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ftpftM 
 
 LIBRARY 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Deceived 
 
 Accessions No.' 
 
 "* /"^ ' "" rv ' ^ 
 
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 *H3WS5i 
 
 t .Art. <5f 
 
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III. 
 
 POSITIONS 
 
 FUNDAMENTAL STARS 
 
 HKIHTF.II KICoM 
 
 OBSERVATIONS MADE AT THE U. S. NAVAL OBSERVATORY 
 
 nr.nvKKN TIIK 
 
 YEARS 1863 ANI) 1867 
 
 SIMON NEWOOMIl. 
 
 OK MATHEMATICS. V. S. SAW 
 
 !'Kl:i'Ai:r.|i AT THE 
 
 U. S. NAVAL OBSERVATORY 
 
 IIV OIIUKK OK 
 
 COMMODORE 15. I\ SANDS, U. S. N.. 
 
 - 1 ri: ii I XTKN in. N i 
 
 UJIV1RSIT7 
 
 W ASHING/TON: 
 
 <: (i VK17NMEXT V R I / T I N fi OFFICK. 
 
 187/. 
 
TABLE OF CONTENTS. 
 
 CHAPTER I. EIGHT ASCENSIONS. 
 
 Page. 
 
 >>stcni;itic errors to which concluded right ascensions are liable 5 
 
 Plan lor el i mi until it; these errors 7 
 
 Kate of tin 1 Kescels clock 7 
 
 Kffcct of temperature on this rate 7 
 
 Kllect of the barometric pressure 10 
 
 I '.Meet of the galvanic current 10 
 
 Magnitude of the irregularities of clock rate 1(1 
 
 Mode of detecting the systematic errors of the adopted star positions 10 
 
 Formation of the ei| nations of condition 11 
 
 Solutions of the equations 18 
 
 Discussion of the results 19 
 
 ( 'Directions to the position of the equinox and the obliquity of the ecliptic 5JO 
 
 Concluded systematic correct ion to the adopted positions of the clock stars 21 
 
 Comparison of right ascensions observed directly and by rcllection 22 
 
 Computation of corrections to the right ascensions of the standard stars 22 
 
 Discussion of differences between the results of the transit anil circle 26 
 
 Hight ascensions of I'olaris 2r 
 
 CHAPTER 11. POLAli DISTANCES. 
 
 Preliminary remarks on measured polar distances 33 
 
 Individual results for corrections to polar distances of stars 38 
 
 Concluded mean positions of standard st a rs for the epoch 1870.0 :FJ 
 
 Comparison of the preceding polar distances with those of other catalogues 43 
 
 K'emarks on these comparisons 45 
 
POSITIONS OF 1TNDAMENTAL STARS ftTIXyiBSZTH 
 OBSERVATIONS .MADE AT THE UNITED STATES NAVAL OBSERVATORY 
 
 YEAKS ISOJi TO 1867, INCLUSIVE. 
 
 CHAPTER I. 
 
 11IGIIT ASCENSIONS. 
 
 Tin- agreement between the right ascensions of (lie fundamental stars, resulting from tin- work 
 if tin- different e>hscrvateries, which have of late years made them a subject of regular observation, 
 is very close, and well illustrates tlie approach to perfection which the art of practical astronomy 
 has made. Still, the small outstanding differences are greater than can result from the chance 
 errors of individual observations, thus indicating that hidden sources of systematic error still exist. 
 A classiiication of the differences, with respect to the, positions of the stars, show that they arc 
 mainly a function of this element. In fixing the positions of the stars, one of tiie efforts of the 
 astronomer will be to look for and eliminate every cause which can introduce into his determina- 
 tions errors depending on the position of the stars. 
 
 The possibility of emus depending on the right ascension of the stars being introduced and 
 perpetuated has been pointed out by different astronomers, and especially by Mr. Watford, in the 
 monthly notices of the Royal Astronomical Society for October, 18(51. The existence of this class 
 of errors is more especially to be feared, because under the system of reducing observations in 
 right ascension, now almost universally adopted, they will tend to perpetuate themselves when 
 once introduced. .Moi co\ IT, owing to the diurnal and annual inequality in the conditions to which 
 the observer and the instrument necessarily, and the clock generally, are subjected, the original 
 introduction of the class of errors referred to is very easy. A mathematical examination of the, law, 
 according to which they will be perpetuated, may not be uninteresting. 
 
 In the- system of reduction now generally adopted, the mean of all the clock stars observed b\ 
 one- observer during a tour of duty is assumed to lie free from error. Whatever error this mean 
 maybe affected with, the same error will affect the mean of the concluded positions. The alge- 
 braic aggregate of the errors in the adopted positions will be distributed among the concluded 
 positions. If the adopted clock rate' be correct, this distribution will be a uniform one, otherwise 
 it will vary with the position of the star in the group. 
 
 Suppose, now, that the adopted positions are affected with an error of the form n sin <i + b cos n. 
 Then, throughout one-half the circle the star positions will be systematically too small, and in the 
 other half systematically too great. And all clock errors not derived equally from the two classes 
 of stars will be erroneous, and the error will thus perpetuate itself. It will, indeed, tend to grow 
 a litth' smaller with each revision of the- clock stars; but this tendency will be counteracted by the 
 probable erroneous proper motions, and, under the actual circumstances of obsci A at ions, will be 
 very small. If we examine the published observations we shall liiul that only a small fraction of 
 the stars observed are distant more than three hours from the mean of the group on which they 
 depend, nearly all the stars of a group being included in a space of from four to six hours. If we 
 suppose; the groups to be of a uniform length of six hours, and to be equally distributed around the 
 circle, the right ascension of any one star will depend wholly upon the' adopted positions of stars 
 
6 POSITIONS OF FUNDAMENTAL STARS. 
 
 within isix hours of it, and the stars within a space of two hours on each side will have more weight 
 in fixing its position than all the others combined, the weight of each star, or the number of times 
 it is compared with the star in question, increasing in arithmetical progression as we approach the 
 latter. In algebraic language, the number of comparisons will be proportional to O 1 ' J, J 
 being the difference of right ascension. If we represent the number of comparisons with any one 
 star by n, and the error of the adopted position of this star by y>, the error of the concluded posi- 
 tion of the star compared will be represented by 
 
 ~np 
 Tw ' 
 
 To change the terms of this fraction into definite integrals, we have only to multiply each of 
 them by da, and substitute / for I. The fraction thus becomes 
 
 fnp da 
 fn d a 
 
 Put for the right ascension of the star, the error of whose concluded position is sought, 
 and a for the right ascension of any star with which it is compared. Then, on the above 
 hypothesis, we have 
 
 *=||*d=(-*o)}j 
 
 the sign being yo taken that the difference ot right ascension shall always be negative. The factor 
 c depends on the entire number of observations, and may be supposed equal to unity, as it disap- 
 pears from the fraction. Substituting this value of n, and putting c for the final error in the. con 
 eluded position of the star resulting from the errors in the adopted positions of the clock stars, we 
 have 
 
 J* C" 
 
 (i~ u o "f" ")j"' tt "t~ I 
 !*o ^ " Jo 
 
 7*"o /'"c 
 
 Jo i ~ " /o 
 
 The value of the denominator of this fraction is 
 
 i*. 
 
 Let the adopted right ascensions of the clock stars now be affected with a periodic error 
 
 sin + b cos + a' sin '2 a -f b' cos 2 
 Tut 
 
 a = fe cos fi, 
 b = fc siii ^9, 
 ft' = k' cos ft', 
 b' = k' siii ,5', 
 x = a + ft, 
 X' = 2a + ft';' 
 which gives 
 
 p = Tc sin x + k' siii x', 
 
 The substitution of these values reduces the numerator of c to the form 
 
POSITIONS OF FI'NDAMKNTAI. STAlis. 
 The value of tlio tirsl term of tliis expression is 
 
 -t sin (a + ,3); 
 that ol' tin- second 
 
 (li--)Jtsiu( + ,;): 
 
 th;it of tin- third vanishes, ; uid that of the fourth is 
 
 /.-' sin (1> C + ,;') 
 The \alue ol' r therefore lieconies 
 
 1H- sin ( 
 
 or, writing for , so that now re])resents the right ascension of any star, the position of which 
 is determined by observation, 
 
 S I 
 
 e = -^j- (a sin a + ft cos ) -f- , (n 1 sin 2a + ft' cos li) . 
 
 It appears, then, that in the case supposed, that in which the groups are of a uniform length 
 of six hours, and the clock stars are scattered uniformly through each group, each revision of the 
 fundamental catalogue will tend to diminish the error of single period by rather less than one-ufth, 
 and that of double period by more than one half. The latter will therefore be cut down much more 
 rapidly than the former. 
 
 In addition to this, it may be noted that errors of single, period are those most likely to have 
 found entrance into the original catalogue, arising, as they do, from the ett'ect of the diurnal change 
 of temperature upon the instrument and the clock. It is also to be remembered that this same 
 cause may perpetuate the errors in question. It is true that the effect of a uniform diurnal change 
 will be eliminated from a symmetrical year's work. But the diurnal change of temperature is not 
 uniform throughout the year, and it is also unsafe to assume that its ett'ect upon the clock is the 
 same in all seasons. 
 
 This same uncertainty will att'eet the results of comparisons of single stars or groups of stars. 
 The comparison must alwa\s be made with a clock rate deduced from its change of error during a 
 period of at least twenty-four hours, while the interval of comparison is only a fraction of a day, 
 during which the clock rate may be systematically different from its mean rate during the twenty- 
 four hours. 
 
 In arranging the transit circle observations for 1800 and 1807, the following arrangements 
 were planned as necessary to a reliable determination of the possible systematic error in the adopted 
 right ascensions of the clock stars of the form a sin + /J cos : 
 
 1. That the clock should be placed in a position where it would be tree from all diurnal ine- 
 quality of temperature. 
 
 '_'. That when practicable the same observer should observe as many as six clock stars between 
 -I' 1 and .'!'' of the day, and a corresponding group between O' 1 and l.V' mean time of the night. 
 Also, that similar combinations of groups twelve hours apart should be made in the morning and 
 evening when practicable. The systematic errors would then be of equal magnitude, and of oppo- 
 site signs in each pair of groups compared. K.s continuing the observations through an entire 
 year all regular diurnal inequalities arising from the observer or the instrument would be elimi- 
 nated. And, by using the instrument in opposite positions during the two years, all diurnal ine- 
 qualities in its collimation, whether regular or irregular, will be eliminated. 
 
 Kate of the clwJc. During the year 18G(i the Kessels clock was in the superintendent's room, 
 where it was supposed to be tree from all appreciable diurnal inequality of temperature. This con- 
 dition was well fulfilled, except during the summer months, when it was found that the night 
 temperature, as indicated by a pointer on the pendulum rod, was about 5 lower than the highest 
 day temperature. As such a change might be deleterious, the clock was, in February, 1807, 
 removed to a niche in the base of the great pier of the equatorial, where its temperature varies 
 but a very few degrees during the entire year. 
 
 Deeming it advisable to test the rate of the clock under changes of temperature as severely as 
 possible, it was. during the months of November and December, ISOC-flj^aaed to changes of 
 
 it^S^s 
 
 [VIXYl&SXTTl 
 
8 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 temperature several times more wide and rapid than any it had met with in actual use, while its 
 changes of rate were determined by comparison with the standard mean time clock in the chro- 
 nometer room, which had about as even a rate; as the Kessels clock. The changes of temperature 
 were effected by closing the door of the room, opening the windows, and cutting oil' the heat 
 for periods of one day or more during exceptionally cold weather, and reversing the process when 
 the temperature nearly ceased to fall. The clock comparisons wew made at irregular intervals. 
 The results are presented in the following table, which gives : 
 
 The mean dates and sidereal times of coincidence of beats of clocks. 
 
 The sidereal interval following each comparison. 
 
 The reduction of this interval to solar time. 
 
 The length of the sums of one or more of these intervals in hours. 
 
 The relative loss of the Kessels (sidereal) clock during these intervals. 
 
 The resulting daily losing relative rate of the sidereal clock. 
 
 The mean reading of the temperature pointer during the rate-interval. Each unit of r corre- 
 sponds to about .'5 Fahrenheit. 
 
 Menu date. 
 
 Sidereal 
 time of coin- 
 cidence. 
 
 Sidereal 
 intervals. 
 
 Reduction to 
 solar time. 
 
 Intervals 
 of time. 
 
 Relative 
 lossol'sid. 
 clock. 
 
 Relative 
 
 daily rate 
 
 T 
 
 1866. 
 
 /I. Ml. . 
 
 /I. Ml. 8. 
 
 X. 
 
 /i. 
 
 V. 
 
 K. 
 
 
 Nov. 25. 9 
 
 13 43 33 
 
 8 8 15 
 
 79. 988 
 
 8.1 
 
 .012 
 
 . 030 
 
 + 3.2 
 
 26 
 
 21 51 48 
 
 ii 30 38 
 
 6.002 
 
 
 
 
 
 
 22 28 26 
 
 334 
 
 29.991 
 
 3.7 
 
 .(MIT 
 
 .047 
 
 + 1.8 
 
 
 1 31 30 
 
 3 58 46 
 
 39. 117 
 
 
 
 
 
 
 5 30 1C 
 
 2 49 44 
 
 27.807 
 
 6.8 
 
 .076 .268 
 
 1.4 
 
 
 8 20 
 12 36 13 
 
 4 16 13 
 
 1 49 50 
 
 41.974 
 17.994 
 
 4.3 
 
 .026 
 
 .144 
 
 - 3.4 
 
 
 14 26 3 
 
 289 
 
 20. 995 
 
 4.0 
 
 .011 
 
 .066 
 
 1.9 
 
 27 
 
 16 34 12 
 
 2 44 51 
 
 27. 006 
 
 2.7 
 
 + .006 
 
 + .053 
 
 + 1.0 
 
 
 19 19 3 
 
 3 52 7 
 
 38.027 
 
 3.9 
 
 + .027 
 
 + .106 
 
 + 1.8 
 
 
 23 11 10 
 
 
 
 
 
 
 
 Dco. 2. 9 
 
 13 47 41 
 
 3 27 27 
 
 33. 986 
 
 3.4 
 
 .014 
 
 . 1)1)8 
 
 0.3 
 
 3 
 
 17 15 8 
 
 2 32 32 
 
 24. 989 
 
 2.5 
 
 .011 
 
 .108 
 
 0.5 
 
 
 19 47 40 
 
 6 24 25 
 
 62. 977 
 
 6.4 
 
 .023 
 
 .088 
 
 + 1.3 
 
 
 2 12 5 
 
 22 17 27 
 
 219. 109 
 
 22.3 
 
 + .109 
 
 + . 115 
 
 + 2.5 
 
 4 
 
 29 32 
 
 13 5fl 45 
 
 137. 082 
 
 13.9 
 
 + .082 
 
 + .142 
 
 + 2.8 
 
 
 14 26 17 
 
 10 28 55 
 
 162.010 
 
 16.5 
 
 + .inn 
 
 + .015 
 
 + 3.5 
 
 5 
 
 6 55 12 
 
 
 
 . 
 
 
 
 
 11 
 
 22 54 48 
 
 16 52 28 
 
 165. 868 
 
 16.9 
 
 .132 
 
 .187 
 
 - 4.4 
 
 
 15 47 16 
 
 7 37 42 
 
 74. 983 
 
 7.6 
 
 .017 
 
 . 054 
 
 8.3 
 
 12 
 
 23 24 58 
 
 15 15 14 
 
 149.939 
 
 15.3 
 
 . 081 
 
 .096 
 
 9. 5 
 
 
 14 40 12 
 
 II 51 :,5 
 
 8.996 
 
 
 
 
 
 15 35 7 
 
 4 28 28 
 
 13. 981 
 
 5.4 
 
 .023 
 
 .1(15 0.2 
 
 18 
 
 20 3 35 
 
 3 51 58 
 
 :!8. 003 
 
 3.9 
 
 + .003 
 
 + . 018 j- 1. 3 
 
 
 23 55 33 
 
 15 34 25 
 
 33.061 
 
 15. 6 
 
 + .081 
 
 + . 124 0. 
 
 
 15 29 58 
 
 4 59 18 
 
 49. 033 
 
 5.0 
 
 + . 033 
 
 + .159 +0.8 
 
 14 
 
 20 2!) l(i 
 
 3 27 28 
 
 33. 988 
 
 3. 5 
 
 .012 
 
 .082 
 
 
 23 56 44 
 15 12 21 
 
 15 15 37 
 3 27 31 
 
 150. 002 
 33. 997 
 
 15. 3 
 3. 5 
 
 + .002 
 .003 
 
 + .003 -- 5.5 
 . 021 
 
 15 
 
 18 39 52 
 
 
 
 
 
 
 
POSITIONS OK KfNDAMKNTAL STARS. 9 
 
 The probable result of these comparisons is that the losing daily rate of the clock increases 
 by O s .()4 for each unit of increase in r. or by O s .0i:$ for each rise of 1 in flic temperature. If we 
 suppose a periodic diurnal change of (5 in the temperature, or 3 on eacli side of the mean, the 
 resulting inequality in the clock rate will be 
 
 ilt 
 
 < being the inequality of clock correction, and the unit of t being one day. Integrating, we have 
 for the resulting inequality in the clock error, and in the reduced right ascensions of stars, 
 
 cos 
 
 = O a .OOG cos 
 
 The discordance of the results is such as to leave the magnitude of this small correction 
 doubtful. The rates were therefore compared with the actual recorded changes of temperature 
 during the summer of ISiiii,* and the result was that the effect of change of temperature was not 
 nearly so great as this, and was, indeed, in the opposite direction. The temperatures and rates 
 are compared in the following table: 
 
 Limiting ilatrs. 
 
 Mran rates 
 bet. (lairs. 
 
 Mean tem- 
 peratures. 
 
 d. h. 
 
 8. 
 
 o 
 
 l-(*i. May 23 12.4 
 
 + 0.25 
 
 64.6 
 
 25 5.5 
 
 + 0.07 
 
 70.5 
 
 28 10.6 
 
 + 0.14 
 
 65.6 
 
 31 11.0 
 
 + 0.09 
 
 71.0 
 
 June 4 I Mi 
 
 + 0.04 
 
 74. 5 
 
 18 14. 
 
 + 0.06 
 
 6!. '.' 
 
 20 12. 6 
 
 + 0. 12 
 
 72.0 
 
 21' 12.0 
 
 + 0.14 
 
 75.8 
 
 23 10. 4 
 
 + 0. 12 
 
 81.6 
 
 26.9 5.7 
 
 + 0.00 
 
 75. 1 
 
 28. 9 4. 8 
 
 + 0.13 
 
 72.1 
 
 July 3 11.6 
 
 + 0.11 
 
 80.2 
 
 8.9 5.1 
 
 + 0.00 
 
 76.6 
 
 13 15. 1 
 
 + 0.01 
 
 84. H 
 
 19 11.4 
 
 
 
 Taking the differences of the successive numbers in the columns of rate and temperature, we 
 have a series of changes of rates corresponding to changes of temperature. If we change the 
 signs of the corresponding pairs in which the temperature change is negative, and then take the 
 sum of each series, we find 
 
 Sum of changes of temperature 60 
 
 Sum of changes of rate 0. R 26 
 
 The daily rate, therefore, appears to diminish by O s .004 for each rise of 1 in the temperature. 
 
 The apparent difference between the e fleet of natural and artificial changes of temperature 
 may be due to the greater rapidity of the latter. In a rigorous investigation the rate ought to IM> 
 supposed to depend upon the rate of change of the temperature, as well as the absolute amount of 
 the latter. In a mercurial pendulum such an effect would be likely to arise from the different 
 degrees of rapidity with which the mercury and the rod would answer to changes of temperature. 
 The experiments just detailed seem, however, to show that ill the Kessels clock the effect is very 
 small, if not altogether insensible a result not improbable in the case of a gridiron pendulum. 
 
 found in Washington Observations for IHIiti, Introduction, pp. xx.xix ami xl. 
 
10 POSITIONS OF FUNDAMENTAL STARS. 
 
 I conclude that the effect of the diurnal change of temperature to 'which the clock was actually 
 exposed may be safely pronounced insensible. 
 
 Effect of the barometric pressure on the clock. During the month ending February 7, 18C7, the 
 barometer was subject to unusually wide, and rapid fluctuations. The comparison with the clock 
 rates indicated an increase of O s .27 in the daily losing rate for every inch in the rise of the barome- 
 ter. This correction has not been employed, as it can give rise to no systematic diurnal inequality. 
 
 Effect of the galvanic current. An opinion has prevailed that the passage of the galvanic cur- 
 rent through the pendulum might affect the clock rate. This was tested by throwing the current 
 on and off during alternate intervals of from 4Jto 13 hours, and comparing with the mean-time clock 
 at each change. The result was 
 
 8. 
 
 With battery on the mean relative hourly rate was 0.038 
 
 With battery off it was 0.040 
 
 Not knowing any way in which the current could appreciably influence the motion of the pen- 
 dulum, I regard this difference as accidental. 
 
 Irregularities of clock rate. During several months from April, 1867, observations were made 
 with great regularity. This period was divided into intervals of as near ten days each as practica- 
 ble, the dividing points being epochs of determination of clock error. The errors "thus arbitrarily 
 selected were interpolated to the times of such intermediate determinations as were three days or 
 more distant from each end of the period, and compared with these determinations. The mean dis- 
 cordance was O s .12. It appears, then, that if the clock error were determined but once in ten days, 
 the intermediate errors would average about OM2 during the period in question. But I think that 
 during this period the rate was more regular than the average one, and that the mean result for the 
 two years would be from 8 .1(5 to OM8. 
 
 As the clock corrections are published in full in the introduction to each volume of observa- 
 tions, it seems unnecessary to repeat the data on which these results are founded. 
 
 A diurnal change in the pointing of the instrument will have the same effect as one in the clock 
 
 rate. The collimation error is known to undergo a change of 8 .003 for every change of 1 Falnvn- 
 
 .heit in the temperature. A regular diurnal change in the pointing of the instrument may, therefore, 
 
 be inferred. Its effect will, however, be eliminated from the mean of the results of the two years 
 
 by the reversal of the instrument. 
 
 There are few results for diurnal change of level, it being considered very improbable that there 
 should be such a change. These few do not indicate such a change. 
 
 A diurnal change of azimuth can be most certainly detected from the observed transits of 
 Polaris. Its discussion is, therefore, deferred for a subsequent section. 
 
 Having considered the sources of diurnal inequality, the possibility of which may be seen a 
 priori, we now proceed to the discussion of the observations of stars. The method of discussion is 
 founded on the consideration that there may be a systematic difference between the clock correc- 
 tions determined at different times of the day. Such a difference would result from a regular diur- 
 nal change either in the clock, the instrument, or the personal equation of the observer. However 
 improbable its existence may seem, the question of its reality is to be finally settled by the observa- 
 tions themselves. Let us, then, consider the transits of two groups of stars several hours apart. 
 We compare the observed sidereal interval between the transits with the computed difference of 
 right ascensions. The clock rate being supposed accurately known, the difference between the 
 observed and computed intervals may be due to systematic error in the right ascensions of the two 
 groups of stars, and to changes in the observer or instrument. The first source of error will be con- 
 sidered to depend on the right ascension, and to be of the form a sin All + !> cos All; the second 
 will be supposed to depend on the hour of the solar day. In any one day it will be impossible to 
 distinguish between the effects of these two causes. Hut, in the course of a year, the first cause will 
 undergo ;>(!( changes while the second will undergo 305, and the effects may, therefore, be completely 
 separated. 
 
 Since the second cause may not change regularly in the course of the day, the latter will be 
 
1'OSITIONS OF l<'rM>AMKNTAI. STAKS. 1 1 
 
 divided into six parts, in each of wliicli the second elfeet will have separate and independent values. 
 The ilala have, therefore, been divided into three classes, as follows: 
 
 1. Comparisons of groups of stars observed in the forenoon, with corresponding groups observed 
 by the same observer during the evening following;'. 
 
 "2. Similar comparisons in which the first group was observed in the afternoon, and the second 
 near or soon after midnight. 
 
 ;{. Similar comparisons in which the lirst group was observed in the early evening, and the sec- 
 ond in the early morning. . 
 
 Each difference between the observed and computed intervals of a pair of groups gives an equa- 
 tion of the form 
 
 d = a + ma-\-nb, 
 
 where 
 
 J, excess of computed over observed interval. 
 
 , amount by which the lirst group is systematically observed too late, as compared with the sec- 
 ond, or the amount by which the observed interval is systematically too small. 
 M,n, differences between the mean values of sin a and cos for the two groups. 
 
 The data for the separate comparisons are given in the following table, which shows 
 
 (1.) The date, the day beginning with the tour of duty of the observer. 
 
 (li.) The initial of the observer. 
 
 (3.) The sidereal hour corresponding to the mean of the first group of stars. 
 
 (4.) The number of stars in the group. 
 
 (.">.) The mean correction in hnndredths of seconds to the computed right ascensions of tl;e stars 
 of the group. In the year 1866 these computed positions are taken from the American Ephemeris, 
 without correction, and the mean given is simply that of the " miscellaneous corrections" in the last 
 column of the printed observations. In 1867 the corrections refer to the adopted positions, and are 
 the mean excesses of the "adopted" over the "apparent" clock correction. 
 
 (6,) (7,) (8.) The corresponding quantities for the opposite group of stars. 
 
 (9.) The values of J, or the excess of the computed over the observed difference of right ascen- 
 sion of the groups. A is the difference between columns (5) and (8), corrected for the change in the 
 collimation of the instrument due to the change of temperature between the times of observation. 
 
 J forms one side of the equation of condition of the form already given, only that in compari- 
 sons of the second and third classes is replaced by /Sand y respectively. 
 
 In columns (5,) (8,) and (9) the units represent huudredths of seconds of time. 
 
12 
 
 POSITIONS OK FUNDAMENTAL STARS. 
 
 Date. 
 
 Obs. 
 
 Hour. 
 
 No.of 
 stars. 
 
 Mean 
 correc'i). 
 
 Hoar. 
 
 No.of 
 
 stars. 
 
 Mean 
 
 ronvc'n. 
 
 Equation of condition. 
 
 1866. 
 
 
 
 
 
 
 
 
 
 January 9 
 
 R. 
 
 1.9 
 
 2 
 
 + 6 
 
 14.1 
 
 2 
 
 + 4 
 
 + 3 = : 7 + 1.0 a + 1. 6 ft 
 
 H 
 
 H. 
 
 21.0 
 
 3 
 
 1 
 
 6.8 
 
 4 
 
 2 
 
 + 3 = - 1. 5 + 0. 9 
 
 31 
 
 N. 
 
 19.1 
 
 3 
 
 + 3 
 
 7.0 
 
 3 
 
 y 
 
 + ll = a - 1.7 + 0.6 
 
 31 
 
 N 
 
 -22.1 
 
 3 
 
 7, 
 
 10.6 
 
 3 
 
 + 5 
 
 - 11 = /3 - - 0. 9 +1.5 
 
 February 1 
 
 R. 
 
 19.1 
 
 2 
 
 + 5 
 
 7.0 
 
 3 
 
 
 
 + 6 = - - 1.7 +0.6 
 
 1 
 
 R. 
 
 23.9 
 
 3 
 
 1 
 
 11.3 
 
 3 
 
 + 3 
 
 - 8 = - - 0.9 +1-7 
 
 2 
 
 H. 
 
 22.8 
 
 2 
 
 2 
 
 12.0 
 
 4 
 
 3 
 
 + 3 = 0. 3 +1.7 
 
 8 
 
 T. 
 
 0.0 
 
 3 
 
 + 3 
 
 12. 9 
 
 3 
 
 1 
 
 + 6 = y + 0.3 +1.8 
 
 6 
 
 H. 
 
 18.9 
 
 5 
 
 + r, 
 
 5.9 
 
 6 
 
 4 
 
 + 10 = a - 1.7 +0.3 
 
 6 
 
 H. 
 
 0.8 
 
 5 
 
 -' 2 
 
 14.0 
 
 3 
 
 3 
 
 + 3 = 7 + 0.7 + 1.5 
 
 16 
 
 H. 
 
 18.3 
 
 . 4 
 
 + 1 
 
 5.9 
 
 3 
 
 3 
 
 + 5 = a - 1.8 0. 
 
 1(> 
 
 H. 
 
 1.3 
 
 3 
 
 1 
 
 11.4 
 
 5 
 
 + 2 
 
 -2 = y + 0.2 +1.7 
 
 17 
 
 T. 
 
 20.8 
 
 3 
 
 + 4 
 
 9.5 
 
 2 
 
 8 
 
 + 13 = a - 1. 3 + 1.3 
 
 20 
 
 R. 
 
 1.0 
 
 4 
 
 + 4 
 
 12.4 
 
 3 
 
 2 
 
 + 8 = + 0.4 + 1.7 
 
 21 
 
 T. 
 
 20. 7 
 
 2 
 
 + 6 
 
 10.0 
 
 3 
 
 6 
 
 + 13 = a - 1.2 +1.3 
 
 26 
 
 H. 
 
 18.6 
 
 3 
 
 + 3 
 
 7.2 
 
 4 
 
 4 
 
 + 8 = a . 1.7 + 0.5 
 
 March 5 
 
 H. 
 
 1.9 
 
 2 
 
 + 10 
 
 13.0 
 
 6 
 
 3 
 
 + 15 = ;? + 0.8 +1.6 
 
 5 
 
 H. 
 
 6.6 
 
 3 
 
 6 
 
 18.1 
 
 2 
 
 + 4 
 
 - 10 = y + 1. 8 - 0. 2 
 
 8 
 
 N. 
 
 23.2 
 
 4 
 
 
 
 11.3 
 
 5 
 
 2 
 
 + 3 = -- 0. 4 +1.7 
 
 8 
 
 N. 
 
 6.8 
 
 2 
 
 6 
 
 17.9 
 
 3 
 
 + H 
 
 -17 = y + 1.7 - 0.2 
 
 10 
 
 T. 
 
 0.2 
 
 3 
 
 + 4 
 
 11.7 
 
 5 
 
 1 
 
 + 6 = 0.0 +1.8 
 
 14 
 
 N. 
 
 21.4 
 
 2 
 
 3 
 
 10.7 
 
 4 
 
 6 
 
 + 4 = o - 1.0 +1.5 
 
 16 
 
 H. 
 
 6.1 
 
 2 
 
 + 6 
 
 18.0 
 
 4 
 
 2 
 
 + 8 = 7 + 1.8 0.0 
 
 22 
 
 R. 
 
 23.8 
 
 2 
 
 + 4 
 
 11.9 
 
 4 
 
 6 
 
 + 11 =a 0. 1 +1.9 
 
 26 
 
 N. 
 
 1.3 
 
 3 
 
 + 3 
 
 13.0 
 
 3 
 
 + 3 
 
 + 2 = + 0.7 + 1.6 
 
 27 
 
 R. 
 
 22.3 
 
 2 
 
 9 
 
 10.5 
 
 3 
 
 + 2 
 
 10 = a 0. 8 +1.5 
 
 30 
 
 N. 
 
 22.1 
 
 3 
 
 + 4 
 
 11.3 
 
 3 
 
 7 
 
 + 12 = o - - 0. 7 +1.5 
 
 April 26 
 
 R. 
 
 0.3 
 
 2 
 
 + 4 
 
 14.0 
 
 2 
 
 4 
 
 + 9 = a + 0. 6 + 1. 5 
 
 27 
 
 H. 
 
 5.0 
 
 ^ 3 
 
 5 
 
 13.5 
 
 3 
 
 + 2 
 
 -5 = + 1.2 +1.1 
 
 May 4 
 
 H. 
 
 0.3 
 
 2 
 
 4 
 
 13.0 
 
 4 
 
 + 2 
 
 - 5 = a + 0. 4 +1.7 
 
 12 
 
 T. 
 
 5.2 
 
 4 
 
 + 1 
 
 15.4 
 
 4 
 
 + 1 
 
 + 2 = + 1.5 +0.8 
 
 14 
 
 N. 
 
 5.4 
 
 3 
 
 + 2 
 
 16.0 
 
 4 
 
 + 3 
 
 + 1=0 + 1.6 + 0.7 
 
 15 
 
 R. 
 
 5.2 
 
 2 
 
 2 
 
 16.1 
 
 4 
 
 + 3 
 
 -3 = + 1.6 +0.7 
 
 22 
 
 H. 
 
 1.3 
 
 2 
 
 + 8 
 
 12.8 
 
 5 
 
 5 
 
 + 14 = n + 0. 6 +1.6 
 
 22 
 
 H. 
 
 5.4 
 
 3 
 
 + o 
 
 17.6 
 
 4 
 
 1 
 
 + 4 = 0+1.7 +0.3 
 
 83 
 
 T. 
 
 0.6 
 
 3 
 
 + 5 
 
 12.6 
 
 2 
 
 1 
 
 + 7 = a + 0. 5 +1.7 
 
 24 
 
 N. 
 
 1.9 
 
 2 
 
 
 
 15.1 
 
 3 
 
 ^ 
 
 + 2 = + 0.9 +1.5 
 
 24 
 
 N. 
 
