On the Results of Periodical Observations of the Positions and Distances of Nineteen of the Stars in Sir John Herschel's Lists of Stars, Favourably Situated for the Investigation of Parallax, Contained in Part III. Of the Philosophical Transactions for 1826, and Part I. 1827

PHILOSOPHICAL TRANSACTIONS. XIII. On the Results of Periodical Observations of the Positions and Distances of Nineteen of the Stars in Sir John Herschel's Lists of Stars, favourably situated for the investigation of Parallax, contained in Part III. of the Philosophical Transactions for 1826, and Part I. 1827*. By Lord Wrottesley, F.R.S. &c. Received November 14, 1850,—Read January 16, 1851. In these communications, Sir John Herschel shows, that if the component members of a double star occupy a certain position with reference to the pole of the ecliptic, and one of them be supposed to be situated within a given distance from the earth, a change will be periodically produced in the angle of position, and in the distance of the two stars forming the double star, consequent on the motion of the earth in her orbit; that the maximum of the change in the angle of position will occur at two periods of the year distant from each other about six months; and he gives formulæ by which the epochs at which that maximum occurs may be computed, and by which the amount of parallax due to a given change in the angle of position may be also found for each star; also lists of stars favourably situated for the investigation of that element, with the times of the year at which they should be observed, and the amount of parallax, which an observed change of $30'$ in the angle of position would indicate in the case of each star. On the erection of my observatory in the autumn of 1842, comprising among its instruments an equatoreal of very considerable power, I determined to employ it in the observations of the double stars contained in these lists, with the view of ascertaining whether they exhibited such decided differences in their positions, when observed at the proper periods, as to give good grounds of hope that some definite conclusion might be arrived at, as to the existence of a parallax in the objects observed, capable of being measured, or at the least, confidently announced as subsisting in fact. * I have to acknowledge my obligations to Mr. Main of the Royal Observatory, Greenwich, for many valuable suggestions during the preparation of this communication for the press. MDCCCLXI. In conducting the observations, however, difficulties arose that had not been anticipated: Sir John Herschel's lists contain sixty-nine stars; many of these, at the periods announced in the lists as proper for observation, if observed at all, must be observed at distances from the meridian too great, when the delicate nature of the inquiry is considered; many of them, having south or small northern declinations, are near the horizon when the proper period for their observation arrives. Another very serious impediment existed in the obligation imposed of obtaining half of the measures in the early morning hours; the observer, if employed in the observatory on the preceding night, was sometimes fatigued and unequal to the task; heavy fogs frequently came on at that time, and an enormous deposit of dew on the interior surface of the object-glass often seriously incommoded the observer; an evil which, until an opening was made in the tube near it, was irremediable, since the use of dew-tubes failed in preventing it. To these and other causes it is owing, that after more than six years devoted to this course of observation, I am compelled to apologise for the meagre results which, for reasons about to be mentioned, I have still ventured to lay before the Royal Society in their present shape. Of sixty-nine stars I have only obtained observations of forty-eight, and of these forty-eight, twenty-nine have only been observed at one period of the year. It is a most discouraging feature in this class of observations, that, however numerous and trustworthy the measures obtained at one period of the year may be, there may still be a failure to procure, at the expiration of six months from their date, measures worthy to be compared with them; and the function of the parallax, being the difference between the two results, the value of that element is of course affected by the whole amount of error with which either result is charged. It has often happened that a star has been observed at one of the assigned periods, and that no corresponding observations have been procured at the expiration of six months, or the next succeeding period; thus, for example, calling the first epoch in the year at which the star is marked for observation, the early, and the second the late period, a star has been observed two or more times successively at the early period, when no corresponding observations could be procured at the following late period. The question then naturally occurs, whether the communication of the measures actually obtained may not be deemed premature. I consider, however, that I have proceeded sufficiently far to demonstrate the impolicy of further perseverance, with the means at my command; the rather that instruments are now erected both at Liverpool and Oxford, which are pre-eminently suited to this class of observations, and therefore it would be only a waste of time and force, which may be more profitably employed in other ways, to devote any further attention to the inquiry. I proceed, therefore, without further apology, to describe the means employed, the mode of employing them, and the results obtained. The instrument employed was an equatoreally mounted telescope of 10 feet 9 inches focal length, with an object-glass of $7\frac{3}{4}$ inches clear aperture, of which the flint-glass is by Guinand, and the crown glass English, the whole having been finished and perfected by Dollond. This telescope is mounted in the manner usually adopted by the opticians of this country in a fixed observatory, in the immediate vicinity of my residence in Staffordshire; the polar axis is formed of four mahogany planks 14 feet 3 inches long and 10 inches square in the middle, the pivots of which are of hard bell-metal, and rest above and below on Ys attached to large and solid stone piers, which are supported by a foundation of brick-work, joined with cement, and formed into a solid mass of great extent by filling up the space enclosed by an outward circuit of brick with stones and mortar pounded together: this mass of brick-work and stone extends beyond the equatoreal room, and forms also the support of the piers of a 5-foot transit. The Declination and the Hour Circle are each 3 feet in diameter; the two verniers of the former read off to $10''$ in space, and that of the latter to seconds of time. To the telescope there is attached a parallel-wire micrometer with one equatoreal fixed, and two moveable wires; the screw heads are divided into 100 parts; the micrometer is provided with the usual position circle, graduated on silver, with its vernier which reads to $6'$ in space. The value of one part of the micrometer first employed was $0''$.15628, but from the 1st of January 1847 the value $0''$.15641 was used, the first having been determined by Mr. Beaumont, the former possessor of the instrument, and the latter by myself. There are six eye-tubes that can be used with the micrometer, with powers varying from 85 to 820, but the power almost invariably used in the observations about to be described was 450; one of 320, and sometimes a lower power, was occasionally, but very rarely, employed, and when this occurs a notice to that effect will be found in the Table containing the results of observations subjoined. The telescope is provided with a clock-work motion; the performance of the object-glass, so far as its powers have been tested, leaves nothing to be desired, but the mounting of the telescope, notwithstanding the precautions above mentioned, does not appear to be equally steady with that of some other recently erected equatoreals. Whenever the night admitted of it, ten measures both in position and distance were obtained of each object observed; when in the sequel I speak of a set of observations, the term is to be understood as applying to all the observations of a single night, which almost always comprised that number of measures both of position and distance. To each individual measure, whether of position or distance, an arbitrary weight was assigned, and registered at the time of making it, the number 10 being supposed to express a result with which the observer was entirely satisfied, and smaller numbers to denote a less degree of confidence in the value obtained; in point of fact, however, no higher number than 8 seems to have been used, and the weights employed generally range from 4 to 7. The sum of the weights of the indi- vidual measures, or the weight of the set, has been divided by 10 prior to its entry in the subjoined tables; while therefore the number 5 should express the weight of a set