UC-NRLF CM GO r r- UJ BOOKS WITH CARE. Per.. Date 'af FROM THE OXFORD UNIVERSITY PRESS, CORNER, LONDON. I With the Compliments of the Delegates of the Prefi Oxford REDUCTION OF THE OBSERVATIONS MADE BY BRADLEY AT KEW AND WANSTED, TO DETERMINE THE QUANTITIES OF ABERRATION AND NUTATION. BY DR. BUSCH, // ASSISTANT ASTRONOMER AT THE ROYAL, OBSERVATORY OF KONIGSBERG. OXFORD, AT THE UNIVERSITY PRESS. MDCCCXXXVIII. Astronomy GIFT REDUCTION "V OF BRADLEY'S OBSERVATIONS. V/F Bradley's original observations on Aberration and Nutation, those results only were known which Bradley himself published in the Philosophical Transactions (No. 406. vol. xxxv. p. 637. and No. 485. vol. XLV. p. 1). It was known, how- ever, that these observations were very complete; and it was supposed that a strict and accurate discussion of them would give the values of the constants of Aberration and Nutation with greater exactness, than had hitherto been attained : for, though Bradley himself had gone through the investigation, yet on account of the more extended developement, which the theory of Nutation has undergone in later times, and the recently invented methods of deducing the most probable results from observations, there was reason to expect that we might now obtain much greater precision. A wish was therefore expressed (Bessel " Fundamenta Astronomia? pro anno 1755," p. 122) that this series of observations, which had been lost sight of for nearly a century, might again be brought forward. This wish has been gratified by professor Rigaud of Oxford, who had the good fortune to discover, among the books of the late professor Hornsby, a great many papers of Bradley, and among them the original observations for Aberration and Nutation. Mr. Rigaud thereupon imparted his discovery to astronomers in a work, containing much valuable information relating to Bradley, published at Oxford, in 1832, under the title of " Miscellaneous Works and Correspondence of the reve- rend James Bradley." This work contains not only the observations made by Bradley at Wansted, but those also which had been instituted at an earlier period by Molyneux at Kew, and continued there by Molyneux and Bradley conjointly. It contains likewise all the data requisite for a complete investigation of the con- stants of both elements, resulting from Bradley's observations. The Royal Society of Sciences of Copenhagen were therefore induced to pro- pose, in 1832, as the subject of their prize, " Observationes Bradleyanas, hoc anno Oxonii editas, ad calculos revocare, et in illarum vim inquirere." This prize question gave rise to the following inquiry. The above-mentioned work of Mr. Rigaud contains an account drawn up by Molyneux himself of his instrument at Kew, from which I shall extract such B 287 2 REDUCTION OF portions as are necessary for understanding the observations. The instrument was constructed for observing those stars only which passed very near the zenith, especially 7 Draconis, which, besides possessing this advantage, is sufficiently brilliant to be visible in the day-time. This instrument, which Molyneux erected at his house at Kew, to repeat the earlier but unsuccessful experiments of Hooke, was a telescope, made by Graham, fixed in the direction of the zenith, and pro- vided with means for measuring variations of zenith distances of stars a . To the object-end of the telescope there was attached a strong ring of brass, from which proceeded the pivots on which the instrument moved. Both pivots were of the same length and thickness, and their common axis passed through the centre of the object-glass. The supports for the pivots were fixed to the chimney wall of the house, which was built of brick, and 300 years old. The pivots were so contrived as to admit of being made perfectly horizontal, and of being moved in a direction perpendicular to the meridian. On the side of the telescope, to the west, hung the plummet, attached to a silver wire, which passed down the whole length of this side of the tube. On the telescope itself, at the part where the cross wires were inserted, there was screwed a small brass plate, bearing a black dot. The measurements depend on the supposition that, when the telescope has been so placed that the plumbline bisects the above-mentioned dot, its optical axis always preserves the same position with respect to the horizon. In the lower room, into which the eye end of the telescope passed, there was fastened to the same strong chimney wall a frame work, to which was attached a micrometer screw, by which the telescope could be moved in the direction of the meridian, and brought immediately upon the star : a weight suspended by a string, which passed over a pulley, always caused the telescope to bear against the screw. Prior to any observation, the telescope was so placed, by means of the micrometer screw, as to make the plumbline bisect the fixed dot ; it was then moved, (also by the micrometer screw,) so that the star about to be observed might run along the wire stretched in the direction of its diurnal motion. The number of revolutions made by the micrometer screw, between the position in which the plumbline bisected the fixed point, and that in which the wire of the telescope was brought on the star, was the quantity to be observed. In order to convert the number of revolu- tions into seconds, it was ascertained that 42 revolutions of the screw were equal to an inch, and that the focal length of the object-glass was 24 ft. 3.15 in. : hence it follows, that the value of one revol. = 16".86785. The head of the screw was 16" 86785 divided into 17 equal parts, each one of which therefore = - =0".992226. a For a description of this instrument, see " Miscellaneous Works and Correspondence of Bradley." p. xiv. and p. 96, note c : also Smith's Optics. [EDITOR.] BRADLEY'S OBSERVATIONS. 3 The examination of the position of the fixed dot with respect to the plumbline was generally repeated after the observation. To avoid parallax in placing the fixed dot under the plumbline, a small lens of 1.5 inch focal length was made to bear upon the plumbline. It is clear from this description, that an alteration in the position of the brick work, on which the apparatus was fixed, could have no effect on the observation. I will illustrate the method of observing by an example. On the 1st of Jan. 1726, [N.S.] 7 Draconis was observed. Before the observation, when the plumbline bisected the fixed dot, the index stood at 8.00 ; after the observation, at 8.33 : the mean therefore = 8. 17. After the telescope had been directed to the star, the index pointed to 11.75. The difference between the two readings = 3.58 divisions ( = 3". 55) gives the distance of the star from that point of the heavens to which the axis of the telescope was directed when the fixed dot was bisected by the plumbline. In this manner every observation made at Kew is recorded. The instrument was erected on the 7th of Dec. 1725, and the first observation was made on the 14th of Dec. Little reliance, however, is to be placed on the observations before the 29th of Dec. ; for on that day the deviation of the star's path, through the telescope, from the horizontal wire was noticed for the first time, and care was taken afterwards, on that account, to bring the star upon the wire at the instant of culmination. The series of observations commences then on the 1st of Jan. 1726, and ends on the 9th of Jan. 1728. During this period we find 83 observations of 7 Dra- conis, 7 of a Persei, 12 of a small star in Auriga, and 5 of Ursae majoris. Bradley not having succeeded during the observations at Kew in finding an explanation of the variation of the zenith distances of stars indicated by the observations, proceeded to determine the amount of those variations more accu- rately, by means of new observations directed to a greater number of stars. But as there were only a few stars, of sufficient brightness to be seen in the day- time, within the range of the instrument hitherto employed, he induced Graham to construct another, with which he might be able to observe all the stars com- prehended in a zone of 12^, having the zenith point for its centre. This instru- ment (the first specimen of a zenith sector) was not erected at Kew, but at Wansted. Bradley's zenith sector had, for the most part, the same construction and apparatus as Molyneux's instrument ; with this difference, however, that instead of the dot fixed on the telescope of the latter, in Bradley's instrument the divi- sions of an arc, attached to the telescope, graduated to every 5' as far 12^, were used for the same purpose. The graduation was so contrived, that the readings of the arc corresponded nearly with the polar distance of the observed star. The REDUCTION OF object-glass was 12 ft. 6.6 in. in focal length ; and the eye-glass, always used, 2.2 in. The head of the micrometer screw was divided into 34 equal parts. To determine the value of one revolution of the screw in seconds of arc, Bradley measured with the zenith sector, on the 14th of Sept. 1747, the difference of the apparent zenith distances of the two stars /3 and 7 Draconis, and found it 103 rev. 26.8 div. of the screw; at the same time, the same distance, according to the mural quadrant, was = 58'. 9"-5 : hence, // Ca-i o '^ 1 rev. = 34 div. = 33".6213, and 1 div.= 34 = 0".98886. The first observation with this instrument was made on the 30th of Aug. 1727, on the star 7 Draconis. Before the observation, the sector was so placed that the point answering to 38. 25' on the graduated arc exactly coincided with the plumb- line, and the index of the micrometer screw pointed to 18 rev. 31.0 div.: at the place of the star the index marked 21 rev. 1.6 div. So that the star was south of the point in the heavens, which corresponded to 38. 25' on the graduated arc, by the difference of the two readings, viz. 2 rev. 4.6 div. = 1'. ll // .79- The ob- served polar distance of the star, therefore, inclusive of refraction and error of collimation, = 38. 26'. 11 ".79. In this way is given the result of every individual observation, made from the 30th of Aug. 1727 to the 14th of Sept. 1747. The following list contains the names of the stars observed, and the number of observations of each, made during this period. Names of Stars. Numb, of Observ. Names of Stars. Numb. of Observ. Names of Stars. Numb. of Observ. X Cassiopese 42 108 8 18 1 19 4 2 2 17 58 65 79 44 21 222 36 36 44 23 13 Lyncis t Ursae maj. f 9 9 10 10 50 24 11 54 2 129 9 133 17 166 247 70 61 315 7 9 * Cygni 17 5 16 12 17 12 8 4 14 3 18 6 3 3 1 16 4 10 19 107 a a J a lir . eh . . . * a Y Andromedae 4 Persei h P * 3 y a -^^~ 8 9 Aurigae 18 Camelopardi 8 Aurigae 35 Camelopardi 46 Aurigae & 3 Lacertae 3 Andromedae 7 T Cassiopeae d < Persei ft Cassiopese * The same as 34 Cass. [EDITOR.] BRADLEY'S OBSERVATIONS. 