27 19 6.18 19 6.12 19606 19 6.18 196 12
'9 5.96 19 6.01 iy 6.07 19 6 .w '9 594 I l ) 4 . 0 ;
* I I , - - ~ . j s 6.39 -0.21 -0.45 6.07 . 0.11 -0.45 6.17 :O.CI 9-o .0~ 6.31 - 0 . 1 2 i - 0 . q 6.22 -0.04
I 0.04 6.22 -1 0.13 6.25. -0.07 :-o.13 609 -1-0.9 -.-o. 13 6.14 -0 04 : 0.13 6.20 -0.01 - 0 . 1 3 6.13 .:o.o5 f 0.13 6.v7 . 0.11 * - l . j 0 0.22 - l l . < l J
-:-o.oJ 6.16 - 0.02 1 0 . q 6.10 ., 0.d
Riglit r\\ccrision.
,\I I<lioch of t'orr, I . : ~ I I K I I 'late.
I'lnrc. fur!). 1~75.
I is3 36 56.99 -u. j o 56.$ - V . I I 11 3656.91 -0.30 56.61 - 0 . 1 3
I 1 1 3656.47 -0.30'56.17 -. 0.31 I\' 36 56.51 . n 03 56.5.1 -0 06 v 3656.49 I 0.03 56-51 --WM
V I 365b.41 $0.0.) 56.44 : 0.04 V I I 36 56.02 * 0.03 56 05 z-o.43
V I I I 3656,;7 to.oJ 5 6 . k - 0 . j 2
S 36 56.58 .: 0.09 56 67 -0.19 X I 3656.18 .Lo.q 56.2; . ~ 1 . 2 1 SI1 36 56.33 70.09 56.4; : o.v1 i l l 1 36566; : 0.9 56.76 -0.2'3 K1V 3656.23 ' 0 . q 5632 i v . 1 6
0 , I ,
'5 In$%; X h
I' -0:iMt "rr;.0197
)ntc of Oliscrvntion, 1874.6
468 KIiE'I'L.
STAK 7. ~
Right Ascension.
'late. ,\I Epoch of Corr. I<yuch I'late. for ) I . 137s.
I 11
111 I \ V
v I Y I I
L'I I I IS S
1 1 X I 1
S l l l
v .
- 0 . d -43 03 -i 0.0s 4 . 1 3
-i 3.06 -0.02
-: 0.20
Declination.
\ C Epoch of Corr. Epoch . Hate. furp'. 1875. .'
26"37'16:63 -dbz 1c61 -'-d.'o7 37 16.71 ,--no2 16.69 -0.01 37 16.80 -0.02 16.78 -0.10 37 16.58 .a, 16.58 -+O.IO 37 16.76 .m 16.76 -0.0s 37 16.So .ov 16 80 -0 .12 37 16.67 .oo 16.67 0.01 j7 16.71 .oo '16.,7r -0.03 37 16.50 -. 0.01 16.51 t 0.17 37 16.66 i0.01 16.67 -r0.01 37 16.81 Co.01 16.82 -0.14 3; 16 79 .: o.ni 16& -0.12 37 16.49 4 0.01 16.50 C o . 6 37 16.63 . 0.01 1664 to.04 :7 1h.6,; !-n.o; 1h.711 -11.02
4 , 6 3 7 1c;:Os I h t e of Obwvation, 1874.7
1" -0.W c d k ~ 3 8
Declination.
I'lnte. f o r d . 1875. ''' \ t I'pcl i of Corr. K p c h
1 I ,, I
26 2455.40 -00g 55.;1 -n 1 2 2455.30 -0.q 55 .21 -0.03 2 J 55.37 - c . q $5.28 4 . I C 14 55.66 I 0.01 55 17 -'o.ni 24 5 5 . ~ 3 n.ot 55.09 0.9 24 55.20 0.01 55.21 -0.03
2455.14 :oat 55.15 '0.03 2.1 $5.09 0.03 55.12 :-0.06 24 55.07 t - m q 55.m Lo.&
24 55.23 .. n.oi 55.26 --o& 2.1 5 5 . 1 8 1 on3 55.21 4 . 0
24 s 5 . w ZJ.Y./.0? l'..:,? .C.j..?~I - 1 ) 0s
4 rcizr's: i rl
I" -6:m co:bo27
Z j 5 5 . 2 1 L O O l 5 5 . 2 2 4 . 0 4
24 5.i.10 -0.03 55-13 0.05
0 u3 55.10 i o . rd
Ihtc of 1 hrrvntion, 1874 7
Ilcclinntioii. I Right Ascension.