 5.5 
 
 3 
 
 
 
 18.1 
 
 3 
 
 + 2 
 
 + 1=0 + 1.8 +0.1 
 
 25 
 
 H. 
 
 1.1 
 
 4 
 
 + 1 
 
 14.4 
 
 2 
 
 
 
 + 2 = a + 0.9 +1.5 
 
 28 
 
 N. 
 
 6.0 
 
 6 
 
 1 
 
 15. 8 
 
 5 
 
 + 2 
 
 = + 1.6 +0.5 
 
 30 
 
 T. 
 
 1.9 
 
 2 
 
 3 
 
 13.8 
 
 2 
 
 
 
 l = a + 0.9 +1.5 
 
 30 
 
 T. 
 
 7.4 
 
 2 
 
 14 
 
 17.1 
 
 3 
 
 + 12 
 
 23 = + 1. 6 - 0. 1 
 
 June 4 
 
 N. 
 
 7.0 
 
 3 
 
 7 
 
 16.3 
 
 3 
 
 + 4 
 
 -8 = + 1.6 +0.1 
 
 8 
 
 R. 
 
 6.9 
 
 3 
 
 2 
 
 17.8 
 
 3 
 
 + .7 
 
 6 = + 1.8 - 0.2 
 
 11 
 
 N. 
 
 7.5 
 
 3 
 
 5 
 
 18.6 
 
 3 
 
 + 2 
 
 -4 = + 1.8 - 0.6 
 
 12 
 
 R, 
 
 3.7 
 
 2 
 
 n 
 
 15.0 
 
 2 
 
 3 
 
 + 5 = a + 1.4 +1.2 
 
 16 
 
 T. 
 
 3.6 
 
 2 
 
 
 
 15.6 
 
 3 
 
 + 4 
 
 -2 = o + 1.5 +1.2 
 
 18 
 
 N. 
 
 7.6 
 
 2 
 
 6 
 
 18. 5 
 
 4 
 
 + 3 
 
 -6 = + 1.8 - 0.5 
 
 22 
 
 R. 
 
 6.2 
 
 4 
 
 4 
 
 18.0 
 
 3 
 
 + 1 
 
 8 = + 1.9 - 0.1 
 
 
 
 
 
 
 ( 
 
 
 
I'OSITIONS OK FUNDAMENTAL STA 
 
 13 
 
 Hair. 
 
 01. 
 
 Hour. 
 
 No. of 
 
 stars. 
 
 Mean 
 
 i mi i i-'n. 
 
 Hour. 
 
 No.of 
 
 stars. 
 
 Mean 
 convc'ii. 
 
 Equation of condition. 
 
 L866. 
 
 
 
 
 
 
 
 
 
 .lunc 23 
 
 11. 
 
 7.6 
 
 2 
 
 4 
 
 15.8 
 
 I 
 
 + 6 
 
 - 7 = + 1.6 a + 0. Ib 
 
 25 
 
 N. 
 
 6. II 
 
 2 
 
 - 10 
 
 18.5 
 
 3 
 
 + 5 
 
 -12 = a + 1.9 0.2 
 
 26 
 
 R. 
 
 4.8 
 
 2 
 
 4 
 
 16.4 
 
 4 
 
 4 3 
 
 -5 = + 1.7 +0.8 
 
 n 
 
 II. 
 
 14.3 
 
 2 
 
 4 
 
 1.7 
 
 S 
 
 + 5 
 
 -9 = 7 0.8 1.7 
 
 July 2 
 
 N. 
 
 4.8 
 
 2 
 
 + 2 
 
 17.4 
 
 4 
 
 + 5 
 
 1 = + 1.8 +0.5 
 
 2 
 
 N. 
 
 13.4 
 
 2 
 
 !l 
 
 1.9 
 
 2 
 
 4- 2 
 
 11 = 7 - - 0.9 1.7 
 
 5 
 
 N. 
 
 5.2 
 
 2 
 
 6 
 
 If.. 7 
 
 4 
 
 + 1 
 
 -5 = a + 1.8 +0.5 
 
 5 
 
 N. 
 
 11.6 
 
 2 
 
 6 
 
 1.6 
 
 2 
 
 + 8 
 
 11 = 7 0.3 1.7 
 
 6 
 
 K. 
 
 4.8 
 
 2 
 
 4 
 
 16.7 
 
 3 
 
 + 3 
 
 -5 = o + 1.8 +0.7 
 
 6 
 
 K. 
 
 14.0 
 
 2 
 
 4 
 
 1.6 
 
 2 
 
 + 4 
 
 - 8 = 7 - - 0.9 -1.7 
 
 7 
 
 11. 
 
 13.4 
 
 2 
 
 1 
 
 2.4 
 
 2 
 
 + 3 
 
 4 = y - - 1.0 1.6 
 
 11 
 
 T. 
 
 5.1 
 
 3 
 
 
 
 16.8 
 
 4 
 
 + 2 
 
 . l = a' + 1.8 +0.6 
 
 11 
 
 T. 
 
 i-.'. i; 
 
 3 
 
 9 
 
 21.1 
 
 2 
 
 + 10 
 
 - 16 = 7 + 0. 1 -1.8 
 
 111 
 
 H. 
 
 5.2 
 
 4 
 
 4 
 
 17.2 
 
 5 
 
 4- 4 
 
 -7 = + 1.8 +0.5 
 
 a 
 
 H. 
 
 ;i. f, 
 
 2 
 
 - 14 
 
 r.t. :, 
 
 4 
 
 4- 7 
 
 -18 = + 1.4 0.1 
 
 13 
 
 II. 
 
 13.7 
 
 3 
 
 5 
 
 1.7 
 
 2 
 
 4- 3 
 
 - 8 = 7 - - 0.9 -1.7 
 
 14 
 
 T. 
 
 5.4 
 
 4 
 
 4 
 
 17.3 
 
 4 
 
 + 2 
 
 4 = + 1.8 +0.5 
 
 14 
 
 T. 
 
 I-'..', 
 
 3 
 
 
 
 0.5 
 
 3 
 
 4 
 
 + 7 = 7 - 0.3 -1.8 
 
 16 
 
 N. 
 
 f>. 5 
 
 3 
 
 - 5 
 
 18.0 
 
 4 
 
 4- 3 
 
 - 6 = + 1.8 + 0.2 
 
 19 
 
 K. 
 
 5.3 
 
 3 
 
 3 
 
 17.5 
 
 3 
 
 4- 2 
 
 -3 = o + 1.8 +0.3 
 
 23 
 
 N. 
 
 13.6 
 
 2 
 
 4 
 
 1.9 
 
 2 
 
 
 
 - 2 = 7 - 0. 9 -1.7 
 
 26 
 
 N. 
 
 6.2 
 
 2 
 
 4 
 
 18.4 
 
 5 
 
 + 4 
 
 - 6 = + 1.8 - 0.2 
 
 26 
 
 N. 
 
 11.5 
 
 4 
 
 2 
 
 1.1 
 
 2 
 
 
 
 + 1 = - - 0. 2 -1.8 
 
 27 
 
 H. 
 
 11.5 
 
 3 
 
 6 
 
 20.9 
 
 3 
 
 4 5 
 
 -8 = + 0.8 1.5 
 
 31 
 
 H. 
 
 f.. 2 
 
 5 
 
 1 
 
 18.9 
 
 4 
 
 4- 4 
 
 -3 = o + 1.8 0.4 
 
 August 3 
 
 T. 
 
 6.6 
 
 3 
 
 5 
 
 18.4 
 
 3 
 
 + 8 
 
 -ll = o + 1.8 0.3 
 
 3 
 
 T. 
 
 12.5 
 
 2 
 
 1 
 
 23.0 
 
 2 
 
 6 
 
 + 8 = 7 + 0.2 -1.8 
 
 I 
 
 N.. 
 
 7.0 
 
 3 
 
 * 3 
 
 19.4 
 
 4 
 
 + 2 
 
 - 3 = o + 1.7 0.7 
 
 10 
 
 H. 
 
 7.2 
 
 3 
 
 7 
 
 19.3 
 
 5 
 
 4- 8 
 
 13 = a + 1. 8 0. 7 
 
 10 
 
 11. 
 
 12.0 
 
 3 
 
 7 
 
 1.1 
 
 2 
 
 4 
 
 = - - 0. 3 1.8 
 
 15 
 
 T. 
 
 13.6 
 
 2 
 
 4 
 
 0.2 
 
 2 
 
 4 
 
 + 3 = 7 - 0.4 -1.8 
 
 16 
 
 R. 
 
 7.5 
 
 3 
 
 5 
 
 19.8 
 
 4 
 
 + 2 
 
 5 = + 1.7 0.9 
 
 16 
 
 R. 
 
 II. n 
 
 2 
 
 11 
 
 23.2 
 
 3 
 
 4- 5 
 
 - 13 = 7 - 0. 3 1. 7 
 
 17 
 
 II. 
 
 7.2 
 
 5 
 
 1 
 
 19. 
 
 P 
 
 4 2 
 
 l = o + 1.7 1.8 
 
 17 
 
 H. 
 
 12.5 
 
 3 
 
 3 
 
 22.6 
 
 4 
 
 + 3 
 
 - 3 = + 0.2 1.7 
 
 18 
 
 T. 
 
 7.3 
 
 3 
 
 8 
 
 19.2 
 
 3 
 
 + 13 
 
 -20 = o + l. 8 0.7 
 
 20 
 
 N. 
 
 7.6 
 
 4 
 
 7 
 
 21.2 
 
 4 
 
 + 6 
 
 -12 = o + 1.6 .1 
 
 20 
 
 N. 
 
 11.4 
 
 2 
 
 5 
 
 0.8 
 
 2 
 
 + 5 
 
 - 7 = 0.0 .8 
 
 22 
 
 T. 
 
 7.6 
 
 2 
 
 9 
 
 21.2 
 
 2 
 
 + 6 
 
 -13 = a+1.5 .1 
 
 S..|,i,.|,il.cr 5 
 
 T. 
 
 13.6 
 
 2 
 
 4 
 
 23.6 
 
 2 
 
 4 
 
 + 3 = -- 0.3 .7 
 
 8 
 
 T. 
 
 9.5 
 
 2 
 
 14 
 
 21.1 
 
 4 
 
 + 5 
 
 -18 = a + 1.3 .4 
 
 8 
 
 T. 
 
 13.1 
 
 2 
 
 7 
 
 0.4 
 
 2 
 
 4 3 
 
 7 = 0.5 .8 
 
 12 
 
 T. 
 
 0.8 
 
 2 
 
 11 
 
 21.0 
 
 3 
 
 4- 9 
 
 -18 = a + 1.2 - .5 
 
 13 
 
 R, 
 
 '.'. 6 
 
 2 
 
 
 
 21.2 
 
 4 
 
 1 
 
 + 3 = a + 1.2 .5 
 
 14 
 
 T. 
 
 14.4 
 
 2 
 
 12 
 
 23.8 
 
 2 
 
 4 2 
 
 - 11=0 - - 0.5 .7 
 
 15 
 
 R. 
 
 13.8 
 
 2 
 
 7 
 
 23. 
 
 3 
 
 + 3 
 
 - 7 = 0.2 .7 
 
 22 
 
 N. 
 
 12.4 
 
 3 
 
 - 5 
 
 22.3 
 
 4' 
 
 4 6 
 
 8 = + 0.3 .8 
 
 27 
 
 28 
 
 N. 
 R. 
 
 9.8 
 12.1 
 
 3 
 2" 
 
 1 
 12 
 
 23.0 
 23.5 
 
 3 
 4 
 
 + 7 , - 6 = + 0.8 .6 
 + 6 - 16 = o + 0. 1 .ft 
 
14 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 r 
 
 Date. 
 
 Obs. 
 
 Hour. 
 
 No.of 
 
 btars. 
 
 Mean 
 orrec'n. 
 
 Hour. 
 
 No.of 
 tars. 
 
 Mean 
 orrec'u. 
 
 Equation of condition. 
 
 1866. 
 
 
 
 
 
 
 
 
 
 October 3 
 
 H. 
 
 10.4 
 
 3 
 
 4 
 
 22.3 
 
 4 
 
 + 8 
 
 11 = o + 0.8a - 1.7 6 
 
 4 
 
 R. 
 
 15.6 
 
 2 
 
 4 
 
 0.2 
 
 2 
 
 + 8 
 
 - 9 = /3 - - 0. 8 -1.5 
 
 5 
 
 H. 
 
 10.4 
 
 3 
 
 7 
 
 21.8 
 
 4 
 
 + 2 
 
 7 = + 0.9 1.6 
 
 5 
 
 H. 
 
 14.4 
 
 2 
 
 3 
 
 0.8 
 
 2 
 
 1 
 
 + l = l) + 0.8 -1.6 
 
 6 
 
 N. 
 
 11.0 
 
 3 
 
 1 
 
 22.7 
 
 2 
 
 + 4 
 
 3 = a + 0. 7 1. 8 
 
 8 
 
 N. 
 
 12.3 
 
 3 
 
 4 
 
 0.5 
 
 4 
 
 + 2 
 
 4 = a - - 0. 2 - 1. 8 
 
 8 
 
 N. 
 
 15.1 
 
 3 
 
 1 
 
 1.9 
 
 2 
 
 + 1 
 
 = ,i - 1.2 - 1.5 
 
 17 
 
 H. 
 
 11.4 
 
 2 
 
 3 
 
 0.3 
 
 3 
 
 + 6 
 
 8 = a + 0. 1 -.1.8 
 
 17 
 
 H. 
 
 17.1 
 
 4 
 
 3 
 
 6.2 
 
 3 
 
 1 
 
 + 1 = 7 - 1. 8 - 0. 2 
 
 18 
 
 R. 
 
 15.6 
 
 2 
 
 + 6 
 
 4.4 
 
 3 
 
 6 
 
 + 14 = f) - - 1. 6 . 1. 
 
 19 
 
 H. 
 
 17.7 
 
 4 
 
 2 
 
 5.1 
 
 3 
 
 + 2 
 
 1 = y - - 1. 8 - 0. 4 
 
 20 
 
 N. 
 
 -14.1 
 
 3 
 
 + 3 
 
 0.1 
 
 4 
 
 + 3 
 
 + 2 = /J -- 0.5 -1.7 
 
 25 
 
 R. 
 
 13.6 
 
 2 
 
 6 
 
 1.4 
 
 3 
 
 + 1 
 
 5 = a 0. 8 1.7 
 
 31 
 
 H. 
 
 11.0 
 
 5 
 
 4 
 
 22.9 
 
 4 
 
 
 
 3 = a + 0.5 -1.8 
 
 November 2 
 
 H. 
 
 12.2 
 
 2 
 
 - 11 
 
 1.3 
 
 3 
 
 + 5 
 
 - 14 = a - - 0. 5 1.8 
 
 2 
 
 H. 
 
 16.6 
 
 4 
 
 
 
 4.8 
 
 3 
 
 + 4 
 
 1 = p - - 1. 7 - 0. 7 
 
 5 
 
 N. 
 
 12.8 
 
 2 
 
 + 4 
 
 1.9 
 
 2 
 
 2 
 
 + 7 = o - - 0.7 -1.7 
 
 7 
 
 T. 
 
 12.9 
 
 2 
 
 4 
 
 2.5 
 
 3 
 
 + 9 
 
 12 = a 0. 9 -1.7 
 
 7 
 8 
 
 12 
 
 T. 
 
 N. 
 
 N. 
 
 17.3 
 13.5 
 
 17.7 
 
 2 
 3 
 3 
 
 - 6 
 
 
 
 + 10 
 
 4.8 
 2.5 
 5.0 
 
 2 
 
 2 
 4 
 
 + 1 
 + 8 
 + 2 
 
 5 = f) - - 1. 8 - 0. 5 
 - 7 =a - - 1.0 -1.6 
 + 10 = /3 - - 1. 8 - 0. 4 
 
 13 
 
 R. 
 
 13.8 
 
 2 
 
 + 2 
 
 1.2 
 
 2 
 
 + 2 
 
 + l = a -- 0.8 - 1.7 
 
 17 
 
 T. 
 
 13.8 
 
 2 
 
 5 
 
 3.3 
 
 2 
 
 + 7 
 
 - ll = o - 1.2 - 1.5 
 
 20 
 
 R. 
 
 13.8 
 
 2 
 
 5 
 
 1.9 
 
 3 
 
 4 
 
 + = a - - 0. 9 1.7 
 
 / 21 
 
 T. 
 
 13.5 
 
 4 
 
 + 5 
 
 2.7 
 
 3 
 
 6 
 
 + ll = a 1.0 1.5 
 
 26 
 
 T. 
 
 14.8 
 
 3 
 
 + 3 
 
 1.5 
 
 3 
 
 + 3 
 
 + 1 = 1.0 1.6 
 
 26 
 
 T. 
 
 18.3 
 
 3 
 
 + 2 
 
 8.0 
 
 4 
 
 3 
 
 + 7 = /3 - - 1.7 +0.6 
 
 December 4 
 
 R. 
 
 19.2 
 
 2 
 
 4 
 
 6.5 
 
 5 
 
 + 2 
 
 4 = /3 1.8 +0. 4 
 
 5 
 
 N. 
 
 14.6 
 
 2 
 
 + 3 
 
 3.3 
 
 3 
 
 4 
 
 + 7 = o - - 1.3 - 1.4 
 
 5 
 
 N. 
 
 19.2 
 
 4 
 
 + 6 
 
 7.4 
 
 3 
 
 2 
 
 + 10 = /3 1. 7 + 0. 7 
 
 10 
 
 R. 
 
 17.0 
 
 2 
 
 2 
 
 3.2 
 
 2 
 
 3 
 
 + 3 = a 1.6 1.0 
 
 12 
 
 R. 
 
 19.1 
 
 2 
 
 2 
 
 6.6 
 
 4 
 
 + 2 
 
 - 2 = /3 - - 1.8 +0.5 
 
 20 
 
 T. 
 
 16.2 
 
 3 
 
 + 5 
 
 2.8 
 
 4 
 
 8 
 
 + 14 = a - - 1.5 - 1.1 
 
 20 
 
 T. 
 
 19.4 
 
 4 
 
 + 8 
 
 7.0 
 
 2 
 
 10 
 
 + 20 = /3 -- 1.8 + 0.7 
 
POSITIONS OF FUNDAMENTAL, STARS. 
 
 If) 
 
 Hate. 
 
 ni,*. 
 
 Hour. 
 
 No.,,1 
 stars. 
 
 Mean 
 
 OITCC'II. 
 
 Hour. 
 
 No.of 
 
 St. 'IIS. 
 
 Mean 
 OITCC'II. 
 
 Initiation of condition. 
 
 1887. 
 
 
 
 
 
 
 
 
 
 January l. r > 
 
 H. 
 
 22. 3 
 
 2 
 
 J 
 
 7.8 
 
 2 
 
 1 
 
 - 2 = - - 1.3 a + 1.36 
 
 18 
 
 11. 
 
 17.9 
 
 3 
 
 + 1 
 
 5.6 
 
 4 
 
 
 
 = o - - 1.8 0.2 
 
 19 
 
 T. 
 
 Ukl 
 
 8 
 
 
 
 6.5 
 
 2 
 
 + 5 
 
 - 6 = - 1.8 +0.5 
 
 22 
 
 H. 
 
 22.3 
 
 2 
 
 4 
 
 CM 
 
 2 
 
 + 2 
 
 - 8 = - - 0.4 +1.7 
 
 23 
 
 T. 
 
 1-." 
 
 2 
 
 + 5 
 
 6.9 
 
 3 
 
 4> 
 
 + 6 = 1.9 +0.3 
 
 23 
 
 T. 
 
 1.5 
 
 2 
 
 + 2 
 
 11.7 
 
 3 
 
 2 
 
 + 3 = 7 + 0.3 +1.8 
 
 24 
 
 N. 
 
 17.6 
 
 4 
 
 2 
 
 7.5 
 
 2 
 
 + 6 
 
 - 9 = o - 1.8 +0.3 
 
 24 
 
 N. 
 
 22.1 
 
 2 
 
 + 7 
 
 10.7 
 
 4 
 
 4 
 
 + 9 = - - 0.8 +1.7 
 
 28 
 
 N. 
 
 1-. 1 
 
 3 
 
 + 4 
 
 5.4 
 
 3 
 
 2 
 
 + 5 = 1.9 0.1 
 
 .".I 
 
 H. 
 
 18.6 
 
 2 
 
 6 
 
 6.5 
 
 2 
 
 + 4 
 
 - 11 = o - - 2.0 +0.2 
 
 29 
 
 H. 
 
 3.2 
 
 2 
 
 + 5 
 
 15.1 
 
 2 
 
 
 
 + 3= x + 1.5 + 1.3 
 
 Kcliniary 1 
 
 H. 
 
 19.1 
 
 2 
 
 6 
 
 6.3 
 
 3 
 
 + 4 
 
 - 11 =o - 1.8 +0.4 
 
 5 
 
 II. 
 
 3.5 
 
 3 
 
 1 
 
 13.6 
 
 2 
 
 + 7 
 
 -9 = y + 1.2 +1.4 
 
 6 
 
 T. 
 
 19.1 
 
 3 
 
 1 
 
 7.2 
 
 2 
 
 3 
 
 + l=a - 1.8 + 0. 7 
 
 6 
 
 T. 
 
 0.4 
 
 2 
 
 8 
 
 12.4 
 
 4 
 
 + 5 
 
 - 14 = y + 0. 1 +1.8 
 
 7 
 
 N. 
 
 19.7 
 
 2 
 
 4 
 
 7.4 
 
 2 
 
 + 2 
 
 -7 = a 1.8 +0. 8 
 
 7 
 
 N. 
 
 22.8 
 
 2 
 
 2 
 
 9.5 
 
 2 
 
 + 4 
 
 - 8 = - - 0.9 +1.7 
 
 11 
 
 N. 
 
 23.5 
 
 2 
 
 + 2 
 
 9.3 
 
 3 
 
 + 2 
 
 - 2 = 0.8 +1.6 
 
 12 
 
 H. 
 
 19.4 
 
 3 
 
 3 
 
 4.7 
 
 3 
 
 + 8 
 
 - 12 = a - 1.7 + 0.1 
 
 26 
 
 II. 
 
 7.4 
 
 2 
 
 + 2 
 
 17.2 
 
 2 
 
 4 
 
 + 6 = y+1.7 - 0.1 
 
 27 
 
 T. 
 
 19.6 
 
 3 
 
 
 
 8.2 
 
 2 
 
 + 2 
 
 - 3 = o 1.6 +0.9 
 
 March 18 
 
 N. 
 
 22.1 
 
 2 
 
 + 2 
 
 9.2 
 
 2 
 
 + 1 
 
 = a - 1.2 +1.5 
 
 28 
 
 N. 
 
 7.1 
 
 4 
 
 2 
 
 19.7 
 
 3 
 
 
 
 -2 = y + 1.7 - 0.8 
 
 80 
 
 II. 
 
 21.8 
 
 2 
 
 + 2 
 
 11.1 
 
 2 
 
 2 
 
 l = o - - 0.8 +1.7 
 
 29 
 
 H. 
 
 2.5 
 
 3 
 
 - 2 
 
 13.5 
 
 4 
 
 + 2 
 
 - 6 = + 1,0 + 1.0 
 
 30 
 
 T. 
 
 21.8 
 
 3 
 
 
 
 10.7 
 
 3 
 
 
 
 l = a - - 0.9 +1.7 
 
 April 2 
 
 H. 
 
 2.9 
 
 3 
 
 3 
 
 12.3 
 
 3 
 
 + 1 
 
 -6 = + 0.8 +1.7 
 
 2 
 
 H. 
 
 9.5 
 
 2 
 
 + 2 
 
 18.6 
 
 2 
 
 + 2 
 
 1 = 7 + 1.6 0.9 
 
 3 
 
 T. 
 
 0.4 
 
 2 
 
 3 
 
 12.1 
 
 3 
 
 2 
 
 -2 = o + 0.2 +1.9 
 
 5 
 
 H. 
 
 2.4 
 
 2 
 
 2 
 
 11.2 
 
 2 
 
 + 2 
 
 -6 = + 0.4 +1.7 
 
 6 
 
 T. 
 
 1.0 
 
 3 
 
 + 4 
 
 12.9 
 
 8 
 
 1 
 
 + 3 = + 0.6 +1.7 
 
 13 
 
 N. 
 
 22.8 
 
 2 
 
 2 
 
 11.1 
 
 3 
 
 
 
 - 3 = a - - 0. 6 +1.8 
 
 17 
 
 T. 
 
 4.4 
 
 2 
 
 1 
 
 15.1 
 
 3 
 
 + 5 
 
 -8 = + 1.5 +1.1 
 
 18 
 
 II. 
 
 0.0 
 
 2 
 
 2 
 
 11.1 
 
 3 
 
 + 3 
 
 - 6 = a - - 0.3 +1.9 
 
 18 
 
 11. 
 
 4.1 
 
 2 
 
 2 
 
 14.0 
 
 2 
 
 
 
 4 = + 1.3 + 1.3 
 
 26 
 
 H. 
 
 2.8 
 
 3 
 
 5 
 
 13.0 
 
 4 
 
 + 4 
 
 - 11 =0 + 1.0 + 1.6 
 
 May 9 
 
 N. 
 
 4.3 
 
 5 
 
 5 
 
 14.1 
 
 5 
 
 + 4 
 
 -12 = + 1.3 +1.2 
 
 17 
 
 H. 
 
 0.4 
 
 2 
 
 + 2 
 
 12.4 
 
 4 
 
 3 
 
 + 3 = a + 0.2 +1.9 
 
 18 
 
 T. 
 
 1.2 
 
 2 
 
 + 4 
 
 14.1 
 
 2 
 
 + 3 
 
 1 = + 0.9 +1.7 
 
 18 
 
 T. 
 
 6.0 
 
 3 
 
 5 
 
 17.1 
 
 3 
 
 
 
 - 8 = + 1.8 + 0.2 
 
 23 
 
 N. 
 
 11.0 
 
 7 
 
 3 
 
 21.4 
 
 4 
 
 + 2 
 
 -6 = 7 + 0.9 1.6 
 
 24 
 
 II. 
 
 1.2 
 
 3 
 
 li 
 
 12.2 
 
 5 
 
 + 4 
 
 - 12 = o + 0. 4 + 1 . - 
 
 31 
 
 11. 
 
 2.3 
 
 4 
 
 o 
 
 14.2 
 
 5 
 
 + 1 
 
 -5 = o + l.l +1.5* 
 
 June 1 
 
 N. 
 
 1.6 
 
 4 
 
 + 2 
 
 15.0 
 
 2 
 
 2 
 
 + 2 = a + 1.1 +1.5 
 
 1 
 
 V 
 
 (Cs 
 
 5 
 
 2 
 
 1 :>.!) 
 
 3 
 
 + 1 
 
 -6 = + 1.7 +0.3 
 
 4 
 
 T. 
 
 1.9 
 
 2 
 
 ~" ~~ J 
 
 13.8 
 
 5 
 
 1 
 
 -6 = + 1.0 +1.6 
 
 4 
 
 T. 
 
 7.6 
 
 2 
 
 4 
 
 17.4 
 
 2 
 
 + 12 
 
 - 19 = + l.s 0.3 
 
 5 
 
 a. 
 
 1.9 
 
 3 
 
 
 
 13.8 
 
 3 
 
 + 2 
 
 -3 = a + 1.0 +1.7 
 
 8 
 
 N. 
 
 1.6 
 
 3 
 
 + 3 
 
 12.3 
 
 3 
 
 5 
 
 + 7^a + 0.5 +1.7 
 
16 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 Date. 
 
 Obs. 
 
 Hour. 
 
 No.of 
 stars. 
 
 Mean 
 corrcc'n. 
 
 Hour. 
 
 No.of 
 stars. 
 
 Mean 
 correc'n. 
 
 Ktjnation of condition. 
 
 1867. 
 
 
 
 
 
 
 
 
 
 Juno 10 
 
 N. 
 
 5.2 
 
 2 
 
 + 1 
 
 16.6 
 
 2 
 
 + 4 
 
 - 5 = a + 1.8 a + 0.66. 
 
 10 
 
 T. 
 
 0.8 
 
 2 
 
 + 3 
 
 12.4 
 
 2 
 
 4 
 
 + 7 = 7 + 0.3 +1.9 
 
 11 
 
 T. 
 
 1.4 
 
 6 
 
 7 
 
 13.7 
 
 5 
 
 
 
 -8 = 7 + 0.8 +1.7 
 
 11 
 
 T. 
 
 7.5 
 
 3 
 
 5 
 
 17.4 3 
 
 + 8 
 
 -10 = + 1.8 0.2 
 
 13 
 
 N. 
 
 3.3 
 
 4 
 
 + 3 
 
 16.6 
 
 3 
 
 + 2 
 
 . ]= a + 1.6 + 1.0 
 
 14 
 
 H. 
 
 4.4 
 
 4 
 
 7 
 
 16.2 
 
 5 
 
 + 5 
 
 - 14 = a + 1.7 + 0. 9 
 
 15 
 
 T. 
 
 0.5 
 
 2 
 
 + 7 
 
 13.6 
 
 2 
 
 6 
 
 13 = y + 0. 6 +1.8 
 
 20 
 
 N. 
 
 4.4 
 
 2 
 
 5 
 
 16.3 
 
 3 
 
 + 1 
 
 - 8 = a + 1.7 + 0.8 
 
 20 
 
 N. 
 
 7.5 
 
 2 
 
 4 
 
 18.4 
 
 2 
 
 + 8 
 
 - 15 = /J +1.9 - 0.5 
 
 21 
 
 H. 
 
 .4.1 
 
 2 
 
 6 
 
 15.9 
 
 4 
 
 + 2 
 
 - 10 = a + 1.6 +1.0 
 
 21 
 
 H. 
 
 7.5 
 
 2 
 
 8 
 
 18.5 
 
 3 
 
 + 9 
 
 - 20 = p + 1.9 0. 6 
 
 July 1 
 
 N. 
 
 3.8 
 
 3 
 
 + 1 
 
 17.0 
 
 3 
 
 1 
 
 = a + 1.7 +0.8 
 
 2 
 
 H. 
 
 5.1 
 
 3 
 
 4 
 
 14.0 
 
 2 
 
 + 6 
 
 - 12 = a +' 1. 4 + 0. 1 
 
 10 
 
 T. 
 
 5.3 
 
 3 
 
 3 
 
 16.9 
 
 5 
 
 1 
 
 - 4 = a + 1.8 + 0.5 
 
 .11 
 
 N. 
 
 4.4 
 
 3 
 
 9 
 
 16.8 
 
 4 
 
 + 6 
 
 - 17 = a . + 1.7 + 0. 7 
 
 11 
 
 N. 
 
 8.9 
 
 4 
 
 8 
 
 19.6 
 
 4 
 
 + 12 
 
 -23 = /3 -{ 1.6 1.1 
 
 15 
 
 N. 
 
 5.6 
 
 4 
 
 1 
 
 16.5 
 
 3 
 
 + 8 
 
 -ll = a + 1.8 +0.5 
 
 17 
 
 T. 
 
 5.4 
 
 4 
 
 8 
 
 17. 5 
 
 3 
 
 + 10 
 
 20 = a + 1.8 + 0. 3 
 
 17 
 
 T. 
 
 9.9 
 
 3 
 
 8 
 
 20.3 
 
 3 
 
 + 8 
 
 - 19 = ,3 + 1.3 -1.4 
 
 18 
 
 N. 
 
 9.8 
 
 3 
 
 3 
 
 19.9 
 
 3 
 
 + 5 
 
 11 = p + 1.3 1.3 
 
 19 
 
 H. 
 
 5.6 
 
 6 
 
 4 
 
 18.7 
 
 4 
 
 + 5 
 
 -ll = a + 1.8 0.1 
 
 19 
 
 H. 
 
 10.1 
 
 2 
 
 8 
 
 21.7 
 
 3 
 
 + 2 
 
 - 13 = p + 1. 1 1.6 
 
 20 
 
 T. 
 
 5.4 
 
 4 
 
 11 
 
 18.3 
 
 3 
 
 + 2 
 
 - 15 = a + 1. 8 + 0. 1 
 
 22 
 
 X. 
 
 5.9 
 
 5 
 
 6 
 
 17.9 
 
 5 
 
 + 5 
 
 -13 = o + 1.8 0.0 
 
 23 
 
 H. 
 
 5.2 
 
 6 
 
 6 
 
 18.8 
 
 3 
 
 + 12 
 
 20 = a + 1.8 0.0 
 
 24 
 
 T. 
 
 5.8 
 
 3 
 
 7 
 
 18.6 
 
 3 
 
 + 7 
 
 16 = a + 1. 9 - 0. 1 
 
 27 
 
 T. 
 
 5.5 
 
 3 
 
 5 
 
 18.7 
 
 2 
 
 + 4 
 
 -ll = a + 1.9 0. 
 
 30 
 
 H. 
 
 6.1 
 
 3 
 
 11 
 
 18.7 
 
 2 
 
 + 6 
 
 19 = a + 1. 9 0. 1 
 
 30 
 
 H. 
 