5 Bradley, who had probably discovered the true explanation of the phenomena of Aberration and Nutation as early as the year 1728, and observed that the first comprehended an annual period, the latter a much longer one, (about 20 years,) might have perceived, that, although the Kew observations were sufficient for the determination of aberration, it was necessary to continue them in order to deter- mine the constant of Nutation. A great many observations, however, were made at Wansted, which might serve for determining the amount of Aberration, and its effect on a greater number of stars than were observed at Kew. This is particu- larly the case at the beginning of the series. But when Bradley considered, as he had every right to do, that he had obtained the amount of Aberration with great precision, by the observations undertaken for that purpose, he contented himself, for the most part, with observations made at a particular time of the year. These he continued to the year 1747 ; thus extending them over a complete period of the Nutation. For this purpose he always left Oxford (where he filled the astro- nomical professorship) for Wansted ; for it would have been injudicious to have taken the sector to Oxford, as thereby the relation of the observations to one zero point on the graduated scale would have been lost, and the termination likewise of the period of Nutation would have been thrown somewhat later. II. I now proceed to describe the manner in which I have discussed the ob- servations. First, I have reduced all the observations to one epoch ; for which I have selected the beginning of the year 1730. The auxiliary tables requisite for this purpose, containing the corrections for Precession, Aberration, and Nutation, which I shall annex to this memoir, I have computed in the following manner. (1) The mean places of the observed stars, for the beginning of 1730, were computed by the formula in the Fundamenta Astron. p. 136. Loc. 1730 = loc. 1755-25 />-- (/-/ In which p and p' denote the annual precession for 1755 and 1800, according to the formula Tab. Reg. [16] ; M the annual proper motion in declination. I have obtained the values of /* by comparing the places given in the Fundam. Astron. with more recent ones. If a star, observed at the Konigsberg observatory, is to be found in the Catalogue of Declinations published in the 7th vol. of the Konigsberg Observations, then the place there given for 1820 was selected as the basis of the determination of M- If it be not found there, but is contained in Pond's catalogue for 1828, then its determination depends on a comparison with c 6 REDUCTION OF Pond's place. If it be not found in that catalogue, then / was determined by comparison with Piazzi's declination for 1800. The mean places are as follow : Names of Stars. Annual Precession for 1730. Declination for 1730. Annual proper Motion. Names of Catalogues. X Cassiopeae 4 15 55.5 Con si fi 53 ]'36!'09 CC Q t\ QQ + 0.'l38 On AH Piazzi T Persei 38 49 57.4 41 21 4H fi 51 37 56.46 so 05 1712 -0.045 it hi Pond y .. a s 46 18 21.4 50 57 40 Q 48 52 15.84 4fi 5*i ^4 ot -0.050 Omo Bessel Prnrl 9 Aurigse 18 Camelopardi 8 Aurigse 35 Camelopardi 71 24 23.0 74 12 5.2 77 22 41.0 84 19 51.2 85 46 16.1 91 1185 51 11 51.66 45 41 0.71 56 58 59.19 54 12 58.30 51 32 10.54 49 23 4 5 -0.216 -0.419 -0.232 + 0.160 -0.067 001 Piazzi Bessel Piazzi Pond Piazzi ft Ursse maj. llr 161 19 48.6 163 35 14 1 57 49 25.75 45 57 28 21 -0.371 0077 Pond r 174 52 5.4 i on in J.Q 55 11 44.26 K*7 OK Plfi QQ -0.020 OflKA Bessel f 1OQ 14 5Q 5 fi Oft Q7 CQ 009. \ >? j3 Draconis t Herculis 204 12 52.4 261 5 16.6 262 57 28.2 2fi7 11 105 50 40 16.33 52 30 50.45 46 9 54.81 5fi 55 29 12 -0.024 -0.005 + 0.013 i nco Bessel Pond 9fi7 ^ 111 Kl 00 JQ n n^fi n i /3 Cassiopeae 358 44 56.9 57 39 36.87 -0.203 Pond Let us denote the value of the annual precession in declination for 1730 by 20".06636. Cos. R. A. 1730, and the annual proper motion by m ; then the mean declination for the epoch 1730 + * = Dec. 1730 + tm + it . t E 90 in which p'p was taken from the Fund. Ast. Table I. of the Appendix contains the value of tm + tt . - 1- } according to this formula, for the beginning of every year from 1727 to 1747, and for every star, when all whole numbers from 3 to + 17 are substituted for t. The continuation of the same table gives, moreover, the mean motion for every 10th day of the year, or the value of rm ; where log. T is taken from Tab. 7. of Tab. Reg. (2) If in the formulae for Nutation, first given in Fund. Astron, p. 127, and afterwards amended b , viz. AL={(-18!'0377 sin. Q +o'21720 sin. 2 S3 -0^21633 sin. 2 5 ) .(1 +>)} -(l"l3640-2'86868) sin. 2 O A={(+ 9.6480 cos. S -0.09428 cos. 2 S3 +0.09391 cos. 2 ]) ) .(1 +0} + (0.49330-1.24527 ) cos.2 b Bessel in Schumacher's Astronomische Nachrichten, Nos. 34 and 83. BBADLEY'S OBSERVATIONS. 7 we make t= 0".069541, according to the calculations of Lindenau, then the above becomes changed into c AJL= 16J8332 sin. 8 + 0/20209 sin. 2 8 1-33589 sin. 2 (K20128 sin. 2 ]) A <*>= + 8.97707 cos. S -0.08773 cos. 2 8 +0.57990 cos. 2 O +0.08738 cos. 2 J . I have denoted the true value of the coefficients of the first term of the expression for A w by S". 97707 (1 + i') ; whence !+ = (!- 0".069541) . ( 1 + i'), or i=- 0".069541 + 0.930459 i' : and the above formula, if instead of being expressed in terms of i, be expressed in terms of i', becomes, Aa>={ -^'.OTTO? cos. Q -0".08773 cos. 2 8 + 0".08?38 cos. 2 ]) } . (l + t') + 0".57990 . (l-1.998i'.) cos.2 0. It will therefore be necessary to multiply the terms of the formulae in the Tab. Reg. by 1 +i' if they depend on the moon, and if on the sun by 1 + 1.998i', or, without sensible error, by 1 + 2z*. In Tab. Reg. [23] we have the formula for the effect of Nutation in de- clination : f 6.68299 sin. 8 cos. + 8.97707 cos. 8 sin. al \ +0.08046 sin.2 8 cos. a 0.08/73 cos. 2 8 sin. a I . (1 +t") [0.08015 sin.2 ]) cos. a +0.08/38 cos. 2 ]) sin. aj + { 0"53194sin.20cos.a+o'.57990cos.2O sin.a} . (l-2f) This formula is derived from the expressions for AZ/ and Aw, when the value is assigned to the obliquity of the ecliptic which it had in 1800. But as the observations to be compared with it were made at a much earlier period, a slight alteration must be made in those expressions, by substituting, for the value there assumed, the obliquity of the ecliptic for 1730 = 23. 28'. 26".8. Thus the formula for Nutation becomes, r_6.'680/9 sin. 8 cos. a+8'.97646 cos. 8 sin. al \ +0.08048 sin. 2 8 cos. a 0.08776 cos.2 8 sin. a I . (1 +") [ 0.08017 sin. 2 J) cos. a + 0.08741 cos. 2 ]) sin. a j + {-0!'53210sin.2Qcos. o + 0"58011 cos.2Q sin.a} . (l-2") Table II. of the Appendix has been computed according to this formula. It gives the amount of that part of Nutation, which depends on the place of the moon's node, for five times in every year, viz. for the beginning, and for 100, 200, 300, 400 sidereal days after. Following the example of Tab. Reg., the year is supposed to begin when the sun's mean longitude = 280. The rule for computing the argument for entering the table is also the same as that explained in Tab. Reg.; c Tab. Reg. [21.] 8 REDUCTION OF for which reason it will not be repeated here. The following table contains the fraction by which the date of the day of observation is to be corrected : 1725 + 0.071 1737 + 0.166 26 -0.170 38 -0.076 27 -0.412 39 -0.319 28 + 0.346 40 + 0.439 29 + 0.104 41 + 0.197 30 -0.139 42 -0.045 31 -0.381 43 -0.287 32 + 0.377 44 + 0.470 33 + 0.135 45 + 0.228 34 -0.107 46 -0.014 35 -0.350 47 -0.256 36 + 0.408 48 + 0.502 The part of Nutation, which depends on the sun's longitude, I have inserted by itself in Table III. For as the unknown quantity i' does not influence the values of the two parts of Nutation, depending on O and 8 , in the same proportion, it was necessary to compute each part separately. If we denote the part depending on & by , and that depending on O by ', then the amount of the quantities taken from Tables II. and III. is equal to + '; and if the effect of i' be added thereto, it is equal to + ' + ( + 2') i'. The sun's longitudes used in computing ', and which have also been used in computing the Aberration, were communicated to me through the kindness of professor Bessel. / Table of the Sun's Longitude. 1730. 1750. 1730. 1750. Jan. 280 3 49.69 280 3 7'.45 July 9 106 29 24"43 106 30 5.07 10 290 13 42.39 290 13 0.18 19 116 15.47 116 55.36 20 300 22 50.90 300 22 10.04 29 125 32 5.53 125 32 43.57 30 310 30 39.19 310 30 0.95 Aug. 8 135 5 24.78 135 5 59.89 Feb. 9 320 36 34.17 320 35 59.72 18 144 40 41.26 144 41 12.44 19 330 40 6.80 330 39 37.16 28 154 18 20.25 154 18 46.61 Mar. 1 340 40 52.93 340 40 28.97 Sept. 7 163 58 43.62 163 59 4.35 11 350 38 34.16 350 38 16.54 17 173 42 8.98 173 42 23.42 21 32 58.11 32 47.29 27 183 28 49.22 183 28 56.90 31 10 23 58.58 10 23 54.81 Oct. 7 193 18 51.80 193 18 52.42 Apr. 10 20 11 35.61 20 11 38.93 17 203 12 18.44 203 12 11.91 20 29 55 55.05 29 56 5.29 27 213 9 4.78 213 8 51.21 30 39 37 8.36 39 37 25.15 Nov. 6 223 9 0.15 223 8 39.89 May 10 49 15 31.88 49 15 54.69 16 223 11 47.81 233 11 21.42 20 58 51 26.27 58 51 54.42 26 243 17 5.18 243 16 33.42 30 68 25 15.97 68 25 48.62 Dec. 6 253 24 24.57 253 23 48.39 June 9 77 57 28.32 77 58 4.54 16 263 33 13.86 263 32 34.36 19 87 28 32.90 87 29 11.68 26 273 42 57.80 273 42 16.21 29 96 59 0.95 96 59 41.22 36 283 52 59.01 283 52 16.63 BRADLEY'S OBSERVATIONS. 9 (3) The formula for the effect of Aberration in declination is the well known one d , 20".255 {sin. <* sin. 8 cos. a cos. 8 sin. <*} cos. Q 20".255 cos. a sin. 8 sin. O* which also in this case, where the amount of the constant of Aberration is not supposed to be known, but is to be determined from the observations, must be multiplied by a factor containing an unknown quantity; which factor I will denote by 1 + K. Table IV. of the Appendix, relating to this point, has been computed by assuming values of , S, to for 1730 as well as 1750 ; and the variation of Aberra- tion in 10 years, given in the same table, was obtained by comparing both results together. On this subject also I need not enter into farther detail, as both the explanation and example in the Tab. Reg. are exactly to the same effect. Let the Aberration taken from the table be denoted by /3, then, when corrected by being multiplied by 1 + K, it becomes /3 + /3/r . Therefore, in order to reduce an observed polar distance to its value, at the beginning of 1730, cleared of Preces- sion, Proper Motion, Aberration, and Nutation, we must apply thereto, Precession + Proper Motion + + a' + @ + (a 2 a') i' + /3/c. Let us denote the mean value of the same, such as all the observations of a star afford, when the proper values of i' and K are assumed, by P x, where P is a quantity near the truth, and x a small correction to be deduced from observation ; then the reduced observation gives an equation, = observed pol. dist. + Prec. + Prop. Mot. + or, expressed more briefly, Q I have, from every individual observation, obtained equations of this form, which are contained in Table V. Since I have considered the lunar and solar Nutation, as well as the Aberration, separately, it was not necessary to introduce the coeffi- cients of i' and K into the tables at all. III. Having given the formulae and quantities used in reducing the observations, I proceed to explain how I combined the equations obtained from them, in order to deduce the two final equations, from which there results the most probable amount of both corrections, for the assumed constants of Aberration and Nutation. A closer examination of the series of observations left by Bradley shews it to be extremely accurate, and that the observations themselves, as the result proves, d Tab. Reg. [27.] D 10 REDUCTION OF are very accordant one with another. Even in the present day a series of observations better adapted to the object in view could not be made. Perhaps the only alteration to be desired is, that the property of reversion had been given to the sector, whereby we might have been altogether independent of any varia- tion in the line of collimation. We should, however, form an erroneous judg- ment, were we to suppose the sector's continuance in one position to have been productive of uncertainty in the results ; partly, because, during the twenty years through which the observations were carried on, there is scarcely one remarkable alteration in the line of collimation ; and partly, because Bradley used to observe stars differing from each other 180 in R. A. in order to detect any important effect, which might be produced by change of position of the instrument. For in stars thus situated opposite to each other, the corrections both for Aberration and Nutation have contrary signs. In order to determine the variation of collimation, I have divided the whole time including the observations into four periods, and have assumed the error of collimation during each of these periods as constant. These periods are as follows : 1st period from 1727 to 1731 2d 1732 1735 3d - 1/361740 4th - 1741 1747 Let the variation which the line of collimation underwent in the last three periods from the position which it held during the first period, be denoted by y, y\ y", then from each observation, according as it was made in the 1st, 2d, 3d, or 4th periods, there results an equation of this form : Now from all the preceding observations (except such as Bradley himself marked as doubtful) I have deduced equations, by the method of least squares, for determining the six unknown quantities i, K, a, y, y', y", which are as follows : 0=( ) + ()* + (O y + (m 3 ) y' + (m 4 ) y" + (a ) f + ( b ) < In which the notation, which, after the example of Gauss, is usually adopted to express the sums generally, if it appear with an index subscribed, refers to the BRADLEY'S OBSERVATIONS. 