of average goodness, the number expressive of that weight is reduced in practice to 4. The measures when made are registered in the printed skeleton forms, originally proposed by Sir John Herschel, and adopted, I believe, by almost all observers of double stars in this country. A number of these forms were bound together in a volume, and care was taken to fill up the different columns, so far at least as they refer to measures of position and distance. Whenever the weather permitted, a set of measures was obtained of each double star, on three separate days, at each period of the year marked out as the proper one for observation. The common arithmetical mean was used in taking the average of the partial measures, comprising each set, without taking the arbitrary weights into account. At the commencement of the series, the zero of the position circle was frequently determined; but it was found to undergo no alteration that might not be attributed to error of observation; from that time it became the practice to ascertain it about every two months; but it was never found to vary more than about $2'$, a quantity very much within the error of observation in determining an angle, as will appear in the sequel; no zero was required for distance, as it was the practice to take an equal number of positive and negative readings. The observations were commenced on the 15th February 1843, and terminated the 9th October 1849; and they were made almost exclusively by three gentlemen, who acted successively as my astronomical assistants, during the progress of the work. I have always found, that observations are better made when entrusted to one competent individual, who after a short time gains experience, and a facility of manipulation, which cannot be acquired by one who only occasionally observes; and this uniformity in the mode of observing is particularly desirable, where the quantities to be determined depend on comparisons of observations made at different periods; it was a subject of great regret to me, therefore, that I was compelled to make any change in the staff of my observatory during the course of this investigation, and I only observed myself on a few nights at the time of the first appointment of each assistant. Mr. Goddard observed from the commencement of the observations to October 2, 1843; Mr. Simms from that time to the 11th of June 1844; and Mr. Philpott, my present assistant, from thence to the conclusion. The results of the observations are embodied in five tables, and it now remains to explain the manner in which those tables have been formed. The First Table.—In the first table the stars are arranged in the order of their R.A.'s; and the observations of each day, or sets, follow one another in the order of their date. An asterisk will be found attached to four of the stars in the list; these are stars, which, on comparing their mean positions as ascertained in the course of this inquiry, with those given by other observers, exhibit changes of such an amount in their angle of position as to afford satisfactory evidence of orbital motion. This fact being admitted, it is plain that these stars cannot be rendered available in the present inquiry; it was deemed unnecessary therefore to extend to them the method of reduction employed in the case of the other stars; the observations, however, are given with the others in their proper place. The third and seventh columns of the table contain the arithmetical mean of the individual measures, both in position and distance, obtained on the day specified in the first column. The quantities inserted in the fourth and fifth columns headed "probable error" and "computed weight," refer to the positions only, and have been computed from the formulae \[ P^2 = \frac{0.45494}{n(n-1)} \times \text{sum of } \varepsilon^2, \] \[ W = \frac{1}{P^2}, \] where \[ P = \text{probable error of a single set of measures}, \] \[ n = \text{the number of measures}, \] \[ \varepsilon = \text{the individual errors}, \] and \[ W = \text{the weight of the result}; \] numbers proportional to the computed values of \( W \) being inserted in the Table. The average probable error of all the sets, 211 in number, is 8'98, and the average weight, 0'0124. The quantities inserted in the sixth and eighth columns, headed "assigned weight," represent the sum of the weights, divided by 10, assigned by the observer to the individual measures of position and distance forming the set, or the arbitrary weights of the sets. The magnitudes and colours of the stars were noted on each night of observation, and are inserted in the ninth and tenth columns; where one colour only is named, it is to be understood as applying to both stars; and where two are specified, the colour of the brighter component, or, in cases of equal brightness, of the star called A, is placed first in order. The eleventh column contains the initial of the observer's name. The results of each epoch and year are for the sake of distinctness separated by a blank space. ### Table I. | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |---------------------|-----------------|----------|---------------|----------------|----------------|----------|----------------|------------|--------|----------| | **γ Arietis.** | | | | | | | | | | | | 1843. July 11 | 0.523179 | 44 | 21:18 | 2 | 5 | 9:383 | 5 | 5—5 | White. | G. | | Aug. 7 | 0.597178 | 59 | 14:02 | 5 | 7 | 9:103 | 7 | 6—6 | Yellowish green. | G. | | 11 | 0.608179 | 8 | 9:40 | 11 | 8 | 8:865 | 8 | 6—6 | Yellowish. | G. | | 1844. Jan. 13 | 0.033179 | 42 | 8:66 | 13 | 5:3 | 8:976 | 5:1 | 5—5 | White. | S. | | Feb. 8 | 0.104179 | 43 | 15:23 | 4 | 4:1 | 8:933 | 4:2 | 5—5 | White. | S. | | 1845. Jan. 21 | 0.055178 | 48 | 13:96 | 5 | 3:2 | 8:720 | 2:8 | 5—5 | Yellowish. | P. | | 24 | 0.063181 | 24 | 8:94 | 13 | 2:9 | 8:943 | 3:1 | 5:6—5:6 | Yellowish. | P. | | Feb. 1 | 0.085180 | 59 | 11:98 | 7 | 1:9 | 8:837 | 1:8 | 5:6—5:6 | Yellowish. | P. | | 17 | 0.129179 | 57 | 16:02 | 4 | 7:1 | 8:794 | 7:3 | 5:6—5:6 | Yellow. | P. | | 1847. Jan. 29 | 0.077178 | 13 | 7:36 | 19 | 5:7 | 8:796 | 5:8 | 5—5 | Yellow. | P. | | 31 | 0.082178 | 15 | 9:86 | 10 | 5:8 | 8:750 | 5:9 | 5:6—5:6 | Yellow. | P. | | Aug. 3 | 0.586179 | 19 | 11:04 | 8 | 5:6 | 8:736 | 5:8 | 5—5 | Yellowish. | P. | | 19 | 0.630178 | 36 | 8:14 | 15 | 6:1 | 8:700 | 6:2 | 5:6—5:6 | Yellowish. | P. | | **32 Eridani.** | | | | | | | | | | | | 1843. Aug. 18 | 0.627346 | 29 | 9:91 | 10 | 8 | 6:866 | 8 | 6:7—8 | White. | G. | | Sept. 7 | 0.674345 | 24 | 7:10 | 20 | 6 | 6:784 | 6 | 6—7 | White. | G. | | 7 | 0.683345 | 56 | 7:58 | 18 | 7 | 6:981 | 7 | 6:7—8 | White. | G. | | 1845. Feb. *7* | 0.101351 | 51 | 9:28 | 12 | 2:9 | 6:677 | 3:2 | 6:7—8 | Yellow and blue. | P. | | 16 | 0.126350 | 42 | 10:35 | 9 | 7 | 6:998 | 6:8 | 6:7—8:9 | Red. | P. | | 17 | 0.129349 | 41 | 11:72 | 7 | 6:8 | 6:758 | 6:6 | 6:7—8:9 | Orange. | P. | | 1846. Feb. 10 | 0.110348 | 23 | 8:44 | 14 | 4:1 | 6:664 | 4:2 | 7—9 | White and bluish. | P. | | 1847. Jan. 31 | 0.082347 | 12 | 6:60 | 23 | 4:8 | 6:642 | 5 | 7—9 | Yellow and blue. | P. | | 1849. Feb. 17 | 0.129346 | 39 | 11:97 | 7 | 2:2 | 6:714 | 2:1 | 6—8 | Yellow and bluish. | P. | | **ω Aurigae.** | | | | | | | | | | | | 1843. Sept. 8 | 0.684349 | 28 | 11:46 | 8 | 7:4 | 6:588 | 7:4 | 7:8—9:10 | White. | G. | | 16 | 0.706350 | 20 | 14:38 | 5 | 7 | 6:367 | 7 | 7:8—9:10 | White. | G. | | 24 | 0.729351 | 19 | 10:55 | 9 | 7 | 6:343 | 7 | 8—10 | White. | G. | | 1844. Sept. 25 | 0.734351 | 37 | 12:30 | 7 | 6:6 | 6:724 | 6:7 | 7:8—10 | Yellowish and light blue. | P. | | 26 | 0.736351 | 6 | 13:43 | 6 | 6:9 | 6:546 | 6:6 | 7:8—10 | Yellowish and light blue. | P. | | Oct. 10 | 0.775351 | 19 | 14:92 | 5 | 5:5 | 6:539 | 5:6 | 7:8—10 | Yellowish and light blue. | P. | | 1845. Sept. 22 | 0.723351 | 4 | 11:93 | 7 | 5:7 | 6:229 | 5:8 | 7:8—10 | Yellowish and light blue. | P. | | 30 | 0.745351 | 59 | 23:20 | 2 | 3:5 | 6:384 | 3:1 | 7—10 | Yellowish and light blue. | P. | | 1846. Mar. 7 | 0.178350 | 37 | 9:35 | 11 | 4:8 | 6:457 | 4:8 | 7:8—10 | Yellow and whitish. | P. | | 12 | 0.192351 | 37 | 14:81 | 5 | 5:8 | 6:442 | 5:9 | 7—10 | Yellow and white. | P. | | 13 | 0.194349 | 51 | 13:15 | 6 | 4:8 | 6:292 | 4:9 | 7—9:10 | Yellow and blue. | P. | | 1847. Mar. 12 | 0.192351 | 10 | 12:52 | 6 | 5:6 | 6:250 | 5:5 | 8—9:10 | White and pale blue. | P. | | 24 | 0.225351 | 35 | 20:59 | 2 | 2:2 | 6:297 | 2:1 | 7:8—9:10 | Pale yellow and pale blue. | P. | * A power of 190 used. ### Table I. (Continued.) | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |---------------------|-----------------|----------|----------------|----------------|----------------|----------|----------------|------------|--------------------------|---------| | 1848. Mar. 31. | '246 | 351° 47' | 11·05 | 8 | 5 | 6·233 | 5 | 6·7—9 | Yellow and pale yellow. | P. | | Apr. 1. | '249 | 352° 8' | 10·61 | 9 | 5·8 | 6·230 | 5·4 | 6·7—8·9 | Yellow. | P. | | 1849. Mar. 17. | '205 | 351° 14' | 12·01 | 7 | 5·4 | 6·260 | 5·5 | 7·8—9·10 | Yellow and white. | P. | #### 118 Tauri. | Year | Month | Day | Position | Fraction | Error | Weight | Weight | Magnitude | Colour | Observer | |--------------------|-------|-----|----------|----------|-------|--------|--------|-----------|-------------------------|----------| | 1843. | Sept. | 24. | '728 | 196° 46' | 11·31 | 8 | 7 | 4·866 | 8—9 | G. | | | | 27. | '736 | 196° 36' | 5·48 | 33 | 7 | 4·612 | 8—9 | G. | | 1844. | Mar. | 10. | '189 | 195° 20' | 5·53 | 33 | 3·6 | 5·065 | 8—9·10 | S. | | | | 29. | '241 | 195° 22' | 8·57 | 14 | 5·8 | 4·967 | 8—9·10 | S. | | | | 31. | '246 | 196° 40' | 8·73 | 13 | 4 | 5·030 | 8—9·10 | S. | | | Sept. | 24. | '731 | 193° 25' | 10·71 | 9 | 5·4 | 5·129 | 8—9 | P. | | | | 25. | '734 | 195° 9' | 8·93 | 13 | 7 | 5·087 | 8—9·10 | P. | | | | 29. | '745 | 195° 54' | 13·20 | 6 | 2·2 | 5·232 | 8—9·10 | P. | | 1845. | Feb. | 26. | '153 | 192° 1' | 25·48 | 2 | 5·8 | 4·796 | 7·8—9 | P. | | | Mar. | 7. | '178 | 193° 30' | 8·86 | 13 | 5·5 | 4·939 | 7·8—9 | P. | | | | 8. | '181 | 194° 8' | 15·76 | 4 | 3·3 | 4·984 | 7—9 | P. | | | | *13.