 11.4 
 
 2 
 
 2 
 
 21.6 
 
 3 
 
 + 10 
 
 15 = /3 + 0.7 1.7 
 
 31 
 
 T. 
 
 6.9 
 
 2 
 
 8 
 
 22.0 
 
 2 
 
 + 4 
 
 14 = n + 1.4 -1.1 
 
 31 
 
 T. 
 
 12.6 
 
 2 
 
 
 
 23.9 
 
 2 
 
 + 2 
 
 5 = /3 - - 0.2 -1.8 
 
 August 5 
 
 N. 
 
 8.8 
 
 3 
 
 4 
 
 18.3 
 
 3 
 
 + 3 
 
 9 = a + 1.6 0.8 
 
 9 
 
 H. 
 
 7.0 
 
 2 
 
 6 
 
 17.8 
 
 3 
 
 + 7 
 
 15 = a + 1.8 - 0.2 
 
 12 
 
 N. 
 
 7.6 
 
 2 
 
 8 
 
 20.2 
 
 3 
 
 + 6 
 
 -16 = a + 1.6 -1.0 
 
 13 
 
 H. 
 
 7.4 
 
 4 
 
 3 
 
 20.0 
 
 2 
 
 + 6 
 
 11 = a + 1.6 0.9 
 
 23 
 
 H. 
 
 12.2 
 
 2 
 
 . 12 
 
 22.2 
 
 5 
 
 + 6 
 
 _ 21 = ,3 + 0. 4 -1.7 
 
 23 
 
 H. 
 
 18.7 
 
 2 
 
 4 
 
 (1.2 
 
 2 
 
 7 
 
 + 3 = y 1.9 + 0. 3 
 
 26 
 
 R. 
 
 10.4 
 
 2 
 
 1 
 
 22.0 
 
 4 
 
 
 
 . 4 + /3 + 0.9 -1.7 
 
 30 
 
 H. 
 
 7.5 
 
 4 
 
 4 
 
 19.8 
 
 3 
 
 + 8 
 
 14 = a + 1.7 0.9 
 
 31 
 
 T. 
 
 8.5 
 
 2 
 
 4 
 
 19.8 
 
 2 
 
 + 5 
 
 11 = + 1.6 -1.1 
 
 September 4 
 
 T. 
 
 12.8 
 
 3 
 
 8 
 
 22.8 
 
 3 
 
 + 4 
 
 -15 = + 0.1 -1.8 
 
 G 
 
 N. 
 
 10.4 
 
 3 
 
 . 10 
 
 22.9 
 
 6 
 
 + 4 
 
 16 = o + 0. 7 1. 7 
 
 11 
 
 T. 
 
 9.6 
 
 3 
 
 9 
 
 20.9 
 
 4 
 
 + 
 
 -17 = a + 1.2 1.4 
 
 11 
 
 T. 
 
 13.3 
 
 2 
 
 6 
 
 0.2 
 
 2 
 
 + 6 
 
 15 = 0.4 1.9 
 
 12 
 
 N. 
 
 8.8 
 
 3 
 
 14 
 
 20.2 
 
 6 
 
 + 6 
 
 -22 = a + 1.5 1.2 
 
 12 
 
 N. 
 
 14.0 
 
 2 
 
 10 
 
 0.3 
 
 2 
 
 + 9 
 
 -22 = -- 0.6 -1.7 
 
 13 
 
 H. 
 
 9.4 4 
 
 7 
 
 19.6 
 
 4 
 
 + 6 
 
 15 = a + 1.4 - 0.1 
 
 13 
 
 H. 
 
 13. 5 4 
 
 4 
 
 23.3 
 
 3 
 
 + 7 
 
 _ 14 = - - 0.2 1.8 
 
 17 
 
 II. 
 
 9.8 4 
 
 6 
 
 21.7 
 
 3 
 
 + 8 
 
 _16 = o + 1.1 1.6 
 
 
 
 
 
 
 
 
 1 
 
POSITION'S OK FUNDAMENTAL STARS. 
 
 17 
 
 Date. 
 
 (IllS. 
 
 Hour. 
 
 No.of 
 
 -l;ll~. 
 
 Menu 
 colTrc'n. 
 
 lluiir. 
 
 Xo.or 
 
 -t:u~. 
 
 Mi-mi 
 oorrec'n. 
 
 Kipiiition of condition. 
 
 186T. 
 
 
 * 
 
 
 
 
 
 
 
 S'lllclllh'rlf* 
 
 T. 
 
 !i. " 
 
 4 
 
 12 
 
 -"-'. ! 
 
 9 
 
 4 4 
 
 -18 = a + 1.0 -1.7 
 
 111 
 
 V 
 
 y.7 
 
 3 
 
 :t 
 
 20.8 
 
 3 
 
 
 
 -5 = a + (i.!) -1.7 
 
 19 
 
 N. 
 
 ii. i 
 
 2 
 
 + 4 
 
 23.6 
 
 2 
 
 4 2 
 
 = - - 0.5 1.7 
 
 22 
 
 11. 
 
 ;i. :; 
 
 6 
 
 1(1 
 
 21.7 
 
 5 
 
 4 8 
 
 -20 = o + 1.2 1.5 
 
 24 
 
 T. 
 
 14.11 
 
 2 
 
 2 
 
 22.8 
 
 2 
 
 
 
 - 5 = - 0.2 1.7 
 
 October 1 
 
 11. 
 
 1(1.2 
 
 4 
 
 13 
 
 91.6 
 
 4 
 
 4 12 
 
 -26 = a + l.ll 1.6 
 
 1 
 
 H. 
 
 1 1.- 
 
 4 
 
 8 
 
 24.2 
 
 2 
 
 4 12 
 
 -22 = -- 0.7 1.6 
 
 -' 
 
 T. 
 
 10.7 
 
 4 
 
 6 
 
 . 19.3 
 
 3 
 
 + 4 
 
 -11 = + 1.2 1.2 
 
 8 
 
 H. 
 
 10.6 
 
 4 
 
 7 
 
 22.5 
 
 2 
 
 4- 10 
 
 - 18 = a + 0. 8 1.8 
 
 8 
 
 H. 
 
 14.6 
 
 2 
 
 2 
 
 1.4 
 
 2 
 
 + 8 
 
 - 12 = , a - i.o .1.7 
 
 11 
 
 II. 
 
 10.6 
 
 9 
 
 G 
 
 21.9 
 
 3 
 
 4 4 
 
 - 11 = + 0.9 . 1.6 
 
 14 
 
 11. 
 
 11.4 
 
 2 
 
 12 
 
 21.6 
 
 3 
 
 4 3 
 
 -16=0 + 0.8 1.7 
 
 14 
 
 H. 
 
 15.6 
 
 3 
 
 4 
 
 1.8 
 
 5 
 
 4 4 
 
 - 10 = - 1.2 1.4 
 
 1C 
 
 T. 
 
 11.4 
 
 2 
 
 2 
 
 1.6 
 
 3 
 
 4 4 
 
 - 7 = o - - 0.2 1.7 
 
 17 
 
 H. 
 
 15. 9 
 
 4 
 
 1 
 
 3.3 
 
 5 
 
 2 
 
 1 = - 1.5 . -- 1.2 
 
 18 
 
 A. 
 
 15.0 
 
 2 
 
 3 
 
 1.9 
 
 3 
 
 3 
 
 - 2 = - 1.2 l.G 
 
 19 
 
 T. 
 
 11.4 
 
 2 
 
 7 
 
 1.1 
 
 4 
 
 4 3 
 
 - 11 = a - - 0. 1 1. 9 
 
 23 
 
 H. 
 
 ir.. !i 
 
 4 
 
 
 
 2.1 
 
 3 
 
 1 
 
 1 = - 1.3 1.3 
 
 24 
 
 A. 
 
 16.3 
 
 3 
 
 4 1 
 
 3.8 
 
 3 
 
 4- 1 
 
 - 2 = - 1.6 1.0 
 
 26 
 
 11. 
 
 12.2 
 
 2 
 
 9 
 
 22.0 
 
 3 
 
 4- 5 
 
 -15 = o + 0.4 1.7 
 
 NoYrllllMT f> 
 
 A. 
 
 13.0 
 
 2 
 
 + 2 
 
 22.3 
 
 3 
 
 4 l 
 
 = o + 0. 1 - 0. 7 
 
 :. 
 
 A. 
 
 15.9 
 
 2 
 
 + 8 
 
 2.4 
 
 2 
 
 10 
 
 + 16 = 0-1.4 -1.3 
 
 G 
 
 T. 
 
 15.4 
 
 2 
 
 5 
 
 2.1 
 
 3 
 
 
 
 - 7 = - 1.2 -1.4 
 
 15 
 
 A. 
 
 17.8 
 
 9 
 
 + 10 
 
 6.6 
 
 3 
 
 1 
 
 + 9 = - l.f +0.1 
 
 18 
 
 H. 
 
 13.5 
 
 4 
 
 2 
 
 0.6 
 
 3 
 
 + 3- 
 
 - 6 = a - - 0.6 1.7 
 
 18 
 
 11. 
 
 18. 
 
 2 
 
 4- 2 
 
 3.6 
 
 2 
 
 
 
 = - 1.8 -0.6 
 
 20 
 
 T. 
 
 13.6 
 
 9 
 
 11 
 
 1.2 
 
 2 
 
 4 12 
 
 24 = o -- 0.7 1.8 
 
 26 
 
 A. 
 
 14.5 
 
 4 
 
 - 2 
 
 2.9 
 
 6 
 
 4 2 
 
 5 = a-1.3 1.5 
 
 30 
 
 T. 
 
 15.2 
 
 3 
 
 4 
 
 1.5 
 
 2 
 
 
 
 - 5 = o - 1.1 -1.5 
 
 Dt'uciuln'r 5 
 
 H. 
 
 15.6 
 
 2 
 
 4 2 
 
 0.8 
 
 2 
 
 
 
 + 1 = a - 1.0 1.5 
 
 5 
 
 H. 
 
 19.2 
 
 7 
 
 
 
 4.2 
 
 2 
 
 4 
 
 + 2 = - 1.7 - 0.2 
 
 7 
 
 T. 
 
 15.2 
 
 3 
 
 + 3 
 
 1.3 
 
 4 
 
 (1 
 
 + 2 = o - 1.1 - 1.6 
 
 7 
 
 T. 
 
 19.3 
 
 3 
 
 4- :i 
 
 4.0 
 
 9 
 
 7 
 
 + 8 = - 1.7 - 0.1 
 
 11 
 
 H. 
 
 14.0 
 
 4 
 
 + -I 
 
 1.2 
 
 4 
 
 2 
 
 + 5 = o-- 0.9 1.7 
 
 !l 
 
 H. 
 
 19.5 
 
 :! 
 
 4 3 
 
 4.4 
 
 9 
 
 6 
 
 + 7=0 - 1.7 0.0 
 
 16 
 
 H. 
 
 1 :,.-.' 
 
 4 
 
 it 
 
 0.8 
 
 4 
 
 6 
 
 + 5 = o - - 0.9 1.6 
 
 17 
 
 A. 
 
 17.0 
 
 9 
 
 
 
 6.0 
 
 4 
 
 4 
 
 + 3 = a 1.8 0.0 
 
 19 
 
 H. 
 
 16.3 
 
 2 
 
 4 4 
 
 1.8 
 
 4 
 
 4 
 
 + 7 = a-1.2 1.4 
 
 23 
 
 H. 
 
 15. 3 
 
 5 
 
 4 1 
 
 2.8 
 
 4 
 
 
 
 = a - 1.4 1.4 
 
 26 
 
 H. 
 
 19.8 
 
 2 
 
 + 2 
 
 6.0 
 
 3 
 
 2 
 
 + 2 = - 1.8 +0.5 
 
18 
 
 POSITIONS OF FUNDAMENTAL, STABS. 
 
 In discussing' these equations the results for the two years arc first treated separately. Equal 
 weight is given to each equation, it appearing that the error, arising from an insufficient number of 
 stars, is generally small. The equations are treated by the method of least squares, except that 
 only the factors 0, 1, and 2 have been used as multipliers. Thus, the following normal equations 
 and solutions are obtained : 
 
 Class a 
 
 1866. 
 
 9* 
 
 70 a + 32.7 16.4 b = 1.13 
 40 u + 142.2 a + 1,'3.8 I = 4.04 
 20 + 7.9 a + 129.0 b + ,'3.99 
 
 Solution. 
 
 8. 
 
 a = + 0.007 
 
 a = 0.034 
 b = + 0.034 
 
 48 ft + 5.1 a 7.9 b = 0.80 
 Glass p { 10 ft + 91.G a + 2.9 b = - 2.75 
 _ 8 ft + 7.5 a + 83.4 b = + 1.98 
 
 ft = 0.009 
 rt = 0.030 
 b = + 0.020 
 
 21 Y 2.6 a 15.16 = 0.83 
 Class Y { 2 r + 24.9 a + 13.G b = + 0.10 
 _ 18 r + 17.2 a + 54.0 6 = + 1.48 
 
 r = 0.022 
 
 = 0.013 
 & = + 0.031 
 
 The small values of a, /9, and f show that during the year 1866 there was no appreciable diur- 
 nal inequality in the apparent course of the stars over the meridian, as measured by the instrument 
 and clock. 
 
 The mean values of and 6 show that the right ascensions of the American Ephemcris, which 
 are the same with those of Dr. Gould's standard Coast Survey Catalogue, require the systematic 
 correction, 
 
 _ o.030 sin + 0".030 cos . 
 
 The corrections applied to this catalogue to obtain the clock correction is of the systematic 
 form 
 
 0".008 sin a. 
 so that the correction to be applied to the adopted positions is 
 
 O s .022 sin a + 9 .030 cos . 
 1867 Normal equations. 
 
 77 + 20.0 a 12.76 = 0.35 
 Class a <; 31 a + 105.8 a 8.3 6 = - 7.42 
 _20a 0.4 a + 134.46= + 4.23 
 
 Solutions. 
 
 8. 
 
 a = 0.009 
 
 a = 0.031 
 b = + 0.021 
 
 f 49/5 2.2 a 18.56= -3.54 
 
 Class /? <J -2/3+ 80.3 a+ 11.26== -3.19 
 
 [ _ 22 ft + 15.5 a + 90.1 6 = + 3.88 
 
 C 12 Y + 5.4 a, 2.2 6 -- 0.29 
 
 Class r \ fi r + -- 3 + 1.7 6 = 0.04 
 
 [ _ 3 r + 3.0a+ 27.0 6 = + 0.02 
 
 t = 0.062 
 a = 0.045 
 6 = + 0.033 
 
POSITIONS OF FUNDAMENTAL 8TAKS. 19 
 
 The tMiuatioiis in ;- art', with one except ion. all found in tin- first half of tin- year, and will there- 
 fore not suffice to give reliable independent values of the unknown quantities. The values of and 
 b from the other equations give (lie systematic correction to the adopted right ascensions of clock 
 stars 
 
 (I'.O.'M sin + O s .O:>.-> cos . 
 
 i omliining this with the above correction Iroin the observations for ISiiii, we have, for the -result 
 of both years' work. 
 
 0".028 sin + O s .028 cos , 
 or. 
 
 + O s .0,'!9 siu ( in 1 ') 
 
 The very large values of ./ and ,; corresponding to the year 1867 are remarkable. They indi- 
 cate that during tliis year stars observed in the day-time seemed to cross the meridian too soon by 
 O s .(l(i.">, when compared with transits at night. Any diurnal inequality in the clock rate during this 
 year has been shown to be out of the question, and it does not seem possible that the instrument 
 could have been subjected to such unequal heating, from any cause whatever, as would change its 
 pointing in right ascension. The inequality is greater in the case of the forenoon observations, 
 made before the sun's rays had had time to heat up the interior of the roof, than in the afternoon. 
 
 It would therefore appear that the cause is to be sought for in the manner in which observers 
 themselves arc a flee ted by the different conditions under which the day and night observations are 
 made. In the day-time the nervous system is braced by the rest of the preceding night, and stim- 
 ulated by sunlight ; the observations are so few that particular attention can be concentrated on 
 each, and this concentration is the more easy from the Hue and sharp definition of the transit wires 
 upon the bright ground of the sky. As night advances the nervous system becomes relaxed by con- 
 tinned labor; attention is no longer concentrated as during daylight, but is divided among rapidly- 
 recurring observations, and the wires are comparatively indistinct upon the feebly-illuminated back- 
 ground. All these causes will tend toward allowing the observer to let the star slip by a little at 
 night, and this is the very result which is indicated by the sensible magnitude of the quantities a 
 and ,;. 
 
 If this explanation be the true one we might expect the work of different observers to exhibit 
 the phenomenon in question in different degrees. Taking the mean values of the J's of the class 
 and ,J, which pertain to observers K, H., and T., during the first nine months of 1S67, we find that 
 
 H. 
 
 ForH J= 0.106 
 
 For N J = 0.063 
 
 For T J = - 0.0"..-. 
 
 Itegarding the irregular differences between the products of a and b by their coefficients in the 
 equations of condition as accidental errors, which we may well do, the differences between the values 
 of J indicate similar differences between the values of the diurnal inequality given by the work of 
 the several observers. That is to say, the mean value of and ,5 given by the work of H. is five- 
 hundredths of a second greater than that given by the work of T. 
 
 The principal difficulty in the reception of this explanation arises from the circumstance that 
 no such inequality is exhibited in the observations of 1866. For the difference I can give no reason 
 except this: that a much greater number of observations of miscellaneous stars were imposed 
 upon the observers during the nights of ISiiT. Although this would increase the effect referred 
 to, the actual increase is much greater than could have been anticipated as the result of that 
 cause. It is also worthy of remark, that had no correction been applied to J for diurnal change 
 of collimation, there would have been no great discrepancy between the values of-/ and ,; resulting 
 from the two years' work. 
 
 Supposing the quantities and ,'; to remain constant throughout each year, neither their mag 
 iiitudes nor the causes whence they originate will affect the quantities a and l>, on which depend 
 
20 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 the systematic corrections to the .adopted star positions. But, if we suppose them irregularly varia- 
 ble between wide limits, or subject to a regular annual variation, we may satisfy all the preceding 
 equations of condition by zero values of a and 6, each equation giving a separate value of a, ,?, or f. 
 Whether there is any reason to suppose them so variable is a question for the judgment of the indi- 
 vidual astronomer. The present discussion will be continued on the supposition that they are not 
 so variable, and that the corrections indicated by a and b are real. 
 
 Deeming it desirable to see what systematic corrections would be given by the observations of 
 1868, their results have also been investigated on the supposition that the correction would be of 
 the form 
 
 with the result, 
 
 sin ( 15 1 '), 
 ft = O s .024. 
 
 If we give half weight to this result, owing to the small number of determinations on which it 
 depends, the definitive systematic correction to the adopted right ascensions will be 
 
 O s .036sin( lo 1 '), 
 indicating an error of O s .07 in the difference of right ascensions between stars in I) 1 ' and in 21 1 '. 
 
 CORRECTIONS TO THE POSITION OF THE EQUINOX, AND TO THE OBLIQUITY OF THE ECLIPTIC. 
 
 The mean corrections to the positions of the sun derived from Hanson's Tables, and given in 
 the American Ephemeris, are as follows. J , Jp, and Jj/ represent the corrections to the right 
 ascension, north polar distance, and ecliptic polar distance, respectively : 
 
 
 
 1866. 
 
 
 
 1867. 
 
 
 
 Aa 
 
 Ay 
 
 A/ 
 
 Aa 
 
 Aj> 
 
 Ap> 
 
 
 8. 
 0.08 
 
 + 1.3 
 
 14 
 
 + 1.1 
 
 8. 
 
 + 0.05 
 
 
 
 + 0.1 
 
 II 
 
 + 0.2 
 
 February 
 March 
 
 - 0. 04 
 0. 05 
 
 + 0.7 
 0.2 
 
 + 0.5 
 - 0.5 
 
 + 0.06 
 0.00 
 
 + 0.6 
 + 1.2 
 
 + 0.9 
 + 1.2 
 
 
 0.01 
 
 + 0.8 
 
 + 0.7 
 
 0.02 
 
 + 0.8 
 
 + 0.7 
 
 May. 
 
 0.00 
 
 + 0.2 
 
 + 0.2 
 
 - 0.01 
 
 + 1.5 
 
 + 1.5 
 
 June 
 
 + 0.01 
 
 + 0.6 
 
 + 0.0 
 
 + 0.03 
 
 + 0.4 
 
 + 0.4 
 
 July .- 
 
 0.01 
 
 + 0.4 
 
 + 0.4 
 
 + 0.03 
 
 + 0.7 
 
 MH> 
 
 
 + 0.02 
 
 + 0.7 
 
 + 0.6 
 
 + 0.02 
 
 + 0.8 
 
 + 0.7 
 
 September 
 October 
 
 0.01 
 -f 0.03 
 
 + 1.4 
 
 + 1.3 
 
 + 1.5 
 + 1.1 
 
 + 0.05 
 + 0.03 
 
 + 1.5 
 + 0.9 
 
 + 1.2 
 
 + 0.7 
 
 November 
 December 
 
 -f 0.07 
 + 0.04 
 
 + 1.1 
 + 0.2 
 
 + 0.9 
 + 0.2 
 
 + 0.06 
 + 0.09 
 
 + 1.0 
 + 1.6 
 
 + 0.8 
 + 1.5 
 
 Put 
 
 z for the constant error in the measures of polar distance ; 
 J u> for the correction to Hanson's obliquity of the ecliptic ; 
 ' A e for the error of polar distance of the ecliptic at the vernal equinox. 
 
 Then each value of J j>' will give an equation of the form 
 
 = c J m sin 7 J e cos /. 
 
POSITIONS OF FUNDAMENTAL STARS. 
 
 21 
 
 The equations tor cadi \ear. \\hen solved ly least squares, will become, with sufficient approxima- 
 tion, 
 
 \->z l'J,,<: 
 
 (5 Je r= - J p 1 cos /: 
 
 and the constant correction to the right ascensions of stars will be 
 
 J = cosec M J e = 2.5 J c. 
 
 The solution for each year gives 
 
 1866. 
 
 iaer. 
 
 ^ + 0".G2 
 
 + 0".S8 
 
 J u> + 0".08 
 
 + 0".03 
 
 J c + 0".-li' 
 
 0".02 
 
 j + s .07 
 
 s .00 
 
 The great divergence iu the value of J for the two years renders the result somewhat uncer- 
 tain. Considering, however, that the divergence may arise from some cause acting iu opposite 
 directions in the two positions of the instrument, and that the preceding four years' observations 
 with the old instruments (lS(52-'(i")) indicate a correction of + O s .05, the correction + O s .03 for the 
 position of the equinox will be admitted. 
 
 The entire systematic correction to the fundamental catalogue is, therefore, 
 
 + O s .0.'i + O s .0:5(i sin ( 15 h ) 
 
 COMl'AIJISON OF RIGHT ASCENSIONS OBSERVED DIRECTLY AND BY REFLECTION. 
 
 Each annual volume contains a comparison of the direct and reflex observations of north polar 
 distance, but none of the right ascensions. As a comparison of the latter will decide with consid- 
 erable probability whether the meridian to which the observations are reduced is really a vertical 
 great circle, the results of one are here presented. The individual discordances in the case of the 
 several stars may be seen at a glance by reference to the means given under the head " Corrections 
 to the positions of stars in the American Ephemeris." These means were collected in groups, each 
 included in a zone extending through 10 of polar distance. Each discordance was multiplied by 
 sin X. 1'. J)., and the mean by weights taken, with the following results : 
 
 
 1866. 
 
 1867. 
 
 
 Limits of N. P. D. 
 
 
 
 \li.-m f~D 1?^ win ti 
 
 
 
 
 
 jHr.ul ^U ^ Kf Hill 2' 
 
 
 (D E)8inj> 
 
 wt. 
 
 (D R)slnj> 
 
 Wt. 
 
 
 o o 
 
 a. 
 
 
 i. 
 
 
 i. 
 
 32 
 
 + 0.004 
 
 19 
 
 - 0. Oil 
 
 19 
 
 - 0.004 
 
 + 210 
 
 0.009 
 
 9 
 
 0.002 
 
 20 
 
 0.004 
 
 11 20 
 
 + 0.003 
 
 28 
 
 + 0.004 
 
 29 
 
 + 0.004 
 
 21 30 
 
 + 0.017 
 
 .'- 
 
 + 0.032 
 
 15 
 
 + 0.022 
 
 31 .|.-> 
 
 0.028 
 
 19 
 
 0.000 
 
 18 
 
 - 0.014 
 
 .Vi ClI 
 
 - 0. 013 
 
 28 
 
 - 0.034 
 
 25 
 
 0.023 
 
 70 79 
 
 0.009 
 
 40 
 
 - 0.010 
 
 39 
 
 O.IMI 1 .! 
 
 80 89 
 
 0.007 
 
 28 
 
 0.019 
 
 37 
 
 0. 014 
 
 fl> 99 
 
 o.u:;- 
 
 31 
 
 0.028 
 
 24 
 
 0.034 
 
 99 in:. 
 
 - 0. 04.1 
 
 
 
 + 0. 010 
 
 12 
 
 0.008 
 
22 POSITIONS OF FUNDAMENTAL STARS. 
 
 The general result may be summed up as follows : In the north there is a substantial agreement 
 between the transits observed directly and those observed by reflection. In the south the latter 
 exceed the former by the quantity 8 .018. 
 
 If the systematic discordance depended entirely on the instrument, the algebraic sum of the 
 south discordance in one position of the instrument, and of the corresponding north discordance in 
 the reverse position, ought to vanish. They do not so vanish. If, in recording a transit by reflec- 
 tion, the observer should, from his less easy posture, or from any other cause, let a swift-moving 
 star slip by a little, the result would be of the same character with that actually found. 
 
 The above comparison seems to me to indicate, with great probability, that the axis of motion 
 of the instrument is subject to no wabbling amounting to as much as O s .02. 
 
 CORRECTIONS TO THE RIGHT ASCENSIONS OF STANDARD STARS DERIVED FROM OBSERVATIONS WITH 
 THE TRANSIT INSTRUMENT AND WITH THE TRANSIT CIRCLE. 
 
 The results given in the following table are all in the form of corrections to the American 
 Ephemeris for the years 1865-'C9 ; the positions for previous years being found by carrying back 
 those found in the American Ephemeris for 1809, with the proper motions there employed. 
 
 The second column gives the mean correction deduced from the observations with the transit 
 instrument during the four years 1862-'G5, without correction. These are in fact, the standard 
 corrections employed in deducing the clock corrections for the transit circle. The small figures in 
 this and the third column following indicate the number of observations on which the result 
 depends. 
 
 Next we have the amount of the systematic correction + <)*.<).'? + N .03G sin (a 15' 1 ) deduced 
 from the observations with the transit circle. The sum of these two columns gives the final cor- 
 rection resulting from the observations with the transit instrument, found in the next column. 
 
 Column "Eesult of circle" gives the mean -corrections resulting from the observations with the 
 Transit Circle during the years 186G-'67. This column is deduced from the corrections to the right 
 ascensions found in the published volumes for those years, the constant correction, + O s .03, being 
 applied to the result. 
 
 Column C T gives the excess of the transit circle result over that of the transit instru- 
 ment, to which we shall recur presently. 
 
 The next column gives the correction concluded from the work of both instruments. It is formed 
 by giving to each result a weight proportional to the number of observations. 
 
POSITIONS OF FUNDAMENTAL STARS. 
 
 KXimtiT OF roi;i;i:(TioNs TO THE KICHT ASCENSIONS or M \M.\I;I> STAKS. 
 
 23 
 
 8Ur. 
 
 Transit 
 l-i-.-.'-V,:,. 
 
 Sy-li-matii- 
 
 ColTl-ctillll. 
 
 I.V.-nlt of 
 transit. 
 
 KV^nlt of 
 
 rilrlr. 
 
 C T. 
 
 CnnrliiiliMl 
 correction. 
 
 
 H, 
 
 H. 
 
 .s. 
 
 a. 
 
 t. 
 
 . 
 
 n Andromeda' 
 
 4- . 002,4 
 
 f .OH 
 
 f .057 
 
 4- .037 
 
 - .020 
 
 f .050 
 
 ; IVnasi . . . 
 
 - .017,. 
 
 -f . 054 
 
 \- .037 
 
 h .031,., 
 
 - .003 
 
 4- . 035 
 
 ii Cas.-io|ir:r . 
 
 - .08, 
 
 -f- .051 
 
 - .03 
 
 .00,0 
 
 f .03 
 
 .01 
 
 ,< (Vti .... 
 
 -1- .o:;i... 
 
 + .051 
 
 f .089 
 
 f .082 41 
 
 .000 
 
 f .o,-*> 
 
 21 ('assio]>i'a- . 
 
 - - 
 
 
 
 4- .09,:, 
 
 
 4- .09 
 
 I'isrilllll . 
 
 - .05-' 
 
 -)- .049 
 
 . 003 
 
 - .002,., 
 
 4- .001 
 
 .1111:1 
 
 6 Ceti .... 
 
 4- .001 61 
 
 + .nlii 
 
 f . 047 
 
 4- .061,, 
 
 f .014 
 
 4- .050 
 
 A Cassioi>f;r . . 
 
 
 . 
 
 . 
 
 
 . 
 
 . 
 
 V Piscimu . . . 
 
 -f JM- 
 
 + .044 
 
 4- .092 
 
 4- ."H6 
 
 f .024 
 
 4- . 103 
 
 a Piscitim . . . 
 
 - .039 M 
 
 4- .04:! 
 
 4- . .004 
 
 4- .002*, 
 
 - .002 
 
 4- .003 
 
 f} Arietis . 
 
 4- .OO&j, 
 
 4- .041 
 
 4- . 047 
 
 4- .043 18 
 
 - .004 
 
 4- . 045 
 
 ."ill ('a>Mi>|>r;i> . 
 
 
 . 
 
 
 4- .04,,, 
 
 
 .04 
 
 a Arietis . 
 
 + . 
 
 + .O:H 
 
 4- . 044 
 
 4- .032K 
 
 - ."012 
 
 4- .038 
 
 P (Vti .... 
 
 + .o::i 
 
 + .oils 
 
 4- .069 
 
 4- .070,, 
 
 4- .007 
 
 4- .072 
 
 t Cassio],i-;<. . . 
 
 - 
 
 - -. 
 
 
 4- -268 
 
 
 
 + .26 
 
 y Ceti .... 
 
 .11117 
 
 + .034 
 
 4- . 027 
 
 4- .03*.,, 
 
 4- .oil 
 
 4- .032 
 
 a Ceti .... 
 
 4- .01-:, 
 
 + .o:!l 
 
 + .049 
 
 4- .052^ 
 
 4- .003 
 
 4- .050 
 
 48 (H)CViilii . . 
 
 . 
 
 . 
 
 
 4- .12u 
 
 . 
 
 4- .12 
 
 f Arietis . . . 
 
 - .027,,, 
 
 + .029 
 
 4- ."002 
 
 - .014 14 
 
 .016 
 
 .007 
 
 a Pereei . . . 
 
 - .052,o 
 
 + .d->f 
 
 . 024 
 
 4- -09,, 
 
 4- .11 
 
 4- .04 
 
 il Tanri 
 
 4- .0054, 
 
 + .1^5 
 
 4- .030 
 
 4- .04*., 
 
 4- .018 
 
 4- .036 
 
 f Pereei . 
 
 . (HK>3 
 
 + .oi:t 
 
 4- .023 
 
 4- .022 r , 
 
 .(Mil 
 
 4- .022 
 
 y Eridani . . . 
 
 + .o:u.. 
 
 + .022 
 
 4- . 053 
 
 4- .095,, 
 
 4- .042 
 
 4- .06* 
 
 y Tauri . . . 
 
 + "- 
 
 + . 019 
 
 4- . 042 
 
 4- .034.:,, 
 
 .008 
 
 4- . o:w 
 
 e Tauri . . 
 
 4- -004*, 
 
 4- .018 
 
 4- . 022 
 
 4- .014,, 
 
 .()() 
 
 4- .019 
 
 a Tauri 
 
 4- .(Mil., 
 
 + .017 
 
 4- .018 
 
 4- .(MHi M 
 
 .012 
 
 4- .014 
 
 i: (':lllli>liip;ir<li 
 
 
 
 . 
 
 4- .1",:, 
 
 . 
 
 4- .17 
 
 Auriga- . . . 
 
 .031 ; 
 
 4- .014 
 
 . 022 
 
 4- .002,., 
 
 4- .024 
 
 .010 
 
 11 Orionis . . . 
 
 - .UK),, 
 
 4- .013 
 
 . 027 
 
 _ .066 
 
 .028 
 
 . 037 
 
 a Auriga- . . . 
 
 - .or 1 .,, 
 
 4- .011 
 
 . 0*2 
 
 .OSr, 
 
 
 
 .03 
 
 ; Orionis . 
 
 4- .012, e 
 
 4- .oil 
 
 4- .023 
 
 4- .030 
 
 4- .007 
 
 4- .025 
 
 /3 Tauri . . . 
 