11 sums of the observations made within each of the periods specified by such index ; but if there be no index, then it refers to the whole of the observations. I have computed the values of all the coefficients occurring in these equations from the observations of every individual star, and I give them in order in the following table : Names of Stare. Periods () () (*) (on) (*) (at) (aa) (64) () (m) a Auriga I. + 4.24 + 1159.20 - 199.00 + 49.33 + 264.32 -1182.66 8953.11 6856.20 254.15 153 II. + 26.73 + 11-71 - 46.26 + 32.92 + 104.16 + 389.61 425.56 1530.66 78.69 32 III. + 2.00 - 89.80 + 68.33 - 17.89 + 34.16 - 474.07 627.29 639.93 35.47 13 IV. + 10.28 - 15.26 + 20.85 - 37.39 + 62.16 - 90.50 66.46 196.25 30.99 4 Sums + 43.25 + 1065.85 156.08 + 26.97 + 464.80 - 1357.62 9072.42 9223.04 399.30 202 V' Ursae maj. I. + 6.06 + 5.17 - 98.19 + 14.44 -167.90 - 146.79 25.35 2026.48 30.32 21 i Herculis I. + 24.59 - 450.26 + 265.41 -187.08 + 134.12 -1766.63 3302.06 15165.21 107-35 64 8 Persei I. -12.60 + 266.21 + 140.37 - 91.42 -111.39 + 722.90 2055.39 2734.76 37.80 35 a Persei 1. -34.31 + 408.53 + 30.13 -271.08 - 2.81 + 276.33 3186.03 4886.80 63.35 53 II. - 0.05 + 24.71 + 35.07 + 8.34 + 27.04 + 358.16 167.82 900.63 1.73 7 III. + 3.01 - 29.60 + 44.57 22.23 + 33.18 329.82 219.05 496.81 3.25 4 Sums -31.35 + 403.64 + 109.77 284.97 + 57.41 + 304.67 3572.90 5284.24 68.33 64 46 Aurigae I. + 16.29 + 158.00 + 48.23 + 130.38 + 81.56 + 364.90 1272.00 986.71 22.30 20 17 Ursae maj. I. -26.39 - 516.86 + 32.15 + 187.08 + 3.34 -2335.98 3219./6 13230.37 52.55 85 II. - 1.84 - 109.19 + 217.01 - 12.80 - 64.27 - 271.75 616.44 6296.71 16.82 28 III. -30.25 + 111.30 + 238.66 -190.47 -388.88 + 1414.02 692.69 3544.54 79.27 19 IV. + 0.69 + 42.23 + 191.50 5.16 + 6.41 + 528.62 520.16 2345.79 8.02 16 Sums -57-79 - 472.52 + 679.32 - 21.35 -443.40 - 665.09 4049.05 25417.41 156.66 148 9 Aurigae I. 0.94 + 146.12 + 90.09 - 11.09 - 35.90 + 741.50 1231.44 1018.55 11.85 17 II. + 0.64 + 6.03 + 29.33 + 0.90 + 5.24 + 57.98 35.73 287.00 0.16 3 III. + 0.34 - 5.34 + 9.59 - 1.82 + 3.26 - 52.40 28.52 91.97 0.12 1 Sums + 0.04 + 146.81 + 129.01 - 12.01 - 27.40 + 750.08 1295.69 1397.52 12.13 21 y Draconis I. + 26.45 -1138.62 + 1021.45 215.96 + 553.88 -6226.26 8342.52 39927.15 77.61 166 II. + 7-78 + 91.57 + 514.6-2 - 54.91 + 95.97 + 1656.09 700.78 12819.94 38.24 48 III. -38.57 + 319.39 + 488.37 -298.08 -490.28 + 3953.89 2480.95 11845.41 70.40 42 IV. + 1.62 - 27.54 + 586.21 - 14.77 + 26.24 - 743.87 564.06 12303.46 15.78 35 Sums - 2.72 755.20 + 2510.65 -583.72 + 185.81 1360.15 12088.31 76895.96 202.03 291 35 Camelopardi I. + 14.48 + 239.54 + 48.70 + 89.29 + 53.96 + 519.32 1843.79 2071.26 29.93 32 II. + 0.39 + 2.33 + 8.60 + 0.91 + 3.35 + 20.03 5.43 73.96 0.15 1 III. + 1.07 - 28.72 + 34.85 3.48 + 8.43 - 203.49 171-38 255.90 1.82 5 IV. + 1.90 + 7.12 + 9.52 + 13.53 + 18.09 + 67.78 50.69 90.63 3.61 1 Sums + 17-84 + 220.2; + 101.67 + 100.25 + 83.83 + 403.64 20/1.29 2491.75 35.51 39 T Persei I. + 10.32 + 271.75 + 216.62 + 49.33 45.95 + 1648.70 1929.25 4170.36 46.77 39 II. + 0.82 + 36.04 + 88.62 + 2.1/ + 9.93 + 459.49 201.86 1123.12 1.53 7 III. + 4.25 - 37.5S - 0.09 - 32.77 + 53.04 - 478.28 282.55 812.14 9.82 B Sums + 15.39 + 270.21 + 305.15 + 18.73 + 17-02 + 1629.88 2413.66 6105.62 5fc.l2 51 y Persei I. + 4.46 + 291.81 + 321.07 + 32.63 + 96.9S + 1623.45 2616.15 4/50.53 33.40 40 II. + 3.67 + 28.1)9 + 63.93 + 20.36 + 47.30 + 370.72 171-57 817.62 4.07 5 III. - 4.17 - 45. H5 + 75.33 + 9.27 - 52.11 566.85 339.96 946.67 5.51 6 Sums + 3.9H + 275.64 + 460.33 + 62.26 + 92.1b 4- 142/. 32 312/.6f 6514.8? 42.1* 51 12 REDUCTION OF Names of Stars. Periods () () (*) (an) (4n) (ab) (aa) (bb) (nn) (m) # Draconis A. Cassiopese 8 Aurigae a Cassiopeae y Ursae maj. f Ursae maj. Draconis IsCamelopardi Ursae maj. j3 Cassiopeae Ursae maj. I. II. III. IV. + 128.0J + 25.49 + 43.27 + 9.48 992.56 + 68.33 + 239.03 - 16.53 + 781.99 + 592.10 + 393.07 + 521.47 -909.61 + 99.68 + 340.91 + 52.91 + 235.13 + 208.17 + 489.23 + 96.86 -4883.45 + 1198.02 +3272.65 - 388.28 7522.84 621.99 1982.57 585.37 34079.93 12162.93 9395.83 11339.79 203.41 44.21 71.06 27.21 137 42 30 31 Sums I. II. III. + 20(5.29 - 1(5.91 + 1.40 - 0.47 -701.73 + 111.85 + 25.30 - 11.74 + 2288.63 + 430.27 + 86.41 + 29.24 -416.11 - 68.26 + 2.24 + 2.43 + 1029.39 - 235.90 + 21.12 - 8.14 - 801.06 + 1716.96 + 357.18 - 171.56 10712.77 493.97 121.43 68.94 66978.48 6728.78 1254.45 427.84 345.89 23.07 4.33 4.70 240 31 6 2 Sums I. II. III. IV. - 15.98 - 1.84 - 1.81 + 12.73 + 7-85 + 125.41 + 189.24 - 3.23 - 32.34 + 3.30 + 545.92 - 60.91 + 9.16 + 40.41 + 18.54 - 63.59 - 14.54 + 5.84 - 82.60 + 16.64 - 222.92 + 21.73 + 16.57 + 95.08 + 73.52 + 1902.58 + 524.81 - 29.59 - 265.59 + 42.82 684.34 1411.96 10.43 210.31 66.17 8411.07 2255.45 83.91 342.59 174.33 32.10 19.20 3.28 33.44 31.04 39 26 1 5 2 Sums I. II. III. IV. + 16.93 + 0./9 + 0.23 - 1.45 + 3.01 + 156.9? +357.43 + 33.50 - 7-70 - 3.13 + 7.20 + 341.16 + 9.14 + 60.93 - 16.38 - 74.66 - 53.10 - 1.83 - 0.96 - 8.69 + 206.90 - 240.85 - 14.30 - 21.96 - 29.25 + 272.45 + 1489.99 + 30.95 - 114.97 + 105.46 1698.8/ 1661.52 175.17 82.91 49.74 2856.28 15589.94 1449.96 928.46 276.28 86.96 79.63 4.44 1.43 5.58 34 88 7 4 2 Sums I. III. IV. + 2.58 -!- 6.05 - 1.57 + 6.67 + 380.10 -115.22 + 1.07 + 35.35 + 394.85 + 102.95 + 11.15 + 61.21 - 64.58 - 8.86 + 3.01 + 32.92 306.36 + 116.98 - 6.05 + 99.65 + 1511.43 - 630.14 + 21.72 + 451.72 1969.34 349.61 22.95 258.10 18244.64 7823.05 73.25 943.48 91.08 46.22 1.89 18.57 101 50 2 8 Sums I. II. III. IV. + 11.15 - 17-08 - 7-61 - 8.07 + 30.98 - 78.80 -414.46 - 90.79 + 67.07 + 59.18 + 175.31 + 257.22 + 123.50 + 159.75 + 177-72 + 27.07 + 105.13 + 50.11 - 45.62 + 164.21 + 210.58 + 176.53 + 219.82 - 69.85 + 375.00 - 156.70 -1918.43 - 111.20 + 851.5! + 795.78 630.6( 2328.44 501.95 374.50 508.68 8839.78 13522.90 4949.63 2370.73 2254.86 66.68 63.63 31.91 53.76 82.35 60 76 21 13 15 Sums I. I. III. - 1.78 + 6.46 - 3.38 + 3.08 -379.00 -3/1.09 + 193.96 - 30.28 + 718.19 + 398.53 - 5.09 + 48.43 + 273.83 - 24.13 - 15.84 - 21.38 + 701.50 - 309.52 + 116.16 + 24.04 - 382.26 -2462.40 - 53.82 - 292.65 3713.57 2685.54 1571.01 187.88 23098.12 13045.07 2463.02 478.15 231.65 108.07 43.14 7.03 125 55 25 5 Sums I. II. III. IV. - 0.30 - 29.59 - 15.33 - 8.52 + 0.48 + 163.68 -340.66 -102.22 + 19.62 + 60.06 + 43.34 + 164.36 + 111.98 + 36.08 + 162.05 - 37-22 + 140.59 + 88.86 - 34.20 + 45.50 + 140.20 + 154.03 + 201.74 - 58.12 + 146.64 - 346.47 -1071.99 242.84 + 138.28 + 868.84 1758.89 1646.33 559.38 86.72 545.40 2941.17 14145.01 4643.90 268.65 2280.96 50.17 72.20 50.48 16.65 52.85 30 75 21 5 17 Sums I. II. HI. IV. 52.96 + 30.92 + 3.57 + 5.78 + 7-26 -336.20 + 259.63 + 35.33 - 9.96 4.95 + 474.47 + 340.69 + 39.94 + 77-58 + 8.32 + 240.75 + 156.21 + 19.46 - 21.32 - 6.27 + 444.29 + 811.78 + 86.70 + 90.49 + 16.70 - 307-71 + 963.89 + 232.83 - 153.08 - 72.79 2837.83 1036.72 182.46 105.96 57-47 21338.52 17251.88 1682.25 1204.35 94.89 192.18 117.05 7.26 10.67 29.38 118 85 7 5 2 Sums I. II. + 47.53 + 21.29 + 2.50 + 280.05 - 7-13 - 18.87 + 466.53 + 2.88 + 2.02 + 148.08 - 7-73 - 13.97 + 1005.6/ + 22.88 0.09 + 970.85 - 320.95 - 15.46 1382.61 77.65 121.31 20233.37 5314.54 4.?6 64.36 28.38 3.26 99 38 3 Sums + 23.79 - 26.00 + 4.90 - 21.70 + 22.79 - 336.41 198.96 5319.30 31.64 41 BRADLEY'S OBSERVATIONS. 13 According to this table, therefore, all the observations of any star, a. Aurigae for example, give the following equations : 0=+ 43.25+ 202.00x+ 32y + 13y' + 4y"+1065.85 * 156.08* 0=+ 26.73+ 32.00*+ 32y .... ....+ 11.71 f- 46.26* 0=+ 2.00+ 13.00* + 13 y 89.80." + 68.33* 0=+ 10.28+ 4.00* + 4y"- 15.26 " + 20.85* 0=+* 26.97 + 1065.85*+ 11.71 y-89.80y'- 15.26 y" + 90/2.42 i'- 1357-62 * 0= -1-464.80- 156.08*-46.26y + 68.33y' + 20.85y"- 1357.62 ? + 9223.04 * All the other stars give equations similar to these. The unknown quantity x, which occurs in these equations, is different for each star, and must be eliminated from the remaining equations by means of the first ; whence we have for each star the following expressions : a. Auriga. 0=+ 19.88+ 26.93y- 2.06y' 0.63 y"- 157-14 "- 21.53* 0= 0.78- 2.06y+ 12.16y'- 0.26 y"- 158.39 " + 78.37* 0=+ 9.42- 0.63y 0.26y'+ 3.92y"- 36.37?+ 23.94* 0= -201.24- 157.14y- 158.39 y' - 36.3? y" + 3448.57 "- 534.07* 0=+498.22- 21.53y+ 78.37 y' + 23.94 y"- 534.07 t" + 9102.44* \jr Ursa maj. 0=+ 12.95 + 24.08 1" 122.62* 0=- 139.56 .... - 1 22.62 i'+ 1567-37* i Herculis. 0=- 14.08 + 134.42 f+ 100.64* 0= +32.14 +100.64 ."+14064.54* 8 Persei. 0= + 4.42 + 30.57 "- 344.81 * = -60.86 -344.81 ."+2171.78* a Persei. 0=+ 3.38+ 6.24 y- 0.44 y' .... - 19.41 "+ 23.06* 0=+ 4.97- 0.44 y+ 3.75 / .... 54.83.'+ 37-71* 0=- 87.25- 19.44 y-54.83y' +102/.25?- 387-63* 0= + 111.18 + 23.06y + 37-71y' . - 387-63 ." + 5095.97 * 46 Aurigae. ()=+ 1.69 + 23.77 "- 16-13* 0=+42.28 -16.13. " + 870.40* jj Ursce maj. ()=+ 9.09+ 22./0 y- 3.60 y'- 3.03 y" 19.79."+ 102.11* 0=- 22.83- 3.60 y+ 16.56 /- 2.05 y"+ 171.96."+ 160.69* 0=+ 6.94- 3.03y- 2.05 /+ 14.27 y"+ 93.31.'+ 53.84* 0^-205.85- 19.79y+171-96y' + 93.31y" + 2540.43. v + 1273.87* 0= -206.26+ 102.11 y + 1 60.69 y' + 53.84 y"+ 12/3.87 ." + 22925.35 * E 14 REDUCTION OF 9 Auriga. 0= + 0.03+ 2.57 y- 0.14/ .... - 14.94*" + 10.90* 0=+ 0.34- 0.14y+ 0.95 / ____ - 12.33 i'+ 3.45 0=- 12.29- 14.94 y- 12.33 y 7 ____ + 269.33 '- 151. 82 * 0= -27.65+ 10.90 y+ 3.45 y' ____ -151.82 " + 604.98 K y Draconis. 0=+ 8.23+ 40.08y- 6.93y'- 5.77y"+ 216.14*' + 100.49* 0=- 38.18- 6.93y+ 35.94^- 5.05y"+ 428.39*' + 126.00* 0=+ 1.95- 5.77 y- 5.05 / + 30.79 y"+ 63.29*' + 284.23 * 0=-590.79 + 216.14y + 428.39y' + 63.29 y"+ 101 29.44*' + 5155.56* 0= + 209.28 + 100.49 y + 126.00 y 1 + 284.23 y"+ 5155.56 *" + 55234.92 K 35 Camelopardi. 0=- 0.07 + 0.97 y- 0.13y'-0.03y"- 3.32*' + 5.99* 0=- 1.22-0.13y+ 4.36 y'-0. 13 y" 56.96*" + 21.82 * 0=+ 1.44-0.03y- 0.13^ + 0.97^'+ 1.47 i'+ 6.91 * 0=- 0.51 -3.32 y-56.96 y 1 + 1.47 y" + 827.23 i' 170.59 K T Persei. 