| '194 | 191° 17' | 43·84 | 1 | 1·4 | 5·033 | 7—9 | P. | | | | 20. | '214 | 196° 49' | 17·13 | 3 | 5 | 5·097 | 7—9 | P. | | | Sept. | 22. | '723 | 193° 23' | 13·62 | 5 | 6·2 | 4·835 | 7—9 | P. | | 1846. | Feb. | 28. | '159 | 196° 7' | 10·35 | 9 | 3·9 | 5·035 | 7—8·9 | P. | | | Mar. | 7. | '178 | 195° 11' | 7·59 | 17 | 5·5 | 5·034 | 7—8·9 | P. | #### 41 Aurigæ. | Year | Month | Day | Position | Fraction | Error | Weight | Weight | Magnitude | Colour | Observer | |--------------------|-------|-----|----------|----------|-------|--------|--------|-----------|-------------------------|----------| | 1843. | Feb. | 15. | '123 | 351° 25' | 16·19 | 4 | 4·6 | 7·856 | 7—8 | W.andG. | | | Mar. | 1. | '162 | 352° 22' | 19·92 | 3 | 5·2 | 7·836 | 8—9 | W.andG. | | | | 17. | '205 | 355° 0' | 9·35 | 11 | 7 | 8·445 | 7·8—8 | G. | | | Sept. | 1. | '665 | 352° 0' | 14·44 | 5 | 5·9 | 7·857 | 8—9 | W.andG. | | | | 8. | '684 | 354° 18' | 4·66 | 46 | 7·8 | 7·930 | 8—9 | G. | | | | 16. | '706 | 353° 9' | 10·20 | 10 | 6·8 | 7·820 | 8—9 | G. | | 1845. | Feb. | 26. | '153 | 352° 41' | 11·46 | 8 | 5 | 8·097 | 8—9 | P. | | | Mar. | 7. | '178 | 352° 22' | 19·92 | 3 | 5·2 | 7·836 | 8—9 | P. | | | | 12. | '192 | 351° 57' | 9·54 | 11 | 2·2 | 8·262 | 7·8—8·9 | P. | | | | 17. | '205 | 351° 23' | 9·20 | 12 | 5·8 | 7·681 | 8—9 | P. | | | | 20. | '214 | 351° 20' | 14·94 | 5 | 6 | 7·849 | 7·8—9 | P. | | 1846. | Feb. | 28. | '159 | 351° 34' | 10·90 | 8 | 5·6 | 7·816 | 7·8—9 | P. | | | Mar. | 7. | '178 | 352° 3' | 9·40 | 11 | 6 | 7·949 | 7·8—8·9 | P. | | 1847. | Mar. | 10. | '186 | 352° 42' | 9·79 | 10 | 4·6 | 7·925 | 7·8—9 | P. | | | | 12. | '192 | 353° 11' | 8·71 | 13 | 6·9 | 7·851 | 7·8—8·9 | P. | | 1848. | Mar. | 31. | '246 | 353° 8' | 4·91 | 42 | 5·8 | 7·843 | 7·8—8·9 | P. | | | Apr. | 1. | '249 | 353° 18' | 7·71 | 17 | 5·9 | 7·876 | 7·8—8 | P. | * A power of 320 used. † Ibid. ### Table I. (Continued.) | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |---------------------|-----------------|----------|----------------|----------------|----------------|----------|----------------|------------|--------|---------| | **δ Geminorum.** | | | | | | | | | | | | 1843. Apr. 5. | .257 194 29 | 10·57 | 9 | 5·8 | 7·610 | 5·8 | 3—10 | White. | G. | | 10. | .271 195 34 | 79·59 | 0·2 | 0·4 | 8·400 | 0·4 | 3—10 | White. | G. | | 11. | .274 194 12 | 9·07 | 12 | 5·2 | 7·614 | 4·9 | 3—9 | White. | G. | | 1844. Mar. 29. | .241 197 58 | 12·35 | 7 | 5·5 | 7·310 | 5·7 | 3·4—11 | Red. | S. | | Apr. 1. | .249 198 5 | 13·45 | 6 | 5·2 | 7·468 | 5·5 | 3·4—11 | Red. | S. | | 25. | .315 198 30 | 7·89 | 16 | 4·6 | 7·344 | 4·6 | 3·4—11 | Red. | S. | | 1845. Oct. 31. | .830 197 54 | 17·95 | 3 | 5·8 | 7·295 | 5·6 | 3—11 | Yellow and white. | P. | | Nov. 12. | .862 198 30 | 9·14 | 12 | 5·8 | 7·322 | 5·8 | 3—11 | Orange and light blue. | P. | | 1846. Apr. 9. | .268 198 42 | 9·19 | 12 | 5·8 | 7·355 | 5·8 | 3·4—10·11 | Yellow and white. | P. | | **Anon. Cancri.** | | | | | | | | | | | | 1843. Mar. 18. | .208 353 14 | 24·99 | 2 | 8·6 | 3·802 | 8·5 | 8—8·9 | White. | W.andG. | | 29. | .238 354 33 | 5·25 | 36 | 3·6 | 4·580 | 3·6 | 8—8·9 | White. | G. | | Apr. 11. | .274 352 59 | 9·65 | 11 | 5·8 | 4·015 | 6·9 | 7—7·8 | White. | G. | | 1844. Apr. 1. | .249 351 25 | 8·40 | 14 | 6·6 | 3·557 | 6·6 | 8·9—9·10 | White. | S. | | May 1. | .331 352 24 | 11·06 | 8 | 3 | 3·599 | 3 | 8·9—10 | White. | S. | | 2. | .334 352 10 | 19·26 | 3 | 1·8 | 3·598 | 1·8 | 8·9—10 | White. | S. | | 1845. Apr. 3. | .252 354 3 | 10·23 | 10 | 6 | 3·498 | 6 | 8·9—10 | White. | P. | | 8. | .266 353 11 | 19·53 | 3 | 5·6 | 3·361 | 5·7 | 8·9—10 | White. | P. | | 20. | .298 353 10 | 8·47 | 14 | 5 | 3·314 | 5·3 | 8·9—10 | White. | P. | | Oct. 31. | .830 351 29 | 11·94 | 7 | 5·9 | 3·563 | 5·7 | 7·8—9·10 | Light blue. | P. | | Nov. 12. | .862 352 5 | 15·23 | 4 | 6 | 3·617 | 6·1 | 7·8—9·10 | Light blue. | P. | | 1848. Apr. 3. | .255 353 42 | 9·58 | 11 | 5·8 | 3·479 | 5·7 | 8—9 | Deep yellow and pale yellow. | P. | | **φ² Cancri.** | | | | | | | | | | | | 1843. Mar. 24. | .225 30 59 | 13·26 | 6 | 6·2 | 4·946 | 6 | 7—7 | White. | G. | | 28. | .235 31 10 | 10·52 | 9 | 4 | 5·074 | 3·2 | 7—7 | White. | G. | | Apr. 20. | .298 31 54 | 7·44 | 18 | 6 | 4·930 | 6 | 5·6—5·6 | White. | G. | | 1844. May 2. | .334 33 3 | 10·75 | 9 | 4·2 | 4·835 | 4·2 | 6·7—6·7 | Reddish. | S. | | 5. | .342 32 52 | 8·56 | 14 | 4·3 | 4·889 | 4 | 6·7—6·7 | Reddish. | S. | | 13. | .364 33 16 | 5·40 | 34 | 5 | 5·062 | 4·8 | 6·7—6·7 | White. | S. | | 1845. Mar. 20. | .214 30 49 | 19·04 | 3 | 6 | 5·011 | 6 | 7—7 | Yellow. | P. | | 24. | .225 32 15 | 11·54 | 8 | 6·2 | 4·696 | 5·8 | 7—7 | Yellow. | P. | | Apr. 2. | .249 33 2 | 11·21 | 8 | 4·8 | 4·779 | 4·1 | 7—7 | Yellow. | P. | | 3. | .252 33 4 | 11·88 | 7 | 6·4 | 4·642 | 6·6 | 7—7 | Yellow. | P. | | Nov. 12. | .862 34 47 | 16·35 | 4 | 5·1 | 4·632 | 4·5 | 7—7 | Light blue. | P. | | 22. | .890 33 4 | 11·43 | 8 | 7 | 4·701 | 6·8 | 7—7 | Light blue. | P. | | 1846. Mar. 27. | .233 30 46 | 16·79 | 4 | 4 | 4·763 | 4 | 7—7 | Bluish. | P. | | Apr. 9. | .268 32 34 | 11·38 | 8 | 5 | 4·680 | 4·9 | 7—7 | Bluish. | P. | ### Table I. (Continued.) | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |---------------------|-----------------|----------|----------------|----------------|----------------|----------|----------------|------------|--------|---------| | **2 Comæ Berenices.** | | | | | | | | | | | | 1843. May 2. | .331235 15 38:45 | 1 | 0:6 | 3:939 | 0:6 | 6:7—8:9 | White. | G. | | 3. | .334237 16 14:52 | 5 | 5 | 4:056 | 5 | 6:7—8:9 | Yellowish and white. | G. | | 5. | .339238 47 19:61 | 3 | 4 | 3:947 | 4 | 6:7—9 | White. | G. | | 10. | .353237 8 14:97 | 5 | 4 | 3:777 | 4 | 6:7—9 | White. | G. | | 1844. May 13. | .364243 58 6:72 | 22 | 4:6 | 4:092 | 3:8 | 6:7—9 | Red. | S. | | 23. | .392243 31 14:43 | 5 | 4 | 4:129 | 4 | 6:7—8:9 | Reddish. | S. | | June 10. | .441237 2 6:56 | 23 | 6:4 | 4:145 | 6 | 6:7—8:9 | Orange. | S. | | Nov. 20. | .887237 23 10:20 | 10 | 3:6 | 4:043 | 3:6 | 7—9 | Yellowish blue and blue. | P. | | 1845. May 5. | .339238 46 19:60 | 3 | 4:2 | 3:990 | 4:2 | 6:7—10 | Yellow and light blue. | P. | | 13. | .361236 55 20:89 | 2 | 5:7 | 4:052 | 5:4 | 6:7—9:10 | Yellow and bluish. | P. | | 19. | .378236 38 17:58 | 3 | 5:8 | 4:066 | 5:7 | 6:7—9:10 | Yellow. | P. | | Nov. 22. | .890240 25 9:44 | 11 | 4:9 | 3:817 | 4:8 | 7—9 | White and yellowish. | P. | | 1846. May 7. | .345236 20 13:73 | 5 | 1:5 | 3:829 | 1:5 | 7—9 | White. | P. | | May 8. | .348236 42 22:49 | 2 | 4:6 | 3:809 | 4:5 | 7—9 | White. | P. | | 11. | .356236 41 12:32 | 7 | 5:9 | 3:795 | 5:6 | 7—9 | Orange and pale blue. | P. | | 1847. May 26. | .397238 10 13:91 | 5 | 5:4 | 3:618 | 5:2 | 6:7—8 | Pale yellow and blue. | P. | | 1848. May 3. | .337239 51 11:68 | 7 | 5:7 | 3:709 | 5:2 | 6:7—8 | White and pale blue. | P. | | 5. | .342239 20 17:40 | 3 | 1:7 | 3:868 | 1:5 | 6:7—8:9 | Yellow and pale blue. | P. | | 12. | .361238 28 5:60 | 32 | 4:4 | 3:618 | 3:5 | 6:7—8:9 | Yellow and pale blue. | P. | | **39 Bootis.** | | | | | | | | | | | | 1843. Mar. *2. | .164 41 11 ...... | ... | 0:9 | 3:993 | 0:9 | 7—7:8 | White. | W.and G. | | +4. | .170 43 1 ...... | ... | 2 | 4:080 | 2 | 8—8:9 | White. | W.and G. | | 6. | .175 43 18 ...... | ... | 7:6 | 3:951 | 7:8 | 8—8:9 | White. | G. | | Aug. 18. | .627 43 25 ...... | ... | 6 | 3:764 | 6 | 6—6:7 | White. | G. | | 19. | .630 44 1 ...... | ... | 7 | 3:922 | 7 | 6—6:7 | White. | G. | | Sept. 4. | .674 44 3 ...... | ... | 7 | 3:854 | 7 | 6—7 | White. | G. | | **3 Serpentis.