 .010 TO 
 
 + .010 
 
 .000 
 
 4- .029,, 
 
 4- .029 
 
 4- .011 
 
 t Oriouis . . . 
 
 - .019,, 
 
 4- .009 
 
 .010 
 
 4- .oifei 
 
 4- .022 
 
 .004 
 
 a Leporis . . . 
 
 - .019,5 
 
 + . 009 
 
 .010 
 
 
 . 
 
 . 010 
 
 s Orionis . 
 
 + .010.,, 
 
 4- .008 
 
 4- .018 
 
 4- .O32. w 
 
 4- .014 
 
 4- .023 
 
 a Columbia . 
 
 - .061,6 
 
 + .007 
 
 . 054 
 
 .030 a 
 
 4- .024 
 
 .050 
 
 a Orionis . . . 
 
 - .003,,, 
 
 4- .007 
 
 4- .004 
 
 .000.* 
 
 .004 
 
 4- .003 
 
 H Geuiiuur . . 
 
 .002,. 
 
 4- .004 
 
 + .002 
 
 .029,, 
 
 .031 
 
 .008 
 
 y Geminor 
 
 . 000;,, 
 
 4- .002 
 
 4- .002 
 
 .005,, 
 
 .007 
 
 .(Mil 
 
 51 (H) d-phci . . 
 
 . 
 
 
 
 4- -82 
 
 . 
 
 + 
 
 a Canis Ma.joris . 
 
 .061 
 
 4- .(Nil 
 
 .060 
 
 .(i::.-,,,. 
 
 - .025 
 
 .051 
 
 e Canis Majoris . 
 
 .OiKIa, 
 
 .000 
 
 -.023 
 
 - .oia 
 
 4- .005 
 
 .020 
 
 S Canis Majoris . 
 
 .018 
 
 .001 
 
 .019 
 
 .012s 
 
 -r- .007 
 
 .016 
 
 Geminor 
 
 - J'-'S 
 
 .002 
 
 .030 
 
 - .022,, 
 
 4- .008 
 
 .096 
 
 a 2 Gemiuor ... 
 
 + .869 
 
 .0(C! 
 
 4- .266 
 
 4- .280* 
 
 4- .014 
 
 + . 270 
 
 a Canis Minoris* 
 
 - .013, 1B 
 
 .00:1 
 
 .016 
 
 .045.M 
 
 4- .007 
 
 . 
 
 /} Geminor . . 
 
 + .002*, 
 
 .003 
 
 . 001 
 
 .00953 
 
 .008 
 
 .004 
 
 ij> Geminor 
 
 .040, 
 
 .004 
 
 .044 
 
 - .056, 
 
 .012 
 
 .050 
 
 3 Ursa* Miuoris . 
 
 
 
 
 
 . 
 
 
 p Argus 
 
 .085, 
 
 .005 
 
 .030 
 
 - .032,, 
 
 .002 
 
 . 032 
 
 e Hydra? . . . 
 
 .(KM* 
 
 .006 
 
 .010 
 
 - .012., 
 
 .002 
 
 .011 
 
 t Urea? Majoris . 
 
 - - 
 
 
 
 
 - - 
 
 - 
 
 
 o 3 Ursa; Majoris . 
 
 
 
 
 
 .01,:, 
 
 . 
 
 .01 
 
 K Caiu-ri . 
 
 4- .'oo-j,. 
 
 .'ON 
 
 .004 
 
 + .048,, 
 
 4- .052 
 
 4- .019 
 
 1 (H) Dracouis . 
 
 
 . . 
 
 . 
 
 .17,, 
 
 . 
 
 .17 
 
 a Hydne . 
 
 - .001 
 
 .006 
 
 .007 
 
 4- .005,, 
 
 4- .012 
 
 .000 
 
 d Ursa: Majoris - 
 
 
 - - 
 
 
 
 
 
 6 Ursa! Majoris . 
 
 4- .If.' 
 
 .006 
 
 4- .01 
 
 4- .07., 
 
 4- .06 
 
 4- .04 
 
 e Leonis . 
 
 .01:! . 
 
 .006 
 
 .019 
 
 - .0303T, 
 
 .011 
 
 - . 025 
 
 /i Leonig . . 
 
 + .045, 
 
 . 005 
 
 4- .OKI 
 
 4- .073,., 
 
 4- .033 
 
 4- .051 
 
 a Li-onis 
 
 - .004* 
 
 .III 15 
 
 .009 
 
 - .022 6 , 
 
 .013 
 
 .015 
 
 32 l"r.-a- Majoris . 
 
 
 
 
 
 
 
 
 
 
 
 
 In the case of a Caiiis Miuoris the correction i ;.03G ban been applied to C T on account of the inequality of proper motion given by Anwcrs. 
 
2-1. POSITIONS OF FUNDAMENTAL STARS. 
 
 EXHIBIT OF CORRECTIONS TO THE RIGHT ASCENSIONS OF STANDARD STARS Continued. 
 
 Star. 
 
 Transit 
 1862-'65. 
 
 Systematic 
 correction. 
 
 liV.sillt Of 
 
 transit. 
 
 Result of 
 circle. 
 
 C T. 
 
 Concluded 
 correction. 
 
 
 8. 
 
 s. 
 
 w. 
 
 *. 
 
 e. 
 
 H, 
 
 y Leouis . . . 
 
 4 .017 6 , 
 
 .004 
 
 -f . 013 
 
 4 -017 :H 
 
 4 .004 
 
 4 .014 
 
 9 (11) Draconis . 
 
 . 
 
 . 
 
 
 .08, 
 
 . 
 
 .08 
 
 p Leonis . 
 
 - .036,8 
 
 .003 
 
 - .039 
 
 - .034,4 
 
 4 .005 
 
 .037 
 
 t Leonis . 
 
 4 .07335 
 
 .003 
 
 -)- .070 
 
 4 .081*, 
 
 4 .oil 
 
 4 .074 
 
 a Urea; Majoris . 
 
 h .001*4 
 
 .002 
 
 - .001 
 
 4 -OS,, 
 
 4 .03 
 
 4 .01 
 
 i! Leonis . 
 
 .02055 
 
 .001 
 
 - . 021 
 
 - .08844 
 
 .017 
 
 .028 
 
 (i Crateris . 
 
 4 .005,0 
 
 
 
 + . 005 
 
 4 .004,,; 
 
 - .001 
 
 4 . 005 
 
 T Leonis . 
 
 h .007 13 
 
 + .001 
 
 H- . oiw 
 
 4 -015,5 
 
 4 .007 
 
 4 .012 
 
 A Draconis . . 
 
 . 
 
 . 
 
 . 
 
 4 .19l9 
 
 . 
 
 .19 
 
 v Leonis . . . 
 
 - .012 37 
 
 + .002 
 
 .010 
 
 .005,9 
 
 4- .005 
 
 .008 
 
 3 Leonis . 
 
 H- -Oil,* 
 
 4 .002 
 
 + .013 
 
 4 -019.50 
 
 4 .006 
 
 4 .015 
 
 y Ursse Majoris . 
 
 h .039,! 
 
 + .003 
 
 + .04 
 
 4 .07,,-, 
 
 h .03 
 
 4 .07 
 
 o Virginia . 
 
 - .061 3 i 
 
 + .005 
 
 .056 
 
 .034,0 
 
 h .022 
 
 .047 
 
 4 (H) Draconis . 
 
 . 
 
 
 
 .06,, 
 
 . 
 
 
 ;/ Virginis . . . 
 
 - .01138 
 
 4 .006 
 
 ."005 
 
 4 .019 3 , 
 
 4 .024 
 
 4 .'006 
 
 /? Corvi ... . 
 
 + .064*-, 
 
 4 .008 
 
 + .072 
 
 4 .100* 
 
 4 .028 
 
 4 .087 
 
 K .Draconis 
 
 
 
 
 4 -02 6 
 
 . 
 
 4 .02 
 
 32- Camelopardi . 
 
 . 
 
 
 
 4 -50 
 
 . 
 
 .50 
 
 a CanumVenat. . 
 
 4 .011.2, 
 
 + .010 
 
 + .021 
 
 4 -03049 
 
 4 .009 
 
 4 .(127 
 
 Virginis - 
 
 - .031s, 
 
 + .012 
 
 .019 
 
 4 -006,0 
 
 4 .025 
 
 .013 
 
 a Virginis - 
 
 + .006,00 
 
 4 .014 
 
 + .020 
 
 4 -007V, 
 
 .013 
 
 4 .015 
 
 f Virgiuis . 
 
 4 .004 6 , 
 
 + .016 
 
 + .020 
 
 4 -04143 
 
 4 .021 
 
 4 .029 
 
 t/ Ursse Majoris . 
 
 .094 
 
 4 .02 
 
 .07 
 
 4 -02,0 
 
 4 .09 
 
 .00 
 
 71 Bootis - 
 
 .030 M 
 
 + .019 
 
 .011 
 
 .023*,- 
 
 .012 
 
 .017 
 
 a Dracouis . . 
 
 
 
 - - 
 
 4 -03 ;3 
 
 - - 
 
 4 .03 
 
 a Bootis . 
 
 + .013,.,, 
 
 + . 023 
 
 + .036 
 
 4 .033, B 
 
 .003 
 
 4 . 035 
 
 Bootis - 
 
 + . 043 5 
 
 + .024 
 
 -)- .067 
 
 4 .H9ia 
 
 4 .052 
 
 4 .082 
 
 5 Ursse Miuoris . 
 
 . 
 
 . 
 
 
 4 -13,3 
 
 . 
 
 4 .13 
 
 e Bootis . . . 
 
 .018, 
 
 4 .026 
 
 + ."008 
 
 4 -Oils, 
 
 4 .003 
 
 4 .009 
 
 a- Libra; 
 
 .021;,.. 
 
 -r- .027 
 
 + .006 
 
 4 .040 M 
 
 4 .034 
 
 4 .016 
 
 j3 Ursse Miuoris . 
 
 - .OU4 
 
 + .03. 
 
 + .02 
 
 4 -03, : , 
 
 4 .01 
 
 4 .02 
 
 ft Bootis . . . 
 
 _ 
 
 . 
 
 . 
 
 - .06,, 
 
 
 .06 
 
 ;3 Libra? 
 
 .010,,; 
 
 4 .031 
 
 + . 021 
 
 4 .052% 
 
 4 .031 
 
 4 .031 
 
 ft Bootis . . . 
 
 - .004,, 
 
 4 .032 
 
 + .028 
 
 4 .012,, 
 
 .016 
 
 4 .018 
 
 }- Ursje Miuoris . 
 
 
 
 
 .07,, 
 
 - - 
 
 .07 
 
 a Coronie Boreal is 
 
 . 000,,, 
 
 + .034 
 
 + .034 
 
 4 .021 
 
 .013 
 
 4 .028 
 
 Serpeutis 
 
 . ooo w 
 
 4 .035 
 
 + .035 
 
 4 .069 47 
 
 4 .034 
 
 4 .051 
 
 c Serpentis . . 
 
 .011,,, 
 
 4 .036 
 
 + . 025 
 
 4 -025i9 
 
 .000 
 
 4 .025 
 
 f Ursa? Minoris . 
 
 
 
 
 4 -15,3 
 
 
 .15 
 
 & Scorpii . . . 
 
 + .004" ra 
 
 + "038 
 
 + ."042 
 
 4 .040,, 
 
 ."002 
 
 4 .041 
 
 /3 1 Scorpii . 
 
 4 .054,, 
 
 .039 
 
 4- .093 
 
 4 -106,., 
 
 4 .013 
 
 .101 
 
 6 Ophiuchi . . 
 
 + .017,0 
 
 + .040 
 
 4 .057 
 
 4 .049,7 
 
 .008 
 
 4 .052 
 
 T Herculis. . . 
 
 
 
 
 4 -21.8 
 
 . 
 
 .21 
 
 a Scorpii . . . 
 
 ."021 
 
 4 . 042 
 
 4 .021 
 
 4 .020,, 
 
 .001 
 
 4 .021 
 
 11 Draconis . . 
 
 .47, 
 
 + .04 
 
 .43 
 
 -'.774 
 
 - .34 
 
 .60 
 
 A Dracouis 
 
 
 . 
 
 
 .01 7 
 
 
 .01 
 
 f Ophinchi . - 
 
 .050,4 
 
 + . 043 
 
 .007 
 
 4 .018,, 
 
 4 .025 
 
 4 .005 
 
 ij Herculis. 
 
 . 
 
 . 
 
 
 4 -04,8 
 
 
 .04 
 
 K Ophiuchi . - 
 
 + .0283,1 
 
 4 .047 
 
 4 ."070 
 
 4 .067,, 
 
 ."003 
 
 4 .069 
 
 (I Herculis 
 
 
 
 
 
 
 
 10 Ursse Miuoris . 
 
 
 
 
 .08,, 
 
 
 .08 
 
 a Herculis. 
 
 + ."OOI M 
 
 4 . 049 
 
 4 .050 
 
 4 -0464, 
 
 .004 
 
 4 .049 
 
 6 Ophiuchi 
 
 .002 
 
 4. .050 
 
 4 .048 
 
 4 .071,, 
 
 4 .023 
 
 4 . 057 
 
 a Ophiuchi 
 
 + -012 85 
 
 .051 
 
 4 .063 
 
 4 .06153 
 
 .002 
 
 .062 
 
 u Draconis . . 
 
 . 
 
 . . 
 
 . . 
 
 4 .06,0 
 
 - - 
 
 4 .06 
 
 fi Herculis. 
 
 .007 W 
 
 + .052 
 
 4 .045 
 
 4 .023., 
 
 .022 
 
 4 .034 
 
 4 l Draconis . . 
 
 _ 
 
 
 . 
 
 .05 5 
 
 
 .05 
 
 y Draconis . . 
 
 + .05, 
 
 4 .05 
 
 4 .10 
 
 . 05,, 
 
 ."l5" 
 
 .III! 
 
 y* Sagittarii . . 
 /t 1 Sagittarii . 
 
 .029 18 
 .023s, 
 
 .054 
 4 .055 
 
 4 .025 
 4 .032 
 
 4 -077 7 
 4 .057,, 
 
 4 .052 
 4 .025 
 
 4 .040 
 4 . 035 
 
 6 Ursse Minoris . 
 
 
 
 , 
 
 
 . 
 
 . 
 
 r/ Serpeutis . - 
 
 + ."011,3 
 
 4 .056 
 
 4 .'067 
 
 4 .H*. 
 
 4 .045 
 
 4 .085 
 
 1 Aquilse . . . 
 
 + .033 7 4 
 
 4 .058 
 
 4 .091 
 
 4 -122.7 
 
 4 .031 
 
 4 .097 
 
 a Lyrse. . . . 
 
 + .OOlse 
 
 + .058 
 
 4 .059 
 
 4 .044,, 
 
 .015 
 
 4 -051 
 
 /} Lyra. . . . 
 
 + .01545 
 
 + .060 
 
 4 .075 
 
 4 .031,0 
 
 .044 
 
 4 .061 
 
POSITIONS OF FUNDAMENTAL STARS. 
 
 INHIBIT OK roi;i;i:rnoNs TO Tin: I;K;IIT ASCKNSIONS OF STANDARD STARS Contiim.-.i. 
 
 Star. 
 
 Traii-it 
 
 Systematic 
 correction. 
 
 Result of 
 transit. 
 
 Result of 
 circle. 
 
 C T. 
 
 Concluded 
 correction. 
 
 
 . 
 
 ft 
 
 ft 
 
 ft 
 
 t. 
 
 i. 
 
 r. Sajjittarii . 
 
 .024s, 
 
 4- .060 
 
 4- .036 
 
 4- 035 1:! 
 
 - .001 
 
 4- . O3t; 
 
 .">o Draeoni.f 
 
 
 _ 
 
 . 
 
 i tyt 
 
 , 
 
 4~ . ** 
 
 
 i 04't 
 
 4- .061 
 
 4- . 104 
 
 111 
 
 4- .007 
 
 . 11 Hi 
 
 </ Sagittarii . . 
 
 .IIT-J 
 
 4- . oty 
 
 .010 
 
 . 
 
 
 .010 
 
 it Dracouis . . 
 
 
 - - 
 
 
 4- . lo, 5 
 
 
 4- .10 
 
 T Draconis 
 
 . 
 
 
 
 4- -21, 
 
 
 4- .21 
 
 <i Aquila) . 
 
 4- . oi2< 
 
 4- .'062 
 
 4- "074 
 
 4- .096.37 
 
 4- .022 
 
 . OKi 
 
 K AqililiO . . . 
 
 - .005,7 
 
 .063 
 
 4- .058 
 
 4- .100,9 
 
 4- .042 
 
 .075 
 
 y Aquilie . - - 
 
 4- .005.. 
 
 4- .063 
 
 4- .068 
 
 4- .043,0 
 
 .025 
 
 .059 
 
 a Aquihe . . . 
 
 4- .Oil* 
 
 4- .064 
 
 4- .075 
 
 4- .069 
 
 .006 
 
 4- .073 
 
 e Draeonis 
 
 
 
 
 4- . 18 6 
 
 
 4- .18 
 
 Aqnihr . 
 
 .oo6 
 
 4- .064 
 
 4- ."064 
 
 4- ! 054,9 
 
 - .'OIO 
 
 4- .062 
 
 ). Ursa 1 Minoris . 
 
 . 
 
 
 . 
 
 + -12s, 
 
 
 4- -12 
 
 r Aquilic . 
 
 .098, 
 
 4- ."065 
 
 .033 
 
 .033,., 
 
 ."OOO 
 
 .033 
 
 a* Caprii . . . 
 
 - .00760 
 
 4- .065 
 
 4- .058 
 
 4- .099,,, 
 
 4- .041 
 
 4- .070 
 
 K Cephei . . . 
 
 
 . 
 
 . 
 
 4- .24,. 
 
 
 4- .24 
 
 xr Caprii . . . 
 
 . 
 
 . 
 
 . 
 
 4- -05690 
 
 . 
 
 + .056 
 
 e Dclphiu! . . 
 
 4- .010,, 
 
 4- .066 
 
 4- .076 
 
 4- .082,9 
 
 4- .006 
 
 4- .079 
 
 a Cygni . . . 
 
 4- .002,3 
 
 4- . 066 
 
 4- .068 
 
 4- .040*, 
 
 .028 
 
 4- . 057 
 
 fi Aquarii . . . 
 
 4- -021,, 
 
 4- .066 
 
 4- .087 
 
 4- -123,7 
 
 4- .036 
 
 4- .098 
 
 v Cygni . . . 
 
 4- .033 S 
 
 4- .066 
 
 4- .099 
 
 4- .083,9 
 
 .016 
 
 4- .086 
 
 61 Cygni . . . 
 
 
 . 
 
 
 4- . 350 K 
 
 _ 
 
 4- . 350 
 
 ( Cygui . . . 
 
 - .012 61 
 
 4- .066 
 
 4- .054 
 
 4- .01533 
 
 .039 
 
 4- .038 
 
 a Cephei . . . 
 
 4- -05 1B 
 
 4- .07 
 
 4- .12 
 
 .00^ 
 
 .12 
 
 .04 
 
 1 Pegasi . . . 
 
 .074, 
 
 4- .066 
 
 .008 
 
 - .052,7 
 
 .044 
 
 .037 
 
 /3 Aqnarii . 
 
 .OOSso 
 
 4- .066 
 
 + .061 
 
 4- .064 3 , 
 
 4- .003 
 
 4- .062 
 
 i 1 tvplii-i . . . 
 
 4- -025, 
 
 4- -07 
 
 4- .09 
 
 4- -12,8 
 
 4- .03 
 
 4- .10 
 
 f Aquarii . . . 
 
 - .017,, 
 
 4- .066 
 
 4-. . 049 
 
 + .041, 
 
 .008 
 
 4- .046 
 
 e Pegasi . 
 
 .014 
 
 4- .066 
 
 4- .052 
 
 4- -01536 
 
 .037 
 
 4- .037 
 
 11 Cephei . . . 
 
 
 
 - 
 
 .00,0 
 
 - - 
 
 .00 
 
 ft Capricorn! . . 
 
 - .055,7 
 
 4- .065 
 
 4- .010 
 
 4- -032.W 
 
 4- .022 
 
 4- .019 
 
 79 Draconis . . 
 
 . 
 
 . 
 
 . 
 
 4- .05, 
 
 
 4- .05 
 
 a Aquarii . 
 
 .011.15 
 
 4- .065 
 
 4- .054 
 
 4- -065:,, 
 
 4- .Oli 
 
 4- .059 
 
 ft Aqnarii . 
 
 .oi:^ 
 
 4- .065 
 
 4- .052 
 
 4- .054 2 , 
 
 4- .002 
 
 4- .053 
 
 -. Aquarii . 
 
 .009 2J 
 
 4- .064 
 
 + .055 
 
 4- -041,9 
 
 .014 
 
 4- .048 
 
 9 Aquarii . 
 
 4- .ooi. M 
 
 4- .063 
 
 4- .064 
 
 4- .057.,., 
 
 - .007 
 
 4- .061 
 
 226 Cephei . . . 
 
 . 
 
 . 
 
 . 
 
 . 
 
 . 
 
 
 
 f Pegaai . . . 
 
 4- .041 i3 
 
 4- .063 
 
 4- .104 
 
 4- .082*. 
 
 .022 
 
 4- .093 
 
 t Cephei . . . 
 
 . 
 
 . 
 
 
 4- .12n 
 
 . 
 
 4- .12 
 
 i Aquarii . . . 
 
 4- .060*, 
 
 4- .062 
 
 4- .122 
 
 4- -157,3 
 
 4- .035 
 
 4- .134 
 
 a Piscis Austral! s 
 
 - .012* 
 
 4- .062 
 
 4- .050 
 
 4- .088 16 
 
 4- .038 
 
 4- .065 
 
 a Pegasi . 
 
 4- .016, s 
 
 4- .061 
 
 4- .077 
 
 4- -040,6 
 
 .037 
 
 4- .060 
 
 o Cephei ... 
 
 
 . 
 
 . 
 
 .03, 
 
 . 
 
 .03 
 
 " Piscium . 
 
 . 
 
 . 
 
 
 4- .087, 8 
 
 . 
 
 4- .087 
 
 i Piscinm . . . 
 
 .017 
 
 4- .058 
 
 4- .041 
 
 .006,7 
 
 .047 
 
 4- .028 
 
 >' Cephei . 
 
 4- .25,o 
 
 4- .06 
 
 4- .31 
 
 4- -IS, 
 
 4- .16 
 
 4- -24 
 
 u Piscinm . 
 
 .016*, 
 
 4- .056 
 
 4- .040 
 
 4- .031,, 
 
 .009 
 
 4- . o:t7 
 
26 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 The column G T is that which principally commands our attention. The first feature to 
 be noticed is the magnitude of the discrepancies. Taking their mean value, without regard to sign, 
 for the 109 clock stars observed by both instruments, we find it to amount to 0".017. This is a 
 greater mean difference than we should expect to arise from the purely accidental errors of obser- 
 vation. Let us see how. far it is of a systematic character, depending either upon the right ascen- 
 sion, the polar distance, or the magnitude of the star. 
 
 Dividing the circle of E. A. into eight parts, we find the following mean value of C T for the 
 clock stars of each octant : 
 
 Octant. 
 
 C T 
 
 1 
 
 8. 
 
 + 0.002 
 
 2 
 
 + 0.007 
 
 3 
 
 - 0.006 
 
 4 
 
 + 0.008 
 
 5 
 
 + 0.012 
 
 6 
 
 + 0.007 
 
 7 
 
 + 0.010 
 
 8 
 
 0.010 
 
 We see that the circle results are, on the average, greater by O s .004. After correction for this 
 difference, the results will indicate a cyclical difference, of which the largest term is O s .005 cos , 
 but they are not regular enough to predicate anything certain upon. It will be remembered that 
 no corrections for cyclical error have been applied to the circle results, and the somewhat unex- 
 pected result of this comparison is that they do not seem to need any such correction. 
 
 Arranging the values of C T according to polar distance, and taking the mean for each ten 
 degrees, we have the following mean values of this quantity. For stars less than 50 from the pole, 
 the mean by weights proportional to the number of observations has been taken. For the other 
 stars the mean is taken indiscriminately. 
 
 Limits of N. P. D. 
 
 C T 
 
 o 
 
 o 
 
 8. 
 
 10 
 
 20 
 
 + 0.05 
 
 20 
 
 30 
 
 0.03 
 
 30 
 
 40 
 
 + 0.01 
 
 40 
 
 50 
 
 + 0.02 
 
 50 
 
 CO 
 
 0. 005 
 
 GO 
 
 70 
 
 0.006 
 
 70 
 
 80 
 
 0. 006 
 
 80 
 
 90 
 
 0. 001 
 
 90 
 
 100 
 
 + 0.016 
 
 100 
 
 110 
 
 + 0.017 
 
 110 
 
 120 
 
 + 0.015 
 
 North of the zenith (polar distance 51) the differences fall within the unavoidable errors of the 
 few observations made with the transit. But south of the zenith we find the difference to assume 
 a well-marked systematic character, the positions given by the circle being uniformly less north of 
 the equator and greater south of it by amounts too great to be the result of accidental errors. 
 
 Such a result would follow from a constant error in the collimation of either instrument. Me- 
 ridian transits are referred to a supposed great circle passing through the pole, and coinciding with 
 
POSITIONS OP FUNDAMENTAL STARS. 
 
 27 
 
 tin 1 true meridian of reference on the circle of mean declination of clock stars. If this supposed 
 great circle is really a small one.it will cross the meridian of reference on the circle of mean declina- 
 tion. To express the fact in algebraic form it is easy to see that an error of J c in the collimalion 
 will, by its direct ell'ect and by the resulting errors in the polar a/.imuth and the clock correction, 
 give rise to the error 
 
 J c (tan << sec tan 3 + sec <J ) 
 
 in i star of declination . In this formula, tan <? and sec '5 represent the mean values of tan <> and 
 sec ii for the stars on which the clock correction depends. If we suppose <?= 0, the error will become 
 
 J c (1 + tan <5 sec <5) . 
 The following table shows the value of the coefficient of Sc for different polar distances. 
 
 NPD 
 
 Coefficient. 
 
 o 
 
 
 20 
 
 + 0.82 
 
 30 
 
 + 0.73 
 
 40 
 
 4- 0.64 
 
 50 
 
 + 0.53 
 
 00 
 
 + 0.42 
 
 70 
 
 + 0.30 
 
 80 
 
 + 0. 1C 
 
 90 
 
 0.00 
 
 100 
 
 0.19 
 
 110 
 
 0.43 
 
 120 
 
 0.73 
 
 130 
 
 1.14 
 
 To ascertain whether there is any systematic difference depending upon the magnitude of the 
 star, we collect the values of G T corresponding to those thirteen stars the magnitudes of which 
 are given in the Kphcmcris as 1 or 1.-, and those twelve which are of or below the fifth magnitude. 
 In the case of </ ('anis Minoris, C T has been corrected for the inequality of proper motion given 
 by Auwers in Ifo. 1373 of the Astronomische Nachrichten : 
 
 Bright utare. 
 
 Faint stars. 
 
 a Tauri - . 
 
 0. 012 
 
 ^ Geminor. . 
 
 0. 012 
 
 ft Orion is . 
 
 + 0.007 
 
 /c C'ancri . 
 
 + 0. 0.12 
 
 a Canis Mil.). 
 
 0. 037 
 
 i Leonis . 
 
 + O.dll 
 
 ('anis.M.-ij. 
 
 + 0.005 
 
 T 1 .roll is . 
 
 + 0.007 
 
 a Cauia Mill. 
 
 + 0. 004 
 
 v Leonis . 
 
 4- 0.005 
 
 J) Grmiiior 
 
 0.008 
 
 l> OpbincM 
 
 4- 0.023 
 
 a 1 .1-1 in is . 
 
 o.in:: 
 
 ' AqlliliU . 
 
 + 0.042 
 
 a Virninis 
 
 0. 013 
 
 T Aquilitt . 
 
 0.000 
 
 I!(K)tiM . 
 
 0.003 
 
 // Aquarii . 
 
 + o. o:; 
 
 ii Scnrpii . 
 
 0. 001 
 
 f Aqiuirii . 
 
 (1. (HIS 
 
 a Lynn 
 
 0. 015 
 
 ft Capricorni 
 
 + 0. 022 
 
 a Aqililin . 
 
 0.006 
 
 JT Aquarii . 
 
 0. 014 
 
 a PiscisAus. 
 
 + O.u: 1 .- 
 
 
 
 Mean . . . 
 
 0. 004 
 
 Mean . . . 
 
 + 0.014 
 
 The difference of the means, 8 .018, is more than three times the probable mean difference of 
 two sets of values of T, selected at random from the list. It is, therefore, highly probable that 
 there is a real difference depending on the magnitude of the star, the faint stars being observed the 
 later with the circle. Such a result is not an improbable one. The spider lines of the circle appear 
 much finer than those of the transit, while the illumination of the field is fainter. The effect of the 
 latter cause will probably be to make an observer later in recording a transit. If all stars were 
 recorded later by the same amount, their right ascensions would not be affected. But the stray 
 light which surrounds a bright star forms a bright ground for the dark transit wire a perceptible 
 time before the star reaches the wire, and thus tin- approach of the two objects is distinctly seen. 
 As we take fainter stars the stray light disappears, and the approach is less distinctly seen. Thus, 
 tin- elfect in ipicstion will be exaggerated as the star grows fainter. . 
 
 Whatever be the cause of this etfeet, \\e ha\e abundant evidence that the right ascensions of 
 
28 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 faint objects given by different authorities sometimes exhibit discrepancies which can hardly depend 
 on anything but the magnitude. A striking instance of this is given by the planet Neptune. In 
 the Washington Observations for 1806, p. 400, is given a column of corrections to the Ephemeris of 
 Neptune, found in the appendix to the American Ephemeris for 18(59, from which it appears that 
 the mean correction to that ephemeris given by the observations with the transit circle is + N .09U. 
 But a similar comparison with the Greenwich observations for 18(5(! indicates no correction what- 
 ever. In 18(57 a brighter illumination was given the Held of the Washington, circle, and the dis- 
 crepancy was reduced to O s .03(). 
 
 These circumstances strengthen the view already presented that an observer may observe 
 transits at night systematically later than in the day. 
 
 EIGHT ASCENSIONS OF POLARIS. 
 
 The right ascensions of Polaris demand a separate investigation, on account of the different 
 character of the data on which they depend, and the existence of well-marked personal differences 
 in the results. 
 
 In the following collection of right ascensions all results are omitted except those of consecu- 
 tive transits by the saifie observer. As a single transit gives only an equation of condition between 
 the azimuth and the right ascension, a pair of opposite transits is considered as giving only a single, 
 result for right ascension. As the coefficients of the azimuth in the equations are nearly equal, and 
 of opposite signs, we may take as this single result the mean of the separate results of the two tran- 
 sits reduced with any value of the azimuth reasonably near the truth. 
 
 Classifying the right ascensions according to the observer, we have the corrections to the right 
 ascensions of the American Ephemeris given on the next page. The third column gives the correc- 
 tions as they result immediately from the observations. Large personal differences in the results 
 being evident, the mean result from the work of each observer during each year is taken and is 
 given at the end of the columns. It appears from this that there is a difference of more than, two 
 seconds between the result of Professor Hall's observations and that of Mr. Thirion's. Eeduced to 
 arc of a great circle, this difference amounts to 0".82, or 8 .054 in time. 
 
 It will also be seen that each of the three observers who observed throughout both years gives 
 a smaller correction in 1867 than in 18C6, the differences being as follows: 
 
 This change may be partly due to the different position of the instrument during the second year. 
 
 For the purpose of reducing the results to a common standard, the general mean is taken, and 
 found to be appreciably + 1 8 .0. The systematic correction to reduce the results of each observer to 
 this standard is applied to the results in the third column to obtain those in the fourth. It may be 
 a question whether this correction should be considered the same for both years, or whether the 
 results for each year should be taken and applied separately. A middle course has been adopted by 
 applying the following corrections : 
 
 01 is. 
 
 18>. 
 
 18G7. 
 
 
 8. 
 
 X. 
 
 N. 
 
 0.0 
 
 + 0.4 
 
 II. 
 
 + 1.0 
 
 + 1.0 
 
 i;. 
 
 0.1 
 
 
 T. 
 
 1.4 
 
 -1.1 
 
POSITIONS OF FUNDAMKNTAL STARS. 
 
 29 
 
 Thus, the fourth column Drives the results as they would have been had all the observations 
 
 made b\ a single mean observer. 
 
 KllIlIT ASCMNSIONS or PHI. \1!1S HKIHVKn KUdM DOriH.K TRANSITS ]!V T1IK SKVKIi.U, OI'.SKKVI- I;S. 
 
 _ 
 
 
 Cc.rriTt n In 
 Am. K|ilirm. 
 
 j[ = 
 
 - 
 
 ti 
 
 Corrcct'n If. 
 Am. Ephcin. 
 
 ji 
 
 Date. 
 
 O 
 
 Correct'n to 
 Am. Eiilicin. 
 
 Reduced cor- 
 rection. 
 
 Date. 
 