'late' At Epocli (if C'cirr. I:~HK.II ' I'Inte. forp. 1875. *.
I 18341 45.71 -1.36 44.35 -:07 I1 41 45.61 -1.36 44 25 .! 003
41 45.68 -1.36 44.32 -0.04 I V 41 44.37 ' 0 . 1 2 44.49 - a 2 1
V 41 44.16 ,O.IZ jj.13 .oc
V I I 41 44.23 t 0 . 1 2 44.35 -0.07
IS 41 43.99 4 0.40 44.39 4 . 1 1 S 41 4 3 . Y ~ . 0.40 44.22 0.0b SI 41 4 j . b ' 0.40 J J . ~ O . o.aY
XI1 41 43.69 to.40 4 4 . y ~ 0 . 1 9
L%mr fr,;y. .<,; . +Y,i 4 , f . j ; - t ~ ~ ~ 5
a 0 , ,I It ,,
111
V I 41 44 02 CO.12 44.14 ' 0 . l J
V I I I 41 44.34 . 0.12 44.46
Jl 43 33 -. 0.40 44.23 . 0.05 x1v 41 43.74 0.40 44.14 t 0 . 1 4
c
A t I<JMCII of l'orr. Epnr.11 I'lnte. forp'. 1S75.
25 43 15.23 +&b3 I;.'!% --d.'06 43 15.44 C0.6; 16.07 -0.15 43 15.40 . 0.63 16.03 -0.11 43 15.76 -0.05 15.;1 1 0 . 2 1
43 15.93 --o.oj 15.8s 7 . 0 . 0 ~ 43 16.16 -0.05 16 I I -0.19
43 1 6 . 1 2 - 0 . 1 9 15.93 -0.01 43 15.93 -0.19 15.74 0.1s 43 16.01 -0.19 5 S z ~ 0 . 1 0 43 16.19 -0.19 16.00 -0.a9 43 16.22 --o 19 16.03 - 0 . 1 1
43 1 6 . 9 -0.19 15 cjo t0 .02
V .
0 , I
43 15.92 --O.CY l5.s7 r-0.05
43 16.01 --O.Oj 15 96 -0.04
4,; (5'. 11) -2.21 /.i.t).S --c*.~>b
--O.O!
' 1) 0: 0.0;
-0.d
v. 1.' ' 0.01
.m --O.Ol
.w
. 0.02 -0 1'1
.a:
--11. I 3
( Ion,
470 K I< EI'Z.
S T A R I I .
Dcclinntion.
4t K p x l i of Corr. Epoch ,,, I'lnic. lorpl. 1875.
27 r h 8 . 6 0 -0.01 8.59 -53 18 7.69 -001 7.68 r0.3S
ISS.,S -0.22 s.,v'l .oo
0 , ,, I , I I
18 7.91 4 . 0 1 7.90 i 0.16
1'1 s f 1 8' i*iml Untc of Oi~scrvn~io~i , 18;s.d
I(' [ +;:0131
S'I'AKS I N COMA IJEI11:SICES.
S T A U 14.
471
47'3 KKE'TZ.
I Ikclinnrion.
I p c h _ ,
1875. "
42.56 - a 0 1 42.59 -0.05 42.48 -to.& 42.52 -;-o.oz
42.66 -0 1 2 ~ 1 . 3 7 -0.17 43.61 -0.07 42.63 -0.14 42.49 -ko.o5
42.41 10.13
STARS IN COMA BERENICES.
Right Ascension.