** | | | | | | | | | | | | 1843. Aug. 1. | .580196 8 ...... | ... | 8 | 3:137 | 8 | 4—5 | Yellowish. | G. | | 7. | .597195 37 ...... | ... | 7 | 3:003 | 7 | 3—4 | White. | G. | | 10. | .605195 1 ...... | ... | 5 | 2:950 | 5 | 3—4 | White. | G. | | 1844. July 26. | .567197 15 ...... | ... | 1:5 | 3:146 | 1:7 | 3—5 | Yellowish and light blue. | P. | | Aug. 4. | .591192 13 ...... | ... | 4 | 3:718 | 4 | 3—5 | Yellowish and light blue. | W.and P. | | 9. | .605192 58 ...... | ... | 1:6 | 3:133 | 1:6 | 3—5 | Yellowish and light blue. | P. | | 28. | .657197 34 ...... | ... | 5 | 3:310 | 5 | 3—5 | Yellowish and light blue. | P. | | 29. | .660197 16 ...... | ... | 5 | 3:151 | 5 | 3—5 | Yellowish and yellowish blue. | P. | | 1845. Feb. 13. | .118192 18 ...... | ... | 5:4 | 3:185 | 5:2 | 3—5 | Yellow. | P. | | 17. | .129190 47 ...... | ... | 7:6 | 3:135 | 7:6 | 3—5 | Yellow and yellowish. | P. | | 17. | .129192 26 ...... | ... | 6:8 | 3:105 | 6:3 | 3—5 | Yellow and yellowish. | P. | * A power of 320 used. † Ibid. | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |--------------------|-----------------|----------|---------------|----------------|----------------|----------|----------------|------------|--------|----------| | 1845. Aug. 7 | .597 | 194 40 | | 5·4 | 3·105 | 5·2 | 4·5—6 | Yellow | P. | | | .621 | 194 53 | | 5·4 | 2·910 | 5·6 | 4·5—6 | Yellow | P. | | Aug. 28. | .654 | 195 20 | | 6·6 | 2·990 | 6·6 | 4—6 | Yellow and light blue. | P. | | 1846. July 25 | .561 | 194 35 | | 4·9 | 2·829 | 4·6 | 3·4—5·6 | Yellow and light blue. | P. | | | .575 | 195 4 | | 1·5 | 2·970 | 1·4 | 3·4—5 | Yellow and pale blue. | P. | | Aug. 5. | .591 | 194 19 | | 4·9 | 2·764 | 4·7 | 3·4—5 | Yellow and pale blue. | P. | | 1847. Mar. 10 | .186 | 192 41 | | 6 | 2·903 | 5·4 | 3·4—5·6 | Yellow and yellowish. | P. | | July 29. | .572 | 193 32 | | 4·9 | 3·021 | 4·4 | 3·4—6 | Orange and pale yellow. | P. | | | .575 | 193 3 | | 4·6 | 2·974 | 4·2 | 3·4—5·6 | Orange and yellow. | P. | | Aug. 1. | .580 | 193 35 | | 6·2 | 2·805 | 6·3 | 3·4—6 | Orange and yellow. | P. | | 1848. Aug. 19 | .632 | 195 9 | | 0·8 | 2·847 | 0·7 | 4·5—6·7 | Yellow and pale yellow. | P. | | | .663 | 196 3 | | 4·3 | 2·908 | 4·3 | 4—6 | Yellow. | P. | | Sept. 4. | .676 | 195 11 | | 4·9 | 2·986 | 4·7 | 4—6 | Yellow and pale yellow. | P. | **178 (Bode) Librae.** | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |--------------------|-----------------|----------|---------------|----------------|----------------|----------|----------------|------------|--------|----------| | 1843. Aug. 1 | .580 | 7 39 | 7·92 | 16 | 7 | 12·374 | 7 | 8—8 | White. | G. | | | .597 | 6 49 | 11·65 | 7 | 5·4 | 11·798 | 5·4 | 8—8 | White. | G. | | | .608 | 8 14 | 8·47 | 14 | 5 | 12·195 | 5 | 8—8 | White. | G. | | 1845. Feb. 14 | .120 | 7 15 | 15·12 | 4 | 3 | 12·232 | 3 | 8—8 | Yellow and white. | P. | | 1847. Aug. *2 | .583 | 7 39 | 5·25 | 36 | 4·2 | 11·706 | 4·6 | 7·8—7·8 | White. | P. | | | .586 | 7 15 | 7·55 | 18 | 5·1 | 11·844 | 4·6 | 7·8—7·8 | White. | P. | **μ Draconis *.** | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |--------------------|-----------------|----------|---------------|----------------|----------------|----------|----------------|------------|--------|----------| | 1843. Mar. †8 | .181 | 15 0 | | 0·8 | 2·844 | 0·9 | 7—7—8 | Bluish. | W. | | | .205 | 17 12 | | 4·3 | 3·693 | 4·3 | 8—8 | White. | G. | | | .225 | 17 27 | | 5·7 | 3·402 | 5·3 | 7—7—8 | Bluish. | W.andG. | | Aug. 22. | .638 | 17 47 | | 6 | 3·793 | 6 | 8—8 | White. | G. | | | .649 | 16 36 | | 6 | 3·233 | 6 | 8—8 | White. | G. | | | .649 | 15 19 | | 6·1 | 3·271 | 6·1 | 7·8—7·8 | Bluish. | W. | | 1844. Aug. 24 | .657 | 17 46 | | 4 | 3·241 | 4 | 7·8—7·8 | Light blue. | P. | | | .663 | 16 40 | | 5 | 3·238 | 5 | 7—7 | Light blue. | P. | | | .665 | 17 5 | | 5 | 3·285 | 5 | 7—7 | Light blue. | P. | | Sept. 2. | .671 | 17 16 | | 4·2 | 3·110 | 4·2 | 7—7 | Light blue. | P. | | 1845. Aug. 24 | .643 | 13 16 | | 6·1 | 3·202 | 6·1 | 7—7 | Bluish. | P. | | | .652 | 12 27 | | 6·8 | 3·209 | 6·4 | 7—7 | Bluish. | P. | | | .654 | 12 58 | | 7 | 3·199 | 6·9 | 6·7—6·7 | Bluish. | P. | | 1846. Mar. 9 | .183 | 13 16 | | 6·9 | 3·074 | 6·8 | 7—7 | Blue. | P. | | | .214 | 12 29 | | 5·3 | 3·063 | 4·8 | 7—7 | Blue. | P. | | Sept. 1. | .665 | 11 36 | | 1·8 | 2·943 | 1·7 | 6·7—6·7 | Pale yellow. | P. | | | .668 | 11 35 | | 6·5 | 2·996 | 6·3 | 6·7—6·7 | Yellow. | P. | | | .674 | 11 52 | | 6 | 3·007 | 5·9 | 6·7—6·7 | Yellow. | P. | | 1849. Sept. 5 | .676 | 10 0 | | 5·2 | 2·980 | 5·3 | 6—6 | Yellow. | P. | | | .684 | 9 24 | | 4·6 | 3·023 | 4·2 | 6·7—6·7 | Pale yellow. | P. | * A power of 190 used. † The powers of 320 and 450 used. | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |--------------------|-----------------|----------|---------------|----------------|----------------|----------|----------------|------------|--------|---------| | **100 Herculis.** | | | | | | | | | | | | 1843. Mar. 28. | .235 | 1 25 | 10-02 | 10 | 6 | 13-855 | 6 | 6-7—7 | Bluish. | G. | | Apr.* 13. | .279 | 0 50 | 18-24 | 3 | 4-5 | 14-471 | 4-2 | 5—5-6 | Bluish. | W.and G. | | 18. | .293 | 2 6 | 10-87 | 9 | 5 | 14-508 | 5 | 6—6 | Bluish. | G. | | Aug.+ 22. | .638 | 2 52 | 6-02 | 28 | 8 | 14-276 | 8 | 6—6 | White. | G. | | 24. | .643 | 2 20 | 2-77 | 130 | 8 | 13-951 | 8 | 6—6 | White. | G. | | 30. | .660 | 2 34 | 6-62 | 23 | 7 | 14-057 | 7 | 7—7 | White. | G. | | 1844. Aug. 30. | .663 | 2 12 | 10-24 | 10 | 5 | 13-916 | 5 | 6—6 | Light blue. | P. | | Sept. 7. | .684 | 2 41 | 6-33 | 25 | 5 | 13-941 | 5-7 | 6—6 | Bluish. | P. | | 10. | .693 | 2 38 | 4-44 | 51 | 5 | 14-031 | 5-9 | 6—6 | Bluish. | P. | | 1845. Mar. 11. | .189 | 1 34 | 10-94 | 8 | 5-3 | 13-986 | 5-1 | 6—6 | Blue. | P. | | 17. | .205 | 1 44 | 11-08 | 8 | 6 | 14-031 | 6 | 6-7—6-7 | Bluish. | P. | | 19. | .211 | 1 41 | 13-06 | 6 | 6-3 | 13-858 | 6-3 | 6-7—6-7 | Yellowish blue. | P. | | Aug. 24. | .643 | 2 11 | 3-80 | 69 | 7 | 13-772 | 6-7 | 6-7—6-7 | Blue. | P. | | 27. | .652 | 1 54 | 3-26 | 94 | 6 | 14-022 | 6 | 6-7—6-7 | Bluish. | P. | | 28. | .654 | 2 1 | 4-61 | 47 | 7 | 13-900 | 6-9 | 6—6 | Yellow. | P. | | 29. | .657 | 2 18 | 3-63 | 76 | 6 | 14-015 | 6 | 6—6 | Yellow. | P. | | 1846. Aug. 29. | .657 | 2 32 | 6-24 | 26 | 2-3 | 13-944 | 2-4 | 6-7—6-7 | Pale yellow. | P. | | Sept. 2. | .668 | 2 9 | 6-51 | 24 | 6-1 | 13-893 | 5-8 | 7—7 | Pale yellow. | P. | | 4. | .674 | 2 9 | 7-13 | 20 | 5-6 | 13-970 | 5-9 | 7—7 | Pale yellow. | P. | | 1847. Mar. 18. | .208 | 2 45 | 4-73 | 45 | 5-1 | 13-989 | 5-2 | 6-7—6-7 | Bluish. | P. | | 28. | .235 | 2 57 | 8-09 | 15 | 4-2 | 13-977 | 4-3 | 6-7—6-7 | Pale yellow. | P. | | Sept. 8. | .684 | 2 45 | 5-49 | 33 | 6-8 | 13-993 | 6-5 | 6-7—6-7 | Pale yellow. | P. | | 27. | .736 | 2 10 | 6-00 | 28 | 6-6 | 13-941 | 6-5 | 6-7—6-7 | Pale yellow. | P. | | 1848. Sept. 4. | .676 | 2 30 | 4-99 | 40 | 5-5 | 13-826 | 5-7 | 6-7—6-7 | Yellow. | P. | | 16. | .709 | 2 25 | 4-61 | 47 | 6-7 | 13-993 | 6-6 | 6-7—6-7 | Yellow. | P. | | 1849. Sept. 8. | .684 | 1 4 | 4-52 | 49 | 5-3 | 14-083 | 5-6 | 7—7 | Yellow. | P. | | Oct. 9. | .769 | 1 41 | 5-22 | 37 | 5-2 | 14-057 | 5-3 | 6-7—6-7 | Yellow. | P. | | **579 Struve.** | | | | | | | | | | | | 1843. Sept. 9. | .687 | 159 56 | 6-83 | 22 | 7 | 5-249 | 7 | 9—9 | White. | G. | | 16. | .706 | 159 29 | 12-44 | 7 | 7 | 5-056 | 7 | 9—9 | White. | G. | | 20. | .717 | 159 25 | 11-14 | 8 | 6 | 4-850 | 6 | 9—9 | White. | G. | | 1844. Oct. 5. | .761 | 160 8 | 12-41 | 7 | 5-1 | 5-441 | 4-9 | 8—8 | Bluish. | P. | | 7. | .767 | 159 28 | 26-85 | 1 | 3-4 | 5-240 | 3-6 | 8-9—8-9 | Light blue. | P. | | 10. | .775 | 160 8 | 10-14 | 10 | 5-7 | 5-332 | 5-5 | 8-9—8-9 | Bluish. | P. | | 15. | .789 | 159 36 | 14-68 | 5 | 5-9 | 5-299 | 5-6 | 8-9—8-9 | Light blue. | P. | | 1845. Apr. 6. | .260 | 159 2 | 20-31 | 2 | 6-2 | 5-188 | 6 | 8-9—8-9 | Light blue. | P. | | Oct. 5. | .758 | 158 4 | 14-47 | 5 | 5-5 | 4-981 | 5-5 | 8-9—8-9 | Bluish. | P. | | 11. | .775 | 158 44 | 21-23 | 2 | 5-5 | 5-092 | 5-2 | 8-9—8-9 | Bluish. | P. | | 13. | .780 | 158 37 | 10-08 | 10 | 5-2 | 5-111 | 5-4 | 8-9—8-9 | Bluish. | P. | | 1847. Oct. 7. | .764 | 159 22 | 13-02 | 6 | 4-5 | 4-875 | 5 | 8—8 | White. | P. | | 12. | .778 | 159 20 | 16-32 | 4 | 3-3 | 4-976 | 3-1 | 8—8 | Pale blue. | P. | * A power of 140 used. † A power of 320 used. | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |--------------------|-----------------|----------|---------------|----------------|----------------|----------|----------------|------------|--------|----------| | **287 h and s.** | | | | | | | | | | | | 1844. Oct. 5 | .761289 | 28 | 19.90 | 3 | 0.8 | 7.775 | 0.8 | 7.8—9 | Light blue. | P. | | 15. | .789291 | 22 | 13.60 | 5 | 3.4 | 8.486 | 3.4 | 7.8—9 | Blue and light blue. | P. | | 18. | .797291 | 2 | 6.63 | 23 | 4.3 | 8.205 | 4 | 7.8—9 | Blue and bluish. | P. | | 23. | .810291 | 17 | 4.72 | 45 | 0.8 | 8.557 | 0.9 | 7.8—9 | Blue and bluish. | P. | | 1845. Apr. 6 | .260290 | 54 | 8.44 | 14 | 3.5 | 8.486 | 3.4 | 7.8—8.9 | Bluish. | P. | | Oct. 5. | .758291 | 57 | 18.50 | 3 | 4.8 | 8.080 | 4.6 | 7.8—9 | Whitish and bluish. | P. | | 11. | .775291 | 37 | 15.61 | 4 | 4.8 | 8.076 | 4.9 | 7.8—9 | Whitish and bluish. | P. | | 16. | .789290 | 31 | 12.92 | 6 | 4.2 | 7.949 | 4 | 7.8—8.9 | Whitish and bluish. | P. | | **δ Draconis.** | | | | | | | | | | | | 1843. Apr. 18 | .293357 | 24 | 24.33 | 2 | 4 | 3.212 | 5 | 5—10 | Yellowish and bluish. | G. | | 19. | .296354 | 19 | 43.84 | 1 | 3.4 | 2.986 | 3.4 | 4—10 | Bluish and white. | W.andG. | | 28. | .320355 | 34 | 43.64 | 1 | 4.2 | 3.060 | 4 | 4—9 | White. | W.andG. | | 1845. Oct. 24 | .810354 | 40 | 38.58 | 1 | 1.8 | 2.802 | 1.7 | 5.6—10.11 | Yellow and white. | P. | | 25. | .813355 | 18 | 30.57 | 1 | 5.2 | 2.938 | 5.4 | 5—10 | Yellow and white. | P. | | 31. | .830357 | 28 | 16.91 | 4 | 5.8 | 2.982 | 6.2 | 5—9.10 | Yellow and white. | P. | | Nov. 1. | .832356 | 9 | 9.02 | 12 | 6 | 2.972 | 6 | 5—9.10 | Yellow and white. | P. | | **I of H 95.