 Observer. 
 
 Correct'n to 
 Am. Ephem. 
 
 If 
 
 1866. 
 
 
 1. 
 
 ,. 
 
 1866. 
 
 
 ,. 
 
 . 
 
 1867. 
 
 
 .. 
 
 s. 
 
 1867. 
 
 
 I. 
 
 #. 
 
 .h.u. 4 
 
 R. 
 
 + 2.0 
 
 + 1.9 
 
 July 11 
 
 T. 
 
 + 14 
 
 ao 
 
 Jau. 7 
 
 K. 
 
 1.2 
 
 0.8 
 
 Sept. IB 
 
 N. 
 
 + 0.6 
 
 + 1.0 
 
 5 
 
 11. 
 
 + 1-4 
 
 + 2.4 
 
 13 
 
 H. 
 
 0.0 
 
 + 1.0 
 
 11 
 
 H. 
 
 + 0.4 
 
 + 1.4 
 
 23 
 
 11. 
 
 0.0 
 
 + 1.0 
 
 8 
 
 H. 
 
 2.5 
 
 1.5 
 
 14 
 
 T. 
 
 + 1.4 
 
 o.o 
 
 17 
 
 X. 
 
 + 0.8 
 
 + 1.2 
 
 24 
 
 T. 
 
 + 1.7 
 
 + 0.6 
 
 9 
 
 R. 
 
 + 0.3 
 
 + a 2 
 
 26 
 
 X. 
 
 + 0.8 
 
 + 0.8 
 
 23 
 
 T. 
 
 + 0.3 
 
 0.8 
 
 27 
 
 H. 
 
 + 1.3 
 
 -( 2.3 
 
 Feb. 1 
 
 R. 
 
 0.1 
 
 0.2 
 
 August 3 
 
 T. 
 
 + 0.6 
 
 - 0.8 
 
 84 
 
 X. 
 
 0.5 
 
 0.1 
 
 28 
 
 T. 
 
 + 4.4 
 
 + 3.3 
 
 3 
 
 T. 
 
 + 2.3 
 
 + 0.9 
 
 4 
 
 R. 
 
 + 1-7 
 
 + 1-6 
 
 28 
 
 X. 
 
 0.0 
 
 + 0.4 
 
 30 
 
 X. 
 
 + 2.5 
 
 + 2.9 
 
 :, 
 
 R. 
 
 + 1.0 
 
 + 0.9 
 
 r, 
 
 N. 
 
 + 1.2 
 
 + 1.2 
 
 29 
 
 H. 
 
 0.0 
 
 + 1.0 
 
 Oct. 1 
 
 H. 
 
 0.8 
 
 + 0.2 
 
 6 
 
 H. 
 
 0.4 
 
 + 0.6 
 
 9 
 
 R. 
 
 + 1.6 
 
 + 1.5 
 
 31 
 
 N. 
 
 + 2.4 
 
 + 3.8 
 
 7 
 
 X. 
 
 0.0 
 
 + 0.4 
 
 15 
 
 R. 
 
 2.7 
 
 2.8 
 
 10 
 
 H. 
 
 0.4 
 
 + 0.6 
 
 Feb. 5 
 
 H. 
 
 1.2 
 
 0.2 
 
 8 
 
 H. 
 
 0.4 
 
 + 0.6 
 
 16 
 
 H. 
 
 0.0 
 
 + 1.0 
 
 15 
 
 T. 
 
 + 1.6 
 
 + 0.8 
 
 6 
 
 T. 
 
 + 2.5 
 
 + 1.4 
 
 12 
 
 T. 
 
 + 3.1 
 
 + 1.0 
 
 20 
 
 R. 
 
 2.2 
 
 2.3 
 
 16 
 
 R. 
 
 0.1 
 
 -0.2 
 
 7 
 
 N. 
 
 0.7 
 
 0.3 
 
 14 
 
 H. 
 
 + 1.5 
 
 + 2.5 
 
 Jl 
 
 T. 
 
 + 3.4 
 
 + 2.0 
 
 17 
 
 H. 
 
 0.8 
 
 + 0.2 
 
 26 
 
 H. 
 
 -1.7 
 
 0.7 
 
 15 
 
 A. 
 
 + 1.5 
 
 
 
 22 
 
 R. 
 
 1.0 
 
 1.1 
 
 1- 
 
 T. 
 
 + 4.0 
 
 + 3.6 
 
 27 
 
 T. 
 
 + 0.4 
 
 0.7 
 
 16 
 
 T. 
 
 + 2.5 
 
 + 1.4 
 
 March 5 
 
 II. 
 
 0.4 
 
 + 0.6 
 
 22 
 
 T. 
 
 + 3.4 
 
 + 8.0 
 
 March 18 
 
 N. 
 
 + 1.5 
 
 + 1.9 
 
 18 
 
 A. 
 
 + 1.7 
 
 
 8 
 
 X. 
 
 r 1.2 
 
 + 1.2 
 
 Sept. 5 
 
 T. 
 
 + 3.2 
 
 + 1.8 
 
 28 
 
 N. 
 
 + 0.5 
 
 + 0. 9 
 
 19 
 
 T. 
 
 + 2.0 
 
 + 0.9 
 
 10 
 
 T. 
 
 + 3.7 
 
 + 2.3 
 
 8 
 
 T. 
 
 1.0 
 
 2.4 
 
 29 
 
 H. 
 
 -0.6 
 
 + 0.4 
 
 23 
 
 H. 
 
 2.2 
 
 1.2 
 
 26 
 
 X. 
 
 1.2 
 
 1.2 
 
 12 
 
 T. 
 
 + 0.7 
 
 -0.7 
 
 30 
 
 T. 
 
 + 2.7 
 
 + 1.6 
 
 24 
 
 A. 
 
 + 0.4 
 
 . 
 
 27 
 
 R. 
 
 + 2.0 
 
 + 1.9 
 
 14 
 
 T. 
 
 + 1.0 
 
 0.4 
 
 April 1 
 
 X. 
 
 0.6 
 
 0.2 
 
 M 
 
 6. 
 
 1.2 
 
 0.2 
 
 30 
 
 N. 
 
 0.9 
 
 0.9 
 
 15 
 
 R. 
 
 f 2.0 
 
 + 1.9 
 
 2 
 
 H. 
 
 1.1 
 
 - 0,1 
 
 Xov. 5 
 
 A. 
 
 + 0.3 
 
 
 April 5 
 
 R. 
 
 + 0.8 
 
 + 0.7 
 
 17 
 
 T. 
 
 + 1.8 
 
 + 0.4 
 
 3 
 
 T. 
 
 + 2.2 
 
 + 1.1 
 
 6 
 
 T. 
 
 + 2.4 
 
 +- 1.3 
 
 11 
 
 T. 
 
 + 3.3 
 
 + 1.9 
 
 22 
 
 N. 
 
 + 2.2 
 
 + 2.2 
 
 5 
 
 H. 
 
 0.8 
 
 + .0.2 
 
 8 
 
 A. 
 
 + 2.2 
 
 
 1!' 
 
 X. 
 
 + 1.4 
 
 + 1.4 
 
 27 
 
 K. 
 
 + 2.6 
 
 1 2.6 
 
 6 
 
 T. 
 
 + 8.2 
 
 + LI 
 
 12 
 
 A. 
 
 \- 0.1 
 
 
 20 
 
 R. 
 
 + 0.4 
 
 + 0.3 
 
 28 
 
 R. 
 
 + 0.8 
 
 + 0.7 
 
 13 
 
 T. 
 
 (- 1. 4:) 
 
 ( 2.5) 
 
 18 
 
 H, 
 
 0.1 
 
 + 0.9 
 
 May 3 
 
 R. 
 
 + 1.3 
 
 + 1.2 
 
 Oct. 4 
 
 R. 
 
 + 2.4 
 
 + 2.3 
 
 17 
 
 T. 
 
 + 1.8 
 
 + 0.7 
 
 19 
 
 A. 
 
 + 1.6 
 
 . 
 
 4 
 
 H. 
 
 0.8 
 
 + 0.2 
 
 5 
 
 H. 
 
 + 0.6 
 
 + 0.4 
 
 18 
 
 H. 
 
 + 1.0 
 
 + 2.0 
 
 20 
 
 T. 
 
 + 0.4 
 
 0.7 
 
 5 
 7 
 14 
 15 
 19 
 21 
 
 T. 
 X. 
 N. 
 R. 
 T. 
 N. 
 
 + 1.7 
 
 + 0.3 
 0.2 
 
 + 1.8 
 + 2.2 
 + 0.8 
 2.0 
 
 6 
 8 
 15 
 16 
 17 
 18 
 
 X. 
 X. 
 X. 
 R. 
 H. 
 R. 
 
 + 1.2 
 + 3.3 
 + M 
 + 3.0 
 + 1.3 
 + 8.0 
 
 + 1.2 
 + 3.3 
 
 + M 
 
 + 8.3 
 + 1.9 
 
 96 
 May 9 
 11 
 14 
 17 
 18 
 
 H. 
 
 N. 
 T. 
 T. 
 H. 
 T. 
 
 + 2.9 
 + 1.2 
 + 3.7 
 + 0.1 
 0.4 
 + 1-2 
 
 + 3.9 
 + 1.6 
 + 2.6 
 1.0 
 + 0.6 
 + 0.1 
 
 Dec. 9 
 Mean. . 
 
 H. 
 
 N. 
 H. 
 T. 
 A. 
 
 + 1.3 
 
 + 2.3 
 
 + 1.8 
 + 2.3 
 + 2.2 
 2.0 
 
 + 0.39 
 0.10 
 + 2.00 
 + 1. 11 
 
 22 
 
 H. 
 
 0.1 
 
 + 0.9 
 
 19 
 
 H. 
 
 + 1.0 
 
 + 3.0 
 
 23 
 
 N. 
 
 + 0.1 
 
 + 0.5 
 
 
 
 
 
 23 
 
 T. 
 
 + 3.6 
 
 + 2.2 
 
 20 
 
 X. 
 
 + 2.6 
 
 + 2.6 
 
 24 
 
 H. 
 
 0.0 
 
 + 1.0 
 
 
 
 
 
 24 
 
 N. 
 
 + 1-1 
 
 + 1.1 
 
 23 
 
 R. 
 
 + 1.4 
 
 + 1.3 
 
 27 
 
 N. 
 
 0.8 
 
 0.4 
 
 
 
 
 
 
 
 H. 
 
 + 1.0 
 
 + 2.0 
 
 27 
 
 X. 
 
 + 2.2 
 
 + 2.2 
 
 31 
 
 H. 
 
 + 0.4 
 
 + 1-4 
 
 
 
 
 
 
 
 X. 
 
 + 0.1 
 
 + 0.1 
 
 31 
 
 H. 
 
 0.2 
 
 + 0.8 
 
 June 1 
 
 N. 
 
 + 0.6 
 
 + 1.0 
 
 
 
 
 
 30 
 
 T. 
 
 + 5.0 
 
 + 3.6 
 
 Xov. 1 
 
 R. 
 
 Kl 
 
 + 0.4 
 
 4 
 
 T. 
 
 + 2.8 
 
 + 1-7 
 
 
 
 
 
 31 
 
 N. 
 
 + 8.4 
 
 + 2.4 
 
 2 
 
 II. 
 
 0.9 
 
 + 0.1 
 
 6 
 
 X. 
 
 + 0.7 
 
 + 1.1 
 
 
 
 
 
 June 4 
 
 X. 
 
 + 1.6 
 
 + 1.6 
 
 5 
 
 X. 
 
 + 3.4 
 
 + 3.4 
 
 10 
 
 N. 
 
 + 1.2 
 
 + 1.6 
 
 
 
 
 
 6 
 
 II. 
 
 + 1.2 
 
 + 2.2 
 
 6 
 
 R. 
 
 + 2.3 
 
 + 8.9 
 
 11 
 
 T. 
 
 + 2.6 
 
 + 1.5 
 
 
 
 
 
 7 
 
 X. 
 
 0.2 
 
 0.2 
 
 7 
 
 T. 
 
 + 5.6 
 
 + 4.2 
 
 15 
 
 T. 
 
 + 0.8 
 
 0.3 
 
 
 
 
 
 11 
 
 N. 
 
 + 1.8 
 
 + L8 
 
 8 
 
 R. 
 
 0.8 
 
 0.9 
 
 21 
 
 H. 
 
 0.8 
 
 + 0.2 
 
 
 
 
 
 13 
 
 JI. 
 
 + 1.8 
 
 + 3.8 
 
 9 
 
 H. 
 
 + 1-2 
 
 + 2.2 
 
 July 24 
 
 T. 
 
 + 2.4 
 
 + 1.3 
 
 
 
 
 
 15 
 
 H. 
 
 0.3 
 
 + 0.7 
 
 12 
 
 X. 
 
 + 4.1 
 
 + 4.1 
 
 27 
 
 T. 
 
 + 2.0 
 
 + 0.9 
 
 
 
 
 
 n 
 
 R. 
 
 + 0.6 
 
 + 0.5 
 
 13 
 
 R. 
 
 + 3.8 
 
 + 17 
 
 31 
 
 T. 
 
 + 2.0 
 
 + 0.9 
 
 
 
 
 
 20 
 
 T. 
 
 + 3.8 
 
 + 1.8 
 
 
 
 R. 
 
 + 4.2 
 
 + 4.1 
 
 Ang. 23 
 
 H. 
 
 1.4 
 
 0.4 
 
 
 
 
 
 SI 
 
 X. 
 
 + 1.0 
 
 + 1.0 
 
 21 
 
 T. 
 
 + 3.1 
 
 I- 0.7 
 
 Sept. 4 
 
 T. 
 
 + 2.7 
 
 + 1.6 
 
 
 
 
 
 '-T. 
 
 N. 
 
 + 1.0 
 
 + 1.0 
 
 M 
 
 T. 
 
 + 8.8 
 
 1 1.4 
 
 5 
 
 H. 
 
 + 0.6 
 
 + 1.6 
 
 
 
 
 
 2fi 
 30 
 .Inly 5 
 6 
 
 7 
 
 R. 
 H. 
 X. 
 R. 
 H- 
 
 f 2.0 
 0.0 
 0.3 
 + 1.4 
 + 0.4 
 
 + 1.9 
 1.0 
 0,3 
 
 i.:i 
 + 1.4 
 
 Mora. - 
 
 X. 
 
 X. 
 II. 
 R. 
 T. 
 
 -0.4 
 
 -0.4 
 
 6 
 
 n 
 
 12 
 13 
 
 18 
 
 X. 
 T. 
 X. 
 II. 
 T. 
 
 + 0.5 
 + 1.5 
 1.0 
 
 M 
 
 + 2.7 
 
 + 0.9 
 + 0.4 
 0.6 
 + 1.9 
 + 1.6 
 
 
 
 
 
 + 1.18 
 + 0.14 
 + 1.13 
 + 9.48 
 
POSITIONS OF FUNDAMENTAL STARS. 
 
 The principal object of this fourth column is to furnish the means of detecting any diurnal 
 change in the pointing of the instrument near the pole. The old transit instrument is known to be 
 affected with such a change.* The existence of this state of things will be manifested by a corre- 
 sponding inequality in the time of transit of Polaris, depending upon the time of d ; iy at which the 
 transit takes place ; there will, therefore, be a corresponding annual inequality in the right ascen- 
 sions of this star deduced from observations. Let us put n for the error of pointing of the instru- 
 ment near the pole, a west azimuth being considered positive. Put, also, w,, and for the values 
 of n at upper and lower transits, respectively ; then the upper transit will be too late by 
 
 n u sec <5; 
 and the lower transit by 
 
 n a sec S. 
 
 The right ascension, deduced from the transits, will therefore be too late by 
 
 i (n u n*) sec S. 
 
 If the pointing of the instrument undergoes a periodic diurnal change, we shall have 
 
 n a sin D + b cos D, 
 
 a and b being constants, and D being the time of day expressed in arc. Put D u for the time of day 
 at which upper transit takes place ; the lower transit will then take place at D u + ll" 1 , and we shall 
 have 
 
 M U = a sin D u + b cos D u ; 
 
 n a = a sin D n b cos D u ; 
 
 and the error of right ascension will be 
 
 da = (a sin D u + b cos D u ) sec <5. 
 
 About April 7 of each year the upper transit takes place at noon, and we then have D u = 
 and we have at any time thereafter 
 
 D n = y, 
 
 y being the fraction of a year counted from April 7, and expressed in arc. Sec S being about 40.7, 
 we have 
 
 8 a = 40.7 ( a sin y + b cos y). 
 
 We shall consider the fourth column of the preceding table as giving a series of values of 3 a 
 plus an unknown constant, extending through a period of two years. Combining the correspond- 
 ing months, and taking the mean value of 3 a + c for each month, we have, with the omission of 
 December 
 
 Month. 
 
 Mean and equation of condition. 
 
 No. of obs. 
 
 Wt. 
 
 January- 
 
 s. 
 + 0. 68 = c + 0. 99 X 40. 7 a + 0. 14 X 40. 7 b 
 
 12 
 
 1 
 
 February . 
 
 0. 11 = c + 0. 79 +0. 62 
 
 14 
 
 1 
 
 March 
 
 + 0. 87 = c + 0. 37 +0. 93 
 
 10 
 
 1 
 
 April 
 
 '+ 1. 08 = o 0. 14 + 0. 99 
 
 12 
 
 1 
 
 May - . . 
 
 + 0. 96 = c 0. G2 + 0. 79 
 
 24 
 
 2 
 
 June . 
 
 + 0. 19 = c 0. 93 + 0. 37 
 
 19 
 
 2 
 
 July . 
 
 -f 0. 73 = c 0. 99 0. 14 
 
 10 
 
 1 
 
 August - 
 
 + 0. 77 = c 0. 79 0. 62 
 
 11 
 
 1 
 
 September . 
 
 + 1.12 = c 0.37 0.93 
 
 22 
 
 2 
 
 October.. . 
 
 + 1.35 = c + 0.14 0.99 
 
 22 
 
 2 
 
 November . 
 
 + 1.70 = + 0.62 0.79 
 
 17 
 
 2 
 
 Washington Observations for 1862, pp. xv. x\ i. 
 
POSITIONS OF FUNDAMENTAL STARS. 31 
 
 The solution of those equations gives 
 
 40.7 a = -<U7 
 10.7 b = 0.29 
 
 // 
 
 a = 0.03 
 b = 0.11 
 
 If we consider those minute values of a and b as due to parallax and error in the constant of 
 aberration, \vo shall lind a value of the parallax sensibly equal to , and a correction to the con- 
 stant of aberration sensibly equal to b; we shall, therefore, have 
 
 // 
 Parallax of Polaris ........... 0.03 
 
 Constant of aberration .......... 20.55 
 
 In other words, the apparent annual inequality in the observed mean right ascension of Polaris 
 may be accounted for indifferently by a diurual inequality in the pointing of the instrument, or by 
 parallax and error of aberration constant. 
 
CHAPTER II. 
 POLAR DISTANCES OF FUNDAMENTAL STAES. 
 
 If the pole were a visible point in the heavens, the polar distance of an object would be deter- 
 mined in the following way : We should point the telescope upon the pole, and determine the circle 
 reading for this pointing exactly as in the case of a star. This circle reading, corrected for all 
 known errors pertaining to the instrument, and for refraction, we shall represent by C p . The tele- 
 scope is then pointed on the star. The circle reading, corrected for the effect of all known sources 
 of error, will be called C,. We shall then have 
 
 N. P. D. = C. C p . 
 
 A separate and independent result may be obtained by pointing upon the images of the pole 
 and star reflected from the surface of quicksilver. If we represent the corrected circle readings by 
 C'. and C' p , the result will be 
 
 N. P. D. = C' P C'.. 
 
 If we find in this way, C. C p = C' p C'. or, C. + C'. = C p + C' p , the results will be accord- 
 ant ; otherwise there will be discordance. 
 
 We see that neither latitude nor zenith point enters into the expression for either the direct or 
 reflected polar distance. 
 
 The pole not being a visible point, the direct application of this method is not practicable. Our 
 present object is to deduce, from the usual system of observations, the result which would follow if 
 the pole were a visible point and distances were measured from it in the way described. 
 
 In the above diagram let S N represent the horizon, P the pole, C, D, and E, the directions of 
 three stars at culmination ; and Ci and Dj the positions of C and D at lower culmination. Let the 
 5 
 
34 POSITIONS OP FUNDAMENTAL STARS. 
 
 accented letters represent the directions of the same objects as seen by reflection from a truly hori- 
 zontal surface. For the purposes of analysis let us represent the circle readings corresponding to 
 each direction by the letter marking the direction, and the polar distances by the letters inclosed in 
 parentheses. Then, 
 
 For the polar distance of the star E, we shall have the two values . . . E P ; 
 
 P' E'. 
 For (D) we shall have the three values ........... D P ; 
 
 P-D 15 
 
 P' D'. 
 For (C) we may have the four values ............ C P; 
 
 P-C,; 
 
 P' C'; 
 
 C'i P' . 
 
 The agreement of these polar distances would furnish a check upon the accuracy of the 
 measures. 
 
 If the value of P were invariable, we should put 
 
 which would still leave us with two independent values of (E) and (D), and three of (C), with an 
 equation of condition between (C) and (D). 
 
 Since C and Cj cannot be determined simultaneously, we shall suppose an invariable point O, 
 the circle reading corresponding to which can be determined at any time. Such a point is the 
 " zenith point ;" but for our present purposes it is quite indifferent whether it be in the true zenith 
 of the place or not. Our data, therefore, consist of a series of values of E', E, D, &c., determined 
 irregularly on various dates, with a separate value of O for each. We shall suppose each determi- 
 nation reduced to a mean epoch, so that the reduced values of E O, O D, &c., are invariable, 
 errors of observation excepted. We then have 
 
 O P = {O-C + O Ci} = {O D + O D,}. 
 The second equation is equivalent to 
 
 so that the agreement or disagreement between the values of O P, or of the colatitudes, derived 
 from stars of different polar distances, is indicative of a corresponding agreement or disagreement 
 between measures made above and below the pole. 
 In the same way we have 
 
 P' O = J{C' O + C't O}. 
 
 Commonly, however, the number of determinations of the class C'j, or of reflection observa- 
 tions below the pole, is too small to determine P'. But (C) and (D) being determined from the 
 direct observations, we have several independent values of P' O from the equations 
 
 P' O = C' O+(C) = D' O+(D), &c. 
 
 If these different values agree, it shows that the measured arc C' D' is equal to the measured 
 arc C D, or that the direct and reflection polar distances agree. 
 
 Let us now represent the mean value of O P thus obtained by p, and that of P' O by <p' ; 
 let us also put Z >= E O : Z' O E'. 
 
POSITIONS OF FUNDAMENTAL STARS. 35 
 
 "We then have 
 
 These values of (E) and (E') will be the same as if they were measured from a visible pole in the 
 heavens, corresponding to the mean of the stars by which the value of <p was deduced. 
 
 If we represent by < the inclination of the direction O toward the north, we shall have 
 
 O D + O D' = 180 2i. 
 
 Each star observed both directly and by reflection, will give an independent value of t, and 
 the agreement or disagreement between the values oft thus obtained will indicate a corresponding 
 agreement between the distances of the stars deduced from direct and reflection observations, since 
 
 O C + O' C' = O E + O' E' 
 is equivalent to 
 
 E-C=E' C'. 
 
 Having thus explained a rigorous system of deducing several independent sets of polar dis- 
 tances from observations as usually made, let us apply the principles of this system to the obser- 
 vations and reductions under discussion. The published volumes of Washington Observations for 
 the years ISGtf and 1867 give us a system of circle measures made and reduced in the following man- 
 ner: Corresponding to O was a "zenith point" determined from observations of the collimators and 
 nadir point. Were the determinations free from all source of error, this zenith point would be the 
 true one, and we should have i = ; but as the determination may be liable to systematic errors, 
 we shall regard i as an unknown quantity to be determined. The observations were further reduced 
 by supposing 
 
 o ' " 
 
 O P = y> = 61 6 21.20 ; 
 6 21.20. 
 
 These quantities being applied to the measured values of E O = Z and O E' = Z', values 
 of the reduced polar distances of the stars were thus obtained. Let us represent these assumed 
 values of y and ?' by p and f' , the true values not being known. Let us also put 
 
 3y and H<f' being the unknown quantities to be determined. The polar distances actually found by 
 the reductions given in the published volumes, are 
 
 Z -f <F C (from direct observations.) 
 Z' 4- f'o (from reflection observations.) 
 
 It will be remembered that in the preliminary reductions given in the volumes of observations 
 under the title, Observations with the Transit Circle, no corrections have been applied for flexure or 
 error of division, it being thought most convenient to apply the same once for all to the mean results. 
 
 In what follows we shall suppose Z and Z' to have received these corrections. From the equations 
 
 Z = E O Z' = O E' 
 
 O E + O E' = 1800 _ 2 1 
 we obtain, first, 
 
 Z Z' = E O+E' O = 180 + 2t, 
 
 and next, 
 
36 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 or, the value of i, deduced from the observations of any star, is simply the discordance between the 
 direct and reflection polar distances of that star found by the preliminary reductions. This result 
 will be made evident by considering that, proceeding as we are, upon the supposition that all meas- 
 ures of arcs are correctly made, or that all circle readings are affected with only a common error in 
 the zero point, the only source of discordance will arise from the inclination of the adopted zenith 
 line, and this inclination will produce a discordance of double its amount in the zenith distances 
 derived by the two methods. 
 
 In the published volume, the mean values of the discordance in question is given for every 10 
 of Z. D. The following are the resulting values of i : 
 
 Z. D. 
 
 Value of i. 
 
 1866. 
 
 1867. 
 
 o 
 
 // 
 
 // 
 
 310 
 
 + 0.78 
 
 + 0.44 
 
 321 
 
 + 0.96 
 
 + 0.54 
 
 330 
 
 + 0.90 
 
 -f 0.44 
 
 340 
 
 4- 1.38 
 
 + 0. 36 
 
 350 
 
 + 1.01 
 
 + 0.48 
 
 10 
 
 -f 0.54 
 
 0.09 
 
 20 
 
 + 0.44 
 
 - 0.14 
 
 30 
 
 + 0.49 
 
 0.13 
 
 40 
 
 + 0.70 
 
 - 0.24 
 
 48 
 
 + 0.48 
 
 0.16 
 
 It has been shown that an agreement or disagreement between the values of i, obtained from 
 different stars, indicates a corresponding agreement or disagreement between the arcs of polar dis- 
 tance included between those stars as measured directly and by reflection, the disagreement being 
 double the difference between the values of i. It appears, therefore, that the measures in question 
 exhibit the following peculiarities : During the year 1866, as we measure from the pole toward the 
 southern horizon, we find, as we approach the zenith, that the reflected arcs are a little less than those 
 measured directly, the difference at 30 of N. P. D. being more than 1". But, as we pass the zenith, 
 there is a sudden increase in the reflected measure, which remains sensibly constant as far as the 
 reflected arcs extend. During the year 1867 there is no sensible discordance, except a sudden 
 extension of the reflected measure by 1".2 near the zenith, such that all arcs which do not pass 
 over the zenith agree, while those which pass over it exhibit the difference in question. 
 
 Were reflection observations extended to the horizon, the values of <p and </>' could be deter- 
 mined independently. As they cannot be so extended, we have to employ the auxiliary i in the 
 expressions 
 
 y = i(Z +Z,); 
 
 /, <<> p' = 180 2i. 
 
 Since ?' is used only to fix the position of the reflected pole, the value of i to be employed should 
 be derived solely from those stars which may be observed on both sides of the pole. Actually it has 
 been derived from the reflection observations north of the zenith, which leads to nearly the same 
 result. The values of i employed are, therefore, 
 
 for 1866, i = + 0".!)(i 
 1867, i = + 0".45 
 
 The further investigation of y is substantially the same with that for the correction of latitude 
 
POSITIONS OF FUNDAMENTAL STARS. 
 
 already {riven, with the differenee thai i has been applied to the provisional polar distances in 
 advance. The results are as follows: 
 
 Had the pole been a visible point in the heavens, the pointing on which corresponded to the 
 mean pointing on cm-unipolar stars above and below the pole, we should have found for the 
 measured arc, from that point to the adopted zenith point derived from collimator observations, 
 
 o ' " " 
 
 in 1866, <p = 51 6 20.74 ; Sy = 0.46 ; 
 1867, f = 51 6 21.25 ; 8<f = + 0.05 . 
 
 And for the arc between the adopted zenith point and the reflected pole, 
 
 o i n n 
 
 in 1866, y.' = 231 6 22.66 ; Sy' = + 1.46 ; 
 1867, <f' =231 6 22.15 ; 8<p' = + 0.95 . 
 
 It will be seen that the values of <p -(- <?', or the measured arcs between the direct and reflected 
 poles, agree perfectly in the two years ; this agreement has, however, been brought about by first 
 adopting the value zero for the cosine flexure of the telescope,* which made the difference very 
 small, and then combining the results of the two years on the supposition that the two measures 
 were equal. 
 
 Applying the above values of <p and y>' to the observed zenith distances, we shall obtain the 
 results already set forth, that the polar distances north of the zenith exhibit no great discordances, 
 whether measured above or below the pole, directly or by reflection, while in arcs which extend 
 south of the zenith, the reflected polar distances are constantly greater by a nearly constant 
 amount. 
 
 The corrections which have to be applied to the positions obtained by the preliminary reduc- 
 tions to reduce them to actual measures from the pole to the stars are simply, flexure + division 
 + S<forS<f'. The corrections for flexure and division are discussed in the introductions to the 
 several volumes of Observations ; 6<p and S<p' have just been given. As already indicated, we shall 
 find, on applying these corrections, that the reflection measures which extend south of the zenith 
 are greater than the direct ones by about 1". As a last correction to reduce both measures to a 
 uniform system, we shall divide this discrepancy between the two classes of observations. More- 
 over, instead of supposing the change to take place suddenly at the zenith, it will be spread over a 
 space of 5 on each side. The concluded corrections thus obtained are the same as those finally 
 given in the introductions to the two volumes of Observations. Applying them to the preliminary 
 means, we have the following corrections to the north polar distances of the American Kphemeris, 
 with the number of standard independent observations to which the actual observations made are 
 considered equivalent : 
 
 * Washington Observations for 1866, pp. xxiv, xxv, and for 1867, p. xx. 
 
38 
 
 POSITIONS OB' FUNDAMENTAL STARS. 
 
 CORRECTIONS TO THE NORTH POLAR DISTANCES OF THE STARS OF THB AMERICAN EPHEMERIS, DEDUCED FROM 
 
 OBSERVATIONS WITH THE TRANSIT CIRC I. K. 
 
 Star.' 
 
 1866. 
 
 1867. 
 
 Mean. 
 
 Star. 
 
 1866. 
 
 1867. 
 
 Mean. 
 
 D. 
 
 R. 
 
 D. 
 
 R. 
 
 D. 
 
 E. 
 
 D. 
 
 R. 
 
 a Andromeda? . 
 
 + 1.4, 
 
 + 0.9, 
 
 + 1.6. 
 
 + 1.3, 
 
 + 1.52 
 
 * Cancri .... 
 
 + 1.1, 
 
 " 
 
 + 0. 2 S 
 
 
 
 + 0.46 
 
 y Pegasi .... 
 
 + 0. 5, 
 
 
 + 1.1. 
 
 + 2.0, 
 
 + 1.03 
 
 1 (H) Draconis 
 
 
 
 + 1. Oj 
 
 + 0.4, 
 
 + 0.70 
 
 a Cassiopero . . 
 
 + 0.7, 
 
 - 0.2, 
 
 + 0.9, 
 
 + 0.4, 
 
 + 0.43 
 
 1 (H) Drac., S. P. . 
 
 
 
 - 0.7 4 
 
 
 0.70 
 
 a Cassiopera, S. P. . 
 
 
 
 0.2 
 
 
 0.20 
 
 a Hydra .... 
 
 + 1.4 4 
 
 + 0.8, 
 
 + i. o. 
 
 + 2.0 3 
 
 + 1.27 
 
 ft Ceti 
 
 - 0.4, 
 
 
 - 0.2, 
 
 
 0.28 
 
 Ursae Majoris . 
 
 
 
 - 0.5, 
 
 
 0.50 
 
 21 CassiopeaB . . 
 
 - 2.1, 
 
 
 - 0.5, 
 
 - 2.0, 
 
 1.78 
 
 t Leonis .... 
 
 + 0.5 4 
 
 
 + 0.8, 
 
 + 0.4, 
 
 + 0.64 
 
 21 Cassiopeae, S. P. . 
 
 + 2. 7, 
 
 
 + 1.6, 
 
 
 + 1.91 
 
 p Leonis .... 
 
 - 0.1, 
 
 + 0.9, 
 
 + 0. S, 
 
 
 + 0.59 
 
 t Piscium . . 
 
 + 0.5, 
 
 
 + 1.2, 
 
 
 + 0.88 
 
 a Leonis .... 
 
 + i.o. 
 
 - 0.1, 
 
 + 1.3, 
 
 + 0.4, 
 
 + 0.92 
 
 Polaris .... 
 