At I p c l i of Corr. E&li Plate. Cnr ! I . 1875.
11 I Q O 1 i l l j l - 12.71 - 0 . 1 1
\’I 18 12.70 - 12.70 -0.10
5 l d l U 1i;w
:,,
Y N
V IS 12.4s -- 12.48 1 0 . 1 2
VIII x8 12.50 - 12.50 : 0.10 . .
Date of Obscrvatioii, 1874. I
P ?
473
Declination.
I’Inte. Gorp'. 1875. ‘‘. 27 15 32.59 - 32.59 - r o . ~ t
32.72 -!-0.03
A t 1:pocIi of Corr. , K p c l i
0 I I , I , ,I
32.77 -0.01 1532.77 -- 15 32.92 -- 32.92 -0.17 15 32.72 -
4 ‘l<lS‘39:\5
I d f ? Date of Obscrwion, 1874. I
~~
Riglit Ascension
AKNAIS N. Y. AcAn. Scr., hloy 43 Igoo.--p.
(133)
474
0 , I , I , I ,
26 32 42.76 0.00 42.76 to.0: 32 42.74 .W 42.74 t O . 0 ; 32 42.79 .W 42.79 $0.0: 3242.87 .UJ 42.87 4.d 3 2 42.81 .w 42.S’ .a 3 2 42.85 .w 42.85 4 . 0 4 32 42.76 .oo 42.76 -1-0.05
32 4Z74 .m 42.74 to.0’2 3 2 42.86 .w 4 2 , s -0.05 3 2 42.80 .w 42.60 fo.01 3242.90 .w 42.90 4.q
.7-? 42.75 + I I . O Z 42.77 t 0 . 0 4
3 2 41.93 .W 41.93 -0.11
3242.77 .W 42.77 $0.04 3242.75 .W 42.75 70.06
KKETL.
I Declinstion. Right Ascension. I
‘ I I I
111 IV V
V I V I I
V I l l IS S XI
X I 1 K I l I X I V Xnsr
0 * 9, 184 26 44.13 4 : ; 4 4;.’S9
26 44.24 4 . 2 4 44.00 26 44.15 -0.24 43.91 26 44.17 -10 .02 44.19 26 44.03 -4 0.01 J4.Oj 2643.80 -r0.02 43.81 2643.77 b V . 0 2 43.79 26 43.94 10.02 43 96 2643.77 -: 0.07 4384 26 43.81 t o 07 43.39 2643.90 ! 0.07 43.97 2643.93 ‘-0.07 44.03 2643.80 $0.07 43.87 26 43.85 $0.07 43.92 26 43.09 L-c.8.j 4.i.94
-: 0.05 4.06
j 0.03 -0 .25 -0. I I
I -: 0 . 1 2 --0.15 4 . 0 2 : 0.IC
- , - 0.05 -0.03 4.06 2 0.07 -j-0 0 2
.Ol)
“ I 130 !ld 4d:M hte of Obscrvation, 1674.7
STAR 22.
1 I I
111 I\: v
V I v11
V I l l IS x SI
XI1 i l l 1 SIV X r r r
0 I I . I , I,
134 30 2 9 . a ~ -0.19 Z S . S ~ 4 n 3 30 29.16 -0.19 28 97 -0. I I 30 2 9 . ~ 6 -0.19 28.87 -0.01 30 29.69 :-o.oz 28 71 -: 0.15 j o 28.70 .: 0.02 28.72 t o . 1 4 3028.84 1-0.02 29.56 .m 30 29.01 - : - 0 . 0 2 29.03 -a17 30 28.73 $0 .02 28.75 + O . I I 30 28.75 1-0.06 28.81 - ! 0.05 30 28.88 -:-0.06 29.94 -4.d 30 28 79 : 0.06 28.85 To .o~ 30 29.78 +0.06 28.84 $o.oz 30 28.83 - i -o .d 28.39 -0.03
: I ) 23.21 1 o 68 28.89 -0 .0 .~ 30 28.8; i-0.06 28 9J 4.07
, I , ,# n 2947 33.51 .-0.03 ,33.54 -:-<K
47 33.60 : 0.03 433.63 $0.01
47 33.62 .oo 33.62 So.01 47 33.69 -; 0.03 33.72 -0.08
47 33.54 .w 33.54 t 0 . m 47 33.72 .u3 33.72 -0.4 47 33.78 .W 33.78 4 . 1 4 47 33.61 .a, 33.61 -0.03
47 33.62 -0.01 33.61 i0.03 47 33.67 -0.01 33.66 4.01
47 33.69 -0 .01 33.68 -0.04 47 33.67 -0.01 33.66 -0 .02
47 33.63 -0.01 33.62 +o.W
47 33.56 4 0 1 33.55 i 0 . q
4733.75 -0.12 33.63 t O . O r
STARS IN COMA DERENICIS.