** | | | | | | | | | | | | 1843. May 22 | .386336 | 24 | 26.29 | 1 | 1.2 | 3.380 | 1.2 | 6.7—10 | White. | G. | | 24. | .392338 | 21 | 15.83 | 4 | 4 | 3.334 | 4 | 6.7—10 | White. | G. | | 25. | .394336 | 54 | 14.29 | 5 | 5 | 3.075 | 5 | 6.7—10 | White. | G. | | June 5. | .424336 | 33 | 28.04 | 1 | 4.5 | 3.002 | 4.5 | 6.7—10 | White. | G. | | Nov. 23. | .893344 | 44 | 46.49 | 1 | 1.5 | 3.523 | 1.5 | 6—8 | White. | W.andS. | | 29. | .909341 | 24 | 9.19 | 12 | 2.5 | 3.450 | 2.4 | 6—8 | White. | S. | | Dec. 24. | .977342 | 29 | 25.38 | 2 | 3.8 | 3.149 | 3.2 | 6—8 | White. | S. | | 1844. Jan. 2 | .003344 | 3 | 21.48 | 2 | 1.2 | 3.677 | 1.1 | 6—8 | White. | S. | | 7. | .016342 | 24 | 12.01 | 7 | 5.5 | 3.115 | 5.3 | 6—8.9 | White. | S. | | June 1. | .416341 | 43 | 9.27 | 12 | 5 | 3.252 | 4 | 6—8.9 | Orange and white. | S. | | 3. | .422341 | 44 | 14.52 | 5 | 1.4 | 3.294 | 1.3 | 6.7—9 | Orange and white. | S. | | 10. | .441341 | 44 | 17.58 | 3 | 4.7 | 3.286 | 4.4 | 6.7—9 | Orange and white. | S. | | July 29. | .575339 | 26 | 10.39 | 9 | 3.2 | 3.085 | 3.2 | 6.7—9 | Bluish white. | P. | | Aug. 4. | .591338 | 12 | 12.65 | 6 | 4.2 | 3.065 | 4.2 | 6.7—9 | Bluish white. | P. | | 14. | .619341 | 42 | 12.49 | 6 | 4.4 | 3.230 | 4 | 6.7—9 | Bluish and light blue. | P. | | 24. | .646341 | 27 | 24.86 | 2 | 2.4 | 3.113 | 2.4 | 6.7—9 | Bluish white. | P. | | Nov. 21. | .890340 | 16 | 16.77 | 4 | 6.7 | 3.069 | 6.7 | 6.7—9 | Bluish white. | P. | | 25. | .901339 | 36 | 15.45 | 4 | 7 | 3.125 | 7.5 | 6.7—9 | Bluish white. | P. | | 26. | .903340 | 27 | 11.75 | 7 | 5.8 | 3.155 | 5.7 | 6.7—9 | Bluish white. | P. | | 1845. Oct. 31 | .830342 | 36 | 11.32 | 8 | 7 | 3.179 | 6.9 | 7—9 | Light blue. | P. | | Nov. 3. | .838339 | 55 | 14.47 | 5 | 5.2 | 3.162 | 5.3 | 7—9 | Bluish. | P. | | 4. | .841342 | 26 | 22.19 | 2 | 4.3 | 3.163 | 4.2 | 7—9 | Bluish. | P. | | 1846. May 10 | .353342 | 23 | 10.17 | 10 | 4.8 | 3.115 | 4.9 | 7—9 | Pale yellow and pale blue. | P. | | 29. | .405342 | 12 | 13.47 | 6 | 6.7 | 3.010 | 6.6 | 7—9 | Pale yellow and pale blue. | P. | | Oct. 30. | .827340 | 51 | 12.59 | 6 | 4.1 | 3.049 | 3.5 | 7—8.9 | Pale yellow and pale blue. | P. | ### Table I. (Continued.) | Year, Month and Day | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | Colours | Observer | |---------------------|-----------------|----------|----------------|----------------|----------------|----------|----------------|------------|--------|----------| | **P XXII 306** * | | | | | | | | | | | | 1843. June 25. | .479143 | 2 | | | | | | | | G. | | July 3. | .501143 | 56 | | | | | | | | G. | | 6. | .509144 | 17 | | | | | | | | G. | | Dec. 17. | .958145 | 46 | | | | | | | | S. | | 1844. Jan. 11. | .027145 | 34 | | | | | | | | S. | | 13. | .033144 | 13 | | | | | | | | S. | | Nov.* 27. | .906146 | 0 | | | | | | | | P. | | 1846. Dec. 14. | .950146 | 18 | | | | | | | | P. | | 22. | .972146 | 3 | | | | | | | | P. | | 1847. Dec. 28. | .988146 | 16 | | | | | | | | P. | | 1848. Dec. 21. | .972145 | 37 | | | | | | | | P. | * A power of 190 used. **The Second Table.**—This table contains the means of all the results obtained at the same period of each year, when observations have been obtained on two or more days. The second column contains the mean epoch of the results from which the means are formed. The positions in the third column are computed in the ordinary mode by multiplying each individual set by its computed weight as contained in the fifth column of Table I., adding the products, and dividing by the sum of all the weights. The fifth column contains the sum of the computed weights of the individual sets, from which the probable error of the mean in the preceding column is calculated from the equation \[ P = \frac{1}{\sqrt{W}}. \] The computed weights inserted in the Tables have been multiplied by 1000. The mean distances in the seventh column are computed in the same manner, using, however, the arbitrary or assigned weights in column 8 of Table I., instead of weights computed as above explained; for it was not deemed necessary, for reasons which will appear in the sequel, to apply the calculus of probabilities to the reduction of any of the observations of the distances. The quantities in the sixth and eighth columns, headed “Assigned weight,” are the sums of the weights assigned to the individual sets, from which each mean is formed. In the case of the four binary stars, to which an asterisk is attached in the Tables, the means, both of the positions and the distances, given in this table are obtained by employing the assigned or arbitrary weights, as before described. In deference to the objections which may be urged to this mode of reduction, I had originally intended to use the common arithmetical mean in all these cases; but out of fifty-four means of positions computed strictly by the usual formulae, and compared with means obtained as last described, and also with the arithmetical means of the same quantities, it was found that the mean obtained by using the arbitrary weights differed only in thirteen cases more than $9'$ from the strict mean, and that in eight out of the thirteen cases, the result was rendered more erroneous by using the arithmetical mean, instead of the mean derived from the use of arbitrary weights: there were seven cases out of the fifty-four in which the computed and arbitrary weights gave precisely the same result. ### Table II | Name | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | |---------------|------------------|----------|----------------|-----------------|----------------|----------|----------------| | **γ Arietis** | | | | | | | | | 1843. -576 | 179 10 | 7-33 | 19 | 20 | 9-078 | 20 | | 1844. -069 | 179 42 | 7-54 | 18 | 9 | 8-957 | 9 | | 1845. -083 | 180 38 | 5-92 | 29 | 15 | 8-816 | 15 | | 1847. -080 | 178 14 | 5-89 | 29 | 12 | 8-773 | 12 | | 1847. -608 | 178 51 | 6-55 | 23 | 12 | 8-717 | 12 | | **32 Eridani**| | | | | | | | | 1843. -661 | 345 50 | 4-59 | 48 | 21 | 6-881 | 21 | | 1845. -119 | 350 55 | 6-04 | 27 | 17 | 6-800 | 17 | | **ω Aurigæ** | | | | | | | | | 1843. -706 | 350 26 | 6-84 | 21 | 21 | 6-436 | 21 | | 1844. -748 | 351 22 | 7-76 | 17 | 19 | 6-607 | 19 | | 1845. -734 | 351 16 | 10-60 | 9 | 9 | 6-283 | 9 | | 1846. -188 | 350 37 | 6-77 | 22 | 15 | 6-400 | 16 | | 1847. -209 | 351 17 | 10-66 | 9 | 8 | 6-263 | 8 | | 1848. -248 | 351 58 | 7-65 | 17 | 11 | 6-231 | 10 | | **118 Tauri** | | | | | | | | | 1843. -732 | 196 38 | 4-93 | 41 | 14 | 4-739 | 14 | | 1844. -225 | 195 38 | 4-10 | 59 | 13 | 5-012 | 13 | | 1844. -737 | 194 45 | 6-10 | 27 | 15 | 5-124 | 14 | | 1845. -184 | 193 58 | 6-73 | 22 | 21 | 4-951 | 21 | | 1846. -169 | 195 31 | 6-13 | 27 | 9 | 5-034 | 9 | | **41 Aurigæ** | | | | | | | | | 1843. -163 | 353 54 | 7-69 | 17 | 16 | 8-290 | 15 | | 1843. -685 | 353 56 | 4-07 | 60 | 21 | 7-873 | 21 | | 1845. -188 | 351 52 | 5-17 | 37 | 24 | 7-899 | 24 | | 1846. -169 | 351 51 | 7-13 | 20 | 12 | 7-885 | 12 | | 1847. -189 | 352 58 | 6-51 | 24 | 12 | 7-880 | 11 | | 1848. -248 | 353 11 | 4-14 | 58 | 12 | 7-860 | 12 | | **δ Geminorum**| | | | | | | | | 1843. -267 | 194 24 | 6-62 | 23 | 11 | 7-640 | 11 | | 1844. -268 | 198 18 | 5-96 | 28 | 15 | 7-375 | 16 | | 1845. -846 | 198 23 | 8-14 | 15 | 12 | 7-309 | 11 | | **Anon. Cancri**| | | | | | | | | 1843. -240 | 354 10 | 4-53 | 49 | 18 | 4-027 | 19 | | 1844. -305 | 351 49 | 6-31 | 25 | 11 | 3-575 | 11 | | 1845. -272 | 353 30 | 6-19 | 26 | 17 | 3-895 | 17 | | 1845. -846 | 351 43 | 9-41 | 11 | 12 | 3-591 | 12 | | **ε³ Cancri** | | | | | | | | | 1843. -253 | 31 32 | 5-40 | 33 | 16 | 4-967 | 15 | | 1844. -347 | 33 8 | 4-20 | 57 | 14 | 4-935 | 13 | | 1845. -235 | 32 34 | 6-29 | 25 | 23 | 4-779 | 23 | | 1845. -876 | 33 37 | 9-37 | 11 | 12 | 4-674 | 11 | | 1846. -251 | 32 0 | 9-45 | 11 | 9 | 4-717 | 9 | | **2 Comæ Berenices**| | | | | | | | | 1843. -339 | 237 25 | 8-94 | 13 | 14 | 3-937 | 14 | | 1844. -399 | 240 42 | 4-46 | 50 | 15 | 4-126 | 14 | | 1845. -359 | 237 24 | 11-11 | 8 | 16 | 4-040 | 15 | | 1846. -350 | 236 53 | 8-48 | 14 | 12 | 3-805 | 12 | | 1848. -347 | 238 46 | 4-85 | 43 | 12 | 3-701 | 10 | | **39 Bootis** | | | | | | | | | 1843. -170 | 43 4 | .... | .... | 11 | 3-979 | 11 | | 1843. -644 | 43 51 | .... | .... | 20 | 3-851 | 20 | | **6 Serpentis**| | | | | | | | | 1843. -594 | 195 40 | .... | .... | 20 | 3-043 | 20 | | 1844. -616 | 195 46 | .... | .... | 17 | 3-326 | 17 | | 1845. -125 | 191 46 | .... | .... | 20 | 3-139 | 19 | | 1845. -624 | 194 59 | .... | .... | 17 | 2-999 | 17 | | 1846. -576 | 194 32 | .... | .... | 11 | 2-819 | 11 | | 1847. -576 | 193 25 | .... | .... | 16 | 2-916 | 15 | | 1848. -657 | 195 33 | .... | .... | 10 | 2-941 | 10 | | Name | Fraction of year | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | |--------------|------------------|----------|----------------|-----------------|-----------------|----------|----------------| | **178 (Bode) Librae.