 0. 34, 
 
 + 0. 26 4 
 
 + 0.26,, 
 
 + 0.35 6 
 
 + 0.13 
 
 y Leonis .... 
 
 - 0. 3 4 
 
 0.0, 
 
 + 0.8, 
 
 + 1.0, 
 
 + 0.42 
 
 Polaris, S. P. . . 
 
 0.06, 
 
 0. 46 4 
 
 - 0.04,, 
 
 + 0.03, 
 
 0.09 
 
 9 (H) Draco. . . 
 
 0.8, 
 
 - 1.2, 
 
 - 1.1, 
 
 1.9, 
 
 1.22 
 
 9 Ceti .... 
 
 + 0.2 4 
 
 + 1.6, 
 
 + 0. 2, 
 
 
 + 0.34 
 
 9 (H) Draco., S.P. . 
 
 
 
 K L4 4 
 
 
 + 1.40 
 
 A Cassiopese, S. P. . 
 
 + 1.0, 
 
 
 
 
 + 1.00 
 
 p Leonis .... 
 
 0.0, 
 
 
 0.0, 
 
 
 0.00 
 
 n Piscium . . 
 
 + 0.4, 
 
 + 0. 9, 
 
 + 1.0, 
 
 
 + 0.77 
 
 I Leouis .... 
 
 0.0 4 
 
 - 0.3, 
 
 + 0.7 4 
 
 0.0, 
 
 + 0.21 
 
 a Piscium . . . 
 
 - 0. 2 4 
 
 + 0. 7, 
 
 + 1.2, 
 
 
 + 0.69 
 
 a Ursse Majoris 
 
 + 0.6, 
 
 - 1.5, 
 
 - 0.3, 
 
 - 1.1. 
 
 0.63 
 
 Arietis . . . 
 
 + 0. 4 6 
 
 
 + 1.6, 
 
 
 + 1.09 
 
 i Leonis .... 
 
 + 0.3, 
 
 + 0.8, 
 
 + 0.9, 
 
 
 + 0.68 
 
 50 Cassiopeae . . 
 
 - 1.7, 
 
 0.0, 
 
 0.0, 
 
 
 0.68 
 
 i Crateris . . . 
 
 0.0, 
 
 - 2.7, 
 
 0. 6 
 
 
 0.30 
 
 50 Cassiopere, S. P. . 
 
 - 0.4, 
 
 
 + 0. 6, 
 
 
 + 0.20 
 
 r Leonis .... 
 
 + 1.0, 
 
 
 + 0.2, 
 
 
 + 0.47 
 
 a Arietis . . . 
 
 + 0.9, 
 
 + 1-5, 
 
 + 1.4, 
 
 
 + 1.22 
 
 X Draconis . . . 
 
 - 0.7, 
 
 -2.0, 
 
 - 1-4, 
 
 - 1.7 4 
 
 1.48 
 
 f Ceti .... 
 
 + 0.5, 
 
 
 + 1-1, 
 
 
 + 0.92 
 
 A Draconis, S. P. . 
 
 + 1.0, 
 
 
 + 2.2 4 
 
 
 + 1.80 
 
 t Cassiopeae . . 
 
 0.9, 
 
 - 1.0, 
 
 + 0. 6, 
 
 - 1.3, 
 
 0.79 
 
 v Leonis .... 
 
 + 1.8, 
 
 - 1.2, 
 
 + 0.5, 
 
 
 + 0.74 
 
 i Cassiopeos, S. P. . 
 
 + 0.2, 
 
 
 
 
 + 0.20 
 
 Leonis .... 
 
 + 1.5 S 
 
 + 0.5, 
 
 + 1.7, 
 
 + i.o, 
 
 + 1.45 
 
 y Ceti .... 
 
 - 0.8, 
 
 + 1.1, 
 
 - 0.8, 
 
 
 0.63 
 
 y Ursse Majoris . 
 
 0.0, 
 
 + 0.1, 
 
 + 0.2c 
 
 + 1.1, 
 
 + 0.38 
 
 Ceti .... 
 
 0.64 
 
 + 1.3, 
 
 _ 0.1, 
 
 
 0.04 
 
 o Virginia . . . 
 
 - 0.2 4 
 
 
 + 0. 1 6 
 
 
 0.03 
 
 48 (H)Cephei . . 
 
 - 0.8, 
 
 - 1.4, 
 
 - 1.0, 
 
 
 1.07 
 
 4 (H.) Draco. . . 
 
 - 1.6, 
 
 - 3.5, 
 
 - 1.5, 
 
 - 1.7. 
 
 1.87 
 
 48 (H) Cephei, S.P. . 
 
 + 1.6, 
 
 
 + 0. 9 4 
 
 
 + 1.20 
 
 4 (H.) Draco., S.P. . 
 
 + 2.2, 
 
 
 + 1.9, 
 
 
 + 2.05 
 
 S Arietis . . . 
 
 + 0.7, 
 
 
 + 1.5, 
 
 
 + 1.27 
 
 i) Virginis . . . 
 
 + L7 4 
 
 + 0.4, 
 
 + 1.0, 
 
 
 + 1.12 
 
 o Persei .... 
 
 0.0, 
 
 - 0.4, 
 
 + 0.1, 
 
 - 0.9, 
 
 0.26 
 
 Corvi .... 
 
 - 0. 1 4 
 
 
 0.9, 
 
 
 0.61 
 
 1 Tanri .... 
 
 + 0.3. 
 
 + 1.3, 
 
 + 0.5, 
 
 
 + 0.57 
 
 K Draco 
 
 - 1.9, 
 
 - 1.1, 
 
 - 1.2, 
 
 _ 1.2, 
 
 1.27 
 
 g Persei .... 
 
 + 1.6, 
 
 
 + 2.6, 
 
 
 + 1.93 
 
 t Draco., S. P. . . 
 
 
 
 + 1.7, 
 
 
 + 1.70 
 
 y Eridaui . . 
 
 + 0.7 4 
 
 
 + 0.7, 
 
 
 + 0.70 
 
 32 (H.) Camelop. . 
 
 3.3, 
 
 2.4, 
 
 - 1.2, 
 
 - iO, 
 
 2.02 
 
 Y Tanri .... 
 
 + i.o, 
 
 0.6, 
 
 + 0.8, 
 
 
 + 0.72 
 
 a Canum Venat. . 
 
 + 0. 5, 
 
 
 + 0.9. 
 
 
 + 0.75 
 
 t Tauri .... 
 
 + 0.1, 
 
 - 0.2, 
 
 + 0.5, 
 
 
 + 0.35 
 
 e Virginis . . . 
 
 + 0.6 4 
 
 
 + 1.1. 
 
 + 2-0, 
 
 + 1.16 
 
 a Tauri .... 
 
 + 1.7. 
 
 + 2.2, 
 
 + 1.6, 
 
 + 2.4, 
 
 + 1.80 
 
 a Virginis . . . 
 
 + 0.7, 
 
 + 0. 4, 
 
 + 0.9, 
 
 + i.o 4 
 
 + 0.81 
 
 a Camelop. . . 
 
 + 0.5, 
 
 + 0.2, 
 
 + 0.8, 
 
 - 0.3, 
 
 + 0.30 
 
 Virginis . . . 
 
 + 1.1. 
 
 0.2, 
 
 + LI. 
 
 + 0.6 4 
 
 + 0.85 
 
 o Camelop., S. P. . 
 
 
 
 - 1.0, 
 
 
 1.00 
 
 D TTrsse Majoris . 
 
 0.0, 
 
 0.0, 
 
 + 0.5, 
 
 + 0.2, 
 
 + 0.28 
 
 i Aurigae . . . 
 
 + 0. 7, 
 
 
 + 1.0, 
 
 
 + 0.90 
 
 i) Bootis .... 
 
 + 0.6 8 
 
 - 0.2, 
 
 + 0.7, 
 
 + 0.2 4 
 
 + 0.47 
 
 11 Orionis . . . 
 
 + 0.8, 
 
 . 
 
 + 1.7, 
 
 + 1.4, 
 
 + 1.29 
 
 a Draconis . . . 
 
 - 0.7, 
 
 -1.6, 
 
 _ 1.6 4 
 
 _ 1.4 4 
 
 1.38 
 
 o Auriga} . . . 
 
 + 0.2, 
 
 
 + 1.1, 
 
 
 + 0.80 
 
 a Bootis .... 
 
 + 1.5. 
 
 + 1.3, 
 
 + 2.1, 
 
 + 2.3, 
 
 + 1.87 
 
 Orionis . . . 
 
 0. 0, 
 
 + 0.8, 
 
 + 0.7, 
 
 + 0.5, 
 
 + 0.45 
 
 fl Bootis .... 
 
 + 0.4, 
 
 - 0.6, 
 
 - 0.2. 
 
 0.0 4 
 
 0.14 
 
 Tauri .... 
 
 0.3, 
 
 - 0.2, 
 
 + 0.3, 
 
 + 1.9, 
 
 + 0.25 
 
 5 UrsflB Min. . . 
 
 - 0.6, 
 
 - 1.3, 
 
 - 1.7 4 
 
 _ 1.3, 
 
 1.32 
 
 6 Orionis . . . 
 
 + 0.2 4 
 
 
 - 0.2, 
 
 
 0.02 
 
 5 TJrBseMin.,S.P. . 
 
 
 
 + 23, 
 
 
 + 2.30 
 
 t Orionis . . . 
 
 0.0 5 
 
 
 + 0. 8 6 
 
 
 + 0.44 
 
 t Bootis .... 
 
 + 0.1 6 
 
 - 0.1, 
 
 + 0.4, 
 
 + 0.6, 
 
 + 0.28 
 
 a Columbae . . . 
 
 + 3.4, 
 
 
 
 
 + 3.40 
 
 a' Libne .... 
 
 + 1.6, 
 
 
 + 1.4. 
 
 + 1.6, 
 
 + 1.51 
 
 a Oriouis . . . 
 
 + 0.3 6 
 
 + 0.4, 
 
 + 0.8, 
 
 + 1.7, 
 
 + 0.74 
 
 UrsSD Min. . . 
 
 - 2.0, 
 
 - 1.1, 
 
 - 1.1 
 
 _ 1.5, 
 
 1.34 
 
 li Geminornm . . 
 
 0.5, 
 
 
 + 0.2, 
 
 
 0.20 
 
 TTrsas Min.,S. P. . 
 
 + 0.3, 
 
 
 + 0.5, 
 
 
 + 0.42 
 
 y Geminorum . 
 
 + 0. 3 S 
 
 
 + 0.9, 
 
 
 + 0.62 
 
 Librae .... 
 
 + 0.4, 
 
 + 0.2, 
 
 + 2.0, 
 
 - 0.2, 
 
 + 1.00 
 
 51 (H) Cephei . . 
 
 + 0. 3 5 
 
 
 + 0. 6, 
 
 
 + 0.48 
 
 [i Bootis .... 
 
 + 0.2, 
 
 
 0. 5 
 
 
 + 0.08 
 
 51 (H) Cephei, S.P. . 
 
 - 0.6, 
 
 
 + 0.2, 
 
 
 0.24 
 
 y 2 Ursse Minoris 
 
 - 1.3, 
 
 - 0.1, 
 
 + 0.5, 
 
 
 0.30 
 
 a Canis Majoris 
 
 + 1.8, 
 
 
 + 2.4, 
 
 
 + 2.12 
 
 a CorouaeBorealis . 
 
 + 2.1. 
 
 + 1.8, 
 
 + 3.0, 
 
 + 1.6 4 
 
 + 2.30 
 
 i Canis Majoris . 
 
 0. 5 5 
 
 
 - 0.7 6 
 
 
 0.60 
 
 a Serpentis . . . 
 
 + 1.8 6 
 
 + L3 3 
 
 + 1.9. 
 
 + 1.9 S 
 
 + 1.79 
 
 6 Canis Majoris 
 
 + 0.63 
 
 
 
 
 + 0.60 
 
 t Serpentis . 
 
 + i.o. 
 
 0.8, 
 
 + 0.8, 
 
 + 0.2, 
 
 + 0.63 
 
 S Geminorum . 
 
 + 0.4 4 
 
 0.0, 
 
 + 0. 9, 
 
 
 + 0.66 
 
 TJrsSD Minoris 
 
 - i.o, 
 
 - 0.5 4 
 
 i 0. 1, 
 
 + 1-2, 
 
 0. 22 
 
 a 2 Geminorum . 
 
 + 1.3. 
 
 
 + 0. 7 6 
 
 
 + 0.96 
 
 i Scorpii. . . . 
 
 + 1.8, 
 
 
 + 1. 5 
 
 
 + 1.23 
 
 a Canis Minoris 
 
 + 0. 7 6 
 
 
 ;- 1.1, 
 
 + 1.83 
 
 + 1.08 
 
 Scorpii 
 
 1 L6 4 
 
 
 - 0.1, 
 
 
 + 0.66 
 
 Geminorum . 
 
 1- 0. 7 5 
 
 
 !- 0. 7, 
 
 
 + 0.70 
 
 i Opliitichi . . . 
 
 i 1.0 4 
 
 + 0. 5, 
 
 + 0.8, 
 
 + 0.4, 
 
 + 0.72 
 
 <tt Geminornm . 
 
 - 0.1, 
 
 
 { 0. 5 3 
 
 
 + 0.26 
 
 r Herculis . . . 
 
 0.0 4 
 
 0.0, 
 
 - O.l s 
 
 0.3, 
 
 0.09 
 
 15 Argus .... 
 
 -1- 1.1, 
 
 
 + 0. 8 6 
 
 
 + 0.88 
 
 a Scorpii .... 
 
 + 1.9, 
 
 
 h 1.6 S 
 
 
 + 1.74 
 
 c Hydree 
 
 4- 13. 
 
 
 + 1. 7 
 
 + 3. 1, 
 
 i 1 07 
 
 fl Draconis 
 
 
 
 t- 0. 4 3 
 
 
 + 0.40 
 
 i TTrste Majoris 
 
 T i . '; 
 
 - 0.7, 
 
 - 1-7, 
 
 0.6, 
 
 0.0, 
 
 T- x. ^i 
 0.75 
 
 A Draconis . . . 
 
 0.5, 
 
 + 0. 4, 
 
 + 0.8, 
 
 + 0.9, 
 
 + 0.40 
 
 <r 2 Ursae Majoris 
 
 - 2.0, 
 
 - 1.6, 
 
 - 2.2 3 
 
 - 2-4, 
 
 2.18 
 
 I Ophiuchl . . . 
 
 + 1.1. 
 
 + 1.2, 
 
 - 1.3 3 
 
 + 0.9 4 
 
 + 1.13 
 
 o 3 TTrsae Maj., S. P. . 
 
 + 1.8, 
 
 
 T 2.2 4 
 
 
 + 2.07 
 
 ?) Herculis . . . 
 
 + i.o 4 
 
 
 + 0.6 S 
 
 
 + 0.77 
 
POSITIONS OF FUNDAMENTAL STARS. 39 
 
 CORRECTIONS TO THK XOUT11 1'OI.AK DISTA XfKS (II TMK ST MIS OK T1IK AMKHH'AX KIM1KMKHIS. 4T.-<:..nti,nll. 
 
 Star. 
 
 I860. 
 
 1867. 
 
 Mean. 
 
 Star. 
 
 1666. 
 
 1867. 
 
 Meau. 
 
 D. 
 
 R. 
 
 D. 
 
 R. 
 
 D. 
 
 R. 
 
 D. 
 
 R. 
 
 
 
 
 
 
 
 
 
 
 // 
 
 
 
 
 II 
 
 a 
 
 
 
 
 
 r Ophiuchi . 
 
 t 1. 1 4 
 
 - 1.1, 
 
 0.0, 
 
 
 + 0.20 
 
 t Delphiui . . . 
 
 + 0.6, 
 
 + 0.8, 
 
 0.0. 
 
 
 + 0.38 
 
 t r , .! Minoria . 
 
 - 0. 3 4 
 
 - 0.5, 
 
 + 0.2, 
 
 - 0.7, 
 
 0.25 
 
 a Cyglii .... 
 
 + 0.5. 
 
 + 1.3, 
 
 I 0.6, 
 
 + 2.1, 
 
 + 0.74 
 
 Hrculin . . . 
 
 + 1-8, 
 
 + 0.9, 
 
 + 1.8, 
 
 + !, 
 
 + 1.60 
 
 /i Aquarii . . . 
 
 + 0.6, 
 
 + 1.1, 
 
 + 1.4, 
 
 + 1.5, 
 
 + 1.18 
 
 6 Optiiiu'hi . . . 
 
 4- 1. 0, 
 
 
 + 0.8, 
 
 
 + 0.89 
 
 r Cygni .... 
 
 + 1.4, 
 
 
 + 0.5, 
 
 
 + 0.86 
 
 a Ophiurhi . . 
 
 + 2-5. 
 
 + 1.8, 
 
 + 1.8. 
 
 + 1.2, 
 
 -i 1.92 
 
 61 Cygni .... 
 
 0.0, 
 
 
 - 0.2, 
 
 
 0.12 
 
 cj Draconis . 
 
 - 1.6, 
 
 -1.8, 
 
 - 2.2, 
 
 - 1.9, 
 
 1.91 
 
 I Cygni .... 
 
 + 0.4. 
 
 + 0.2, 
 
 + 0.8, 
 
 + 0.5, 
 
 + 0.32 
 
 a lii.irom*. S. P. . 
 
 
 
 i 2.4, 
 
 
 + 2.40 
 
 * Cephei .... 
 
 - 0.9 4 
 
 - 1.3 4 
 
 - 1.2. 
 
 + 0.1, 
 
 0.91 
 
 f Hercnlii . . . 
 
 + 0.9, 
 
 + 1.2, 
 
 0.0, 
 
 
 + 0.18 
 
 a Cephei, S. P. . . 
 
 + 1.6, 
 
 
 
 
 + 1.60 
 
 i/< ]>rai "ni.s 
 
 
 
 1 0. 4, 
 
 
 + 0.40 
 
 1 Pegasi .... 
 
 r 1-7, 
 
 + 3.3, 
 
 1 2. 5, 
 
 
 + 2.50 
 
 y Dracouis . . . 
 
 j 0.3, 
 
 + 1.0, 
 
 + 0.2, 
 
 + 0. 1 4 
 
 + 0.36 
 
 Aqnarii . . . 
 
 + 0.8 4 
 
 0.0, 
 
 + 0. 4, 
 
 + 1-5, 
 
 + 0.66 
 
 r' Sagittarii . . . 
 
 - 0.4, 
 
 
 
 
 0.40 
 
 Cephei. . . . 
 
 - 1.2, 
 
 -0.6, 
 
 - 0.8, 
 
 1.0, 
 
 0.91 
 
 f Suttittarii . . . 
 
 + O.G, 
 
 
 - 0.6, 
 
 
 0.00 
 
 Cephei, S. P. . . 
 
 
 
 + 1.2, 
 
 
 + 1.20 
 
 1 Serpentis . . . 
 
 + i.o, 
 
 
 0.0, 
 
 
 + 0.40 
 
 Aquarii . . . 
 
 + 1-0, 
 
 
 + 0.4, 
 
 
 + 0.64 
 
 1 Ureas Minoria . 
 
 -1.26, 
 
 - 0.37, 
 
 -1.40, 
 
 0.68, 
 
 1.09 
 
 { Pegasi. . . . 
 
 + 0.5 4 
 
 + i.o, 
 
 + 0.5, 
 
 + 0.9, 
 
 + 0.49 
 
 1 UrewMin.,S. P. . 
 
 + 0.57, 
 
 . . 
 
 + 0.99, 
 
 
 + 0.81 
 
 11 Cephei. . . . 
 
 - LI, 
 
 - 1.0 4 
 
 - 0.5, 
 
 
 6.86 
 
 1 Aqnilo; . . . 
 
 - 0.7 4 
 
 + 0.9, 
 
 - 0.5, 
 
 - 1.9, 
 
 0.45 
 
 i\ Capricorni 
 
 + 0.0, 
 
 
 + 0.4, 
 
 
 + 0.57 
 
 a Lyrae .... 
 
 + 0.6, 
 
 
 + 1.3, 
 
 
 + 0.99 
 
 79 Draconis . . . 
 
 
 
 0.5, 
 
 - 1.0, 
 
 0.75 
 
 ff Lyra) .... 
 
 - 0.3 4 
 
 
 - 0.3, 
 
 
 0.30 
 
 79 Draconis, S. P. . 
 
 
 
 + 1.6, 
 
 
 + 1.60 
 
 * Sacittarii . . . 
 
 + 1.0, 
 
 
 + 1.2. 
 
 
 + 1.12 
 
 a Aqnarii . . . 
 
 + 1. 4, 
 
 + 0.9, 
 
 + 0.6, 
 
 + 1.2, 
 
 + 1.00 
 
 50 DraconU . . . 
 
 - 1-1, 
 
 - 12, 
 
 - 1.2, 
 
 - l.I 
 
 1.15 
 
 9 Aquarii . . . 
 
 + 1.4 4 
 
 + 1.2, 
 
 + 0.8, 
 
 + 0.9, 
 
 + 1.M 
 
 g AquilaB . . . 
 
 + 0.9 4 
 
 + 2.2, 
 
 + 1.0. 
 
 + 1.4, 
 
 + 1.15 
 
 JT Aquarii . . . 
 
 - 0.4, 
 
 + 2.4, 
 
 + 0.6, 
 
 
 + 0.48 
 
 i Uraconia . . . 
 
 0.8, 
 
 - 1.1, 
 
 - 0.7 4 
 
 - 0.2, 
 
 0.55 
 
 1 Aquarii . . . 
 
 + 0.9 4 
 
 + 0.4, 
 
 + 0.9, 
 
 
 + 0.85 
 
 T Draconis . . . 
 
 
 
 0.6 
 
 - 0.3, 
 
 0.42 
 
 g Pegasi. . . . 
 
 + 1.5. 
 
 + 0.8, 
 
 + 1.5, 
 
 
 + 1.37 
 
 5 Aqnilffl . . . 
 
 4- 0. G, 
 
 + 1.6, 
 
 1 0. 9, 
 
 + 1.3, 
 
 + 0.97 
 
 i Cephei .... 
 
 - 0.4, 
 
 + 0.1, 
 
 - 0.6, 
 
 - 1.0, 
 
 0.46 
 
 1C Aquil.r . . . 
 
 + 0.6, 
 
 + 0.4, 
 
 + 0.8, 
 
 + 0.6, 
 
 + 0.69 
 
 i Cephei, S. P. . . 
 
 + 1.3, 
 
 
 
 
 + 1.30 
 
 Y AquiliB . . . 
 
 + 1.5 4 
 
 + 3.1, 
 
 + 1.5, 
 
 
 + 1.63 
 
 A Aquarii 
 
 + 0.9, 
 
 + 1.8, 
 
 + 0.1 4 
 
 + 1.1, 
 
 + 0.69 
 
 a Aquihe 
 
 f 1.0, 
 
 
 + 1.4, 
 
 + i.o, 
 
 + 1.19 
 
 a Piscis Australia . 
 
 + 1.3, 
 
 
 r 0.6, 
 
 
 + 0.81 
 
 i Draconis . . . 
 
 
 
 - 1-1, 
 
 - 1.9, 
 
 1.50 
 
 a Pegaai .... 
 
 + 1.8 4 
 
 + 2.8, 
 
 + 2.9, 
 
 + 2.1, 
 
 + 3.15 
 
 Aquilie . . . 
 
 + 0. 7, 
 
 
 + 1.0, 
 
 
 + 0.90 
 
 o Cephei .... 
 
 
 
 - 1.6. 
 
 - 0.8, 
 
 1.30 
 
 A Une Minoris . 
 
 + 0.9, 
 
 
 + 0.2, 
 
 - 0.9, 
 
 + 0. IS 
 
 o Cephei, S. P. . . 
 
 
 
 + 1.6, 
 
 
 + 1.60 
 
 A UnuB Min., S.P. . 
 
 0.0, 
 
 
 - 0.1, 
 
 
 0.05 
 
 8 Piscium . . . 
 
 + 0. 7, 
 
 + 0.2, 
 
 + 0.8, 
 
 0.0, 
 
 + 0.28 
 
 T Aiplil." . . . 
 
 + 0.8, 
 
 + 1.3, 
 
 
 
 + 1.00 
 
 t Piscium . . . 
 
 + 0.5, 
 
 
 + 0.4, 
 
 + 0.5, 
 
 + 0.45 
 
 a 1 Capricorni 
 
 + 1. 0, 
 
 - 0.4, 
 
 + 1. 1. 
 
 + 1.1, 
 
 + 0.85 
 
 y Cephei .... 
 
 - 0.9 4 
 
 - 0.1, 
 
 - 0.3, 
 
 0.5, 
 
 0.53 
 
 K Cephei .... 
 
 
 
 - 1.0, 
 
 0.9, 
 
 0.95 
 
 f Cephei, & P. . . 
 
 2.7, 
 
 
 + 0. 1, 
 
 
 0.37 
 
 <r Cephei, S. P. . . 
 
 
 
 + 0.8, 
 
 
 + 0. 80 
 
 w Piacium . . . 
 
 0.0, 
 
 + i.o,- 
 
 + o., 
 
 
 + 0.64 
 
 ir Capricurni . . 
 
 + 1.9 4 
 
 
 + 1.4, 
 
 
 + 1.62 
 
 
 
 
 
 
 
 MEAN POSITIONS OF THE STANDARD STARS FOR THE FICTITIOUS EPOCH, 1870.0. 
 
 The preceding investigation has resulted in furnishing us for each co-ordinate and each star a 
 certain mean correction applicable to the ephemeris of the star at the epoch corresponding to the 
 mean of the times of observation. The ephemeris in question is that given in the American 
 Ephemeris for the years 1865-'69. The mean epoch is different for every star, but may, without 
 appreciable error in any case, be supposed 18G7.0 for all the polar distances, and for the right ascen- 
 sions of the circumpolar stars, which are not found in the column " result of transit," and 1865.0 
 for the right ascensions of all other stars. If Ae represent the error of the epoch thus assumed, 
 and J IJL the error of the adopted proper motion, the error, from application to the wrong epoch, will 
 be only Je x J,, a quantity which will probably be insensible in all cases. 
 
 The epoch being variable, the decennial epoch 1870.0 has been selected for the preparation of 
 the catalogue. In deducing the right ascensions for 1870.0, the positions are carried forward from 
 the mean epoch to 1870, with the annual variations of the ephemeris of comparison. That is, the 
 deduced correction is applied, not to the mean place of the ephemeris at the mean epoch, but to that 
 for 1870.0. 
 
 The catalogue thus obtained is as follows. 
 
 The column " Weight." of the north polar distances gives the number of independent standard 
 observations to which the observations actually made are considered equivalent. 
 
40 POSITIONS OF FUNDAMENTAL STARS. 
 
 The precessions here given have been independently computed from Struve's value of the con- 
 stant, using the tables in the Washington Observations for 1847. 
 
 The secular variation of the precession means, as usual, one hundred times the second deriva- 
 tive of the co-ordinate for the epoch of the catalogue. But, instead of being independently com- 
 puted, it is deduced from the values given in Table XXI of the " Star Tables of the American. 
 Ephemeris " for I860.* The value for 1870 was supposed the same as for 1860, except in the cases 
 of those circurnpolar stars for which Dr. Gould's standard catalogue gives the mean right ascen- 
 sion developed in powers of the tiine.t Here Dr. Gould gives 
 
 -f-etc., 
 t being reckoned from 1855.0. Differentiating we have 
 
 Whence, for the change ia -ja, between 1860 and 1870, we have, by putting t = 5, and t= 15, and 
 taking the difference, 
 
 ffta 
 
 A 1^ = 600 + 2400 D + etc. 
 
 (it 
 
 The value of 100 J -r^thus obtained was applied to the secular variation given in the star tables to 
 
 Wf 
 
 reduce it to 1870. 
 
 The proper motions here given are those of the catalogue of comparison, and therefore are 
 effectively, those actually employed in bringing forward the positions from the mean epoch to 1870. If 
 we require the positions for the mean epoch, as deduced from the observations, without any hypothesis 
 respecting the proper motion, we have only to reduce each co-ordinate back to the epoch with this 
 given proper motion. And if we take for the mean epochs those already indicated, namely, 1867.0, 
 for all the polar distances, and for the right ascensions of the few stars not determined with the 
 transit instrument, and 1865.0 for all other right ascensions, the epoch will seldom or never be a 
 year in error, and the error introduced will seldom or never exceed the error of the adopted annual 
 proper motion, which will be entirely unimportant. 
 
 The last column corresponding to each co-ordinate gives the difference between the value of 
 the co-ordinate, as printed in this catalogue, and that given in the American Ephemeris for 1870. 
 
 * Tables to facilitate the reduction of places of the fixed stars, prepared for the use of the American Ephemerie and 
 Nautical Almanac. Washington, 1869. 
 
 t Standard mean places of circumpolar and time stars, prepared for the use of the Coast Survey, second edition. 
 Washington, 1866. 
 
POSITIONS OF FUNDAMENTAL STARS. 
 
 41 
 
 MKAN I'osinoNs FIH; wmfl 1.1 \NTAKY o,/. -0,7.11;. WASIIINC niv> UK STAKS OF THE AMERICAN F.I'IIFMF.KIS, DEDUCED 
 
 FROM (HiSFKVATIONS WITH I III: TRANSIT IXSTRTMKXT ANI> THE TRANSIT CIRCLE DURING THE YEARS 1862-'67. 
 
 SI. II. 
 
 ij 
 
 7 ~ 
 i_ 
 
 o 
 
 -i 
 (4 
 
 i 
 
 i 
 
 11 
 
 | 
 
 CHIT'II to Am. 
 EphciiL. 1874 
 
 J 
 
 1 
 
 
 
 a 
 ri 
 ri 
 
 j 
 
 Secular varia- 
 tion. 
 
 i 
 ii 
 
 41 
 
 ii 
 
 
 
 k. m. t. 
 
 >. 
 
 t. 
 
 1. 
 
 t. 
 
 
 O I It 
 
 // 
 
 // 
 
 // 
 
 
 
 Xlnll.'lit. .].. . 
 
 119 
 
 1 40.344 
 
 -i 3.0773 
 
 + . 0182 
 
 + .0102 
 
 + .050 
 
 16 
 
 61 37 39. 10 
 
 20.054 
 
 + 0.011 
 
 t- 0.146 
 
 + 1.96 
 
 ) IVlMM . . 
 
 n 
 
 6 32. 5:i 
 
 a. OBU 
 
 .0100 
 
 j- .0006 
 
 < .035 
 
 15 
 
 75 32 22. 14 
 
 20. 047 
 
 + 0.020 
 
 (- 0.011 
 
 + 1.46 
 
 a C:is.Hi,iiN'jt! . 
 
 18 
 
 33 C.B7 
 
 I 3.3559 
 
 + .0550 
 
 + .0076 
 
 .01 
 
 11 
 
 31 III :tt. ."7 
 
 19.845 
 
 + 0.088 
 
 r 0. 034 
 
 0.08 
 
 li (Yti .... 
 
 90 
 
 37 :l rt>3 
 
 i 2. W3 
 
 . ii:>7 
 
 .11113 
 
 + .083 
 
 13 
 
 III- 12 2.65 
 
 19. 793 
 
 + 0.079 
 
 0.020 
 
 -)- 0. 93 
 
 -'1 * 'llSHiop.-H! . 
 
 u 
 
 37 6. 46 
 
 3. SI7I 
 
 f . 1581 
 
 .0114 
 
 4- .08 
 
 10 
 
 15 43 23.07 
 
 19.792 
 
 + 0.0% 
 
 | 0.060 
 
 1.89 
 
 f I'i-t iUlll . . 
 
 135 
 
 56 11.931 
 
 + 3.1130 
 
 + .0086 
 
 .0035 
 
 4- .052 
 
 13 
 
 8* 48 38. 53 
 
 19.455 
 
 I- 0. 117 
 
 0.000 
 
 4- 1.81 
 
 Polaris . . . 
 
 7 
 
 1 11 17. 34 
 
 +20.014 
 
 + 14.240 
 
 + .073 
 
 .33 
 
 56 
 
 1 23 1.47 
 
 19. 092 
 
 + 0.910 
 
 0.006 
 
 0.07 
 
 H C,.|i . . . 
 
 n 
 
 1 17 31. .V.'l 
 
 ; 3.0113(1 
 
 + .0(117 
 
 . IXI.-,3 
 
 : . UM 
 
 10 
 
 98 51 18. 47 
 
 18.918 
 
 + 0.152 
 
 I 0.220 
 
 + 1 90 
 
 il risciinn . . 
 
 in 
 
 1 24 ::i OH 
 
 :i. I'.i-i 
 
 + .0142 
 
 . IHHI'.I 
 
 1 .IH.C.I 
 
 14 
 
 75 19 31.71 
 
 18. 706 
 
 + 0. 175 
 
 0.000 
 
 + 1.91 
 
 " l'i*rium 
 
 63 
 
 1 3* :u.!ii4 
 
 3. i.v.i 
 
 j .11111 
 
 + .0061 
 
 + .003 
 
 13 
 
 81 29 52. 17 
 
 18.230 
 
 + 0.199 
 
 0.009 
 
 I- 1. 24 
 
 ,1 \ii.ti-. . . . 
 