0=- 1.29+ 6.04y- 0.69 y' ____ - 1.05 *'+ 46.74* 0=+ 2.74- 0.69 y+ 4.51 y' ____ - 64.07 i'- 30.01 K 0=-62.81- 1.05y-64.07y' ____ +981.96i'+ 13.10* 0=-75.06 + 46.74y-30.01y' ____ + 13.10 i' + 4279.83 * y Persei. 0=+ 3.28+ 4.51 y- 0.59 y 1 .... + 1.97 "+ 18.80* 0=- 4.64- 0.59 y+ 5.29 y' .... - 77-59 i'+ 21.17 0= +40.86+ 1.97y-77.59y' ____ +1637.95 i'- 1060.62* 0= +56.44+ 18.80y + 21. 17 y' .... -1060.62 ? + 2359.82* )8 Draconis. 0=- 10.61+ 34.65 y- 5.25 y'- 5.43 y"+ 191.13'+ 193.16* 0=+ 17.48- 5.25y+ 26.25y'- 3.88y"+ 326.75t"+ 108.11* 0=- 17.17- 5.43y- 3.88^+ 27.00 y"+ 74.11 i'+ 218.02* 0= + 187.06+191.13y + 326.75y'+ 74.11 y" + 8661.01 z"+ 5864.23* 0= -930.05+ 193.16 y+ 108.1 1 y' + 21 8.02 y" + 5864.23 i' + 45325.52* \ Cassiopecc. 0=+ 3.86 + 5.08 y 0.31 y' ____ + 6.01 "+ 2.42* 0=+ 0.35-0.31 y+ 1.90/ ____ - 18.17*'+ 1.24* 0=-12.20 + 6.01y-18.17y' .... +281.07 i'+ 147 .08* 0=+ 0.77 + 2.42y+ 1.24 y' .... + 147.08 *' + 769.24 * BRADLEY'S OBSERVATIONS. 15 d Aurigas. 0=- 2.31 +0.97 y- 0.15 /- 0.06 y"- 7.85.'+ 8.95 * 0=+ 10.24-0.15 y- 4.26 /- 0.29 y"- 55.42 ? + 39.35 * 0=+ 6.85-0.06y- 0.29/ + 1.88y"- 5.93," + 18.12* 0=-152.83-7.85y-55.42y'- 5.93 y" + 9/4.1 7 i'+ 239.21* 0= +203.31 +8.95 y + 39.35/ + 18.12 y" + 239.21 ." + 2854.75* a Cassiopeae. 0=+ 0.06+ 6.51 y- 0.28y'- 0.14y"+ 7.16"- 18.23* 0=- 1.55- 0.28y+ 3.84 y - 0.08 y"- 22.75." + 45.29* 0=+ 2.96- 0.14y- 0.08^+ 1.96y" 10.66."- 24.20* 0=- 74.03+ 7.16y-22.75y'-10.66y" + 538.87*" + 25.43* 0=-316.17- 18.23 y + 45.29 /-24.20y"+ 25.43 i'+ 16700.98* y Ursa maj. 0=- 1.94 .... + 1.93/- 0.27 y"+ 3./Ot'+ 5.31* 0=- 8.20 ____ 0.27 y'+ 6.93 y"+ 45.86 i'+ 37.84* 0=+ 41.71 ____ + 3.70y' + 45.86y" + 527.17" + 37.54* 0= + 178.00 ____ + 5.31 y y + 37.84 y"+ 37.54 .' + 8327.54* f Ursae maj. 0=- 7.31 + 17-47y- 2.18/- 2.52y"- 27.12T+ 2.84* 0=- 7.88- 2.18y+ 11.65y'- 1.56y"+ 106.48.'+ 85.06* 0=+ 31.19- 2.52y 1.56/+ 13.20y"+ 104.66f+ 91.54* 0= + 268.43-27.12 y + 106.48 y'+ 104.66 y" + 2564.44 '+ 1795.29 0=+7H./3+ 2.84y+ 85.06/+ 91.54y"+1795.29.' f Draconis. 0=+ 19.46 ............ +181.72."+ 226.54* 0= -356.33 ............ +226.54 ."+10157 .33* 18 Camelopardi. 0=+ 3.13 ____ + 4.17/ ____ - 57.55 v + 41.21* 0=- 35.58 .... -57.55 / .... +866.25."- 582.88* 0= + 140.63 .... +41.21^ .... - 582.88 v + 2878.56* e Ursce maj. 0=- 5.90+17-26y- 0.89^- 3.03y"- 42.39."+ 27-54* = 6.28- 0.89y+ 4.79/- 0.72 y"+ 33.87*"+ 15.98* 0=+ 8.11- 3.03 y- 0.72 /+ 14.55 y"+ 108.50."+ 93.69* 0=+ 89.86- 42.39 y + 33.87 /+ 108.50 y" + 1879.93."+ 1044.13* 0= +657.24 + 27.54 y + 15.98 /+ 93.69 y"+ 1044.13 ," + 19430.69 * ft CassiopecE. 0=+ 0.21+ 6.51 y- 0.35y'- 0.14y"+ 15.50f+ 6.95* 0=+ 3.35- 0.35 y+ 4.75y-- 0.10 y"- 24.13."+ 54.02* 0=+ 6.30- 0.14y- 0.10y'+ 1.96y"- 10.62,"- 1.11* 0=+ 13.41 + 15.50y-24.13y'- 10.62 y" + 587.88,*- 350.97* 0= + /81.69+ 6.95y + 54.02y'- 1.11 y"- 350.97 ."+18034.92* 16 REDUCTION OF /3 Ursa maj, ()= + 0.76+ 2.78 y - 16.97 '+ 1.66 0=- 6.61-16.97 y + 1 82.47 i'- 333.30 0= + 19.93+ 1.66 y -333.30 f + 5318.71 K These equations for all the stars, being added together, give the following equations, indicating the most probable values of y, y , y" i', K : 0=+ 21.29 + 201.27 y- 23.99y'- 20.78y"+ 127.90*"+ 511.85* 0=- 42.70- 23.99 y+ 183.54 y'- 14.39 y" + 468.96z' + 814.75 K (2) 0=+ 49.79- 20.78 y- 14.39 y' + l 17.43 y"+ 427.62 ? + 802.82* 0=- 780.22 + 127.90y + 468.96y' + 427.62y" + 38319.88z'+ 11867.18* <)= + 1568.24 + 511.85 y + 814.75 y' + 802.82y" + 11867. 18 j' + 269274.07* If from these we eliminate y, j/ t y", we have the two following equations for determining i f and K : 0=- 858.50 + 34292.73 f+ 4146.80 K (o) 0= + 1372.76 + 4146.80 i' + 254099.40 * and hence, i'=+o'.0257382 K = -0.0058255. If we substitute these values in the expressions before given, viz. i= -0".069541 + 0".930459 i', and the Constant of Aberrat. = 20".255 (l + c), then we have i=- 0.045593; and consequently the formulae for Nutation for the beginning of the year 1800 becomes, AZ,= -17.'2152 sin. a + 0"20/30 sin. 2 Q- 1. 267 19 sin. 2 Q -0.20647 sin. 2 J A a>= + 9.2080 cos. S3 0.08998 cos. 2 Q +0.55008 cos. 2 Q +0.08963 cos. 2 5 and the Constant of Aberration = 20".l 371. In the same way I have obtained equations of conditions for i' and K from observations of 7 Draconis made by Bradley and Molyneux at Kew, and found 0=+ 9.72+ 64.00.r- 553.04 i'+ 356.54 K = -70.96-553.04.r + 4831.39i'- 2/60.35 it 0= +47.01 +356.54 x--276Q.35i'+ 10825.15 K and by eliminating x, 0= + 13.03+ 52.39 '+ 320.65 K ' 0=- 7. 14 + 320.65 i' + 8838.85 K As all these observations were made within the space of a year, they are but of little use in determining the Nutation (z); and if we were to deduce from them the value of i' as well as K, we should obtain a value of the former with only a BRADLEY'S OBSERVATIONS. 17 small degree of accuracy. On the other hand, the value of K , given by the second of the above equations, depends so little on the value of i', that if we substitute the value of i' obtained from the observations at Wansted, which we have already discussed, we may arrive at as near an approximation to the value of K, as if it were deduced independently from the observations at Kew. Accordingly, if we make i f = 0.0257382, the last equation becomes, 0= + 1. 112 + 8838.85 -, and therefore, K = - 0.000 1258; or the value of the Const, of Aberr. = 20".2527 ; which so far agrees with the result obtained from the Wansted observations alone, that both indicate a diminution of the assumed Constant of Aberration. The best method, of combining together the observations at Kew and at Wansted, is to add together the first and the last equations derived from both series of observations, and to solve them by means of these new equations con- taining both values. They are as follows : 0=- 845.47+34345.12.'+ 4467 .45 0= + 1365.62+ 4467.45 T + 262938.25* which solved, give f=+ 0.025268; or 1= -0.046030 and = -0.0056244. We have then, as the combined result of the Kew and Wansted observations, for the formulae for Nutation, A L= 17'.2076 sin. Q +o!'20720 sin. 2 Q 1 '.26847 sin. 2 O 0"20638 sin. 2 ]) A o>= + 9.2040 cos. 8 0.08994 cos. 2 Q +0.55063 cos. 2 +0.08959 cos. 2 J) and Constant of Aberr. = 20".l 411. Having, in the manner thus explained, found the value of the Constant of Aberration, and the formulae for Nutation, derived from the combined observations of Molyneux and Bradley, it remains for me now to ascertain the amount of the unknown quantities y, y\ y", or the corrections which are to be applied to the observations, made in any one of the assumed periods, on account of any alteration in the line of collimation of the instrument. By solution of equat. (2) I obtain the following values : y =-6.1351 / = +0.1821 y"=- 0.4/98 We see then that, during the 20 years which include the observations, the line of collimation underwent only a slight alteration, and up to the third period we F 18 REDUCTION OF may, without sensible error, assume the collimation as constant, or make y and j/ 0. It is only in the third period that a perceptible change seems to have taken place, for the greater part of the observations concurs in giving the same sign. Lastly, by substituting these values, as well as those of i' and K deduced from equat. (3), I have deduced the value x for each of the following stars, by which to correct their assumed polar distances (P), and found them as follows : Names of Stars. Assumed value OtP. z Place of the Star by the Instrument at the beginning of 1730. a Aurigee ty Ursae maj. i Herculis 8 Persei 44 15+148" 44 0+ 65 43 50- 90 43 5 + 7 41 *\-\- 71 -0.335 -0.322 -0.179 + 0.172 4-0 341 44 I/ 27.665 44 1 4.678 43 48 29.821 43 5 7.172 41 611 341 46 Aurigae 17 Ursae maj. 9 Aurigae y Draconis 35 Camelopardi r Persei 40 35+ 24 39 15 + 189 38 45+ 93 38 25+ 82 38 25+ 72 38 20+ 28 Q7 QK 114 -1.004 + 0.551 -0.135 + 0.180 -0.595 -0.403 172 40 35 22.996 39 18 9.551 38 46 32.865 38 26 22.180 38 26 11.405 38 20 27.597 37 33 5 828 y - |3 Draconis X Cassiopeae 8 Aurigae a Cassiopeae y UrsBe maj. f 37 30-147 36 55+ 99 35 45+ 13 34 55+ 13 34 45+ 95 33 354-160 -0.666 + 0.419 -0.610 -0.087 -0.077 4-0 187 37 27 32.334 36 56 39.419 35 45 12.390 34 55 12.913 34 46 34.923 33 37 40 187 i Draconis 18 Camelopardi t Ursae maj. Cassiopeae (3 Ursae maj. 33 0+133 33 0- 43 32 20+143 32 20- 81 32 15-360 + 0.098 -0.152 + 0.631 -0.515 -0.553 33 2 13.098 32 59 16.848 32 22 23.631 32 18 28.485 32 8 59.447 IV. Here the investigation which is the object of this Memoir might close, if the assumption on which it is based, viz. that the observations of all the stars em- ployed possess an equal degree of certainty, needed no proof. It was convenient to conduct the investigation on this assumption, but it were unpardonable not to examine its accuracy, nor to avail ourselves of the result of such examination. There can be no doubt that the observations of the different stars gave a mean error, greater in proportion to their zenith distance when they passed the meri- dian. This must necessarily be the case, partly, because Bradley has not given us the indications of the meteorological instruments, and we are therefore compelled to neglect the changes of refraction due to such indications ; partly, because the BRADLEY'S OBSERVATIONS. 19 temperature of the upper and lower rooms, through which the Sector passed, could seldom or never have been the same ; consequently the comparative length [vergleichungsweise] of the graduated arc to the radius must have been generally either too great or too small, and for want of observations of the temperature at different heights of the room, we are not in a situation to make allowance for it. It would be wrong, therefore, to allow an equal weight to all the observations of the different stars. In order to ascertain the mean error which they severally indicate, I have taken out the sum of the squares of the errors of each individual star, after the values of the unknown quantities x, y, y, y", if, K (found in the last section) have been substituted. The following table contains these sums, and also the quotients after they have been divided by the number of the observations of each star respectively. Names of Stan. Z. D. No. of O\x.=m. Sums of the Squares of the Errors =**. 7 a Auriga? 5 48 202 384.08 1.3786 ifr Ursa? maj. 5 31 21 30.97 1.2144 i Herculis 5 19 64 97.35 1.2333 8 Persei 4 35 35 34.41 0.9915 2 36 /*! 48 71 8724 i I ' TO*/ I VO/ ^ 46 Auriga? 2 5 20 8.68 0.6588 ij Ursa? maj. 48 148 123.81 0.9147 9 Auriga? 17 21 12.11 0.7594 y Draconis 3 291 170.09 0.7645 35 Camelopardi 3 39 25.63 0.8107 r Persei 9 51 53.09 1.0203 y 57 51 46.15 0.9513 /3 Draconis 1 2 240 227.95 0.9746 X Cassiopea? 1 33 39 24.14 0.7868 8 Aurigae 2 44 34 66.82 1.4020 a Cassiopea? 