** | 1843. -595 | 7 42 | 5·19 | 37 | 17 | 12·144 | 17 | | | 1847. -585 | 7 31 | 4·31 | 54 | 9 | 11·775 | 9 | | **μ Draconis** | | | | | | | | | 1843. -204 | 17 2 | ... | ... | ... | 11 | 3·521 | 11 | | 1843. -645 | 16 34 | ... | ... | ... | 18 | 3·431 | 18 | | 1844. -664 | 17 10 | ... | ... | ... | 18 | 3·222 | 18 | | 1845. -650 | 12 53 | ... | ... | ... | 20 | 3·203 | 19 | | 1846. -199 | 12 56 | ... | ... | ... | 12 | 3·069 | 12 | | 1846. -669 | 11 42 | ... | ... | ... | 14 | 2·994 | 14 | | 1849. -680 | 9 43 | ... | ... | ... | 10 | 2·999 | 10 | | **100 Herculis.** | | | | | | | | | 1843. -269 | 1 36 | 6·82 | 22 | 16 | 14·240 | 15 | | 1843. -647 | 2 27 | 2·35 | 181 | 23 | 14·096 | 23 | | 1844. -680 | 2 36 | 3·43 | 85 | 17 | 13·965 | 17 | | 1845. -202 | 1 39 | 6·68 | 22 | 18 | 13·955 | 17 | | 1845. -652 | 2 6 | 1·87 | 286 | 26 | 13·922 | 26 | | 1846. -666 | 2 18 | 3·81 | 69 | 14 | 13·934 | 14 | | 1847. -222 | 2 48 | 4·08 | 60 | 9 | 13·984 | 10 | | 1847. -710 | 2 29 | 4·05 | 61 | 13 | 13·967 | 13 | | 1848. -693 | 2 27 | 3·39 | 87 | 12 | 13·916 | 12 | | 1849. -727 | 1 20 | 3·42 | 86 | 11 | 14·070 | 11 | | **579 Struve.** | | | | | | | | | 1843. -703 | 159 44 | 5·26 | 36 | 20 | 5·062 | 20 | | 1844. -773 | 159 59 | 6·71 | 22 | 20 | 5·333 | 20 | | 1845. -771 | 158 28 | 7·72 | 17 | 16 | 5·060 | 16 | | 1847. -771 | 159 21 | 10·15 | 10 | 8 | 4·914 | 8 | | **287 h and s.** | | | | | | | | | 1844. -789 | 291 9 | 3·64 | 76 | 9 | 8·307 | 9 | | 1845. -774 | 291 11 | 8·77 | 13 | 14 | 8·040 | 14 | | **ε Draconis.** | | | | | | | | | 1843. -303 | 356 17 | 19·25 | 3 | 12 | 3·101 | 12 | | 1845. -821 | 356 18 | 7·54 | 18 | 19 | 2·951 | 19 | | **I of H 95.** | | | | | | | | | 1843. -399 | 337 18 | 9·29 | 12 | 15 | 3·148 | 15 | | 1843. -960 | 342 6 | 6·58 | 23 | 15 | 3·279 | 14 | | 1844. -530 | 340 40 | 4·82 | 43 | 25 | 3·187 | 24 | | 1844. -898 | 340 10 | 8·17 | 15 | 20 | 3·115 | 20 | | 1845. -836 | 341 42 | 8·25 | 15 | 17 | 3·169 | 16 | | 1846. -379 | 342 19 | 8·11 | 15 | 12 | 3·055 | 12 | | **P XXII 306** | | | | | | | | | 1843. -496 | 143 44 | ... | ... | ... | 18 | 8·420 | 18 | | 1844. -006 | 145 8 | ... | ... | ... | 14 | 8·655 | 12 | | 1846. -961 | 146 6 | ... | ... | ... | 5 | 8·339 | 5 | The Third Table.—This Table contains the general means of all the observations of each star, both in position and distance, reduced to the mean epoch of all the observations, which will be found in column three. The positions in column four, and the probable errors and weights in columns five and six, are obtained by combining the means and individual sets (where one set only has been obtained at any one period) in accordance with the theory of probabilities, as above mentioned, except in the case of the four binary stars, in which the arbitrary weights are substituted for computed ones, as before explained. Where two stars are supposed to be of equal brightness, it has been usual to register always the smaller of the two angles, by which the position may be designated, according as the one or the other component be considered as the larger star. In these cases there is some confusion as to the identity of the two stars, which might be obviated by astronomers agreeing always to designate the northern, or in cases of equal N.P.D., the east star as A. The seventh and ninth columns contain the sums of the assigned or arbitrary weights. The eighth column contains the mean of all the observed distances, obtained in all cases by using the arbitrary weights. The tenth column contains the mean of all the registered magnitudes of each component star, the first No. referring to the brightest of the two components, or in cases of equal brightness, to the star called A. The eleventh and twelfth columns contain the R.A. and N.P.D. of each star, taken from the B. A. C.; and when the star is not found in that Catalogue, from Struve's of 1837. The thirteenth column contains the total number of individual measures in position; the number of measures in distance being equal in every case, except one, that is specified, one column suffices for both position and distance. In the notes will be found notices of any remarkable differences between the measures contained in this Table, and those given by Struve in his Catalogue of 1837:—they are confined to differences exceeding $1^\circ$ in position, and $0''\cdot200$ in distance. ### Table III | No. | Name | Mean epoch | Position | Probable error | Computed weight | Assigned weight | Distance | Assigned weight | Magnitudes | R.A. | N.P.D. | n. | |-----|-----------------------|------------|----------|----------------|-----------------|----------------|----------|----------------|------------|-----|-------|----| | 1 | γ Arietis^a | 1845. | .483 | 179° 18' 29.93 | 117 | 68 | 8.887 | 68 | 5° 3' - 5° 3' | h | m | 145 | 71 | 27 | 118 | | 2 | 32 Eridani | 1846. | .220 | 347° 37' 29.90 | 119 | 49 | 6.803 | 49 | 6° 5' - 8° 2' | 3 | 47 | 93 | 24 | 86 | | | 3 | ω Aurigae | 1846. | .434 | 351° 53' 14.14 | 102 | 89 | 6.401 | 88 | 7° 3' - 9° 7' | 4 | 49 | 52 | 21 | 154| | | 4 | 118 Tauri^b| 1844. | .962 | 195° 27' 23.55 | 182 | 79 | 4.955 | 78 | 7° 6' - 9° 1' | 5 | 20 | 64 | 59 | 150| | | 5 | 41 Aurigae | 1845. | .607 | 353° 52' 15.21 | 216 | 95 | 7.947 | 95 | 7° 6' - 8° 7' | 6 | 0 | 41 | 16 | 162°| | | 6 | δ Geminorum^c| 1844. | .912 | 197° 14' 35.58 | 78 | 44 | 7.422 | 44 | 3° 2' - 10° 5' | 7 | 11 | 67 | 45 | 82 | | | 7 | Anon. Cancri^d| 1845. | .384 | 353° 16' 28.66 | 122 | 64 | 3.655 | 65 | 8° 1' - 9° 3' | 7 | 56 | 62 | 3 | 113| | | 8 | φ² Cancri^e| 1844. | .992 | 32° 36' 27.70 | 137 | 74 | 4.823 | 71 | 6° 8' - 6° 8' | 8 | 18 | 62 | 35 | 137| | | 9 | 2 Comæ Berenices^f| 1845. | .746 | 239° 4° 26.0 | 148 | 82 | 3.916 | 78 | 6° 6' - 8° 8' | 11 | 57 | 67 | 42 | 166| | | 10 | 39 Bootis^g| 1843. | .407 | 43° 35' | ... | ... | 3.896 | 31 | 6° 8' - 7° 4' | 14 | 45 | 40 | 40 | 46 | | | 11 | δ Serpentis^h| 1846. | .119 | 194° 21' | ... | ... | 3.042 | 115 | 3° 5' - 5° 3' | 15 | 28 | 78 | 57 | 215| | | 12 | 178 (Bode) Libraⁱ| 1845. | .433 | 7° 34' 3° 24' | 95 | 30 | 12.038 | 30 | 7° 8' - 7° 8' | 15 | 29 | 98 | 10 | 56 | | | 13 | μ Draconis^k| 1845. | .673 | 14° 15' | ... | ... | 3.217 | 101 | 7° 0' - 7° 1' | 2 | 35 | 20 | 184| | | 14 | 100 Herculis | 1846. | .247 | 2° 14' 1° 02' | 959 | 158 | 14.005 | 158 | 6° 4' - 6° 4' | 18 | 2 | 63 | 55 | 260| | | 15 | 579 Struve | 1845. | .456 | 159° 29' 3° 39' | 87 | 70 | 5.131 | 70 | 8° 5' - 8° 5' | 18 | 31 | 48 | 49 | 124| | | 16 | 287 h and s^l| 1845. | .274 | 291° 7° 12' | 103 | 27 | 8.192 | 26 | 7° 5' - 8° 9' | 18 | 58 | 83 | 7 | 56 | | | 17 | ε Draconis^m| 1844. | .562 | 356° 18' 7° 02' | 20 | 30 | 3.010 | 32 | 4° 8' - 9° 8' | 19 | 49 | 20 | 7 | 64 | | | 18 | I of H 95 | 1845. | .118 | 340° 53' 2° 78' | 129 | 106 | 3.157 | 103 | 6° 5' - 8° 8' | 20 | 14 | 35 | 9 | 211| | | 19 | P XXII 306ⁿ| 1846. | .055 | 144° 56' | ... | ... | 8.475 | 48 | 7° 0' - 9° 1' | 22 | 59 | 58 | 7 | 96 | | --- ^a γ Arietis. Distance, x—W = −0°256, period elapsed = 14°64 years. ^b 118 Tauri. Position, x—W = +1° 2° 20', period = 15°33 years. ^c δ Geminorum. Distance, x—W = −0°277, period = 15°19 years. ^d Anon. Cancri. This star is erroneously termed 11 Cancri in Herschel and South's Catalogue. See Smyth's Cycle; it is 2688 B.A.C. ^e φ² Cancri. Distance, x—W = −0°260, period = 15°54 years. ^f 2 Comæ Berenices. Position, x—W = +1° 33', period = 16°21 years. ^g 39 Bootis. Comparing the place of this star in position with that given by Herschel and South and by Struve, its mean yearly motion by Sh—W = −4°39', period = 20°48 years. x—W = −2°39', period = 13°39 years. Mean = −3°39' ^h δ Serpentis. Comparing the place of this star in position with that given by Herschel and South and by Struve, its mean yearly motion by Sh—W = −12°18', period = 24°80 years. x—W = −13°49', period = 13°05 years. Mean = −12°84' Distance, x—W = −0°380 ⁱ 178 (Bode) Libra. Distance, x—W = −0°225, period = 14°89 years. ^k μ Draconis. The mean yearly motion of this star in position by Sh—W = −35', period = 24°30 years. x—W = −49', period = 13°45 years. Mean = −42' ^l 287 h and s. Position, x—W = +1° 13', period = 15°47 years. ^m ε Draconis. Position, x—W = −1° 46', period = 12°12 years. ⁿ P XXII 306. The mean yearly motion of this star in position by Sh—W = −3°10', period = 22°31 years. x—W = −4°78', period = 15°47 years. Mean = −6°94' The measures of distance are one less in number than those of position in the case of this star. The Fourth Table.