STAR 23.
478
I I1
I l l I V V
v1 VII
V I r I IS s XI
XI1 XI11 X I V LXflW
0 , (4 ,, ,I ,I
184 32 38.57 -0.23 35.34 4 0.11 32 38.55 -0.23 38.32 lt1.13 32 38.63 - 0 . 2 3 33.40 -: 0.05
32 38.65 t o m 38.67 4 . 2 2
32 36.55 $0.02 35.57 - o 1 2 32 35.33 fo.07 3S.40 I 0.05 31 38.39 T ~ . 0 7 39 46 -0.01 32 33.35 -‘0.07 39.42 . 0.03 32 38.49 0.07 38.56 - O . I I 32 36.31 ?mu7 33.35 10.07
32 38.53 4 0.02 35.55 4 . 1 0
32 38.33 -:-0.02 35.40 -: 0.05 32 38.31 -i-0.02 38.33 - 1 0 . 1 2
32 38.46 10.07 38.53 4.0!! .7237.-~7 - 1 ‘>.SO .;.C3j i O . I I , V
“I 18tn3r’3Rk5
11 +d’oo40 3nte of Observation, 1974.7
Declination.
.t E p c h of Corr. EpcIi ,,,
86 16’36.20 -LO.OI 36.21 -:-0.07 16 36.20 -1 0.01 36.21 t 0.07 16 36.14 0.01 36.15 to.13 16 36.33 .m 36.33 - 0 5 16 36.40 .oo 36.40 -0.12 1636.28 .ca 36.2s .m 1636.16 .oo 36.16 - 1 0 . 1 2 1636.29 .oo 36.29 -0.01 1636.32 .co 36.32 -0.04 1636.36 .uo 36.36 -0.d 16 36.32 .oo 36.32 -0.04 16 36.35 .M 36.35 -0.07 16 36.24 .m 36.24 -Lon4 16 36.24 .M 36.14 -:-o.od I f i , f h 2 l -0.0,: $,I,? . ’ 1 1 . I I l
I’lntc. Torp’. 18;s. 0 u “ I, I,
f’, blc;‘:#ii
/I’ i d h ~ -?&a30
.)ate of Olicerv~tion. 1874.7
~
Right Ascension.
i \ t ~pcic11 of (‘orr. ~ p n c ~ i _ ,
I’latc. f i i r p . 1Yj5. ’ . I , ,,
I 1~4”41’3.51’~2 4 3 5 35.47 -:-o.06 11 41 35.90 4 . 3 5 35 55 -0.02
1V 41 35.74 -’.om3 35.77 -0.24 V 41 356% $0.03 35.71 -0.18 VI 41 35.60 -’o.o~ 35.63 -0.10
V I I 4r 35.35 .: 0.03 35.36 to.15 V l I I 41 35.49 2-0.03 55.52 : 0.01
41 35.16 ~ 0 . 1 0 35.16 $ 0 2 7 s 41 35.45 t O . 1 0 35.55 4 . 0 2
X I 41 35 41 . t O . I O 35.51 I 0 . 0 2 X I 1 41 35.41 tO.10 35.51 10.02
SIV 4 1 35.42 10.10 35.52 2-0.01
111 41 35.37 +.35, 35.52 - tO.OI
IS
X I 1 1 41 35.39 10.10 35.49 -:o.o4
“I 164°41’S.’h )ate of Obscrvntion, 1874.7
11 -d.075 *o:oogg
(135)
Decliiintion.