3 34 101 86.66 0.9263 y Ursa? maj. 3 43 60 60.43 .0035 f 4 52 195 209.29 .2940 Draconis 5 27 1 4-f 55 112.83 .4323 18 Camelopardi 5 30 30 48.20 .2676 e Ursae maj. 5 57 118 160.56 .1665 /3 Cassiopeas 6 11 99 130.32 .1473 /3 Ursa? maj. 6 21 41 17-63 0.6558 It appears from this list, as might have been anticipated, that the observations are more uncertain, the farther they are removed from the zenith, and the law of the mean errors is on the whole as regular as could be expected. Nevertheless, in order to determine them still nearer, I have compared them with the simple formula ee = a + 0Z 20 REDUCTION OF depending on the zenith distance ; in which z denotes the zen. dist. expressed in degrees. The values and /3 most nearly corresponding with the above table are a=0.612l =0.1737 Since by assuming these values of a and /3 the formula corresponds as nearly as we can expect with the errors actually found by observation, I have had no hesi- tation in making a new determination of the Constants of Aberration and Nuta- tion based on this hypothesis, instead of that of the equal value of the observa- tions of all stars. Accordingly, by multiplying the equations resulting from the observations of each star by I have given them the weight, which they would have had if the observations on which they depend were as accurate as those made in the zenith, i. e. as accurate as observations whose mean error ^/G.6121 = 0".7824. I shall, in the first place, here give the values of the factors ee Names of Stars. Z. D. | a. cc a Aurigae 5 48 l".2726 0.3/80 i\r Ursae maj. 5 31 1 .2533 0.3897 i Herculis 5 19 1.2394 0.3985 8 Persei 4 35 1.1866 0.4348 2^fl i n^i4 A K7CK oo 1 .UOl *T U.O/ OO 46 Aurigae 2 5 0.9869 0.6286 ij Ursse maj. 48 0.8666 0.8151 9 Aurigse 17 0.8132 0.9257 y Draconis 3 0.7879 0.9861 35 Camelopardi 3 0.7879 0.9861 T Persei 9 0.7989 0.9592 y 57 0.8815 0.7877 /3 Draconis 1 2 0.8897 0.7734 X Cassiopese 1 33 0.9489 0.6799 8 Aurigse 2 44 1.0425 0.5633 a Cassiopese 3 34 1.1098 0.4971 y Ursse maj. 3 43 .1215 0.4867 * 4v> 9fl79 Oi-'nn fc m ._' '/ _ .^iUw f Draconis 5 27 .2485 0.3928 18 Camelopardi 5 30 .2520 0.3906 t Ursse maj. 5 57 .2828 0.3720 Cassiopese 6 11 .2985 0.3631 /3 Ursse maj. 6 21 .3095 0.3570 By multiplying the equations for each star in sect. III. by these factors, we have the five following new final equations, depending on the Wansted observations alone. BRADLEY'S OBSERVATIONS. 21 0=+ 14.52+ 135.62 y- 18.04y'- 14.97y"+ 233.30i'+ 424.67* = - 33.68- 18.04 y + 101. 45 y'- 11.18y"+ 506.75t' + 528.28 * 0=+ 19.03- 14.97y- 11.18y'+ 82.37y" + 277-63i' + 598.15* = - 737.22 + 233.30 y + 506.75 y' + 277-63 y" + 27770.57 i' + 9956.45 * 0= +307 .32 + 424.67 y + 528.28 y' + 598.15y" + 9956.45 i' + 164251.73* By eliminating y, y, y" , we obtain from the above equations for z" and K 0=-667.72 + 22669.73'+ 2619.69 K (5) 0= + 299.10+ 2619.69 " + 152854.05* The solution of which gives ,"=+0.029740 or = -0.041870 an( J *= 0.0024665. After thus assigning to the observations a weight, depending on their zenith distances, the formulae for Nutation for the beginning of the year 1800 become A L= 17".2828 sin. Q + 0.2081 1 sin. 2 Q f.25651 sin. 2 O 0.20728 sin. 2 5 A )0 0.41 0.83 1.23 1.64 + o'.'oo 0.34 0.69 1.03 1.38 + o'.'oo 0.17 0.34 0.51 0.68 +o"oo 0.14 0.28 0.41 0.55 +o".oo 0.11 0.23 0.34 0.45 + o'.'oo 0.06 0.12 0.18 0.23 +o"oo 0.04 0.08 0.12 0.15 19 Mar. 1 11 21 31 2.75 3.30 3.85 4.40 4.95 2.72 3.26 3.80 4.35 4.89 2.13 2.55 2.98 3.40 3.83 1.89 2.26 2.64 3.02 3.40 2.05 2.47 2.88 3.29 3.70 1.72 2.06 2.41 2.75 3.10 0.84 .01 .18 .35 .52 0.69 0.83 0.96 1.10 1.24 0.57 0.68 0.79 0.91 1.02 0.29 0.35 0.41 0.47 0.53 0.19 0.23 0.27 0.31 0.35 Apr. 10 20 30 May 10 20 5.50 6.05 6.60 7.15 7.70 5.43 5.97 6.52 7.06 7.61 4.26 4.68 5.11 5.53 5.96 3.77 4.15 4.53 4.90 5.28 4.11 4.52 4.93 5.34 5.75 3.44 3.78 4.13 4.47 4.82 .69 .86 2.03 2.19 2.36 1.38 1.52 1.65 1.79 1.93 1.13 1.25 1.36 1.47 1.59 0.59 0.64 0.70 0.76 0.82 0.39 0.42 0.46 0.50 0.54 30 June 9 19 29 July 9 8.25 8.80 9.35 9.90 10.45 8.15 8.69 9.23 9.78 10.32 6.38 6.81 7.23 7.66 8.09 5.66 6.04 6.41 6.79 7.17 6.16 6.57 6.98 7.39 7.81 5.16 5.51 5.85 6.19 6.54 2.53 2.70 2.87 3.04 3.21 2.0? 2.20 2.34 2.48 2.62 1.70 1.81 1.93 2.04 2.15 0.88 0.94 0.99 1.05 1.11 0.58 0.62 0.66 0.69 0.73 19 29 Aug. 8 18 28 11.00 11.55 12.10 - 12.65 13.20 10.87 11.41 11.95 12.49 13.04 8.51 8.94 9.36 9.79 10.21 7.54 7.92 8.30 8.68 9.05 8.22 8.63 9.04 9.45 9.86 6.88 7.22 7-57 7.91 8.25 3.38 3.55 3.71 3.88 4.05 2.76 2.89 3.03 3.17 3.31 2.27 2.38 2.50 2.61 2.72 1.17 1.23 1.29 .35 .40 0.77 0.81 0.85 0.89 0.93 Sept. / 17 27 Oct. 7 17 13.75 14.30 14.85 15.40 15.95 13.58 14.12 14.67 15.21 15.75 10.64 11.06 11.49 11.91 12.34 9.43 9.81 10.19 10.56 10.94 10.27 10.68 11.09 11.50 11.91 8.60 8.94 9.29 9.63 9.98 4.22 4.39 4.56 4.73 4.89 3.44 3.58 3.72 3.86 3.99 2.84 2.95 3.06 3.17 3.29 .46 .52 .58 .64 70 0.97 1.00 1.04 .08 .12 27 Nov. 6 16 26 Dec. 6 16.50 17.05 17-60 18.15 18.70 16.30 16.84 17.38 17.92 18.47 12.77 13.19 13.62 14.04 14.47 11.32 11.70 12.07 12.45 12.83 12.33 12.74 13.15 13.56 13.97 10.32 10.67 11.01 11.35 11.70 5.06 5.23 5.40 5.57 5.74 4.13 4.27 4.41 4.54 4.68 3.40 3.52 3.63 3.74 3.86 75 .81 .87 .93 .99 .16 .20 .24 .27 .31 16 26 36 19.25 19.80 20.35 19.01 19.55 20.09 14.89 15.32 15.74 13.20 13.58 13.95 14.38 14.79 15.20 12.04 12.38 12.61 5.91 6.08 6.25 4.82 4.96 5.10 3.97 4.08 4.20 2.05 2.11 2.16 .35 .39 .43 TABLE I. Precession + Proper Motion. 46 Auriga 8 Ursae maj. ^ Ursae maj . y Ursae maj. eUrsKmaj. JUresemaj. r, Ursa maj. 8 Draconis i Herculis | Draconic y Draconis 8 Cassiopew 1727 + L32 + 58J3 + 57.97 + 60"02 + 59.35 + 5/'25 + 54.98 + 9'35 + 7"35 + 2'68 + 2"71 - 59"a8 28 +0.89 + 38.76 + 38.65 + 40.01 + 39.57 + 38.16 + 36.65 + 6.23 + 4.89 + 1.78 + 1.80 39.72 29 +0.45 + 19.38 + 19.32 + 20.01 + 19.78 + 19.08 + 18.33 + 3.11 + 2.45 + 0.89 + 0.90 19.86 30 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 31 0.45 19.38 - 19.32 - 20.01 - 19.78 - 19.08 - 18.33 - 3.11 2.45 - 0.89 - 0.90 + 19.86 32 -0.91 - 38.76 38.65 - 40.01 - 39.57 - 38.16 - 36.65 6.23 4.89 - 1.78 1.80 + 39.72 33 -1.38 - 58.15 57-99 - 60.02 - 59.35 - 57.23 - 54.96 - 9.33 - 7-33 - 2.66 2.69 + 59.58 34 -1.85 - 77-53 - 77-31 - 80.02 - 79-13 - 76.31 - 73.29 -12.44 - 9.76 - 3.55 - 3.58 + 79.44 35 -2.33 - 96.92 - 96.65 -100.03 - 98.91 - 95.38 - 91.61 15.55 -12.20 - 4.44 - 4.48 + 99.30 36 -2.81 -116.31 -115.98 -120.05 -118.68 114.46 -109.92 -18.65 -14.63 - 5.32 - 5.37 + 119.15 37 -3.31 -135.71 -135.31 140.05 - 138.47 -133.63 -128.24 -21.75 -17-07 - 6.20 - 6.26 + 139.02 38 -3.81 -155.11 154.65 -160.06 -158.25 -152.60 -146.55 -24.85 -19.50 - 7-08 - 7-15 + 158.87 39 -4.31 -174.49 -173.98 -180.06 -178.03 -171.67 -164.87 -27.95 -21.92 - 7.96 - 8.03 + 178.73 40 -4.83 -193.90 -193.32 -200.07 -197.80 -190.74 -183.17 -31.04 -24.35 - 8.83 8.91 + 198.59 41 5.35 -213.30 -212.67 -220.09 -217.57 -209.81 -201.49 -34.13 -26.77 - 9./1 - 9.79 + 218.45 42 5.77 -232.70 -232.00 -240.09 -237.35 -228.87 -219.79 -37.23 -29.18 -10.57 -10.66 + 238.31 43 -6.41 -252.10 -251.35 -260.10 -257.13 -247.94 -238.10 -40.32 -31.60 -11.45 -11.54 + 258.17 44 -6.95 -271-51 -270.68 -280.12 -2/6.90 -26/.00 -256.40 -43.41 -34.02 -12.32 -12.41 + 278.03 45 -7-47 -290.91 -290.03 -300.12 -296.66 -286.06 -274.71 46.49 -36.43 -13.19 -13.28 + 297.88 46 -8.05 -310.33 -309.37 -320.14 -316.44 -305.12 -293.00 49.57 -38.84 -14.07 -14.16 +317.74 47 -8.61 -329.73 -328.72 -340.14 -336.21 -324.18 -311.31 -52.66 -41.25 -14.93 -15.03 + 337.60 CONTINUATION or TABLE I. Mean Motion for every 10 Star-days. Jan. 10 20 30 Feb. 9 46 Aurigse \8 Ursae maj. ^ UresB maj. y Ursae maj. Ursae maj. IS Ursae maj >1 Ursae maj 8 Draconis t Herculis | Draconis y Draconis 8 Cassiopeae -o"oo 0.01 0.03 0.04 0.05 - o"oo 0.53 1.06 1.59 2.12 - o'oo 0.53 1.06 1.58 2.11 - 0:00 0.55 1.09 1.64 2.19 - 0:'00 0.54 1.08 1.62 2.16 o'.bo 0.52 1.04 1.56 2.08 - o'.bo 0.50 1.00 1.50 2.00 -o'.'oo 0.09 0.17 0.26 0.34 -o'.bo 0.07 0.13 0.20 0.27 -o'oo 0.02 0.05 0.07 0.10 -0:00 0.03 0.05 0.07 0.10 + o!bo 0.54 1.09 1.63 2.17 19 Mar. 1 11 21 31 0.06 0.07 0.09 0.10 0.11 2.65 3.18 3.71 4.23 4./6 2.64 3.17 3.69 4.22 4.75 2.73 3.28 3.82 4.37 4.92 2.70 3.24 3.78 4.32 4.86 2.61 3.13 3.65 4.17 4.69 2.50 3.00 3.50 4.00 4.50 0.43 0.51 0.60 0.68 0.77 0.33 0.40 0.47 0.53 0.60 0.12 0.15 0.17 0.20 0.22 0.12 0.15 0.17 0.20 0.22 2.71 3.25 3.80 4.34 4.88 Apr. 10 20 30 Mav 10 ' 20 0.12 0.14 0.15 0.16 0.17 5.29 5.82 6.35 6.88 7.41 5.28 5.80 6.33 6.86 7.39 5.46 6.01 6.56 7.10 7-65 5.40 5.94 6.48 7-02 7-56 5.21 5.73 6.25 6.77 7-29 5.00 5.50 6.01 6.51 7-01 0.85 0.94 1.02 1.11 1.19 0.67 0.74 0.80 0.87 0.94 0.24 0.27 0.29 0.32 0.34 0.25 0.27 0.30 0.32 0.34 5.42 5.97 6.51 7.05 7-59 30 June 9 19 29 Julv 9 0.18 0.20 0.21 0.22 0.23 7.94 8.47 9.00 9.53 10.05 7.91 8.44 8.97 9.50 10.03 8.19 8.74 9.29 9.83 10.38 8.10 8.64 9.18 9.72 10.27 7.81 8.34 8.86 9.38 9.90 7.51 8.01 8.51 9.01 9.51 1.28 1.36 1.45 1.53 1.62 1.00 1.07 1.14 1.20 1.27 0.37 0.39 0.41 0.44 0.46 0.37 0.39 0.42 0.44 0.47 8.13 8.68 9.22 9.76 10.30 19 29 Aug. 8 18 28 0.25 0.26 0.27 0.28 0.29 10.59 11.12 11.65 12.17 12.70 10.55 11.08 11.61 12.14 12.66 10.93 11.47 12.02 12.57 13.11 10.81 11.35 11.89 12.43 12.96 10.42 10.94 11.46 11.98 12.50 10.01 10.51 11.01 11.51 12.01 1.70 1.79 1.87 1.96 2.04 1.34 1.40 1.47 1.54 1.60 0.49 0.51 0.54 0.56 0.58 0.49 0.52 0.54 0.57 0.59 10.85 11.39 11.93 12.47 13.01 Sept. 7 17 27 Oct. 7 17 0.31 0.32 0.33 0.34 0.36 13.23 13./6 14.29 14.82 15.35 13.19 13.72 14.25 14.78 15.30 13.66 14.21 14.75 15.30 15.84 13.51 14.05 14.59 15.13 15.fi? 13.03 13.55 14.07 14.59 15.11 12.51 13.01 13.51 14.01 14.51 2.13 2.21 2.30 2.38 2.47 1.67 1.74 1.80 1.87 1.94 0.61 0.63 0.66 0.68 0.71 0.62 0.64 0.66 0.69 0.71 13.56 14.10 14.64 15.19 15.73 27 Nov. 6 16 26 Dec. 6 0.37 0.38 0.39 0.40 0.42 15.88 16.41 16.94 17.46 17.99 15.83 16.36 16.89 17-41 1/.94 16.39 16.94 17.48 18.03 18.57 16.21 16./5 17.29 17.82 18.37 15.63 16.15 16.67 17.19 17-71 15.02 15.52 16.02 16.51 17.01 2.55 2.64 2.72 2.81 2.89 2.00 2.07 2.14 2.20 2.27 0.73 0.75 0.78 0.80 0.83 0.74 0.76 0.79 0.81 0.84 16.27 16.81 17.35 17.89 18.44 16 26 36 0.43 0.44 0.45 18.52 19.05 19.58 18.47 18.90 19.52 19.12 19.67 20.21 18.91 19.45 19.99 18.24 18.75 19.28 17-52 18.02 18.52 2.98 3.06 3.15 2.34 2.41 2.47 0.85 0.88 0.90 0.86 0.89 0.91 18.98 19.52 20.06 TABLE II. Lunar Nutation. Cassiopeee Cassiopeae T Persei a Persei y Persei S Persei 9 Aurlgee a Aurigse 8 Camelop. i Aurigee 5 Camelop. 1727 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 0-064 + 0.668 + 1.261 + 1.844 + 2.417 + 0.386 + 0.989 + 1.579 + 2.156 + 2.720 + 5.084 + 5.576 + 6.019 + 6.413 + 6.757 + 5.986 + 6.428 + 6.815 + 7-146 + 7.421 + 5.400 + 5.877 + 6.301 + 6.674 + 6.995 + 6.498 + 6.905 + 7.253 + 7.542 + 7.772 + 8?198 + 8.424 + 8.579 + 8.664 + 8.680 + 8.354 + 8.552 + 8.679 + 8.735 + 8.720 + &505 + 8.672 + 8.767 + 8.790 + 8.741 + 8^48 + 8.843 + 8.866 + 8.816 + 8.693 + 8.783 + 8.863 + 8.870 + 8.805 + 8.667 1728 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 2.229 + 2.783 + 3.314 + 3.824 + 4.311 + 2.536 + 3.086 + 3.607 + 4.099 + 4.563 + 6.647 + 6.953 +7.201 + 7.390 + 7-520 + 7.336 + 7.569 + 7-739 + 7-845 + 7.888 + 6.894 + 7.176 + 7-398 + 7.559 + 7.659 + 7.701 + 7.887 + 8.007 + 8.061 + 8.049 + 8.683 + 8.649 + 8.544 + 8.369 + 8.123 + 8.733 + 8.669 + 8.534 + 8.328 + 8.052 + 8.765 + 8.666 + 8.497 + 8.258 + 7.949 + 8.741 + 8.530 + 8.276 +7-978 + 7.637 + 8.720 + 8.532 + 8.276 + 7.952 + 7.559 1729 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 4.155 + 4.614 + 5.031 + 5.408 + 5.743 + 4.413 + 4.852 + 5.248 + 5.603 + 5.915 + 7.480 + 7.571 + 7.598 + 7.561 + 7.460 + 7.883 + 7-881 + 7.815 + 7.684 + 7.489 + 7.634 + 7.692 + 7.686 +7.617 + 7.484 + 8.062 + 8.005 + 7.883 + 7.695 + 7.442 + 8.213 + 7.922 +7.567 + 7.148 + 6.666 + 8.154 + 7.832 + 7-447 +7.000 + 6.491 + 8.061 + 7-706 + 7.290 + 6.813 + 6.275 + 7-772 + 7.349 + 6.868 + 6.329 + 5.733 + 7.699 + 7-261 + 6.767 + 6.216 + 5.609 1730 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 5.637 + 5.942 + 6.196 + 6.399 + 6.550 + 5.816 + 6.096 + 6.323 + 6.498 + 6.621 + 7-501 + 7.359 + 7.156 + 6.893 + 6.570 + 7.561 + 7.323 + 7.026 + 6.669 + 6.253 + 7.536 + 7.360 + 7.125 + 6.830 + 6.475 + 7-534 + 7.238 + 6.884 + 6.472 + 6.001 + 6.834 + 6.313 + 5.743 + 5.124 + 4.455 + 6.668 + 6.121 + 5.526 + 4.884 + 4.194 + 6.460 + 5.585 + 5.264 + 4.598 + 3.886 + 