—This Table has been formed for the purpose of exhibiting the results from which, in conformity with the principles explained by Sir John Herschel, the existence or non-existence of parallax in the stars observed must be inferred. These results are the differences between two angles of position, the one observed at one period of the year, say the early one, and the other at another period (the late) distant from the former about six months. For reasons which will appear hereafter, it has not been deemed necessary to include the distances in this table. In so delicate an inquiry as that of parallax, it may not perhaps be considered a legitimate course to pursue, to compare any results except those distant from one another by an interval of about six months, or in other words, results which follow one another immediately at opposite seasons. It is on differences so obtained that many therefore may be disposed to rely exclusively in discussing the questions raised by this investigation; and such differences, when furnished by the observations, are accordingly placed first in the table; but it is in truth only a choice of difficulties; it has been found impossible in the case of some of the stars to obtain such differences at all; and in others, the observations are so few, and their weight consequently so small, at one at least of the periods compared, that little reliance can be placed on the results; it has been thought better therefore to combine in the case of each star, and in the manner already explained, all the observations made in all the years at the early period into one mean result, and all those made at the late period into another, and to insert their difference, leaving it to astronomers to attach whatever importance to the comparison they may think due to it. This difference follows in every case the more legitimate comparisons at intervals of six months. The four binary stars are excluded from this Table. The second column of this fourth Table contains the mean epoch:—in the case of the final means, that is, the means of all the early and all the late periods, the decimal, following an enumeration of several years, is the mean of all the decimals attached to the years of the individual means or sets, from which the final means are formed. The third column contains the positions, obtained by using the computed weights of the results employed, as before explained. The fourth and fifth columns contain the probable errors and weights of these positions. The sixth column contains the differences between the positions, which follow one another in succession, and which have been obtained at opposite periods of the year; or, in other words, the quantity, on which parallax depends, and to which the subjoined remarks on the results of the observations refer. The plus sign is attached to the difference when the change in the angle takes place in that direction, which is in conformity with the hypothesis of a parallax in the stars observed; and the minus sign when the change is in the contrary direction. The eighth column contains the weight of the difference computed from the formula \[ W'' = \frac{WW'}{W + W'}, \] where \( W \) and \( W' \) are the weights of the two positions compared, and \( W'' \) the weight of their difference:—from the value of \( W'' \) so obtained, that of the probable error of the difference, inserted in the seventh column, is computed by the above equation. The ninth column contains the distance, taken from the third Table to the first place of decimals. All the computations have been very carefully examined. ### Table IV. | Name | Epoch | Position | Probable error | Weight | Difference | Probable error of Δ | Weight of Δ | Distance | |------------|-------|----------|----------------|--------|------------|---------------------|-------------|----------| | γ Arietis. | 1843. | -576179 10 | 7·33 | 19 | -32 | 10·52 | 9 | 8·9 | | | 1844. | -069179 42 | 7·54 | 18 | | | | | | | 1847. | -080178 14 | 5·89 | 29 | +37 | 8·81 | 13 | | | | 1847. | -608178 51 | 6·55 | 23 | | | | | | | 1843, 7.| -592178 59 | 4·89 | 42 | -30 | 6·10 | 27 | | | | 1844, 5, 7.| -077179 29 | 3·65 | 75 | | | | | | 32 Eridani.| 1843. | -661345 50 | 4·59 | 48 | +178 | 5·92 | 29 | 6·8 | | | 1845, 6, 7, 9.| -110348 48 | 3·74 | 72 | | | | | | ω Aurigæ. | 1845. | -734351 16 | 10·60 | 9 | -39 | 12·58 | 6 | 6·4 | | | 1846. | -188350 37 | 6·77 | 22 | | | | | | | 1843, 4, 5.| -729350 55 | 4·62 | 47 | +18 | 6·30 | 25 | | | | 1846, 7, 8, 9.| -213351 13 | 4·28 | 55 | | | | | | 118 Tauri.| 1843. | -732196 38 | 4·93 | 41 | +60 | 6·42 | 24 | 5·0 | | | 1844. | -225195 38 | 4·10 | 59 | -53 | 7·35 | 19 | | | | 1844. | -737194 45 | 6·10 | 27 | | | | | | | 1845. | -184193 58 | 6·73 | 22 | +47 | 9·08 | 12 | | | | 1845. | -723193 23 | 13·62 | 5 | -35 | 15·18 | 4 | | | | 1846. | -169195 31 | 6·13 | 27 | -128 | 14·93 | 5 | | | | 1843, 4, 5.| -731195 42 | 3·69 | 73 | +26 | 4·78 | 44 | | | | 1844, 5, 6.| -193195 16 | 3·04 | 108 | | | | | | 41 Aurigæ.| 1843. | -163353 54 | 7·69 | 17 | -2 | 8·22 | 15 | 7·9 | | | 1843. | -685353 56 | 4·07 | 60 | | | | | | | 1843, 5, 6, 7, 8.| -191352 45 | 2·53 | 156 | -71 | 4·79 | 44 | | | | 1843. | -685353 56 | 4·07 | 60 | | | | | | δ Geminorum.| 1845. | -846198 23 | 8·14 | 15 | -19 | 12·29 | 7 | 7·4 | | | 1846. | -268198 42 | 9·19 | 12 | | | | | | | 1843, 4, 6.| -268196 58 | 3·99 | 63 | +85 | 9·06 | 12 | | | | 1845. | -846198 23 | 8·14 | 15 | | | | | | Anon. Cancri.| 1845. | -272353 30 | 6·19 | 26 | +107 | 11·26 | 8 | 3·7 | | | 1845. | -846351 43 | 9·41 | 11 | | | | | | | 1843, 4, 5, 8.| -268353 26 | 3·00 | 111 | +103 | 9·88 | 10 | | | | 1845. | -846351 43 | 9·41 | 11 | | | | | ### Table IV. (Continued.) | Name | Epoch | Position | Probable error | Weight | Difference | Probable error of Δ | Weight of Δ | Distance | |---------------|-------|----------|----------------|--------|------------|---------------------|-------------|----------| | φ² Cancri | | | | | | | | | | | 1845. | -235 | 32 34 | 6-29 | 25 | -63 | 11-28 | 8 | | | 1845. | -876 | 33 37 | 9-37 | 11 | -97 | 13-30 | 6 | | | 1846. | -251 | 32 0 | 9-45 | 11 | | | | | | 1843, 4, 5. | -278 | 32 30 | 2-82 | 126 | -67 | 9-78 | 11 | | | 1845. | -876 | 33 37 | 9-37 | 11 | | | | | 2 Comæ Berenices | | | | | | | | | | | 1844. | -399 | 240 42 | 4-46 | 50 | -199 | 11-14 | 8 | | | 1844. | -887 | 237 23 | 10-20 | 10 | -1 | 15-09 | 4 | | | 1845. | -359 | 237 24 | 11-11 | 8 | +181 | 14-59 | 5 | | | 1845. | -890 | 240 25 | 9-44 | 11 | +232 | 12-70 | 6 | | | 1846. | -350 | 236 33 | 8-48 | 14 | | | | | | 1843, 4, 5, 6, 7, 8. | -365 | 239 4 | 2-80 | 127 | -3 | 7-48 | 18 | | | 1844, 5. | -889 | 239 1 | 6-93 | 21 | | | | | 178 (Bode) Libræ | | | | | | | | | | | 1843, 7. | -590 | 7 35 | 3-32 | 91 | +20 | 15-44 | 4 | | | 1845. | -120 | 7 15 | 15-12 | 4 | | | | | 100 Herculis | | | | | | | | | | | 1843. | -269 | 1 36 | 6-82 | 22 | +51 | 7-21 | 19 | | | 1843. | -647 | 2 27 | 2-35 | 181 | | | | | | 1844. | -680 | 2 36 | 3-43 | 85 | | | | | | 1845. | -202 | 1 39 | 6-68 | 22 | -57 | 7-51 | 18 | | | 1845. | -652 | 2 6 | 1-87 | 286 | +27 | 6-94 | 21 | | | 1846. | -666 | 2 18 | 3-81 | 69 | | | | | | 1847. | -922 | 2 48 | 4-08 | 60 | -30 | 5-58 | 32 | | | 1847. | -710 | 2 29 | 4-05 | 61 | -19 | 5-75 | 30 | | | 1843, 5, 7. | -231 | 2 18 | 3-10 | 104 | -4 | 3-28 | 93 | | | 1843, 4, 5, 6, 7, 8, 9. | -682 | 2 14 | 1-08 | 855 | | | | | 579 Struve | | | | | | | | | | | 1844. | -773 | 159 59 | 6-71 | 22 | -57 | 21-49 | 2 | | | 1845. | -260 | 159 2 | 20-31 | 2 | +34 | 21-82 | 2 | | | 1845. | -771 | 158 28 | 7-72 | 17 | | | | | | 1843, 4, 5, 7. | -755 | 159 30 | 3-43 | 85 | -28 | 20-70 | 2 | | | 1845. | -260 | 159 2 | 20-31 | 2 | | | | | 287 h and s. | | | | | | | | | | | 1844. | -789 | 291 9 | 3-64 | 76 | +15 | 9-20 | 12 | | | 1845. | -260 | 290 54 | 8-44 | 14 | +17 | 12-18 | 7 | | | 1845. | -774 | 291 11 | 8-77 | 13 | | | | | | 1844, 5. | -782 | 291 9 | 3-36 | 89 | +15 | 9-10 | 12 | | | 1845. | -260 | 290 54 | 8-44 | 14 | | | | | ε Draconis | | | | | | | | | | | 1843. | -303 | 356 17 | 19-25 | 3 | +1 | 20-67 | 2 | | | 1845. | -821 | 356 18 | 7-54 | 18 | | | | | I of H 95 | | | | | | | | | | | 1843. | -399 | 337 18 | 9-29 | 12 | +288 | 11-38 | 8 | | | 1843. | -960 | 342 6 | 6-58 | 23 | +86 | 8-15 | 15 | | | 1844. | -530 | 340 40 | 4-82 | 43 | -30 | 9-48 | 11 | | | 1844. | -898 | 340 10 | 8-17 | 15 | | | | | | 1845. | -836 | 341 42 | 8-25 | 15 | | | | | | 1846. | -379 | 342 19 | 8-11 | 15 | -37 | 11-57 | 8 | | | 1846. | -827 | 340 51 | 12-59 | 6 | -88 | 14-99 | 5 | | | 1843, 4, 6. | -436 | 340 28 | 3-78 | 70 | +55 | 5-59 | 32 | | | 1843, 4, 5, 6. | -880 | 341 23 | 4-11 | 59 | | | | Results of the observations. Distances.