 117 
 
 1 47 27. 779 
 
 + 3.2841 
 
 + . 0182 
 
 + .OOC2 
 
 + .045 
 
 14 
 
 69 49 43. 85 
 
 17.891 
 
 + 0.224 
 
 (- 0.109 
 
 + 1.81 
 
 ."41 ( '.i-sii.|if;i- . 
 
 111 
 
 i :_ 2:1.111 
 
 1. '.i.-iil 
 
 I-:. 
 
 .011 
 
 + .04 
 
 7 
 
 18 12 35. 21 
 
 17. 692 
 
 0.345 
 
 0.000 
 
 0.43 
 
 a Aril-tin . . . 
 
 M 
 
 i 59 5o. IKK > 
 
 :i. 3534 
 
 4- .0203 
 
 i .II14-J 
 
 + .038 
 
 16 
 
 67 9 13.53 
 
 17.375 
 
 H- 0.253 
 
 + O.i:t7 
 
 4- 1.35 
 
 i' c,-ii .... 
 
 4* 
 
 2 6 6. 736 
 
 i 3. 1733 
 
 + .0115 
 
 . OtH'J 
 
 + .072 
 
 10 
 
 81 45 52.50 
 
 17. 095 
 
 I 0.248 
 
 I- 0.040 
 
 + 0.86 
 
 t C:iHMiulM-lB . 
 
 8 
 
 2 18 23. 41 
 
 i. -u 
 
 + .1300 
 
 .008 
 
 + .86 
 
 7 
 
 23 11 a 46 
 
 16.508 
 
 H- 0.404 
 
 + 0.020 
 
 0.74 
 
 ) Ci-ti . 
 
 44 
 
 2 36 34. 016 
 
 : 3. Illl. 
 
 + .0092 
 
 .0094 
 
 4- .031 
 
 11 
 
 87 18 49. 43 
 
 15.556 
 
 + 0.291 
 
 |- 0. 191 
 
 -r 1. 18 
 
 a (Vti .... 
 
 71 
 
 2 55 29. 188 
 
 r 3. 1300 
 
 i- .0097 
 
 .0015 
 
 + .050 
 
 13 
 
 86 25 19. 29 
 
 14. 459 
 
 + 0.321 
 
 |- 0. 103 
 
 i 0. 42 
 
 !: C. pll.'i . . . 
 
 M 
 
 3 3 55. 35 
 
 + 7.322 
 
 + .350 
 
 + .016 
 
 + .12 
 
 11 
 
 12 44 50. 92 
 
 13. 9X> 
 
 + 0.770 
 
 + 0.066 
 
 0.13 
 
 a Arii-tis . . . 
 
 24 
 
 3 7 25. 951 
 
 3. 1:11- 1 
 
 + . 0176 
 
 .0015 
 
 .008 
 
 7 
 
 69 26 21. 86 
 
 13.714 
 
 + 0.370 
 
 + 0.071 
 
 + 1.80 
 
 a IVrm-i . . . 
 
 24 
 
 3 15 a 19 
 
 i 4. 245 I 
 
 + .0483 
 
 + .0020 
 
 4- .06 
 
 10 
 
 40 36 14. 58 
 
 13.220 
 
 + 0.470 
 
 + 0.043 
 
 0. 30 
 
 >I Tauri . . . 
 
 68 
 
 3 39 45.629 
 
 i 3.5525 
 
 + .0173 
 
 + .0010 
 
 + .035 
 
 13 
 
 66 17 57.30 
 
 11.520 
 
 + 0.430 
 
 4- 0.060 
 
 4-0.93 
 
 < Pl-Wi . . . 
 
 8 
 
 3 45 57. 894 
 
 i- 3.7551 
 
 + .0222 
 
 + .0006 
 
 + .022 
 
 3 
 
 58 30 19. 58 
 
 11.072 
 
 + 0.460 
 
 + 0.049 
 
 + 2.25 
 
 j- Kriihuii 
 
 38 
 
 3 51 57.948 
 
 2. 7! 120 
 
 + . 0045 
 
 + .0044 
 
 + .067 
 
 7 
 
 103 52 49. 62 
 
 10. 630 
 
 + 0.350 
 
 + 0. 120 
 
 i 2. 30 
 
 y Tauri . . . 
 
 41 
 
 12 23. .-71 
 
 ; a 3983 
 
 + .0116 
 
 + .0085 
 
 + .038 
 
 10 
 
 74 41 19.90 
 
 9. 074 
 
 + 0.447 
 
 + 0.031 
 
 + 1.71 
 
 c Tauri . . . 
 
 55 
 
 21 1. 674 
 
 + 3.4876 
 
 + .0122 
 
 + .0076 
 
 + . 019 
 
 10 
 
 71 6 37. 91 
 
 8.395 
 
 4- 0.467 
 
 + 0.031 
 
 + 1.73 
 
 Tauri . . . 
 
 151 
 
 28 37.806 
 
 + a 4311 
 
 + .0106 
 
 + .0045 
 
 t. (Ill 
 
 18 
 
 73 45 16. 86 
 
 7.793 
 
 + 0.465 
 
 + 0.166 
 
 + 1.71 
 
 a Cami-liipiinli . 
 
 13 
 
 41 .-. i:-j 
 
 + 5.915 
 
 + .070 
 
 .003 
 
 .17 
 
 10 
 
 23 52 56. 91 
 
 6.765 
 
 + 0.814 
 
 0.009 
 
 f 0. 44 
 
 t \illit:;r 
 
 37 
 
 48 31. 808 
 
 + 3.8971 
 
 i- .0146 
 
 .0008 
 
 .011 
 
 9 
 
 57 2 34. 21 
 
 6.153 
 
 + 0.543 
 
 + 0.020 
 
 + 1. 6C 
 
 11 Ormnis . . . 
 
 28 
 
 57 a 536 
 
 | 3. 4-.MI 
 
 4- .0078 
 
 (- .0025 
 
 .037 
 
 8 
 
 74 46 46. 94 
 
 5. 432 
 
 + 0.483 
 
 + 0.031 
 
 + 1.67 
 
 a Aurlgie . . 
 
 17 
 
 5 7 5.30 
 
 f 4.4134 
 
 4- .0160 
 
 + .0086 
 
 .03 
 
 3 
 
 44 8 15.38 
 
 4. 5r 
 
 -j- 0.630 
 
 + 0.420 
 
 + 0.40 
 
 Orion is . 
 
 120 
 
 5 8 17. 481 
 
 + 2.8808 
 
 + . 0040 
 
 .0001 
 
 + .025 
 
 18 
 
 98 21 15. 03 
 
 4.486 
 
 + 0.411 
 
 + 0.017 
 
 4- 1.13 
 
 11 Tiiuri . . . 
 
 111 
 
 5 18 4. 523 
 
 + 3. 7h.V 
 
 . M 
 
 t .0017 
 
 + .010 
 
 17 
 
 61 30 19. 51 
 
 3.648 
 
 + 0.545 
 
 I 0.191 
 
 4-0.96 
 
 <' Idiiinm . . . 
 
 78 
 
 5 2521.970 
 
 3. (MW.I 
 
 4- . 0038 
 
 t- .0009 
 
 .004 
 
 9 
 
 !K> 23 52.65 
 
 3. 019 
 
 + 0.443 
 
 + 0.040 
 
 4. 1.01 
 
 a I . |>"ii- . . 
 
 15 
 
 5 26 59.879 
 
 i- 2.IM44 
 
 . . IXKIII 
 
 . (Klil 
 
 .010 
 
 
 107 55 
 
 2.878 
 
 + 0.383 
 
 0.000 
 
 
 ' Onoiiis . 
 
 79 
 
 5 29 37. 077 
 
 + 3. (Mi! 
 
 + .0036 
 
 .0005 
 
 4- .023 
 
 11 
 
 91 17 14.93 
 
 2.651 
 
 c 0.441 
 
 + 0.011 
 
 + 1.23 
 
 .1 ('"luniliiB . . 
 
 19 
 
 5 34 56. 569 
 
 + 2. 1709 
 
 + .0028 
 
 4- .0026 
 
 .011 
 
 I 
 
 124 8 43. 52 
 
 2.178 
 
 4- 0.316 
 
 0.000 
 
 + 2.53 
 
 a < iiinuis . 
 
 144 
 
 5 48 H. II7-J 
 
 +- 3.-J15I 
 
 + . IKI-JS 
 
 + .11017 
 
 4- .003 
 
 18 
 
 82 37 11.89 
 
 1.038 
 
 4- 0. 474 
 
 0.000 
 
 + l.U 
 
 li 1 M-niiiiornni . 
 
 38 
 
 6 15 5.755 
 
 -f- 3. i;-;n:i 
 
 . 0004 
 
 + .0059 
 
 .007 
 
 7 
 
 67 25 21. 32 
 
 + 1.320 
 
 + 0.529 
 
 4- 0. 140 
 
 4- 1.32 
 
 ) lii'tiiinot inn . 
 
 13C 
 
 6 30 12. 1 l.'i 
 
 i- 3. Hi 111 
 
 .0014 
 
 4- .0040 
 
 .(in 
 
 13 
 
 73 --"I 33. 00 
 
 4- 2.635 
 
 + 0. 501 
 
 4- 0.040 
 
 4- 1.44 
 
 .M c.-pli.-i . . . 
 
 47 
 
 6 38 43. 17 
 
 +30.406 
 
 2.011 
 
 - .106 
 
 4- .17 
 
 21 
 
 2 45 37. 67 
 
 -j- 3.373 
 
 + 4.341 
 
 0. 003" 
 
 O.S8 
 
 CantaMajoris . 
 
 134 
 
 6 39 25. 074 
 
 f 2. GWIB 
 
 .0000 
 
 . 0364 
 
 [- .054] 
 
 13 
 
 106 32 25.02 
 
 4- 3. 371 
 
 4- 0.381 
 
 f 1.383 
 
 4- 2.64 
 
 r I 'llllis M;ij..l i> 
 
 44 
 
 6 53 31.066 
 
 j. x,; i 
 
 1- . 0013 
 
 + .0013 
 
 .019 
 
 10 
 
 118 47 49.74 
 
 + 4.638 
 
 |- 0.333 
 
 + 0.020 
 
 + 1. 32 
 
 t Citnis Miijori.H . 
 
 11 
 
 7 :i ii. 3> 
 
 j. i.i'.i.. 
 
 f .0012 
 
 + .0003 
 
 .1111; 
 
 3 
 
 116 11 18.79 
 
 + 5.453 
 
 + 0.340 
 
 0.009 
 
 + 1.67 
 
 '' < ii-miii"! urn 
 
 53 
 
 7 12 21 455 
 
 :i. .v.nii 
 
 . IXIVJ 
 
 - .0004 
 
 .026 
 
 13 
 
 117 4(1 52. in 
 
 + 6.227 
 
 + 0.496 
 
 + 0.020 
 
 i 1.H1 
 
 0* (iclllill.n Mill 
 
 76 
 
 7 26 18. 121 
 
 3. -.Ml 
 
 .11131 
 
 .IIH'.I 
 
 i . ->7(l 
 
 10 
 
 57 49 45. 77 
 
 + 7. 374 
 
 + 0.527 
 
 + 0.076 
 
 4-0.97 
 
 a Cani> Minmis 
 
 167 
 
 7 33 29. 718 
 
 3. 1III7 
 
 .0042 
 
 .057 
 
 .110 
 
 16 
 
 84 26 39. 52 
 
 + 7.876 
 
 + 0.420 
 
 [+1.040] 
 
 + 1.09 
 
 & Gfininorum . 
 
 149 
 
 7 37 21. -500 
 
 3. 7-J.HI 
 
 .ill-.'.'. 
 
 .11171 
 
 .0114 
 
 14 
 
 111 :I9 44.81 
 
 + R262 
 
 + 0.480 
 
 | 0.060 
 
 t 1.41 
 
 t ' i.'iiiiimriini . 
 
 IS 
 
 1 45 :w. M:, 
 
 
 .11130 
 
 _ 1 
 
 .050 
 
 5 
 
 ii-' M 1.95 
 
 + 8. 913 
 
 + 0.478 
 
 + 0.049 
 
 + 1.71 
 
 l."i Ar^iin . . . 
 
 23 
 
 ii :,!; 
 
 '. Mf.t 
 
 (Mill 
 
 .0046 
 
 . 032 
 
 8 
 
 113 55 53.08 
 
 I 10. 179 
 
 4- 0.317 
 
 0.060 
 
 + 1.83 
 
 Hydno . . . 
 
 60 
 
 8 39 53. 451 
 
 :i. I'.KKI 
 
 .0071 
 
 .11117 
 
 .012 
 
 10 
 
 83 6 22.65 
 
 + 12.884 
 
 I 0.350 
 
 + 0.040 
 
 + 1.98 
 
 i Urai' Mrtji'ii- 1 
 
 
 
 ! 4 1C70 
 
 .0444 
 
 . 0453 
 
 
 4 
 
 41 26 59.65 
 
 + 13. 568 
 
 + 0. 436 
 
 + 0.280 
 
 0.80 
 
 ff 1 Ursa? Majoria . 
 
 13 
 
 8 'S8' 55.' 15 
 
 - 1 . 134 
 
 . IKK 
 
 .'of 
 
 11 
 
 24 20 25. 3 
 
 ! .14.114 
 
 u tee 
 
 h 0.097 
 
 2. 15 
 
 It 1 ':nn-i i . . . 
 
 J4 11 II 42. 254 
 
 3, -ivs _ . INI:I i 
 
 .OIKIO 
 
 + .020 
 
 7 
 
 7." IH 37.92 
 
 14. CM 
 
 0. 3-.-.I 
 
 + 0.011 
 
 + 1.77 
 
 1 DracunU . . 
 
 6 9 If 31. l:t 
 
 U. l(i<l . W07 
 
 _ . IKI- 
 
 .17 
 
 9 
 
 8 10.37 
 
 1- 15. 269 
 
 + 0.873 
 
 0.006 
 
 (- 0.68 
 
 a Hyilrjc . . . 
 
 89 9 21 11.956 
 
 J. 1I.VI7 
 
 .0014 
 
 .0011 
 
 + .001 
 
 16 
 
 98 5 47. 96 
 
 + 15 430 
 
 : 0. 'JCll 
 
 0.040 
 
 + 1.45 
 
 8 TJnw-Mii.j.ni- 
 
 4 9 24 8. 88 
 
 1. I..-7 
 
 .0553 
 
 . nun 
 
 f .04 
 
 2 
 
 37 43 54. 98 
 
 + 15. 594 
 
 + 0.357 
 
 + 0.569 
 
 + 0.05 
 
 r I... mis . . . 
 
 <'-, 9 38 28. l7 
 
 a. oas BITS 
 
 . 002." 
 
 .oil 
 
 U 
 
 115 37 43.56 
 
 + 16. 351 
 
 0.2.-3 
 
 + 0.020 
 
 i 1.54 
 
 (i Leonfo . . . 
 
 37 45 21. nil 
 
 3. 1 (35 . 01117 
 
 .0188 
 
 + .020 
 
 8 
 
 63 22 56. 13 
 
 111. I1!I3 
 
 + 0.270 
 
 + 0.060 
 
 { 1.01 
 
 a I. ..iiis . . . 
 
 119 10 1 26.820 
 
 3. -.'.'IKI .0101 
 
 .0165 
 
 .014 
 
 19 77 23 55. K 
 
 4- 17. 431 
 
 (I. .'il 
 
 fl.Oll 
 
 1. .VI 
 
 j Leoois . . . 
 
 86 
 
 10 12 48. 138 
 
 :i. -JC5 .015'J 
 
 i .0203 
 
 4- .014 
 
 13 
 
 69 30 7.86 
 
 + 17.901 
 
 + 0.213 
 
 + 0.151 
 
 + 2.08 
 
 9 Draronis . . 
 
 7 
 
 10 23 58. 40 
 
 + 5.317 
 
 .284 
 
 .000 
 
 .08 
 
 8 
 
 13 37 6. 92 
 
 + ia320 
 
 + 0.312 
 
 I 0.031 
 
 1.2H 
 
 fLconin . . . 
 
 4v! Ill 25 57.889 
 
 :i. lii.-,d 
 
 .0081 
 
 f .0005 
 
 .036 
 
 8 80 1 31. 85 
 
 + 1R390 
 
 + 0.177 
 
 . 11.034 
 
 ( 1.23 
 
 1 U . . . 
 
 :.:, in 42 25. :-,!> 
 
 3. iui:< 
 
 .0082 
 
 .0006 
 
 + .035 
 
 12 78 46 4.06 
 
 + 18.917 
 
 . 0.146 
 
 i 0.020 
 
 | 1.S4 
 
 a I'ruH-Majorm. 41 10 55 41. 04 
 
 
 _ Jl-,-.' 
 
 . 0195 
 
 . 
 
 14 -27 32 52. 18 
 
 + 19. 270 
 
 + 0.145 
 
 + 0.086 
 
 - 0.41 
 
 HIM . 
 
 'M 11 7 11.525 
 
 -r 3. 1908 
 
 .0134 
 
 + .0117 
 
 - .027 
 
 14 
 
 68 45 5a05 
 
 + 19. 525 
 
 II. 1IKI 
 
 + 0. 140 
 
 ! 1. cl 
 
 A Crati-riH . . 
 
 46 11 12 50.585 
 
 3.IP037 
 
 + .0063 
 
 . C078 
 
 f .005 
 
 9 
 
 104 4 31. 88 
 
 + 19.632 
 
 n. u-.' 
 
 0.180 
 
 + 1.35 
 
 T I.f.tllis . 
 
 2r- 11 21 I.'.. 1-Jli 3.0-112 
 
 .002J 
 
 + .0019 
 
 + . 012 
 
 9 
 
 86 25 II M 
 
 + 19. 769 
 
 + 0.068 
 
 > 0.020 
 
 4- 1.11 
 
 A Draronin . . 
 
 19 11 2.1 3:1. :,:. 3. i;:,:i 
 
 .113 
 
 .011 
 
 + .19 
 
 16 
 
 1957 6.11 
 
 t 19. 803 
 
 . 11.1177 
 
 + 0.060 
 
 1.53 
 
 v Leonifl . . . 
 
 56 11 30 17. 5!i9 3.1171- 
 
 + .0002 
 
 .0000 
 
 - .008 
 
 9 
 
 90 6 23. 29 
 
 + 1!>. 887 
 
 + 0.050 
 
 0. 031 
 
 + 1.59 
 
 II Leonis . . . 
 
 116 11 42 25.660 
 
 T 3. 1001 
 
 .0073 
 
 .0344 
 
 + .015 
 
 17 
 
 74 42 5.56 
 
 + 19. 990 
 
 + 0.026 
 
 + 0. 103 
 
 + 1.B7 
 
 y Urea- Mnjoris . 
 
 18 11 46 58.98 
 
 + 3. 178S 
 
 .0440 
 
 .- .01 in 
 
 + .07 
 
 12 
 
 35 34 57. 42 
 
 4- 20.023 
 
 f 0.019 
 
 0. 003 
 
 + 0.51 
 
 o Virginia . . 
 
 51 11 56 35.224 
 
 3. 1173.', 
 
 .00:12 
 
 .0130 1+ .006 
 
 10 80 32 42. 33 
 
 + 20.055 
 
 0.005 
 
 0.020 
 
 + 1.48 
 
 4 Dnu-mim . . 
 
 18 12 6 4.78 
 
 - 2.900 
 
 . 1-JH 
 
 - .010 '- .06 
 
 16 11 39 411 15 
 
 + 20. H48 
 
 0.019 + 0.008 
 
 _ 1.90 
 
 Virginin . . 
 ft Corvi . . . 
 
 69 
 53 
 
 12 13 15.348 
 12 27 33. 735 
 
 +- a 0721 
 r ai3s 
 
 - . IKM; . (Ki:n - . oofl 
 
 + .0163 U .0041 .006 
 
 13 
 11 
 
 89 56 40. 07 
 112 40 39. S3 
 
 + 20.021 
 + 19. 910 
 
 0. 033 
 0. 062 
 
 + 0.029 
 i 0.069 
 
 + 1.86 
 + 1.87 
 
42 
 
 POSITIONS OF FUNDAMENTAL STARS. 
 
 MEAN POSITIONS FOR 1870.0 (JANUARY Orf. Od.16, WASHINGTON) OF STARS OF THE AMERICAN EI'IIK M El: IS, \ r. ( 'cuit iniii-d. 
 
 Star. 
 
 1 . 
 if 
 
 7 
 
 
 
 i 
 
 4 
 
 M 
 
 Precession. 
 
 Secular varia- 
 tion. 
 
 Proper motion. 
 
 Corr'll to Am. 
 Epliem., 1870. 
 
 A 
 i 
 
 * 
 
 o 
 
 i 
 
 o 
 
 fi 
 
 rf 
 
 Precession. 
 
 Secular varia- 
 tion. 
 
 Proper motion. 
 
 CCIIT'II to Am. 
 Eplicni.. 1.-70. 
 
 
 
 h. m. s. 
 
 s. 
 
 s. 
 
 s. 
 
 ftp 
 
 
 / // 
 
 
 
 
 
 
 
 
 
 IT Draconis . 
 
 5 
 
 12 27 55. 31 
 
 + 2.612 
 
 .055 
 
 .011 
 
 + .02 
 
 8 
 
 19 29 41. 59 
 
 l- 19. 906 
 
 0.054 
 
 + 0.023 
 
 1.32 
 
 32 2 Caiuelopanli . 
 
 9 
 
 12 48 13. 51 
 
 + 0.362 
 
 + .222 
 
 .012 
 
 + .50 
 
 11 
 
 5 52 48. 81 
 
 + 19.612 
 
 0.018 
 
 i- 0.030 
 
 2.02 
 
 a (Jaiium Ven. . 
 
 71 
 
 12 4!) 56. 627 
 
 + 2. 8379 
 
 . 0151 
 
 . 0204 
 
 + .027 
 
 13 
 
 50 58 4.1.11 
 
 19. SSI 
 
 _ 1). 036 
 
 - 0. Hill 
 
 + 1.04 
 
 Virginia . . 
 
 83 
 
 13 3 13. 268 
 
 + 3. 1030 
 
 + .0077 
 
 . 0024 
 
 .OH 
 
 12 
 
 94 50 40. 76 
 
 + 19. 297 
 
 - 0. 130 
 
 i- 0.040 
 
 + 2.09 
 
 a Virginia . . 
 
 200 
 
 13 18 20. 852 
 
 + 3.1551 
 
 t- .0114 
 
 . 1:024 
 
 + . 015 
 
 22 
 
 100 28 55. 51 
 
 f 18. 894 
 
 - 0. 161 
 
 i- 0.034 
 
 :- 1.46 
 
 Virginia . . 
 
 94 
 
 13 28 4. 261 
 
 + 3.0715 
 
 1- . C063 
 
 . 0189 
 
 + .029 
 
 17 
 
 89 55 49.74 
 
 + 18. 592 
 
 0. 173 
 
 I). ODD 
 
 + 1.59 
 
 TI UraD Majoris . 
 
 24 
 
 13 42 24. 99 
 
 + 2.3844 
 
 .01113 
 
 .0102 
 
 .00 
 
 13 
 
 40 2 13. 61 
 
 18.0*7 
 
 0. 156 
 
 0. 020 
 
 ' II. OH 
 
 rt Bootis . . . 
 
 inc. 
 
 13 48 29. 713 
 
 + 2.8617 
 
 .0005 
 
 .0031 
 
 .016 
 
 19 
 
 70 56 59.35 
 
 + 17. 851 
 
 0. 197 
 
 f 0.360 
 
 i- 1.81 
 
 a Draconis . . 
 
 13 
 
 14 52. 30 
 
 + 1.629 
 
 + . 0052 
 
 .007 
 
 + .04 
 
 12 
 
 25 8.22 
 
 + 17. 330 
 
 0. 136 
 
 \- 0.034 
 
 -1.38 
 
 a Bootis . . . 
 
 186 
 
 14 9 43.975 
 
 + 2.8131 
 
 + . 0023 
 
 . 0798 
 
 + . 033 
 
 22 
 
 70 8 23. 46 
 
 + 16. 927 
 
 0.214 
 
 + 1.970 
 
 t- 1.99 
 
 6 Bootis . . . 
 
 18 
 
 14 20 46.31 
 
 + 2.0697 
 
 . 0013 
 
 .0266 
 
 + .08 
 
 13 
 
 37 32 51. 22 
 
 + 16. 390 
 
 0. 176 
 
 i- 0.409 
 
 D.W 
 
 5 Ursa? Miuoris . 
 
 13 
 
 14 27 49.96 
 
 0. 219 
 
 + .122 
 
 + .005 
 
 + .13 
 
 11 
 
 13 43 33. 95 
 
 + 16. 025 
 
 0.012 
 
 + 0. C20 
 
 1.43 
 
 c Bootis . . . 
 
 88 
 
 14 39 18. 612 
 
 + 2.6241 
 
 . 0001 
 
 .0025 
 
 + .009 
 
 15 
 
 62 22 35. 79 
 
 + 15. 402 
 
 0. 250 
 
 0.011 
 
 ; 1.35 
 
 a 2 Libra) . . . 
 
 81 
 
 14 43 41.416 
 
 + 3.3150 
 
 + .0155 
 
 .0085 
 
 + .016 
 
 14 
 
 105 30 0. 22 
 
 + 15. 153 
 
 0. 321 
 
 + 0.054 
 
 + 1. 74 
 
 UrsseMmoris . 
 
 57 
 
 14 51 6.66 
 
 0. 244 
 
 + .104- 
 
 .007 
 
 + .02 
 
 17 
 
 15 18 47. 57 
 
 + 14. 720 
 
 + 0.020 
 
 I- 0.029 
 
 - 1.34 
 
 fi Bootis . . . 
 
 6 
 
 14 57 2. 89 
 
 + 2.2637 
 
 .0000 
 
 .0038 
 
 .06 
 
 
 49 5 . . 
 
 + 14. 362 
 
 0.235 
 
 + 0.060 | . . 
 
 /? Librae . . . 
 
 91 
 
 15 10 0.866 
 
 -|- 3.2265 
 
 + .0118 
 
 .0067 
 
 + .031 
 
 16 
 
 98 54 6. 02 
 
 + M. 548 
 
 0. 3.11 
 
 i 0.009 
 
 + 3.23 
 
 ft Bootis . . . 
 
 88 
 
 15 19 34. 843 
 
 f- 2.2780 
 
 + . 0012 
 
 .0102 
 
 + .018 
 
 8 
 
 52 9 56. 26 
 
 + 12.919 
 
 0. 257 
 
 0. 091 
 
 r 0.61 
 
 y TJrstc Minoris . 
 
 6 
 
 15 20 57. 15 
 
 0. 148 
 
 + .075 
 
 .000 
 
 .07 
 
 6 
 
 17 42 11.57 
 
 + 12.827 
 
 + 0.012 
 
 0. 029 
 
 0.30 
 
 a Corona? Borealis 
 
 140 
 
 15 29 11.084 
 
 + 2.5296 
 
 + .0024 
 
 + .0097 
 
 + .027 
 
 21 
 
 62 50 47. 50 
 
 + 12. 265 
 
 0.299 
 
 + 0.063 
 
 + 1.85 
 
 a Serpentis . 
 
 102 
 
 15 37 51. 987 
 
 r 3.9417 
 
 + . 0061 
 
 + .0085 
 
 + .051 
 
 21 
 
 83 9 49. 83 
 
 + 11. 656 
 
 II. .-,.1.1 
 
 0. 06.P 
 
 4- 1.91 
 
 Serpentis . 
 
 45 
 
 15 44 2il. 269 
 
 + 2.9776 
 
 + . 0065 
 
 + .(1091 
 
 + .026 
 
 13 
 
 85 7 45.52 
 
 + 11. 190 
 
 0. 367 
 
 0. 069 
 
 + 1. 31 
 
 Trail* Minoris - 
 
 13 
 
 15 48 45. 50 
 
 2. 303 
 
 1- .204 
 
 + .013 
 
 + .15 
 
 11 
 
 11 48 24. 52 
 
 + 10. 867 
 
 + O.S77 
 
 + 0.003 
 
 0.22 
 
 o Scorpii . . . 
 
 35 
 
 15 52 39. 031 
 
 + 3.5368 
 
 + . 0160 
 
 .0009 
 
 + .041 
 
 7 
 
 112 14 58.73 
 
 + 10. 579 
 
 0. 442 
 
 + 0.011 
 
 2. " 
 
 /?, Scorpii . . 
 
 31 
 
 15 57 52, 891 
 
 + 3.4787 
 
 + . 0142 
 
 . 0020 
 
 + . 058 
 
 9 
 
 109 26 50. 88 
 
 + 10. 187 
 
 0. 440 
 
 + 0.020 
 
 + 0.95 
 
 <5 Opluuchi . 
 
 47 
 
 16 7 32. 118 
 
 + 3.1413 
 
 + . 0083 
 
 . 0037 
 
 + .053 
 
 17 
 
 93 21 27. 90 
 
 + 9. 451 
 
 0. 407 
 
 -i- 0. 139 
 
 + 8. 1* 
 
 r Herculis . . 
 
 18 
 
 16 15 50. 13 
 
 + 1.8008 
 
 + .0052 
 
 .0029 
 
 + .21 
 
 13 
 
 43 22 33. 26 
 
 + 8.805 
 
 0.239 
 
 0. 031 
 
 + 0.26 
 
 a Scorpii . . 
 
 67 
 
 16 21 26. 431 
 
 + 3.6686 
 
 h .0152 
 
 .0001 
 
 + .021 
 
 11 
 
 116 8 28. 19 
 
 8.361 
 
 0. 489 
 
 + 0.020 
 
 1. .12 
 
 n Dracouis . . 
 
 9 
 
 16 22 14. 18 
 
 + 0.8012 
 
 + .0185 
 
 + .0220 
 
 + .02 
 
 3 
 
 28 11 27. 40 
 
 + 8.297 
 
 0.110 
 
 0.080 
 
 0.36 
 
 A Draconis . 
 
 7 
 
 16 28 14. 94 
 
 0. 144 
 
 i- . 041 
 
 + .001 
 
 .01 
 
 8 
 
 20 57 2. 80 
 
 + 7. 816 
 
 + 0.016 
 
 0.034 
 
 -|- 0. 39 
 
 g Ophiuchi . . 
 
 4C 
 
 10 30 0. 163 
 
 + 3.2066 
 
 -1- . 0079 
 
 + .0012 
 
 + . 030 
 
 16 
 
 100 18 6.14 
 
 + 7. 675 
 
 0. 447 
 
 0. 031 
 
 i- 2. 31 
 
 i? Hercutis . . 
 
 18 
 
 16 38 26. 43 
 
 + 2.0511 
 
 + . 0038 
 
 + .0032 
 
 + .04 
 
 9 
 
 50 49 44.98 
 
 + 6. 987 
 
 0. 3---1 
 
 + 0.071 
 
 ;- 1. 55 
 
 K Ophiuchi . 
 
 59 
 
 16 51 3). '.174 
 
 + 2.8565 
 
 + . 0044 
 
 .0319 
 
 + .070 
 
 11 
 
 80 25 15. 20 
 
 + 5. 904 
 
 0. 394 
 
 0. 023 
 
 4. 1.4.1 
 
 c TJrsno Minoris . 
 
 11 
 
 16 59 22. 74 
 
 6.405 
 
 + .302 
 
 + .015 
 
 .09 
 
 15 
 
 7 45 10.66 
 
 + 5. 243 
 
 + 0.901 
 
 0.000 
 
 0.25 
 
 a Herculis . . 
 
 115 
 
 17 8 43. 263 
 
 + 2.7339 
 
 + . 0035 
 
 .0008 
 
 + .049 
 
 17 
 
 75 27 34. 86 
 
 + 4. 450 
 
 0.390 
 
 0. 049 
 
 1.11.1 
 
 b Opliiuchi . 
 
 C9 
 
 17 18 26. 000 
 
 + 3.6591 
 
 i- . 0075 
 
 .00114 
 
 + .058 
 
 11 
 
 114 3 11.51 
 
 + 3. 618 
 
 0. 526 
 
 + 0.120 
 
 + 3. 14 
 
 o Ophiuchi . . 
 
 138 
 
 17 28 54. 069 
 
 + 2.7746 
 
 + .0033 
 
 + .0074 
 
 .062 
 
 20 
 
 77 20 36. 52 
 
 + 2. 713 
 
 0. 404 
 
 i- 0.200 
 
 + 1.65 
 
 o> Draconis . 
 
 10 
 
 17 37 42. 96 
 
 0. 364 
 
 -i- .011 
 
 + .000 
 
 + .06 
 
 11 
 
 21 10 55. 83 
 
 1- 1.947 
 
 I- 0. 050 
 
 0. 291 
 
 1.94 
 
 fjt Herculis . . 
 