5.937 + 5.306 + 4.635 + 3.924 + 3.172 + 5.818 + 5.177 + 4.496 + 3.776 + 3.017 1731 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 6.506 + 6.617 + 6.680 + 6.695 + 6.663 + 6.587 + 6.666 + 6.701 + 6.693 + 6.642 + 6.685 + 6.287 + 5.910 + 5.556 + 5.224 + 6.398 + 5.904 + 5.445 + 5.024 + 4.638 + 6.600 + 6.168 + 5.763 + 5.385 + 5.034 + 6.165 + 5.613 +5.107 + 4.647 + 4.233 + 4.682 + 3.931 +3.260 + 2.671 + 2.161 + 4.429 + 3.657 + 2.970 + 2.368 + 1.851 +4.127 + 3.335 + 2.631 + 2.017 + 1.492 + 3.425 + 2.595 + 1 .863 + 1.229 + 0.692 + 3.274 + 2.438 + 1.701 + 1.063 + 0.525 1732 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 6.669 + 6.566 + 6.412 + 6.207 + 5.952 + 6.649 + 6.511 + 6.325 + 6.091 + 5.808 + 5.243 + 4.615 + 3.984 + 3.352 + 2.717 + 4.660 + 3.951 + 3.232 + 2.541 + 1.841 + 5.055 + 4.395 +3.736 + 3.079 + 2.424 + 4.256 + 3.487 + 2.735 + 1.999 + 1.279 + 2.188 + 1.263 + 0.384 -0.450 -1.237 + 1.754 + 0.895 + 0.053 -0.771 -1.576 + 1.518 + 0.570 -0.325 -1.167 -1.957 + 0.719 -0.244 -1.146 -1.987 -2.767 + 0.552 -0.412 -1.313 -2.152 -2.929 1733 Jan. + 6.044 + 5.909 + 2.936 + 2.081 + 2.651 0.966 1.312 1.686 2.500 2.664 Apr. 10 + 5.750 + 5.588 + 2.267 + 1.350 + 1.962 1.775 -2.116 -2.493 -3.293 -3.452 Jul. 19 + 5.408 + 5.221 + 1.582 + 0.627 + 1.260 2.563 2.899 -3.273 -4.052 -4.206 Oct. 27 + 5.019 + 4.808 + 0.882 0.110 + 0.546 3.331 3.660 4.027 4.779 4.926 Dec. 66 + 4.582 + 4.348 + 0.165 0.855 0.181 4.079 4.400 4./54 5.472 5.611 1734 Jan. + 4.732 + 4.506 + 0.40^ 0.608 + 0.061 3.833 4.158 4.516 5.246 -5.388 Apr. 10 + 4.266 + 4.019 -0.315 1.349 -0.667 4.559 -4.873 -5.217 -5.909 -6.041 Jul. 19 +3.767 + 3.501 1.026 2 074 1.384 5.241 5.541 5.868 6.516 -6.638 Oct. 27 + 3.235 + 2.952 -1.730 2.783 2.091 5.878 -6.162 -6.469 -7.068 -7-179 Dec. 66 + 2.670 + 2.370 -2.427 -3.47r -2.788 -6.471 -6.738 -7.021 -7.565 -7-663 1735 Jan. 1 + 2.859 + 2.566 2.197 3/248 2.558 6.279 6.552 -6.845 -7.407 -7.509 Apr. 10 + 2.275 + 1.968 -2.881 3.922 3.240 -6.836 -7.089 -7.356 -7.859 -7.949 Jul. 19 Oct. 27 + 1.675 + 1.061 + 1.359 + 0.737 -3.535 -4.159 -4.556 5.151 -3.888 4.504 -7.329 7-759 -7.560 7.965 -7.800 8.1/7 -8.240 8.550 -8.317 -8.613 Dec. 66 + 0.431 + 0.103 -4.753 -5.707 -5.086 -8.125 -8.305 -8.486 -8.789 -8.836 1736 Jan. i + 0.642 + 0.31o 4.55J 5.528 4.897 -8.011 8.199 8.392 8.71J -8.769 Apr. 10 + 0008 032 5.127 605 5450 8.329 8.491 8.651 8.905 8.940 Jul. 1 Oct. 2 Dec. 6 -0.62 -1.244 -1.86 -0.94 -1.56 -2.18 -5.644 -6.113 -6.53 -6.517 -6.92 -7.28 -5.95 6.400 -6.798 -8.573 -8.742 -8.837 -8.706 -8.846 -8.909 -8.833 -8.938 -8.966 -9.013 -9.043 8.994 -9.033 -9.047 -8.982 1737 Jan. 1.65 1.97 6.39 7.17 6.673 8.815 8.897 8.966 -9.01J -9.014 Apr. 1 2.264 2.57 6.77 7.48 7.030 -8.856 8.907 8.940 -8.91f -8.894 Jul. 1 2.84 3.14 7.09 7.72 7.323 8.821 8.841 -8.838 -8.737 -8.700 Oct. 2 3.40 3.69 7.35 7.89 7-55 8.710 8.698 -8.660 -8.483 -8.431 Dec. 6 3.93 4.20 7.54 8.00 7 71 8.522 8.479 8.40o 8.154 -8.087 TABLE II. Lunar Nutation. 46 AurigR 8 Urea maj. ^ Urstemaj. / L'rste maj. e Ursse maj . Uniemaj. i| Urste maj. 3 Draconis i Herculis ; Draconis y Draconte 8 Cauiopee 1727 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 8.860 + 8.885 + 8.838 + 8.718 + 8.526 + 3"399 + 2.840 + 2.262 + 1.665 + 1.049 +3 '073 + 2.505 + 1.921 + 1.322 + 0./06 + l'.385 + 0.789 + 0.190 0.411 -1.013 - 1'.'030 -1.629 -2.210 -2.773 -3.318 -2"207 -2.790 -3.346 -3.875 -4.377 -3'088 3.652 -4.182 -4.678 -5.139 -8.652 -8.781 -8.837 -8.820 -8.731 8.711 -8.820 -8.857 -8.821 -8.712 -8."812 -8.876 -8.868 -8.787 -8.634 -8.818 -8.879 -8.867 -8.782 -8.625 -0?789 -0.187 + 0.411 + 1.007 + 1.599 1728 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 8.597 + 8.355 + 8.047 + 7-673 + 7.232 + 1.254 + 0.631 + 0.008 -0.617 1.243 + 0.911 + 0.290 0.329 0.947 -1.563 -0.814 -1.411 -1.993 -2.560 -3.111 -3.140 3.667 -4.160 -4.621 -5.048 -4.213 -4.691 -5.127 -5.522 -5.875 -4.988 -5.423 -5.810 6.150 -6.441 8.768 -8.629 -8.421 -8.143 -7-796 -8.756 -8.598 -8.3/0 -8.073 -7-707 8.693 -8.490 -8.219 -7-880 -7-473 8.685 -8.491 -8.204 7-824 -7.351 + 1.403 + 1.987 + 2.551 + 3.095 + 3.619 1729 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 7-387 + 6.903 + 6.366 + 5.775 + 5.130 1.035 -1.656 -2.260 -2.846 -3.414 -1.358 -1.967 2.556 -3.125 -3.674 -2.930 -3.466 -3.969 4.441 -4.881 4.910 -5.310 -5.664 -5.972 -6.233 5.763 -6.084 6.354 -6.571 -6./36 -6.350 6.606 -6.807 -6.952 -7-041 -7.921 -7.529 -7-077 -6.566 -5.995 -7-838 -7-427 -6.958 -6.431 -5.845 -7-618 -7-168 -6.661 -6.099 -5.480 -7-597 -7.143 -6.634 -6.069 -5.448 + 3.448 +3.953 + 4.422 + 4.856 + 5.255 1/30 Jan. Apr. 10 Jul. 19 Oct. 27 Dec. 66 + 5.350 + 4.676 + 3.966 + 3.221 + 2.440 -3.227 -3.778 -4.295 -4.777 -5.224 -3.494 -4.024 -4.518 -4.976 -5.397 4.738 -5.152 -5.521 -5.845 -6.124 6.152 -6.380 6.553 -6.672 -6.737 -6.688 6.816 -6.887 -6.901 -6.857 -7-018 -7-068 -7-059 -6.991 6.864 -6.193 -5.586 -4.937 -4.245 -3.511 -6.047 -5.428 -4.766 -4.063 -3.317 -5.694 -5.043 -4.354 -3.626 -2.860 -5.661 -5.008 -4.317 -3.588 -2.821 + 5.126 + 5.497 + 5.819 + 6.094 + 6.320 1/31 Jan. -5.081 6.037 6.722 6.878 6.914 3.762 -3.081 + 6.251 Apr. 10 5.518 6.287 6.739 6.777 6.723 2.948 -2.237 + 6.444 Jul. 19 5.870 6.472 6.719 6.656 6.525 -2.228 1.496 + 6.579 Oct. 27 6.136 6.593 6.664 6.515 6.319 1.601 0.855 + 6.656 Dec. 66 -6.317 6.649 6.5/3 -6.354 -6.106 -1.069 -0.316 + 6.676 1732 Jan. 6.312 6.650 6.582 6.366 6.120 1.097 0.344 + 6.680 Apr. 10 6.591 6.706 6.376 6.035 -5.696 0.139 + 0.621 + 6.670 Jul. 19 -6.796 6.700 6.126 5.671 5.249 + 0.761 + 1.522 + 6.602 Oct. 27 -6.925 6.631 5.833 5.2/4 4.777 + 1.604 + 2.358 +6.477 Dec. 66 6.981 6.500 5.497 4.846 4.282 + 2.389 + 3.129 + 6.295 1733 Jan. 6.967 6.549 5.617 4.997 4.456 + 2.119 + 2.864 + 6.361 Apr. 10 6.989 6.383 5.243 4.530 3.923 + 2.919 + 3.647 + 6.141 Jul. 19 6.951 6.162 4.826 4.026 3.359 + 3.690 + 4.394 + 5.869 Oct. 27 6.853 5.887 -4.366 -3.487 -2.765 + 4.431 + 5.104 + 5.546 Dec. 66 6.696 5 558 3.864 2.911 2.140 + 5.142 + 5.778 + 5-172 1/34 Jan. 6.755 5.6/3 4.035 -3.10/ -2.351 + 4.908 + 5.557 + 5.302 Apr. 10 6.557 5.311 3.509 2.512 -1.712 + 5.591 + 6.198 + 4.896 Jul. 19 6.304 4.905 2.955 1.900 -1.062 + 6.220 + 6.782 + 4.450 Oct. 2/ 5.995 4.455 2.375 1.2/0 0.401 + 6./97 + 7.308 + 3.964 Dec. 66 5.630 3.962 1-76/ 0.622 + 0.2/0 + 7.320 + 7-777 + 3.439 1735 Jan. 5-756 4.130 1.971 0.840 + 0.046 + 7-151 + 7.628 + 3.61/ Apr. 10 5.358 3.612 1 .352 0.186 + 0.71/ + 7.633 + 8.051 +3.070 Jul. 19 4.916 3.067 0.725 + 0.464 + 1.3/6 + 8.045 + 8.402 + 2.500 Oct. 27 4.431 2.494 0.091 + 1.111 + 2.025 + 8.388 + 8.680 + 1.908 Dec. 66 3.901 1 894 + 0.550 + 1-754 + 2.662 + 8.661 + 8.885 + 1.294 1/36 Jan. 4.081 2 096 + 0.336 + 1.540 + 2.452 + 8.577 + 8.825 + 1.500 Apr. 10 3.529 1 484 + 0.9/5 + 2.174 + 3.074 + 8.799 + 8.978 +0.877 Jul. 19 2.950 0864 + 1.599 + 2.784 +3.665 + 8.943 + 9.051 + 0.252 Oct 27 2.346 0236 + 2.210 + 3.3/0 + 4.224 + 9.008 + 9.046 0.376 Dec 66 1 715 + 0399 + 2.806 +3.931 + 4./51 + 8.996 + 8.962 1.005 1737 Jan. 1.926 + 188 + 2.610 + 3./4/ + 4.580 + 9.010 + 9.000 0./97 Apr. 10 1.285 + 0821 + 3.190 + 4.285 + 5.079 + 8.944 + 8.862 1.421 Jul 19 0.640 + 1 440 + 3./37 + 4.781 + 5.529 + 8.801 + 8.649 2.026 Oct 27 +0.010 + 2046 + 4.251 + 5.235 + 5.931 + 8.584 + 8.361 2.614 Dec. 66 + 0.664 + 2.639 +4.732 + S.64/ + 6.284 + 8.290 + 7.99S 3.183 *c CONTINUATION OF TABLE II. Lunar Nutation. /. Casgiopeue a Caseiopese T Persei a Persei y Persei S Persei 9 Aurigee a Aurigee 18 Camelop. S Aurigee 35 Camelop. 1738 Jan. 3759 4.039 7'.490 7^978 7"670 -8.594 8.561 8.499 8272 8"210 Apr. 10 4.266 4.528 7.639 8.037 7.789 -8.355 8.291 8.193 7 894 7 816 Jul. 19 4.731 4.973 7.721 8.027 7 840 -8.046 7.952 7.820 7 451 7 360 Oct. 27 5.154 5.375 7-736 7.947 7 822 -7.669 7.545 7.380 6 945 6841 Dec. 66 5.534 5.732 7.683 7.798 7 736 -7.222 7.070 6.873 6374 6260 1739 Jan. 5.413 5.618 7.709 7.856 7.773 -7.378 7.235 7.050 6571 6460 Apr. 10 5.761 5.991 -7.611 7.660 7 641 -6.889 6.717 6.501 5 964 5 842 Jul. 19 6.055 6.209 7.448 7.401 7 446 -6.346 6.149 5.904 5.312 5 180 Oct. 27 -6.297 -6.423 -7.221 7.079 7.187 -5.750 5.528 5.258 4.617 4.476 Dec. 66 6.485 6.583 6.931 6694 6 865 -5.100 4.857 4.563 3877 3728 1740 Jan. 6.537 7.035 6 830 6 978 -5.322 5.086 4.799 4.127 3980 Apr. 10 6.663 6.734 6440 6646 -4.686 4.430 4.123 3.411 3 258 Jul. 19 6.720 6.321 5 932 6201 -3.932 3.656 3.329 2.583 2 424 Oct. 27 6.711 5.798 5.308 5 642 -3.057 2 764 2.419 1.643 1 480 Dec. 66 -6.633 -5.163 -4.566 4.970 -2.065 -1.753 -1.391 -0.590 -0.424 1741 Jan. 6.628 4.581 1.777 0.615 0449 Apr. 10 6.582 4.263 1.352 175 0007 Jul. 19 6464 3801 0772 + 0414 + 0582 Oct. 27 6275 3 197 0039 + 1 152 + 1 319 Dec. 66 -6.013 2.449 + 0.848 + 2.040 + 2.203 1742 Jan. 6 103 2 682 + 0578 + 1.772 + 1 936 Apr. 10 5 817 1 977 + 1 385 + 2.569 + 2 731 Jul. 19 5486 1 264 + 2 171 + 3.337 + 3494 Oct. 27 5.110 0.542 + 2.938 + 4.075 + 4.226 Dec. 66 -4.688 + 0.188 + 3.684 + 4.783 + 4.926 1743 Jan 4833 0054 + 3 438 + 4551 + 4 697 Apr 10 4.386 + 674 + 4 164 + 5 231 + 5369 Jul. 19 3908 + 1 389 + 4 848 + 5 861 + 5 990 Oct. 27 3.399 + 2.091 + 5.489 + 6.442 + 6.560 Dec. 66 -2.858 + 2./81 + 6.088 + 6.973 + 7-080 1744 Jan. 3041 + 2 553 + 5 895 + 6 802 + 6 914 Apr 10 2485 + 3 226 + 6461 + 7 294 + 7 393 Jul. 19 1.914 + 3.867 + 6.968 + 7.722 + 7 808 Oct. 27 1.328 + 4.475 + 7-418 + 8.085 + 8 158 Dec. 66 -0.728 + 5.050 + 7.809 + 8.384 + 8.444 1745 Jan. 0.929 + 4.863 + 7.686 + 8.292 + 8357 Apr. 10 0.325 + 5.409 + 8.034 + 8.545 + 8595 Jul. 19 + 0.277 + 5.907 + 8.313 + 8.725 + 8 761 Oct. 27 + 0.876 + 6356 + 8524 + 8.833 + 8 855 Dec. 66 + 1.473 + 6.757 + 8.666 + 8.869 + 8.876 1 746 Jan. + 1.276 + 6.630 + 8.627 + 8.865 + 8 877 Apr. 10 + 1.865 + 6993 + 8 721 + 8.853 + 8 849 Jul. 19 + 2.435 + 7.296 + 8.743 + 8.768 + 8 740 Oct. 27 + 2.985 + 7539 + 8 693 + 8.611 + 8 577 Dec 66 +3.515 + 7 723 + 8571 + 8381 + 8 333 ...... 1747 Jan. + 3.342 + 7.670 + 8.621 + 8.466 + 8423 Apr. 10 + 3.854 + 7.810 + 8.451 + 8.189 + 8 132 Jul 19 + 4.331 + 7.886 + 8.213 + 7 846 + 7 776 Oct. 27 + 4.773 + 7-897 +7-907 + 7.439 + 7 355 Dec. 66 + 5.181 + 7.844 + 7.533 + 6.966 + 6870 6 CONTINUATION OF TABLE II. Lunar Nutation. 