—In discussing the results of the observations, little need be said of the measures of distance: it was impracticable, consistently with the due prosecution of the more important task of measuring the angles, to take these measures of distance at shorter intervals, and at the epochs proper for eliminating the changes, if any, due to parallax: the small differences between the measures taken at opposite seasons must be ascribed to errors of observation. The following Table exhibits these differences; it contains the means of the measures of distance obtained at the early and late periods, with the sums of the assigned weights used in the reduction, and which means correspond, in respect to epoch, with the final means of the angles contained in the fourth Table; the mean epochs themselves therefore have been already given in that Table. The four binary stars are excluded from the following Table. Table V. | Name | Mean distance | Assigned weight | Δ | Name | Mean distance | Assigned weight | Δ | |---------------|---------------|-----------------|-----|---------------------------|---------------|-----------------|-----| | γ Arietis | 8°493 | 32 | 105 | 2 Comæ Berenices | 6°917 | 69·7 | 003 | | | 8°838 | 36 | | 178 (Bode) Librae | 3°914 | 8·4 | | | 32 Eridani | 6°881 | 21 | 136 | 12°016 | 26·6 | | 216 | | | 6°745 | 27·9 | | 12°323 | 3·0 | | | | ω Aurigæ | 6°474 | 49·2 | 165 | 100 Herculis | 14°064 | 42·1 | | | | 6°309 | 39·1 | | 13°083 | 115·5 | | 081 | | 118 Tauri | 4°915 | 34·7 | 072 | 579 Σ | 5°136 | 63·8 | 062 | | | 4°987 | 42·9 | | 5°188 | 6·0 | | | | 41 Aurigæ | 7°967 | 74·5 | 094 | 287 h and s | 8°148 | 22·6 | | | | 7°873 | 20·5 | | 8°486 | 3·4 | | | | δ Geminorum | 7°461 | 32·7 | 152 | ε Draconis | 3°101 | 12·4 | | | | 7°309 | 11·4 | | 2°951 | 19·3 | | 150 | | Anon. Cancri | 3°669 | 53·1 | 078 | I of H 95 | 3°145 | 49·7 | | | | 3°591 | 11·8 | | 3°168 | 53·3 | | 023 | | φ² Cancri | 4°851 | 59·6 | 177 | | | | | | | 4°674 | 11·3 | | | | | | Angles of position.—In the discussion of the measures of position, it must be remembered that four of the stars observed, viz. 39 Bootis, δ Serpentis, μ Draconis, and P XXII 306, exhibit differences in their mean positions, as compared with those given by other observers, of an amount sufficient to induce the belief that they are binary systems: the observations of these stars may therefore be at once dismissed with the remark, that they are useless for the purposes of this inquiry. Again, in the case of five other stars, viz. γ Arietis, φ² Cancri, 178 (Bode) Librae, 100 Herculis and 579 Struve, the components are of equal magnitude, and parallax is in this case not only à priori highly improbable, but there is nothing in the actual observations themselves of these stars, which can lead us to any definite conclusion as to its existence in fact. It is proper, however, to direct attention to the large differences in the case of φ² Cancri, accordant in respect of sign. In order to arrive at any decision on the question, whether the changes in the angles of position of the remaining stars, exhibited in the sixth column of the fourth Table headed "Difference," should induce us to suspect the existence of a sensible parallax in any of the objects observed, two points are to be considered,—first, the amount of those changes, as compared with the probable error of the results themselves; and secondly, their direction, considered with reference to the motion of the earth in her orbit. As to the first point, it would appear, that except the change observed bear a very large proportion to the probable error of the determination, it may be justly treated with little respect, so far as the evidence to be derived from amount only be concerned. This conclusion is supported, first, by the great discordances between the partial differences, in the instances of the three stars, 118 Tauri, 100 Herculis, and I of H 95, the only objects that can be said to have been satisfactorily observed, if the delicate nature of the investigation be considered. 2ndly. These discordances are the more remarkable, when we view them in connection with the large ratios which some of the differences bear to their probable errors. Indeed a bare inspection of the measured angles of position given in Table I. in connexion with the computed weights and errors, will convince us that the differences of the results obtained on different evenings are greater in many instances than those of the separate measures obtained on the same evening. This circumstance, which, it is believed, is not unfrequent in observations requiring the same delicacy of estimation as those under consideration, renders the application of the calculus of probabilities embarrassing and its conclusions uncertain. It is certain, in fact, that in the greater number of instances given in this paper, the computed probable errors of the results on which the parallaxes depend, form no probable criterion of the magnitude or even of the existence of parallax. The only probable explanation that can be given in such cases, where purely instrumental errors can scarcely have place, must arise from an unsuspected bias of the observer in the selection of the line of direction passing through the centres of the stars, which causes an estimation constant on the same evening, but differing on different nights. The weight of each evening's result, calculated according to the amount of discordance of the individual measures, may still be an adequate representative of the degree of dependence to be placed on it, as far as the steadiness of the atmosphere and other favourable circumstances are concerned; but the probable errors of combined and final results, calculated on ordinary principles, will not form a good criterion of the accuracy of such results. Supposing, however, the bias of the observer on different evenings likely to be as often in excess as in defect, or not to be of the nature of a constant error, a better estimation of the probable error of the final means would be obtained by considering each evening's set of measures as a single result without regard to their number, and then comparing the separate results in the usual way*. If the results in the present paper had been of a more positive character, a re-reduction of some of them on this principle might have been desirable, but as the case stands this explanation is sufficient. It is proper to add, that I have no reason to * Putting $p$ for the probable error of 10 sets of 118 Tauri for the early period, treated as individual measures, and $p'$ for the mean of the probable errors, as given in Table I., of the same sets, $p : p' :: 24 : 15$. In the case of 10 sets of I of H 95 for the late period, $p : p' :: 11 : 9$. believe, that a single *individual* measure, either in position or distance, however discordant, has been ever rejected on that or any other ground; but all *sets* containing less than four measures have been invariably rejected. It would seem, then, that though, in one point of view, comparisons at opposite seasons must be treated as possessing value, yet we are after all driven to rely in a great measure on the final means; for notwithstanding the well-founded objections that may be urged to combining observations made in different years, the discrepancies above alluded to show, that a greater number of measures are required to eliminate error, than can possibly be obtained in any one, or even two years. Now if we examine the final means of the two periods in Table IV., we shall find five stars only, viz. 32 Eridani, 41 Aurigæ, δ Geminorum, Anon. Cancri, and I of H 95, of which we can affirm that they have any pretensions whatever to be considered as fulfilling the condition above stated:—with respect to δ Geminorum and Anon. Cancri, the small weights of the results of the late period render any conclusions drawn from them extremely liable to doubt: this is the more to be regretted, in the case of the last-mentioned star, inasmuch as the smallness of the distance of its components renders it a very eligible object for observation. When however we examine the results obtained with reference to the *direction* of the changes observed, they seem to be entitled to rather more consideration. In the *nf* and *np* quadrants an apparent motion to the westward of the larger star, assumed to be the nearest to the earth, must increase the angle of position, and in the *sf* and *sp* quadrants the contrary effect must take place:—therefore at that epoch of observation when the sun is to the west, and therefore the earth to the east, of the star observed, the *maximum* angle may be expected to occur in the two first named quadrants, and the *minimum* in the others; in the case of double stars, whose components are equal, it is plain that two different conclusions may be drawn from the periods at which the maxima occur, according as the one or the other be taken as the nearest star. Omitting therefore the five stars, whose components are of equal magnitude, omitting also the four binary stars, and 2 Comæ Berenices and ε Draconis (which exhibit differences less than their probable errors), this interesting result appears, that of the eight that remain, there is only one, that is, 41 Aurigæ, the changes in whose angles, however small and little entitled to confidence they may be, do not conform in direction to those, which would take place, were a sensible parallax admitted in the brighter of the stars themselves. This is most probably only an accidental coincidence, and I am very far from wishing to estimate it at more than its real worth; but in the case of 32 Eridani and I of H 95, where large, and to a certain extent trustworthy, differences concur with normal directions of motion, it may not perhaps be too much to assert, that this constitutes them objects of interest to the astronomer, possessed of adequate means to prosecute an inquiry, which, I fear, I must be said rather to have attempted than to have succeeded in. *Wrottesley, October 22, 1850.*