 73 
 
 17 41 22.380 
 
 f 2.3696 
 
 + . 0038 
 
 .0249 
 
 + .033 
 
 12 
 
 62 18 6.33 
 
 + 1. 629 
 
 0. 338 
 
 + 0.740 
 
 + 1.72 
 
 i// 1 Draconis . . 
 
 5 
 
 17 44 15. 24 
 
 1.086 
 
 + .019 
 
 + .002 
 
 .06 
 
 4 
 
 17 47 17.40 
 
 + 1. 377 
 
 i- 0.157 
 
 + 0.260 
 
 1 0.41 
 
 Y Draconis . 
 
 19 
 
 17 53 35. 37 
 
 r 1.3910 
 
 -|- . 0036 
 
 + .0017 
 
 .03 
 
 14 
 
 38 29 -11.96 
 
 + 0.561 
 
 0.202 
 
 i- 0.037 
 
 + 0. 36 
 
 y z Sagittarii . . 
 
 25 
 
 17 57 27. 502 
 
 + 3.8572 
 
 + . 0035 
 
 .0049 
 
 + .040 
 
 3 
 
 120 25 22. 14 
 
 + 0.222 
 
 0. 561 
 
 + 0.231 
 
 + 0. 57 
 
 p Sagittarii . 
 
 94 
 
 18 5 59.375 
 
 + 3.5876 
 
 + . 0010 
 
 .0015 
 
 + . 035 
 
 6 
 
 111 5 24.82 
 
 0. 524 
 
 0. 522 
 
 + 0.011 
 
 + 1.14 
 
 6 TJrsaj Minoris . 
 
 
 18 14 16. 33 
 
 19. 435 
 
 .430 
 
 f .028 
 
 .03 
 
 38 
 
 3 23 38. 84 
 
 1. 249 
 
 + 2. fc20 
 
 o. on 
 
 ) 0. 14 
 
 n Serpentis . 
 
 22 
 
 18 14 35. 034 
 
 f 3.1405 
 
 + .0018 
 
 .0411 
 
 + .085 
 
 5 
 
 92 55 49. 72 
 
 1.275 
 
 0. 445 
 
 + 0.680 
 
 + 2.06 
 
 1 Aquilte . . . 
 
 91 
 
 18 28 8.001 
 
 + 3.2665 
 
 -i- . 0001 
 
 .0022 
 
 |- . 097 
 
 12 
 
 98 19 57. 58 
 
 2.456 
 
 0. 471 
 
 1 0. 329 
 
 + 1.51 
 
 a Lyi'ce . . . 
 
 177 
 
 18 32 32.263 
 
 2.0131 
 
 + .0010 
 
 + .0184 
 
 + .051 
 
 16 
 
 51 20 9.66 
 
 2.838 
 
 0. 295 
 
 0. 286 
 
 + 0. 66 
 
 ff Lyras . . . 
 
 64 
 
 18 45 16. 873 
 
 -1- 2.2138 
 
 + . 0015 
 
 4- .0004 
 
 + .061 
 
 9 
 
 56 47 12. 62 
 
 3. 937 
 
 0. 315 
 
 I 0.029 
 
 + 0. 71 
 
 a Sagittarii . . 
 
 40 
 
 18 47 12.258 
 
 + 3.7234 
 
 .0051 
 
 4- -0003 
 
 + .037 
 
 8 
 
 116 27 20.08 
 
 4. 1U2 
 
 0.530 
 
 + 0.080 
 
 1.9.1 
 
 50 Draeoms . . 
 
 13 
 
 18 50 33. 35 
 
 1. 893 
 
 .0557 
 
 . C04 
 
 + .24 
 
 11 
 
 14 43 14. 56 
 
 4. 388 
 
 + 0.271 
 
 0. 057 
 
 1. 15 
 
 Aquilrc . . . 
 
 24 
 
 18 59 26. 137 
 
 + 2.7579 
 
 + .0004 
 
 .0030 
 
 + .100 
 
 13 
 
 76 19 40. 52 
 
 5. 143 
 
 0. 386 
 
 + 0.071 
 
 ;- 1.32 
 
 A Sagittarii . 
 
 8 
 
 19 10 1.6S5 
 
 + 3.5156 
 
 .0060 
 
 .0012 
 
 + .046 
 
 
 III!) 10 . . 
 
 6.032 
 
 0.486 
 
 0.011 
 
 
 i Draconis . . 
 
 15 1 19 12 3J.21 
 
 + 0.015 
 
 .023 
 
 + .019 
 
 + .10 
 
 li 
 
 28 34 1.63 
 
 6. 240 
 
 0. 005 
 
 0. 066 
 
 6.55 
 
 T Draconis . . 
 
 3 
 
 19 18 2. 46 
 
 1.080 
 
 .058 
 
 . 026 
 
 + -21 
 
 5 
 
 16 53 12. 16 
 
 6. 698 
 
 4- 0. 149 
 
 0. 097 
 
 0.44 
 
 A Aquilffi . . . 
 
 73 
 
 111 1* 56.643 
 
 + 3.0096 
 
 .0018 
 
 f .0152 
 
 + .083 
 
 14 
 
 87 8 33. 03 
 
 6. 772 
 
 0. 415 
 
 0.100 
 
 + 1.61 
 
 K Aquihu . 
 
 46 
 
 19 29 53. 846 
 
 ]- 3.2308 
 
 .0044 
 
 .0003 
 
 + .074 
 
 14 
 
 '.17 1- .12. 0.1 
 
 7.666 
 
 0. 432 
 
 0.000 
 
 -|- 2. 40 
 
 y Aquilfo . . . 
 
 86 
 
 19 40 4. 792 
 
 + 2.8520 
 
 . 0010 
 
 + .0008 
 
 + .059 
 
 13 
 
 79 42 7. 12 
 
 8.482 
 
 0. 374 
 
 0. 006 
 
 + 1.68 
 
 a Aquilre . . . 
 
 128 
 
 19 44 26.460 
 
 + 2.8921 
 
 .0018 
 
 + .0362 
 
 + .073 
 
 1.1 
 
 M 88 23.81 
 
 8. 836 
 
 0. 385 
 
 0. 383 
 
 + 1. 19 
 
 s Draconis . 
 
 5 
 
 19 48 36. 14 
 
 0. 185 
 
 .043 
 
 + .014 
 
 + .18 
 
 i; 
 
 20 3 17. 26 
 
 9.151 
 
 0.034 
 
 -I- 0.003 
 
 1.50 
 
 /? Aqnilse . . . 
 
 63 
 
 19 48 55. 678 
 
 + 2.9454 
 
 .0014 
 
 J .0015 
 
 + . 062 
 
 9 
 
 83 54 Sa .1" 
 
 9. 177 
 
 0. 379 
 
 + 0.483 
 
 + 1.48 
 
 A Ursit- Minoris . 
 
 33 
 
 19 54 16. 00 
 
 59. 083 
 
 211. 9.14 
 
 .071 
 
 .38 
 
 13 
 
 1 4 .1.1. .16 
 
 9. 591 
 
 + 7.605 
 
 0.014 
 
 II. .12 
 
 T Aquihi 1 - . . 
 
 23 
 
 III 57 47. 380 
 
 2.9310 
 
 , on-ill 
 
 -- .011:17 
 
 + . 047 
 
 6 
 
 83 5 14.56 
 
 9. 860 
 
 0. 369 
 
 0.011 
 
 a, n 
 
 a 8 Capricorn! . 
 
 85 
 
 411 111 5'i. Illl 
 
 3. 3307 
 
 . 0085 
 
 .OOSM 
 
 + .070 
 
 M 
 
 102 .16 45.16 
 
 10. 837 
 
 0. 405 
 
 0. 005 
 
 (- 1.14 
 
 K Cephei . . . 
 
 7 
 
 20 13 13.3.1 
 
 1. 894 
 
 . ir.4 
 
 + .002 
 
 + .24 
 
 4 
 
 12 40 53. 98 
 
 11.012 
 
 0. 2)3 
 
 0.000 
 
 0. 95 
 
 IT Capricorn i . 
 
 20 
 
 20 19 52. 715 
 
 + 3.4418 
 
 .0115 
 
 .0000 
 
 + .057 
 
 9 
 
 108 38 9.70 
 
 11.494 
 
 0. 407 
 
 0.020 
 
 + 1.90 
 
 Delphini . . 
 
 42 
 
 20 27 0. 1711 
 
 + 2.8666 
 
 . 01)13 
 
 . 0000 
 
 + . 079 
 
 11 
 
 79 8 13.57 
 
 11.999 
 
 0. 330 
 
 0.000 
 
 [ 1.83 
 
 a Cygni . . . 
 
 53 
 
 20 37 0. 07 
 
 1- 2.0434 
 
 + . 0022 
 
 + .01:05 
 
 + .05 
 
 12 
 
 45 10 59. 75 
 
 13. 689 
 
 0. 226 
 
 0.000 
 
 + 0.48 
 
 H Aquarii 
 
 58 
 
 20 45 38. 473 
 
 -[- 3.2394 
 
 .0083 
 
 .11(110 
 
 + .098 
 
 12 
 
 99 28 10. 59 
 
 13. 265 
 
 0.350 
 
 + 0.040 
 
 j- 2. 24 
 
 v Cygui . . . 
 
 24 
 
 20 52 19. 70 
 
 + 2.2331 
 
 + . C037 
 
 + .0006 
 
 + .09 
 
 10 
 
 49 19 56. 60 
 
 13. 698 
 
 0.232 
 
 0. Oil 
 
 1. -1 
 
 lil'Cviiui . . . 
 
 22 
 
 21 1 4. 2! 13 
 
 + 2.3340 
 
 + .0149 
 
 . 3390 
 
 . 00.1 
 
 10 
 
 51 53 19. i2 
 
 14.247 
 
 0. 300 
 
 3. 220 
 
 -I- 0. 1-9 
 
 S Cygni . . . 
 
 84 
 
 21 7 24.265 
 
 -f 2.5507 
 
 4- . 00:19 
 
 . 06 
 
 ; . 038 
 
 18 
 
 60 18 19.07 
 
 14. 632 
 
 0. 240 
 
 + 0.071 
 
 1. 1.1 
 
 <i (Yplu-i . . . 
 
 50 
 
 31 1.1 28.56 
 
 I. 41.16 
 
 .0063 
 
 .0317 
 
 -r .04 
 
 16 
 
 27 57 .13. (IT 
 
 15. 105 
 
 0. 131 
 
 0. 003 
 
 0. 93 
 
 1 Pegasi . . . 
 
 26 
 
 21 16 4.517 
 
 i- 2.7660 
 
 - .1018 
 
 1 .0091 
 
 . 023 
 
 9 
 
 70 45 2.68 
 
 15. 1 111 
 
 0. 261 
 
 0. 0.-9 
 
 ; 2. so 
 
 /^ Aquarii. . . 
 
 81 
 
 21 24 42. 895 
 
 -1- 3.1623 
 
 . 0078 
 
 i- .0,,20 
 
 + . 062 
 
 16 
 
 96 8 30.68 
 
 15.685 
 
 0. 2> 1 
 
 0. COO 
 
 I.HI 
 
POSITIONS OF FUNDAMENTAL STAUS. 
 
 43 
 
 MI:\N I'osmnxs FOI; i>7o.(.r.\xrA!:Yo,i_o.;.ii!. WASIIIM; TIINM>FSTAI;SOF TIIK AMKKICAN i:rin:Mi:iils,&c.-ConUinied. 
 
 
 
 
 
 
 1 
 
 | 
 
 ~ = 
 
 
 
 
 n 
 
 \ 
 
 | 
 
 sg 
 
 Star. 
 
 "= 
 
 
 
 I 
 
 
 i 
 
 3 J 
 
 j 
 
 2 
 
 
 '1 a 
 
 1 
 
 3"] 
 
 
 "=i 
 
 
 
 ^ 
 
 
 
 = ? 
 
 *ci 
 
 H 
 
 R 
 
 J: '- 
 
 s 
 
 q B 
 
 
 
 3 
 
 - 
 
 
 
 P 
 
 fcf 
 
 
 li 
 
 9 
 
 g 
 
 e 
 
 ''** 
 
 
 
 ri 
 
 h 
 
 * 
 
 fi 
 
 C^ 
 
 
 ri 
 
 < 
 
 * 
 
 
 
 at 
 
 
 
 h. m. t. 
 
 g. 
 
 
 ( 
 
 t 
 
 
 O ' '/ 
 
 
 
 
 
 
 
 
 
 :ilH'i 
 
 -.11 
 
 21 2li >. 4C. 
 
 
 031 
 
 i .oos 
 
 + .10 
 
 15 
 
 20 35. 00 
 
 15.748 
 
 0.066 
 
 + 0.037 
 
 0.93 
 
 A'|ti:it li . 
 
 81 
 
 21 30 C'. -13 
 
 3. 11124 
 
 - .ton 
 
 2 
 
 + . 047 
 
 5 
 
 98 26 9. 77 
 
 15. 955 
 
 0.277 
 
 0.040 
 
 + 1. 58 
 
 C IY- r ;ihi 
 
 H 
 
 21 37 1- 117 
 
 i 2. '.1451 
 
 .0000 
 
 -j- . 0028 
 
 . . 037 
 
 18 
 
 80 43 11.87 
 
 Hi. 317 
 
 0. 244 
 
 0.000 
 
 + 1.25 
 
 11 C.ph.i . . . 
 
 10 
 
 -.'1 III 0.5.-, 
 
 
 . 0319 
 
 + .026 
 
 .00 
 
 9 
 
 19 17 12.61 
 
 16. 428 
 
 0. 071 
 
 0.071 
 
 0.86 
 
 fi Capricorn! . 
 
 37 
 
 21 46 12. 13^ 
 
 
 .0114 
 
 . 0-J30 
 
 1- -'" ;l 
 
 9 
 
 104 9 45. 35 
 
 16.734 
 
 0.259 
 
 0. 020 
 
 + 2.36 
 
 79 Drao.nis 
 
 8 
 
 21 51 15.02 
 
 + 0.730 
 
 .015 
 
 .IKK 
 
 + .06 
 
 8 
 
 16 54 44. 65 
 
 16.973 
 
 0. 051 
 
 + 0.009 
 
 0. % 
 
 <i Aigunrii . . 
 
 77 
 
 c. i-.'i 
 
 < I. Or-33 
 
 . 0042 
 
 .11005 
 
 | .060 
 
 18 
 
 90 57 1.81 
 
 17. 329 
 
 0. 220 
 
 + 0.003 
 
 + 1.17 
 
 Aquarii 
 
 511 
 
 >> f) ~ t < '{1|| 
 
 + 3.1636 ] .0077 
 
 . . 0070 
 
 : . O.VI 
 
 12 
 
 47.54 
 
 17.7HS 
 
 0. 207 
 
 o. ogii 
 
 ; 1. 57 
 
 - Aipiarii . . 
 
 41 
 
 19 1- 3- 2!i 1 
 
 -j 3. (H150 .00-^ 
 
 i . 0001 
 
 + .047 
 
 10 
 
 i Hi 54. 14 
 
 18. 125 
 
 0. 184 
 
 + o. on 
 
 -f 1.59 
 
 n A.puirii . . 
 
 I- 
 
 in. :,-i 
 
 
 .0032 
 
 .01111 
 
 on 
 
 10 
 
 IKl 17 13. 14 
 
 18.483 
 
 0. 168 
 
 + 0.060 
 
 + 1.43 
 
 I Pt-nasi . . 
 
 12 
 
 gg :ii :,-. -.c.-. 
 
 
 on-'-' 
 
 i- .0030 
 
 + . 093 
 
 11 
 
 79 50 48. 60 
 
 18. 691 
 
 0. 151 
 
 0.000 
 
 r 2.06 
 
 t (Y|.ltri 
 
 II 
 
 3. :,3 
 
 2. 1211 
 
 n. 'T 
 
 .012 
 
 . 12 
 
 'i 
 
 - 58.44 
 
 is. tog 
 
 0.091 
 
 i 0. 1 III 
 
 0.50 
 
 \ Aqiiiti ii 
 
 41 
 
 22 4.-, 111. 1127 
 
 : 3. ]:'! 
 
 .0064 
 
 . IKI21I 
 
 + . 107 
 
 9 
 
 '.If 16 15.36 
 
 19.014 
 
 0. 138 
 
 II. 029 
 
 i 1. 90 
 
 a Pisris Australia !; 
 
 22 M 27. 7H5 
 
 :i. 305i; 
 
 .0214 
 
 .11211 
 
 . lid:, 
 
 20 
 
 120 i :K ii7 
 
 19. 1311 
 
 0. 139 
 
 ) 0. 169 
 
 + 1. 52 
 
 a p..giwl . . . 
 
 -1 
 
 17.240 
 
 2. H.-OI 
 
 + .0056 
 
 + .0043 
 
 + .060 
 
 17 
 
 75 29 38. 08 
 
 19. .132 
 
 0. 108 
 
 t- 0. 0011 
 
 + 1.81 
 
 (Vphri 
 
 8 1 23 13 1 . 
 
 + 2.422 
 
 + .040 
 
 + .014 
 
 .03 
 
 9 
 
 22 35 58. 11 
 
 19. 640 
 
 0.064 
 
 + 0.020 
 
 1.35 
 
 Piscium . . 
 
 1- 
 
 SI 21 22. 501 
 
 + 3. 0499 
 
 .0021; 
 
 . (KI92 
 
 .0-7 
 
 13 
 
 84 20 6.37 
 
 19.771 
 
 0. 067 
 
 + 0.060 
 
 + 2. 31 
 
 ( IMsi'iuill 
 
 tig 
 
 2:1 :ct 15 :>" 
 
 + 3.0587 
 
 -j- . 04130 
 
 . ii J.'i- 
 
 + .028 
 
 11 
 
 85 4 41. 96 
 
 19.919 
 
 0. 045 
 
 0.451 
 
 -f- 1.41 
 
 y (Yphci . . . 
 
 in 
 
 2:1 31 2.01 
 
 2. 4-.-J 
 
 .1171 
 
 .021 
 
 f .24 
 
 17 
 
 13 5 34. % 
 
 l'J.926 
 
 0. 031 
 
 0. 1411 
 
 - 0.27 
 
 ') Pisrium . . 
 
 57 
 
 23 52 38. 243 
 
 + 3.0675 
 
 + .0047 
 
 + .0105 
 
 + .037 
 
 10 
 
 83 51 24. 09 
 
 20. 045 
 
 0.007 
 
 + 0. 129 
 
 + 1.72 
 
 COMPARISONS OF THE PRECEDING POLAR DISTANCES WITH THOSE OF OTHER CATALOGUES. 
 
 I ii the following list are found only the stars of the Tabulae Reductionum of Wolfers, which are 
 arranged in the order of polar distance. 
 
 The second column gives. the zenith distance of the star at upper transit over the meridian 
 of Washington. 
 
 The polar distances of the catalogue were compared with those of Wolfers for 1870, and the 
 differeiK c is -i\ en after the zenith distance of the star. As the catalogue of comparison was really 
 or substantially that of Wolfers, these corrections are applicable at the mean epoch of observation, 
 lMiT.0. 
 
 The corrections to Wolfers. deduced by Auwers, and given on page 111 of the additions to the 
 Conna inxn arc </< v Temps for the year 1868, are then interpolated to the epoch 1867.0, and, being applied 
 to the numbers corresponding to Wolfers, we have the apparent corrections to Auwers' standard 
 positions for the same epoch. 
 
 In Auwers' investigation the differences of the numbers in the columns B and F indicate the 
 differences between his linal results and those given by the different catalogues. Taking the values 
 of these differences for "Airy, 1857," and applying them to the comparison with Auwers, \ve, 
 have, a comparison with the Greenwich seven years' catalogue, which is given in the next column. 
 
 In the A8tronomischN(u;li>-ivhten, No. 1C97, (Band 71, S. 257-264,) Gylden gives several com- 
 parisons of the declinations of the Pulkowa vertical circle with those of other authorities, and 
 especially a comparison of the declinations of the fundamental stars observed since 1863, with the 
 normal catalogue, of Auwers. Applying these numbers to the column Auwers, we have a com- 
 parison \\ith the Pulkowa verticle circle. 
 
 Nearly all the fundamental stars were observed with the Washington mural circle during the 
 years 1864 and 1S65. Carrying the results forward to 1870, the polar distances were corrected by 
 the constant quantity, -f 0".47, for error of the latitude adopted in the reductions, and then sub- 
 tracted from the polar distances of the transit circle. The differences are given in the last column. 
 
44 
 
 POSITIONS OK FUNDAMENTAL STARS. 
 
 COMPARISONS OF THE PRECEDINli NORTH POLAR DISTANCES WITH THOSE Of 
 
 OTHER AUTHORITIES. 
 
 Star's name. 
 
 Zenith distance. 
 
 Apparent corrections to the polar distance of 
 
 Wolfer's 
 Tab. Red. 
 
 Auwer's 
 Standard. 
 
 Greenwich 
 transit 
 circle. 
 
 Pulkowa 
 vertical 
 circle. 
 
 Washington 
 mural 
 circle. 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 Polaris .... 
 
 310 
 
 0.05 
 
 0.05 
 
 0.07 
 
 0.05 
 
 4- 0.27 
 
 S Ursa) Minoris . 
 
 312 
 
 0.83 
 
 0.20 
 
 0.16 
 
 4- 0.65 
 
 4- 0.3 
 
 ft Ursa) Minoris . . 
 
 324 
 
 1.73 
 
 1.17 
 
 0.51 
 
 0.10 
 
 0.3 
 
 3 Cepliei .... 
 
 329 
 
 1.27 
 
 1.06 
 
 0.54 
 
 4- 0.03 
 
 0.2 
 
 a Urs Majoris . 
 
 336 
 
 0.62 
 
 0.34 
 
 0.40 
 
 4- 0.85 
 
 4- 0.6 
 
 a Cephei . 
 
 336 
 
 0.93 
 
 0.80 
 
 0.43 
 
 4- 0.48 
 
 4- 0.2 
 
 a Cassiopeos . 
 
 343 
 
 4- 0.43 
 
 0.31 
 
 4- 0.01 
 
 0.02 
 
 4- 0.3 
 
 y Ursa) Majoris . 
 
 344 
 
 + 0.39 
 
 4- 0.32 
 
 4- 0.03 
 
 4- 0.53 
 
 4- 0.4 
 
 y Draconis . . . 
 
 347 
 
 + 0.36 
 
 0.03 
 
 4- 0.04 
 
 0.03 
 
 - - 
 
 tl Ursa) Majoris . 
 
 349 
 
 4- 0.29 
 
 0.05 
 
 0.35 
 
 0.03 
 
 . . 
 
 c. Persei . . . . 
 
 350 
 
 0.26 
 
 0. 26 
 
 0.07 
 
 4- 0.20 
 
 . 
 
 o Aurigse .... 
 
 353 
 
 4- 0.79 
 
 4- 0.39 
 
 0.05 
 
 4- 0.21 
 
 4- 0.7 
 
 a Cephei .... 
 
 354 
 
 4- 0.74 
 
 4- 0.44 
 
 4- 0.29 
 
 4- 0.42 
 
 0.6 
 
 a Lyra? .... 
 
 
 
 4- 0.99 
 
 4- 0.36 
 
 0.04 
 
 4- 0.34 
 
 0.1 
 
 o 2 Geminorum 
 
 7 
 
 4- 0.96 
 
 4- 1.51 
 
 4- 1.07 
 
 4- 0.82 
 
 4- i.o 
 
 3 Tauri .... 
 
 10 
 
 4- 0.25 
 
 4- 0.68 
 
 4- 0.43 
 
 4- 0.70 
 
 4- 1.8 
 
 a Andromeda) 
 
 11 
 
 + 1. 52 
 
 4- 0.84 
 
 4- 0.32 
 
 4- 0.28 
 
 4- 1.2 
 
 j? Geminorum 
 
 11 
 
 4- 0.70 
 
 4- 0.83 
 
 4- 0. 64 
 
 4- 0.25 
 
 4- 0.7 
 
 a Coronas .... 
 
 12 
 
 4- 2.30 
 
 + 1.55 
 
 4- 0.98 
 
 4- 0.88 
 
 4- 1.4 
 
 a Arietis .... 
 
 16 
 
 + 1.22 
 
 4- 1.25 
 
 4- 0.50 
 
 4- 0.40 
 
 4- 1.4 
 
 o Bootis .... 
 
 19 
 
 4- 1.88 
 
 4- 1. 29 
 
 4- 0.89 
 
 4- 0.36 
 
 4- 1.3 
 
 a Tauri .... 
 
 23 
 
 4- 1.79 
 
 4- 1.32 
 
 4- 0.43 
 
 4- 0.62 
 
 4- 2.0 
 
 /? Leonis .... 
 
 24 
 
 4- 1.45 
 
 4- 1.28 
 
 4- 0.62 
 
 + 0.68 
 
 4- 1.2 
 
 a Herculis 
 
 24 
 
 4- 1.61 
 
 4- 1.12 
 
 4- 0.39 
 
 4- 0.24 
 
 4- l.o 
 
 a Pegasi .... 
 
 24 
 
 4- 2.15 
 
 4- 1.47 
 
 4- 0.66 
 
 4- 0.29 
 
 4- 0.4 
 
 y Pegasi .... 
 
 24 
 
 4- 1.02 
 
 4- 0.90 
 
 4- 0.20 
 
 4- 0.03 
 
 4- 0.8 
 
 a Ophiuchi 
 
 26 
 
 4- 1.92 
 
 4- 1.67 
 
 4- 0.87 
 
 4- 0.17 
 
 4- 1.2 
 
 o Leonis .... 
 
 26 
 
 4- 0.92 
 
 4- 0.89 
 
 4- 0.40 
 
 4- 0.32 
 
 4- 0.7 
 
 y Aquihe ..... 
 
 29 
 
 4- 1.64 
 
 4- 1.52 
 
 4- 0.83 
 
 4- 0.83 
 
 4- 0.8 
 
 a AquiliB .... 
 
 30 
 
 4- 1.19 
 
 4- 0.90 
 
 4- 0.43 
 
 4- 0.26 
 
 4- 1.2 
 
 o Oriouis .... 
 
 32 
 
 4- 0.74 
 
 4- 1.49 
 
 4- 0.80 
 
 4- 0.49 
 
 4- 2.8 
 
 a Serpeutis 
 
 32 
 
 4- 1.79 
 
 4- 1.67 
 
 4- 0.90 
 
 4- 0.54 
 
 4- 0.6 
 
 f) Aquila) .... 
 a Ceti 
 
 33 
 35 
 
 40 
 
 4- 0.90 
 0.05 
 4- 0.99 
 
 4- 0.85 
 4- 0.33 
 4- 1.37 
 
 4- 0.52 
 4- 0.45 
 4- 0.69 
 
 4- 0.28 
 0.34 
 4- 0.57 
 
 4- 1.2 
 
 4- 0.9 
 0.4 
 
 a Aquarii .... 
 
 a Hydra) .... 
 
 47 
 
 4- 1.27 
 
 4- 1.05 
 
 4- 0.52 
 
 4- 0.59 
 
 4-' 0.8 
 
 /3 Orionis .... 
 
 47 
 
 4- 0.45 
 
 4- 0.73 
 
 4- 0.22 
 
 4- 0.46 
 
 + 0.7 
 
 a Virginis .... 
 
 49 
 
 4- 0.81 
 
 4- 0.59 
 
 4- 0.49 
 
 4- 0.54 
 
 4- 0.3 
 
 a" Capricorni . . . 
 
 52 
 
 4- 0.86 
 
 4- 0.66 
 
 4- 0.48 
 
 4- 0.15 
 
 4- 0.3 
 
 a 2 Librse .... 
 
 54 
 
 4- 1.50 
 
 4- 1.10 
 
 + 0.52 
 
 4- 0.48 
 
 4- 0.7 
 
 a Scorpii . 
 
 64 
 
 4- 1.75 
 
 4- 0.84 
 
 4- 1.21 
 
 
 4- 0.2 
 
 a Piscis Australia . 
 
 69 
 
 4- 0.81 
 
 4- 0. 97 
 
 4- 0.26 
 
 - - 
 
 4- 0.8 
 
POSITIONS OF FI'NDAMKNTAL STARS. 45 
 
 Ccrl ain features of these comparisons may at t met attention. Commencing with the last column, 
 \\c lind that the discordance between the results of the mural and the transit circle exhibits the 
 same curious property with the discordance between the direct and reflection observations with the 
 transit circle, namely, that instead of varying continually it is scarcely sensible, accidental errors 
 exceptcd. from the pole to the xeuith, and that it there suddenly acquires a sensible value, which it 
 retains with no change, except a slight diminution through the remainder of the arc within which 
 observations are included. Comparing this result with the difference between the latitudes given by 
 the two instruments, namely, 0".4S,* we find the general result to be that the zenith distances 
 measured with the transit circle are constantly greater than those measured with the mural by a bout 
 half a second of arc, whether the measure be made north or south. The variations from this law 
 are hardly greater than maybe due to the errors of division of the mural circle and the accidental 
 errors of observation. 
 
 This phenomenon is the more interesting that it gives us an instance of those systematic dis- 
 cordances between the polar distances of stars given by different authorities occurring in the case 
 of two instruments in the same building under similar atmospheric conditions. So far as I am 
 aware, Faye is the only astronomer who has ever framed a general theory to account for these dis- 
 cordances. He has attributed them to undetermined flexure of the instruments and local refrac- 
 tion, and has presented a number of ingenious devices for determining an instrumental flexure of 
 
 the form 
 
 2 sin 2Z -(- 6 2 cos 2Z + 03 sin 3Z + etc. 
 
 The existence of any flexure other than that of the form 
 
 a sin Z + b cos Z 
 
 seems to me highly improbable. A well fitted instrument niay be regarded as a solid body, held in 
 equilibrium by the opposing forces of gravity on the one hand, and the action of the counterpoise 
 roller on the other. And that must be a very badly made instrument in which the effect of the 
 latter action in altering the relative positions of the eye-piece and object-glass is different from 
 what it would be if, as the instrument revolved, it always acted rigorously upon the same particles 
 of the instrument like that of gravity. 
 
 It is also laid down by physicists as an observed law of matter that the change of form which 
 a body undergoes through the operation of a force, which is only a small fraction of the rupturing 
 force, is proportional to the intensity of the force. 
 
 Now, from the two hypotheses, (1), that a revolving body is held in equilbrium by opposing forces 
 always acting in the same direction and on the same parts of the body ; and, (2), that the change of 
 position is proportioned to the force, it follows rigorously that the small change of positioli of any 
 part of the body relatively to any system of co-ordinate axes revolving with it is of the form 
 
 sin Z + b cos Z 
 
 without any terms depending upon the multiples of Z. This proposition is demonstrated in the 
 Description of the Transit Circle, 40, 41. 
 
 Iii applying this hypothesis to an actual instrument it is presupposed that all the parts of the 
 latter which are in contact in one position are equally in contact in every other 'position.t There 
 must, therefore, be no play between the parts of the instrument. If these hypotheses are not 
 applicable, the flexure will be altogether irregular, and not capable of representation by a periodic 
 series unless we take an immense number of terms. 
 
 * The latitudes arc as follows : 
 
 o / a 
 
 From mural circle observations, 1861-64 38 53 38. 78 
 
 From transit circle observations, 1866-67 38 53 38.30 
 
 t An an example of the failure of this hypothesis, suppose the body A B turning P 
 
 round O, and sawed nearly through at P. If, in the position represented, the surfaces ^ " Q~~| ~ g 
 
 of P'were separated by the weight of the end B, while in the reverse position they 
 
 were pressed into contact by the same weight, then the law of flexure would not apply, as there would be a break in its 
 continuity at those points of the revolution where the contact and separation of the surfaces occurred. 
 
46 POSITIONS OP FUNDAMENTAL STARS. 
 
 Moreover, the preceding comparisons of the polar distances deduced from the observations of 
 Pulkowa, Greenwich, and Washington, as well as the comparison of direct and reflection observa- 
 tions made here, seem to render the existence of flexure depending on the multiples of Z very 
 improbable, there being an arc of 40 or 50 through which no well marked change occurs. 
 
 That the difference in question is due to local refraction seems improbable from the similarity 
 of the circumstances in which the two instruments are placed. But there is an alfied cause which 
 may not have been without effect. The differences of external and internal temperature which 
 give rise to loctil refraction are due to the difference between the temperature of the external air 
 and that of the walls, floor, and roof of the observing room. Astronomical instruments are thus 
 subjected in rapid succession to radiation from a roof heated by the sun, to accidental currents of 
 warm air from the heated roofs and walls, and to currents of cool external air. The possible effect 
 of these causes on the instrument maybe judged from the circumstance that if one end of the tube 
 of the transit circle telescope were unequally heated, so that one side of it should be one degree 
 Fahrenheit higher than the other, such heating would alter the pointing by 3". The only reason I 
 have to believe that this cause did not act injuriously, is that the results of day and night observa- 
 tions, when it acted in opposite directions, do not appear to exhibit any great systematic discord- 
 ances. 
 
 During the year 1869 the transit circle was mounted in a new observing room which was 
 designed with especial reference to securing the nearest possible equality of the internal and exter- 
 nal temperatures. 
 
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