Plate. f i irp’ . 1875. ‘’.
26’15’1&0 +d.& 18,’i.S --d’o4 15 ‘8.73 -10.03 1 8 3 1 +on3
1 5 16.72 4 . 0 1 13.71 +o.13 rg 1S.S7 4 . 0 1 r8.86 -0.02 15 1S.72 -0.01 1S.71 .: 0.13 15 1S.89 -0.01 1 X . I 4 . q 15 19.00 4 . 0 1 1 8 . 9 -.IS 15 1S.g0 4 . 0 3 1KS7 -0.03 15 18.37 +.oj 18.84 .cc 15 19.86 4 . 0 3 18.83 -:-n.or 15 18.91 -0.0.3 18.68 -0.04 15 r8.73 -0.03 15.75 +o.q 15 18.v -0.03 13.87 -0.03
.\t 1~:pcIi Of Ciirr. 1 p I i
15 18.75 t O . 0 8 18.83 -: 0.01
4
p’ -I-O,OtA -eo.msq
mn t a‘ t n.04 Date of Observation, 1874.7
476 KKbTL.
Catalogue of Results.411 the CATALOGUE OF S r m s ” on p. 477 are collected the final positions and proper motions de- duced by me from thc Kutherfurd Plates. The right ascensions and declinations are obtained from the uI and 3, given on the preceding pages by iiicans of the formula
n 0 , ; 7,, I1 ... 11, + j ’b ,
7; and 7; king tlic transformation corrcctions. are as follows :
‘The columns
I gives my Nuniber of thc star ; 2 gives Chase’s Suniber ; 3 givcs tiic 1% D. Nuniher, and 4 the Mngnitudc of the
star in that cataloguc ; 5 gives the Riglit Ascension for 1575 in degrees, minutes,
aiid seconds of arc, rcduccd to thc nican epoch iisiiig tlrt d i i - cf Chi pi~ojk-r. iiiofioii given in column 6.
7 niid S givc tlic corrcspondiag quantities for thc Declina- tions ;
9 givcs the Rlcaii Date of Obscrvatioii ; and 1 0 givcs the Suniber of Plates on which the position de-
I t may be well to repeat here that the probable error of a sin- pends.
gle observation is
I : O ” q 3 9 , i a - co”.o595,
and of a position depending on fourteen plates
-Z = 0”.025, ra = k d’.o16.
(1%)
Cat
alog
ue o
f 24
Sta
rs o
f th
e C
lust
er i
n C
oma
Ber
enic
es.
Mea
n E
yulo
or o
f 18
15.0
. E
poch
18l5.0.
Ch
ase'
s No
.
1 2
4
3 3
4 4 5 6
2 7
S 0
9 9
I
0
10
I1
11
I
2
14
13
14
cl 15
1
4
16
15
17
18
19
26
20
a4
n, I)
. so.
26.2
324
26.2
326
26.2
329
27.1
114
26.2
330
26.2
33 I
26.2
332
25.2
493
25.2
495
27.2
116
26.2
336
26.2
337
27.2
118
26.2
339
26.2
340
27.2
I 20
27
.21
21
26
.234
3 26
.234
4 26
.234
5 26
,234
7
25.2
487
27.2
117
16.1
338
B.
I).
Mag.
7.3
66
7.
5 6
.3
5.0
8
.9
8.3
8
.2
7.2
7.
5 8.
o y. 9
9.0
5.0'
85
7.
8 9.
1 R.6
9.8
Y.0
7
.0
5.3'
6.3
8
.3
Rlg
bt A8Cep.
1875
.0
Dec
llnat
lon
1875
.0.
tm0
5'4a
33
10 a.03
14 1
6.W
30 16.W
30 3
'1.W
38
57.
60
38 32.08
41 4
8.01
41
53.