46 AurigiE 1 Urs maj. / Ursee maj . X Urse maj. f Urese maj. ' Ursee maj. i] Ursffi maj. 8 Draconis t Herculis Draconis ' Draconis 8 Cassiopeie 1738 Jan + 0"448 + 2"445 + 4577 + 5'.516 + 61 72 + 8"397 + 8!'l29 2"996 Apr. 10 + 1.09fl + 3.022 + 5.030 + 5.894 + 6.488 + 8.053 + 7-720 -3.546 Jul. 19 + 1 733 + 3.567 + 5.435 + 6.217 + 6.744 + 7.644 + 7.248 -4.060 Oct. 27 + 2351 + 4.080 + 5.791 + 6.485 + 6.942 + 7 169 + 6.715 4.537 Dec. 66 + 2.952 + 4.561 + 6.099 + 6.699 + 7-080 + 6.628 + 6.119 -4.978 1739 Jan. + 2755 + 4.405 + 6.002 + 6.634 + 7.041 + 6816 + 6.324 -4.836 Apr. 10 + 3339 + 4.859 + 6.2/4 + 6.809 + 7.137 + 6236 + 5.693 5.248 Jul. 19 + 3888 + 5.266 + 6.490 + 6.923 + 7.171 + 5 610 + 5.020 -5.610 Oct. 27 + 4 402 + 5626 + 6.649 + 6.977 + 7.144 + 4 937 + 4.305 5.923 Dec. 66 + 4.881 + 5.940 + 6.752 +6.970 + 7.054 + 4.217 + 3.549 -6.185 1740 Jan -1-4 726 + 5 841 + 6.724 + 6.979 + 7.091 + 4464 + 3.806 -6.103 Apr 10 + 5 161 + 6 116 + 6795 + 6.947 + 6.979 + 3765 + 3.076 -6.329 Jul 19 + 5 577 + 6344 + 6 791 + 6.828 + 6771 + 2952 + 2.236 -6.500 Oct 27 + 5 973 + 6525 + 6712 + 6621 + 6468 + 2024 + 1.287 -6.618 Dec. 66 + 6.350 + 6.660 + 6.557 + 6.326 + 6.069 + 0.982 + 0.229 -6.681 1741 Jan + 6334 + 6650 + 6556 + 6.328 + 6074 + 1 009 + 0.256 -6.672 Apr. 10 -t-6479 + 6.692 + 6.478 + 6.192 +5.894 + 0.572 -0.186 -6.684 Jul 19 + 6 616 + 6 691 + 6318 + 5.958 + 5 605 0016 0.775 6.644 Oct 27 + 6 746 + 6.647 + 6.077 + 5.626 + 5.206 0755 -1.518 6.551 Dec. 66 + 6.868 + 6.561 + 5.755 + 5.195 + 4.697 -1.644 -2.391 -6.405 1742 Jan + 6 841 + 6598 + 5 864 + 5335 + 4861 1 374 2.125 6.460 Apr 10 + 6 901 + 6.468 + 5.523 + 4.899 + 4.357 2 177 -2.914 -6.276 Jul 19 -4-6 902 + 6 285 + 5 141 +4428 +3 822 2 954 3.671 6.042 Oct 27 -1-6 847 + 6051 + 4.717 +3.922 + 3.258 3704 -4.395 5.758 Dec. 66 + 6.773 + 5.764 + 4.252 +3.380 + 2.663 -4.427 -5.087 -5.425 1/43 Jan -4-6 777 + 5 865 + 4411 + 3.564 + 2.864 4 189 4.860 -5.542 Apr 10 + 6 626 + 5547 +3922 +3.003 + 2.255 4886 5.523 -5.178 Jul. 19 + 6 422 + 5.187 + 3.406 + 2.424 + 1.634 5.537 -6.133 -4.776 Oct. 27 + 6 166 +4.785 + 2.863 + 1.826 + 1.001 6.141 -6.692 -4.336 Dec. 66 + 5.857 + 4.341 + 2.293 + 1.210 + 0.355 -6.698 -7-198 -3.858 1744 Jan. + 5 965 + 4.492 + 2.486 + 1.417 + 0.571 6.51" -7.035 -4.020 Apr 10 + 5 624 + 4.024 + 1.904 + 0.794 0.076 7.036 -7.501 -3.521 Jul 19 + 5 240 +3.528 + 1.312 + 0.170 0.716 7.492 -7.901 -2.997 Oct 27 + 4 814 + 3003 + 0.710 0.454 1.349 7.886 -8.236 -2.450 Dec. 66 + 4.346 + 2.451 + 0.099 -1.078 -1.9/5 -8.217 -8.505 -1.878 1 745 Jan + 4 506 + 2 637 + 0.301 0.871 1 .768 8.113 -8.423 -2.071 Apr. 10 + 4013 + 2.071 0.311 -1.490 -2.383 8.399 -8.645 -1.489 Jul 19 + 3 491 + 1 492 0916 2.090 2.974 8614 -8.794 -0.900 Oct 27 + 2 94 9 + 0902 1 513 2.674 3.540 8758 -8.872 -0.304 Dec. 66 + 2.364 + 0.299 -2.102 -3.239 4.081 -H.S31 -8.877 + 0.299 1746 Jan. + 2 558 + 0.500 1.904 3.052 3.903 8.815 8.883 + 0.099 Apr. 10 + 1 966 0.105 2.484 -3.601 4.423 8.839 -8.839 + 0.701 Jul 19 4- 1 36-' 0704 3038 4.116 4.902 8791 -8.722 + 1.293 Oct 2/ -1-0747 1 298 3.567 4.598 5.341 8.6/0 -8.534 + 1.875 Dec. 66 + 0.119 -1.887 -4.071 -5.046 5.740 -8.476 -8.273 + 2.447 1747 Jan -4- 3-?<> I 692 3 907 4.901 5 612 8 540 8.36fc + 2.258 Apr 10 0300 9 272 4.390 5.322 5.982 8.309 -8.061 + 2.816 Jul 19 923 2 829 4.833 5.697 6.296 8.002 -7-691 + 3.350 Oct. 27 1.540 3.364 -5.237 -6.026 -6.564 -7-628 -7.256 + 3.860 Dec. 66 2.150 3.877 -5.602 -6.308 6.777 -7-187 -6.756 + 4.346 TABLE III. Solar Nutation. Jan. 10 20 30 Feb. 9 K Cassiopese Cassiopeffi T Persei * Persei y Persei S Persei 9 Aurigte a Aurigte 8 Camelop. S Auriga; 35 Camelop. + O''l42 + 0.311 + 0.442 + 0.517 + 0.529 + O"l22 + 0.294 + 0.431 + 0.512 + 0.532 -O.'l99 -0.008 + 0.184 + 0.352 + 0.478 -0.267 -0.080 + 0.116 + 0.298 + 0.443 -0?223 -0.033 + 0.162 + 0.335 + 0.467 -0.308 -0.125 + 0.072 + 0.261 + 0.417 -0.458 -0.308 -0.121 + 0.082 + 0.273 -0.474 -0.331 -0.147 + 0.056 + 0.251 -0.492 -0.356 -0.175 + 0.027 + 0.224 -0.524 -0.405 -0.236 0.038 + 0.164 -0"529 -0.414 -0.249 -0.051 + 0.152 19 Mar. 1 11 21 31 + 0.476 + 0.365 + 0.211 + 0.033 -0.148 + 0.485 + 0.380 + 0.231 + 0.054 -0.128 + 0.543 + 0.543 + 0.478 + 0.356 + 0.192 + 0.532 + 0.558 + 0.515 + 0.412 + 0.261 + 0.540 + 0.548 + 0.491 + 0.375 + 0.216 + 0.520 + 0.561 + 0.535 + 0.445 + 0.302 + 0.431 + 0.536 + 0.575 + 0.547 + 0.454 + 0.414 + 0.527 + 0.575 + 0.555 + 0.471 + 0.393 + 0.515 + 0.573 + 0.564 + 0.488 + 0.345 + 0.484 + 0.564 + 0.576 + 0.521 + 0.335 +0.477 + 0.561 +0.577 + 0.527 Apr. 10 20 30 May 10 20 -0.311 -0.437 -0.513 -0.531 -0.490 -0.294 -0.425 -0.508 -0.533 -0.498 + 0.008 -0.176 -0.339 -0.464 -0.536 + 0.082 -0.107 -0.283 -0.426 -0.521 + 0.033 -0.152 -0.320 -0.452 -0.532 + 0.126 -0.064 -0.245 -0.398 -0.507 + 0.309 + 0.129 -0.064 -0.249 -0.401 + 0.331 + 0.155 -0.038 -0.226 -0.388 + 0.356 + 0.183 -0.008 -0.199 -0.366 + 0.406 + 0.245 + 0.056 -0.138 -0.316 + 0.416 + 0.257 + 0.069 -0.125 -0.304 30 June 9 19 29 July 9 -0.395 -0.256 -0.090 + 0.086 + 0.253 -0.409 -0.275 -0.11J + 0.066 + 0.234 -0.549 -0.501 -0.398 -0.253 -0.079 -0.557 -0.533 -0.450 -0.318 -0.152 -0.553 -0.513 -0.417 -0.276 -0.105 0.558 -0.548 -0.478 -0.356 -0.195 -0.517 -0.571 -0.563 -0.493 -0.369 -0.506 -0.569 -0.569 -0.507 -0.389 -0.493 -0.565 -0.574 -0.521 -0.412 -0.457 0.549 -0.580 -0.54/ -0.455 0.449 0.544 -0.579 -0.552 -0.464 19 29 Aug. 8 18 28 + 0.391 + 0.488 + 0.531 + 0.515 + 0.442 + 0.377 + 0.479 + 0.529 + 0.520 + 0.453 + 0.103 + 0.274 + 0.416 + 0.512 + 0.551 + 0.032 + 0.212 + 0.369 + 0.486 + 0.549 + 0.079 + 0.254 + 0.411 + 0.504 + 0.551 -0.013 + 0.171 + 0.336 + 0.465 + 0.543 -0.204 -0.017 + 0.172 + 0.342 + 0.476 -0.230 -0.044 + 0.147 + 0.322 + 0.461 -0.257 -0.074 + 0.118 + 0.298 + 0.444 -0.314 -0.137 + 0.055 + 0.241 + 0.401 -0.325 -0.151 + 0.041 + 0.229 + 0.392 Sept. 7 17 27 Oct. 1 7 17 + 0.319 + 0.158 -0.021 -0.199 -0.354 + 0.335 + 0.178 0.000 -0.180 -0.339 + 0.528 + 0.445 + 0.311 + 0.139 -0.049 + 0.551 + 0.489 + 0.371 + 0.210 + 0.023 + 0.537 + 0.461 + 0.333 + 0.164 -0.025 + 0.560 + 0.513 + 0.406 + 0.253 + 0.068 + 0.556 + 0.574 + 0.525 + 0.416 + 0.256 + 0.550 + 0.577 + 0.536 + 0.434 + 0.280 + 0.542 + 0.578 + 0.548 + 0.454 + 0.306 + 0.517 + 0.575 + 0.567 + 0.492 + 0.360 + 0.511 + 0.574 + 0.569 + 0.499 + 0.371 27 Nov. 6 16 26 Dec. 6 -0.469 -0.527 -0.521 -0.452 -0.326 -0.458 -0.524 0.525 -0.463 -0.344 -0.234 -0.391 -0.501 -0.550 -0.531 0.168 -0.340 -0.471 -0.545 -0.552 -0.212 -0.374 -0.491 -0.549 -0.540 -0.126 -0.305 -0.449 -0.537 -0.560 + 0.066 -0.133 -0.318 -0.464 -0.553 + 0.091 -0.109 -0.297 -0.449 -0.546 + 0.121 -0.079 -0.272 -0.430 -0.538 + 0.184 -0.015 -0.213 -0.386 -0.512 + 0.197 -0.002 -0.201 -0.377 -0.506 16 26 36 -0.160 + 0.026 + 0.209 -0.181 + 0.004 + 0.189 -0.447 -0.307 -0.129 -0.491 -0.368 -0.200 -0.463 -0.328 -0.153 -0.514 -0.404 -0.243 -0.574 -0.523 -0.408 0.576 -0.535 -0.427 -0.578 -0.546 -0.447 -0.575 -0.565 -0.486 -0.573 -0.569 -0.494 8 TABLE III. Solar Nutation. Jan. 10 20 30 Feb. 9 46 Auriga & Ursa maj. If Una maj. / Urae maj. Urae maj. | Urue maj. if Ursee maj. 3 Draconis i Herculis Draconis / Draconis 3 Cusiopee 0.548 -0.447 -0.291 -0.100 + 0.104 -0'.348 -0.468 -0.531 -0.527 -0.459 -0'330 -0.456 0.525 -0.530 -0.469 -0''231 -0.384 -0.487 -0.531 -0.510 -0.081 -0.259 -0.405 -0.500 -0.534 -o'oos -0.189 -0.352 -0.471 -0.531 + 0'056 -0.134 -0.308 -0.442 -0.522 + 0'510 + 0.383 + 0.208 + 0.008 -0.193 + 0.519 + 0.396 + 0.224 + 0.026 -0.176 + 0.535 + 0.424 + 0.260 + 0.064 -0.138 +0"536 + 0.426 + 0.263 + 0.069 -0.135 +0'l95 + 0.355 + 0.470 + 0.528 + 0.520 19 Mar. 1 11 21 31 + 0.294 + 0.447 + 0.546 + 0.580 + 0.545 -0.334 -0.170 + 0.014 + 0.196 + 0.353 -0.351 -0.191 -0.009 +0.174 + 0.334 -0.426 -0.290 -0.121 + 0.062 + 0.237 -0.502 -0.410 -0.268 -0.096 + 0.087 -0.527 -0.458 -0.335 -0.172 + 0.008 -0.539 -0.489 0.381 -0.229 -0.050 0.368 -0.499 -0.569 0.571 -0.507 -0.355 0.491 -0.566 -0.575 -0.515 -0.323 -0.469 -0.557 -0.5/9 -0.533 -0.320 0.467 -0.556 -0.580 -0.534 + 0.447 + 0.322 + 0.159 -0.023 -0.201 Apr. 10 20 30 May 10 ' 20 + 0.448 + 0.299 + 0.117 -0.077 -0.262 + 0.468 + 0.529 + 0.530 + 0.471 + 0.360 + 0.456 + 0.523 + 0.532 + 0.481 + 0.376 + 0.383 + 0.484 + 0.531 + 0.516 + 0.445 + 0.258 + 0.400 + 0.494 + 0.533 + 0.512 + 0.188 + 0.345 + 0.462 + 0.527 + 0.533 + 0.133 + 0.300 + 0.433 + 0.515 + 0.541 -0.384 0.217 -0.026 + 0.167 + 0.340 -0.397 0.233 0.044 + 0.150 + 0.326 -0.424 -0.269 -0.083 + 0.112 + 0.293 -0.427 -0.272 -0.086 + 0.108 + 0.290 -0.355 -0.466 -0.525 -0.524 -0.465 30 June 9 19 29 July 9 -0.416 -0.526 -0.577 -0.565 -0.492 + 0.209 + 0.036 -0.141 -0.302 -0.430 + 0.229 + 0.058 -0.118 -0.282 -0.416 + 0.325 + 0.169 -0.005 -0.178 -0.333 + 0.435 + 0.311 + 0.151 0.023 -0.196 + 0.479 + 0.373 + 0.226 + 0.055 -0.122 + 0.506 + 0.415 + 0.280 + 0.114 -0.064 + 0.474 + 0.557 + 0.578 + 0.536 + 0.436 + 0.465 + 0.553 +0.580 + 0.543 + 0.447 + 0.441 + 0.540 + 0.579 + 0.556 + 0.472 + 0.438 + 0.538 + 0.579 + 0.558 + 0.474 -0.355 -0.205 -0.034 + 0.140 + 0.301 19 29 Aug. 8 18 28 -0.364 -0.194 -0.007 + 0.183 + 0.355 -0.511 -0.537 -0.503 -0.414 -0.278 -0.503 -0.536 -0.509 -0.428 -0.297 -0.450 0.518 -0.530 -0.483 -0.382 -0.347 -0.461 -0.523 -0.529 -0.475 -0.286 -0.419 -0.506 0.537 -0.509 -0.236 -0.382 0.486 -0.537 -0.528 + 0.288 + 0.108 -0.084 -0.268 -0.422 + 0.303 + 0.125 -0.067 -0.253 -0.410 + 0.337 + 0.164 -0.028 -0.216 -0.382 + 0.339 + 0.167 -0.024 -0.213 -0.380 + 0.427 + 0.507 + 0.532 + 0.498 + 0.408 Sept. 7 17 27 Oct. 7 17 + 0.487 + 0.564 + 0.577 + 0.523 + 0.407 -0.110 + 0.071 + 0.245 + 0.392 + 0.493 -0.132 + 0.049 -t- 0.225 + 0.376 + 0.483 -0.237 0.065 + 0.116 + 0.284 + 0.420 -0.368 -0.217 -0.042 + 0.140 + 0.306 -0.423 -0.288 -0.120 + 0.064 + 0.230 -0.460 0.338 -0.177 + 0.005 + 0.188 -0.530 0.573 -0.559 0.475 -0.335 -0.523 -0.5/6 -0.564 0.486 -0.350 0.505 -0.572 -0.5/2 -0.506 -0.381 -0.503 0.571 -0.572 0.508 -0.384 + 0.271 + 0.104 -0.077 -0.249 -0.394 27 Nov. 6 16 26 Dec. 6 + 0.242 + 0.046 0.155 0.338 -0.480 + 0.537 + 0.515 + 0.432 + 0.294 + 0.121 + 0.533 + 0.520 + 0.444 + 0.302 + 0.142 + 0.506 + 0.532 + 0.493 + 0.395 + 0.247 + 0.436 + 0.515 + 0.532 + 0.483 + 0.375 + 0.390 + 0.492 + 0.536 + 0.515 + 0.430 + 0.348 + 0.469 + 0.533 + 0.532 + 0.465 -0.155 + 0.045 + 0.241 + 0.408 + 0.525 -0.171 + 0.028 + 0.226 + 0.395 + 0.518 0.209 -0.011 + 0.189 + 0.366 + 0.499 -0.212 -0.015 + 0.186 + 0.363 + 0.497 -0.492 -0.532 -0.506 -0.419 -0.280 16 26 36 -0.563 -0.576 -0.517 0.068 0.249 -0.399 -0.046 -0.229 -0.383 + 0.067 -0.121 -0.293 + 0.220 + 0.037 -0.150 + 0.291 + 0.116 -0.074 + 0.340 + 0.173 -0.015 + 0.577 + 0.557 +0.469 + 0.5/6 + 0.563 + 0.497 + 0.571 + 0.572 + 0.501 + 0.5/0 + 0.572 + 0.503 -0.107 + 0.082 + 0.259 9 TABLE IV. Aberration. Jan. 10 20 30 Feb. 9 A Cassiopeae a Cassiopeae r Persei a Persei y Persei 1730 -122 -160 -201 -234 -260 Varia- inn in 10 yrs. 1730 -114 -149 -191 -227 -256 Varia- tion in 10 yrs. 1730 + 39 - 7 - 47 - 86 -121 Varia- tion in 10 yrs. 1730 + 53 + 16 - 21 - 56 - 89 Varia- tion in 10 yrs. 1730 + 45 + 6 - 34 - 73 -110 Varia- tion in 10 yrs. + 15'.234 + 13.846 + 12.026 + 9.835 + 7-345 + 17 + 24 + 30 + 35 + 38 + 15J34 + 14.467 + 12.750 + 10.638 + 8.202 + 14 + 22 + 28 + 33 + 37 + 12'903 + 13.037 + 12.762 + 12.090 + 11.044 -16 - 8 + 1 + 10 + 18 + 1L219 + 11.556 + 11.530 + 11.145 + 10.412 -22 -16 - 8 - 2 + 7 + 12702 + 12.965 + 12.822 + 12.278 + 11.356 -17 - 7 + 3 + 13 + 24 J9 Mar. 1 11 21 31 + 4.638 + 1.803 - 1.073 - 3.902 - 6.599 -277 -286 -285 -276 -259 + 41 + 42 + 42 + 41 + 39 + 5.522 + 2.687 - 0.215 - 3.095 - 5.868 -276 -287 -289 -283 -268 + 40 + 42 + 42 + 41 + 39 + 9.662 + 7.992 + 6.088 + 4.013 + 1.831 -153 -179 -199 -213 -220 + 25 + 32 +37 + 41 + 44 + 9.366 + 8.036 + 6.471 + 4.720 + 2.839 -119 -145 -166 -182 -192 + 13 + 21 + 26 + 31 + 35 + 10.087 + 8.516 + 6.696 + 4.684 + 2.547 -142 -170 -192 -202 -217 + 32 + 40 + 46 + 52 + 55 Apr. 10 20 30 May 10 ' 20 - 9.087 -11.299 -13.177 -14.672 - 15.750 -235 -205 -169 -129 - 86 + 35 + 30 + 25 + 19 + 13 - 8.453 -10.778 -12.784 -14.419 -15.642 -246 -217 -182 -143 -100 + 36 + 31 + 26 + 21 + 15 - 0.392 - 2.592 - 4.706 - 6.676 - 8.456 -221 -216 -204 -188 -165 + 46 + 46 + 45 + 43 + 42 + 0.887 - 1.081 - 3.007 - 4.840 - 6.528 -196 -195 -188 -176 -159 + 38 + 40 + 41 + 41 +39 + 0.347 1.852 - 3.985 - 5.996 - 7-829 -220 -217 -207 -192 -172 + 57 + 57 + 55 + 53 + 48 30 June 9 19 29 July 9 -16.384 -16.564 -16.286 -15.562 -14.410 - 41 + 5 + 50 + 94 + 135 + 6 - 8 -14 -20 -16.424 -16.751 -16.614 -16.022 - 14.988 - 55 - 10 + 36 + 81 + 124 + 8 + 2 - 5 -11 -18 9.984 -11.237 -12.177 -12.782 - 13.035 -139 -110 - 77 - 43 - 7 + 35 + 30 + 24 + 18 + 10 - 8.028 - 9.301 -10.318 -11.048 -11.474 -139 -115 - 87 - 58 - 27 +37 + 33 + 29 + 24 + 17 - 9.438 -10.781 -11.825 -12.543 -12.916 -148 -119 - 88 - 55 - 20 + 42 + 35 + 28 + 20 + 11 19 29 Aug. 8 18 28 -12.861 -10.954 - 8.739 - 6.273 - 3.620 + 173 + 206 + 234 + 256 + 271 -25 -30 -34 -37 -40 - 13.543 -11.721 - 9.570 - 7-145 - 4.507 + 163 + 199 + 229 + 253 + 271 -23 -28 -32 -35 -39 -12.931 -12.472 -11.660 - 10.524 - 9.088 + 28 + 64 + 97 + 129 + 157 + 3 - 3 -12 -20 -26 11.587 -11.379 - 10.855 -10.027 - 8.914 + 5 + 37 + 68 + 97 + 124 + 12 + 5 - 2 - 8 -15 -12.934 -12.594 -11.906 -10.883 - 9.550 + 16 + 51 + 86 + 113 + 147 + 2 - 9 -17 -26 -34 Sept. 7 17 27 Oct. 7 17 - 0.852 + 1.955 + 4.720 + 7-364 + 9.802 + 279 + 279 + 270 + 254 + 230 -41 -41 -40 -38 -34 - 1.731 + 1.109 + 3.934 + 6.658 + 9.202 + 281 + 283 + 277 + 263 + 241 -40 -40 -40 -38 -35 - 7-386 - 5.469 - 3.374 - 1.172 + 1-077 + 184 + 201 + 215 + 223 + 224 -32 -35 -41 -45 -47 - 7.543 - 5.948 - 4.172 - 2.204 - 0.278 + 148 + 169 + 184 + 195 + 200 -21 -27 -32 -36 -39 - 7-939 - 6.093 - 4.061 - 1.897 + 0.335 + 173 + 194 + 210 + 220 + 223 -42 -47 -52 -55 -57 27 Nov. 6 16 26 Dec. 6 + 11.962 + 13.770 + 15.166 + 16.100 + 16.535 + 198 + 160 + 117 + 68 + 18 -29 -24 -18 -11 - 3 + 11.483 + 13.428 + 14.972 + 16.060 + 16.653 + 211 + 174 + 132 + 84 + 33 -31 -26 -20 -13 - 6 + 3.306 + 5.446 + 7-431 + 9.192 + 10.676 + 218 + 206 + 187 + 162 + 132 -47 -46 -44 -39 -34 + 1.728 + 3.691 + 5.551 + 7-247 + 8.723 + 198 + 196 + 178 + 159 + 134 -41 -42 -41 -39 -36 + 2.570 + 4.738 + 6.771 + 8.604 + 10.175 + 220 + 210 + 193 + 170 + 141 -57 -56 -52 -47 -40 16 26 36 + 16.456 + 15.860 + 14.767 - 34 - 84 -133 + 5 + 13 + 19 + 16-727 + 16.277 + 15.314 - 19 - 76 -138 + 2 + 9 + 17 + 11.829 + 12.572 + 12.976 + 95 + 57 + 18 -26 -21 -13 + 9.932 + 10.829 + 11.389 + 105 + 74 + 42 -32 -26 -21 + 11.433 + 12.334 + 12.848 + 108 + 76 + 45 -32 -23 -14 10 CONTINUATION OF TABLE IV. Aberration. Jan. 10 20 30 Feb. 9 5 Persei 9 Aurigae a Auriga; 18 Camelop. S Auriga 35 Camelop. 