47
I1 1
5.64
51
46.
01
54 5
8.26
18
3 55
4.
46
134
3 18
.13
3 31
.65
426.
37
6
z.14
14
53.
13
18 1
8.24
21
21.
96
'M 4
3.88
9
0 *L
A3
41 m
.15
34 31.39
Pro
per
Mot
. in
R.
A.
-0.0;o
-0,0
39
-0.181
+.oqo
--o 064
-0.025
4.0
57
-0
. 28
9 -0
.039
[+
0.0
11
]
[--0
.oJ2
1 -
__
--
0.03
4 4.02s
[-0.
056]
_
_
--
-_ __
-0.05
I 4
.04
1
4.O
J8
4
.07
5
2d 3i
58:m
26 4
a 1
0s
25 4
.5 11
.90
26 4
1 42
.87
57 1
9 4.
41
56 2
7 30
.29
'20 37 1
4.00
25 4
3 14
.55
25 4
1 28
.2'2
47 1
8 1.
43
4;
14 31.99
26 P
2 46
.80
26 34
a3.8
'1
20 3
1 M
.*L
a; 18
st,o
z 28
30
i.aa
28 *2
44
.22
ar is
81.
81
51 1
'1 45
.20
26 32
40.8
9 ae
41
31.0
3 26
16
33.3
2 20
15
13.7
8
as N
53.58
Pro
per
Mot
. d
e,
in D
ecl.
of (
t 007
3 1
'0
.d
1
-0.0
36
1 d
.09
6
1 ., 0
.004
1 -0
.004
1 4
.0
10
1
--0.
014
1 [+
0.0
13
] 1 1 1
-; 0
.q
1
---0
.007
1
[-0
.02
03
1 1 1 1 1
d.
WI
1
i0.0
07
1 0
.00
2
1 .i
0.01
8 1
[-io
.oll
] 1
iO.1
33
1
-
-
__
_
_
-
~
n 1'
'6 E 6 6 E b I! (i b (i 8 (i a a a a a a a a a 6 6 I!
I D
ate
h'o
.of P
late
! re
rvat
. u
sed
. - .
-
.-
15.1
13
15.1
13
15.4
I
A.l
14
i4
.6
'3
14.1
14
'4.7
14
:4.;
14
:4.7
14 3
a.1
:5.4
,
3 5.4
4 '4
.7
14
:4.7
'
14
5.4
2
'5.1
2
'5
.3
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478 KRETZ.
On tlie foregoing pages have been recorded the nieasures and mcthods of reduction leading to the ‘ I CATALOGUE OF STARS,” p. 477. In gencral it will be better to measure a largc number of plates with less elaboration than has been done in the present case. But owing to the very small number of existing photographs of so early a date it was gecessary, in order to get the best re- sults, to employ all possible precautioll to guard against errors. The excellcnt agreement between Chase’s determinations and the photographic positions speaks well for the accuracy of both researches. Thc proper motions cannot, of course, be verified until a later date, but it seems safe to assume that all of thosc de- pending on fourteen plates and on Chase’s observations are very nearly correct. It is to be regretted that their number is not larger. The group is not well adapted to photographic work, however. The range of magnitudes is largc and the stars are very scattered. In fact, it may be doubted whether the term Group may properly bc applied to thesc stars. Thc proper motions certainly do not indicate any physical connection. This matter, howcvcr, is of ulterior intcrest.
I n co~iclusion, I wish again to thank Messrs. Schlcsinger and Hays for aiding me in measuring tlie plates ; Dr. Davis for in- valuable assistance in the catalogue work, and for frcely placing at my disposal his experience in all mattcrs connccted there- with ; Professor Jacoby for his ever-ready counsel on all diffi- cult points, and Professor Rees, Director of the Observatory, for the interest he has shown in the work, and for securing its pub- lication. It may also be mentioncd that free use has been made of thc Observatory Contributions, especially of Dr. Davis’ “ Fifty-Six Stars “ and of Dr. Schlesinger’s ‘ I Prasepe.”