1730 + 58 + 26 - 7 - 39 - 70 Varia- tion in 10 yrs. 1730 + 137 + 113 + 87 + 58 + 28 Varia- tion in 10 yrs. 1730 + 115 + 95 + 74 + 52 + 26 Varia- tion in 10 yrs. 1730 + 179 + 156 + 131 + 104 + 70 Varia- tion in 10 yrs. 1730 + 172 + 160 + 142 + 119 + 92 Varia- tion in ioyr. 1730 + 158 + 150 + 134 + 113 + 90 Varia- tion in 10 yrs. + 10J048 + 10.476 + 10.576 + 10.344 + 9.793 -25 -18 -11 - 3 + 5 + 6'.471 + 7-720 + 8.727 + 9.458 + 9.894 -46 -40 -34 -25 -16 + 5J38 + 6.181 + 7.030 + 7-658 + 8.046 -42 -38 -33 -27 -20 + 5^544 + 7.223 + 8.672 + 9.848 + 10.714 -48 -44 -38 -32 -24 + 3^396 + 5.081 + 6.604 + 7-918 + 8.982 59 -56 -51 -45 -38 + 2JB09 +4.375 + 5.803 +7-047 + 8.068 -54 -49 -43 -36 -27 19 Mar. 1 11 21 31 + 8.941 + 7.821 + 6.470 + 4.934 + 3.260 - 98 -124 -144 -161 -172 + 13 + 20 + 26 + 31 + 36 + 10.024 + 9.846 + 9.372 + 8.621 + 7-618 - 2 - 33 - 61 - 88 -111 - 7 + 3 + 13 + 21 + 29 + 8.184 + 8.072 + 7-717 + 7.132 + 6.341 + 1 - 23 - 47 - 69 - 88 -13 - 5 + 3 + 11 + 18 + 11.248 + 11.436 + 11.276 + 10.780 + 9.969 + 36 + 1 - 33 - 65 - 96 -16 - 8 + 2 + 11 + 19 + 9.766 + 10.247 + 10.417 + 10.273 + 9.827 + 63 + 33 - 30 - 59 -29 -19 -10 + 1 + 11 + 8.837 + 9.333 + 9.543 + 9.468 + 9.113 + 63 + 35 + 7 - 22 49 -18 - 9 + 2 + 11 + 20 Apr. 10 20 30 May 10 20 + 1.500 - 0.294 - 2.069 - 3.779 5.373 -178 -1/8 -174 -165 -152 + 39 + 41 + 42 + 43 + 41 + 6.399 + 5.002 + 3.468 + 1.844 + 0.176 -131 -147 -158 -165 -167 + 37 + 42 +47 + 51 + 52 + 5.367 + 4.244 + 3.007 + 1.690 + 0.331 -105 -118 -128 -134 -136 + 25 + 31 + 36 + 39 + 42 + 8.870 + 7-522 + 5.965 + 4.247 + 2.417 -122 -145 -164 -177 -186 + 27 + 33 + 39 + 44 +47 + 9.097 + 8.107 + 6.891 + 5.486 + 3.933 - 86 -110 -131 -148 -161 ^169 -172 -171 -165 -155 + 20 + 29 + 37 + 44 + 49 + 8.493 + 7-631 + 6.556 + 5.301 +3.902 - 74 - 97 -117 -133 -145 + 2.8 + 36 + 43 + 47 + 51 30 June 9 19 29 July 9 - 6.814 - 8.061 - 9.084 - 9.856 -10.352 -134 -114 - 90 - 63 - 36 + 39 + 35 + 31 + 26 + 20 - 1.492 - 3.113 - 4.646 - 6.050 - 7.287 -164 -157 -147 -132 -114 + 53 + 52 + 49 + 46 + 41 -1.032 -2.363 -3.626 -4.788 -5.818 -135 -130 -121 -110 - 95 + 44 + 44 + 43 + 41 +38 + 0.527 - 1.373 - 3.232 - 4.999 - 6.629 -190 -188 -181 -170 -154 + 49 + 50 + 49 + 47 + 44 + 2.274 + 0.560 - 1.169 - 2.862 - 4.477 + 54 + 56 + 58 + 57 + 55 + 2.398 + 0.834 -0.750 -2.314 3.812 -153 -157 -157 -153 -145 + 54 + 55 + 59 + 52 + 49 19 29 Aug. 8 18 28 -10.573 -10.499 -10.133 - 9.484 - 8.565 / + 22 + 51 + 78 + 104 + 13 + 7 - 7 -14 - 8.325 - 9.135 - 9.693 - 9.983 9.994 - 92 - 68 - 42 - 15 + 14 +35 + 29 + 20 + 12 + 3 -6.690 -7.378 -7.864 -8.131 -8.172 - 78 - 59 - 38 - 15 + 8 + 34 + 29 + 24 + 17 + 10 - 8.078 - 9.307 -10.280 -10.971 -11.356 -134 -110 - 83 - 54 - 22 + 40 + 34 + 27 + 20 + 12 - 5.970 - 7-30J - 8.433 - 9.334 - 9.976 -141 -123 -102 77 - 50 + 52 + 47 + 41 + 34 + 25 5.207 6.462 -7-540 -8.411 -9.049 -133 -117 - 97 - 75 - 51 + 44 + 38 + 31 + 23 + 14 Sept. 7 17 27 Oct. 7 17 - 7.399 - 6.015 - 4.449 - 2.743 - 0.947 + 128 + 148 + 164 + 175 + 182 -21 -26 -32 -37 -40 - 9.722 - 9.169 - 8.347 - 7.277 - 5.985 + 41 + 69 + 95 + 118 + 139 - 6 -15 -24 -32 -38 -7-981 -7.560 -6.917 -6.069 -5.035 + 31 + 53 + 75 + 94 + 111 + 2 - 5 -13 -20 -27 -11.420 -11.158 -10.571 - 9.6/1 - 8.480 + 10 + 42 + 74 + 105 + 132 + 4 - 5 -13 -21 -29 -10.338 -10.406 -10.172 - 9.639 - 8.817 - 22 + 8 + 38 + 68 + 96 + 16 + 7 4 14 -23 9.434 9.550 -9.391 -8.949 -8.252 - 25 + 2 + 30 + 57 + 83 + 5 - 4 -14 -26 -31 27 Nov. 6 16 26 Dec. 6 + 0.887 + 2.705 + 4.449 + 6.061 + 7-495 + 183 + 1/8 + 168 + 152 -(-132 -42 -43 -43 -41 -40 - 4.506 - 2.883 - 1.163 + 0.599 + 2.348 + 155 + 167 + 1/4 + 176 + 171 -44 -49 -53 -55 -54 3.845 -2.532 -1.137 + 0.300 + 1.733 + 125 + 135 + 142 + 144 + 142 -33 -38 -41 -44 -45 7.026 - 5.353 - 3.508 - 1.548 + 0.468 + 156 + 176 + 190 + 198 + 201 -36 -42 -47 -50 -52 - 7-727 - 6.397 - 4.864 - 3.176 - 1.382 + 121 + 143 + 161 + 174 + 182 32 -41 -48 -53 -57 -7-297 -6.116 -4.739 3.217 -1.586 + 107 + 128 + 145 + 158 + 156 + 158 + 156 + 145 -38 -45 -52 -54 -57 16 26 36 + 8.691 + 9.564 + 10.203 + 103 + 76 + 52 -34 -28 -22 + 4.028 + 5.585 + 6.966 + 162 + 147 + 125 -53 -49 -44 + 3.116 + 4.402 + 5.550 + 133 + 122 + 105 -46 -44 -40 + 2.474 + 4.405 + 6.198 + 197 + 186 + 168 -52 -50 -47 + 0.458 + 2.287 + 4.045 + 183 + 179 + 172 -59 -60 58 + 0.098 + 1.781 + 3.410 -56 -55 -52 11 CONTINUATION or TABLE IV. Aberration. Jan. 10 20 30 Feb. 9 46 Aurigae Ursse maj. -33 -17.409 -15.627 -13.406 -10.817 - 7.936 + 153 + 200 + 241 + 2/4 + 299 -32 -30 -28 -25 -21 -17.119 - 15.484 -13.416 - 10.977 - 8.241 + 139 + 185 + 225 + 259 + 285 - 6 - 9 -11 -13 -15 -18.441 -16.880 -14.844 -12.397 - 9.614 + 130 + 170 + 224 + 262 + 291 - 4 6 - 8 - 9 -10 -18.133 - 16.624 -14.647 -12.264 - 9.548 + 125 + 174 + 218 + 255 + 284 - 6 - 8 - 9 -12 -13 -10.27S -12.574 -14.50C -16.007 -17.053 -245 -211 -172 -128 - 81 +34 + 29 + 24 + 19 + 11 30 June 9 19 29 July 9 + 9.243 + 11.680 + 13.792 + 15.521 + 16.824 + 257 + 227 + 192 + 152 + 107 -30 -26 -22 -17 -12 - 4.844 - 1.626 + 1.631 + 4.839 + 7-912 + 316 + 324 + 323 + 314 + 297 -17 -12 - 8 - 3 + 4 - 5.284 - 2.191 + 0.958 + 4.076 + 7-082 + 303 + 312 + 313 + 306 + 291 -16 -16 -17 -17 -16 - 6.572 - 3.357 - 0.056 + 3.243 + 6.453 + 313 + 331 + 330 + 325 + 312 -11 -11 -11 -11 -11 6.5/5 - 3.429 - 0.195 + 3.042 + 6.194 + 306 + 319 +324 + 319 + 307 -14 -14 -14 -14 -13 -17.623 -17-705 -17-296 -16.417 -15.084 - 33 + 16 + 64 + 111 + 154 + 4 - 2 - 9 -15 -21 19 29 Aug. 8 18 28 + 17-665 + 18.020 + 17.878 + 17.236 + 16.107 + 60 + 11 - 39 - 89 -136 - 6 + 1 + 6 + 12 + 18 + 10.772 + 13.339 + 15.544 + 17.322 + 18.620 + 271 + 239 + 199 + 154 + 104 + 8 + 13 + 17 + 21 + 25 + 9.896 + 12.442 + 14.649 + 16.456 + 17.807 + 268 + 238 + 201 + 158 + 110 -15 -14 -12 -10 7 + 9.487 + 12.266 + 14.711 + 16.755 + 18.336 + 292 + 261 + 224 + 181 + 132 -10 - 9 7 - 6 - 5 + 9.179 + 11.916 + 14.330 + 16.351 + 17.922 + 286 + 258 + 222 + 180 + 132 -13 -12 -11 8 7 -13.335 -11.215 - 8.780 - 6.091 - 3.220 + 193 + 228 + 256 + 278 + 292 -27 -32 -35 -39 -41 Sept. 7 17 27 Oct. 7 17 + 14.516 + 12.499 + 10.111 + 7-412 + 4.479 -180 -220 -254 282 -301 + 23 + 28 + 32 + 35 +37 + 19.397 + 19.621 + 19.279 + 18.369 + 16.910 + 50 - 6 - 63 -118 -172 + 28 + 29 + 31 + 31 + 31 + 18.65^ + 18.981 + 18.755 + 17-977 + 16.664 + 59 + 5 - 50 -105 -157 - 5 3 + 1 + 5 + 8 + 19.404 + 19.921 + 19.865 + 19.225 + 18.014 + 79 + 23 - 35 93 -148 - 4 - 1 + 2 + 3 + 5 + 18.991 + 19.522 + 19.490 + 18.887 + 17-721 + 80 + 25 - 32 - 88 -144 5 - 2 + 1 + 4 + 6 - 0.244 + 2.752 + 5.689 + 8.474 + 11.024 + 298 + 297 + 286 + 267 + 239 -42 -41 -40 -37 -34 27 Nov. 6 16 26 Dec. 6 + 1.394 - 1.749 - 4.853 - 7.819 -10.554 -311 -312 -304 -285 -257 + 38 +38 +37 + 34 +31 + 14.935 + 12.498 + 9.667 + 6.527 + 3.173 -221 -263 -298 -325 -341 + 31 + 29 + 26 + 22 + 18 + 14.842 + 12.562 + 9.887 + 6.896 + 3.680 -205 -248 -283 -310 -328 + 11 + 14 + 16 + 18 + 19 + 16.254 + 13.993 + 11.293 + 8.235 + 4.909 -201 -248 -288 -319 -341 + 7 + 9 + 11 + 12 + 14 + 16.017 + 13.818 + 11.187 + 8.199 + 4.948 -195 -242 -282 -312 -333 + 9 + 12 + 14 + 16 + 17 + 13.258 + 15.100 + 16.491 + 17.377 + 17.727 + 204 + 162 + 114 + 62 + 7 -29 -23 -16 - 8 - 1 16 26 36 -12.965 - 14.973 -16.511 -221 -177 -126 + 27 + 21 + 15 - 0.289 - 3.747 - 7-087 -346 -340 -324 + 13 + 8 + 2 + 0.342 - 3.013 - 6.273 -335 -331 -315 + 20 + 21 + 19 + 1.422 - 2.115 - 5.586 -351 -350 -339 + 15 + 15 + 14 + 1.533 - 1.935 - 5.343 -344 -344 -334 + 18 + 18 + 18 + 17.524 + 16.772 + 15.492 - 48 -102 -154 + 7 + 14 + 22 13 TABLE V. Reduction of the Wanstead Observations. \ CASSIOPE^:. Assuming P= 36 55' + 99". Day of Observation Observation Precession Lunar Nutation Solar Nutation Aberration Sum Reduced to 1730 Division of Microm. Seconds a // 1727 Sept. 10 145.5 143.88 - 46.56 + L55 + 0'.32 - OJ9 - 45.48 98.40 15 143.1 141.51 - 46.28 + 1.60 + 0.20 + 1.27 - 43.21 98.30 26 139.0 137.45 - 45.68 + 1.66 + 0.01 + 4.33 - 39.68 97-77 27 140.4 138.84 - 45.62 + 1.67 -0.01 + 4.61 - 39.35 99.49 30 139.7 138.14 - 45.46 + 1.69 -0.07 + 5.42 - 38.42 99.72 Nov. 23 124.9 123.51 - 42.49 + 2.00 -0.48 + 15.83 - 25.14 98.37 25 123.6 122.22 - 42.38 + 2.01 -0.47 + 15.99 - 24.85 97-37 Dec. 3 123.3 121.93 - 41.94 + 2.05 -0.37 + 16.43 - 23.83 98.10 16 122.4 121.04 - 41.22 + 2.13 -0.17 + 16.46 - 22.80 98.24 23 122.3 120.94 - 40.84 +2.17 -0.04 + 16.14 - 22.57 98.37 24 122.2 120.84 - 40.78 + 2.18 -0.02 + 16.05 - 22.57 98.27 25 122.4 121.04 - 40.73 + 2.18 0.00 + 15.98 - 22.57 98.47 1728 Jan. 1 123.4 122.03 - 41.17 + 2.24 + 0.18 + 14.94 - 22.81 99.22 9 123.8 122.42 - 39.73 + 2.28 + 0.32 + 13.79 - 23.34 99.08 14 124.3 122.92 - 39.46 + 2.30 + 0.38 + 12.93 - 23.85 99.07 Nov. 28 101.0 99.88 - 22.02 + 3.98 -0.42 + 16.25 - 2.21 97.67 Dec. 3 101.3 100.18 - 21.75 + 4.01 -0.36 + 16.46 - 1.64 98.54 10 100.3 99.19 - 21.36 + 4.04 -0.25 + 16.56 - 1.01 98.18 11 101.0 99.88 - 21.31 + 4.04 -0.23 + 16.56 - 0.94 98.94 12 101.0 99.88 - 21.25 + 4.05 -0.22 + 16.55 - 0.87 99.01 15 101.0 99.88 - 21.09 + 4.06 -0.17 + 16.48 - 0.72 99.16 20 100.2 99.09 - 20.81 + 4.08 -0.09 + 16.26 - 0.56 98.53 24 99.5 98.39 - 20.59 + 4.10 -0.02 + 16.00 - 0.51 97.88 1729 Jan. 1 99.5 98.39 - 20.13 + 4.15 + 0.14 + 15.22 - 0.62 97-77 Dec. 9 78.7 77-82 - 1.28 + 5.55 -0.28 + 16.57 + 20.56 98.38 13 78.5 77.62 - 1.06 + 5.56 -0.21 + 16.53 + 20.82 98.44 14 76.2 75.35 - 1.01 + 5.56 -0.19 + 16.51 + 20.87 96.22 16 79.5 78.61 - 0.89 + 5.57 -0.16 + 16.45 + 20.97 99.58 21 78.5 77.62 - 0.62 + 5.59 -0.08 + 16.22 + 21.11 98.73 22 78.3 77.43 - 0.56 + 5.59 -0.06 + 16.16 + 21.13 98.56 1730 Dec. 23 56.7 56.07 + 19.63 + 6.49 -0.04 + 16.11 + 42.19 98.26 1731 Jan. 4 56.5 55.87 + 20.35 + 6.51 + 0.20 + 14.77 + 41.83 97-70 1732 Jan. 19 39.0 38.57 + 41.42 + 6.65 + 0.44 + 11.96 + 60.47 99.04 1733 Jan. 10 19.0 18.79 + 61.01 + 6.02 + 0.32 + 13.83 + 81.18 99.07 1734 Dec. 22 19.8 19.58 + 100.16 + 3.02 -0.06 + 16.17 + 119.29 99.71 1735 Jan. 2 19.0 18.79 + 100.82 + 2.85 + 0.17 + 15.04 + 118.88 100.09 5 20.0 19.78 + 100.99 + 2.83 + 0.22 + 14.64 + 118.68 98.90 1739 Jan. 2 95.0 93.94 + 181.40 -5.42 + 0.17 + 15.04 + 191.19 97.25 8 91.5 90.48 + 181.73 -5.44 + 0.27 + 14.20 + 190.76 100.28 14 TABLE V. Reduction of the Wanstead Observations. a CASSIOPK