337,338 C. RAGOONATHA CHAREY, on the Determination of Personal Equation. 338, 339 VOL. XIX. Supplemental Notice. On the Determination of Personal Equation by Observations of the Projected Image of the Sun. (Letter from C. Ragoonaiha Charey to Captain W. S. Jacob.) 'I beg to trouble you once more on the subject of the Observation of the Sun's Image. Prior to your departure to England, you were good enough to approve the observations of the above, taken by me with the transit instrument of the observatory, and you yourself continued to make a few observations, together with two or three observers simultaneously; and on my addressing you while here, on the 23rd April, 1858, (a copy of which is herein enclosed), you were pleased to apprise me that find you no deficiency in the mode of observation, that you will consult on the subject with some of the scientific friends in England, and will inform me the same. "Having had in view for personal conference on the subject after your arrival in India, I was hitherto unmindful of intruding upon your valuable time; but, to our greatest misfortune, we came to know that you gave up your appointment as astronomer at Madras. Though I have a very poor knowledge in scientific matters, yet I presume to think from little experience that this mode of observing the sun is in no way adverse to accuracy, but it only adds a greater weight (than that we have hitherto obtained) to the result of observations, in proportion to the increase of the number of simultaneous observers; and, further, it affords ample opportunities to ascertain the personal equation of the observers easily. "I happened to see a few months ago in the introduction of the first volume of the Washington Observations, p. 49, where Lieutenant Maury, the Director of the Observatory, states as follows, I have made trials for a personal equation, but could not succeed in establishing any uniformity as to the difference of eye and ear among the observers.' "One of these experiments consisted in casting, by a proper adjustment of the eye-piece, a sharp image of the sun and wires at the time of transit, upon a screen placed at a little distance from the telescope, and to require each of the four officers to observe and record in silence the transit of the sun. The difference among them as to the mean of the seven wires was altogether insignificant. "From the above I see that the transit of the sun's image is only taken for ascertaining the personal equation, and that also for an experimental purpose, without recommending the mode as one that can be employed daily for the general use of the observatory. "I beg leave herewith to show the results of the personal equation deduced from the observations of the sun's image, with the transit instrument here, by yourself with the assistants of the observatory, together with the results derived from recent observations, made with the 5-feet achromatic telescope on the outside of the observatory, when the sun's altitude was about 50 degrees. "For observing the sun's image on the outside of the observatory, I selected a spot where the action of the wind may not shake the instrument, and a shade for protecting the chronometer and the observers from the sun, and made the following contrivance to obtain the observations. No. 10. "I made a cylindrical cage of about ten inches in diameter, of bamboo slits and black cloth, covered its mouth with an oiled white paper, containing nine parallel lines, finely ruled in ink, at an interval of one inch in lieu of wires, introducing the same to the eye-end of the telescope, leaving a projection of about one foot and a half from it, and tieing up the other end on the body of the telescope, adjusted the eye-piece so as to cast a sharp image of the sun's limb on the paper, and thereby made a series of observations with a chronometer, for both the upper and lower limbs of the sun by myself, Sashoo Iyengar and Mootosamy Pillay. "The following are the results of personal equation, deduced from the observations made by the transit instrument, between the months of February and May 1858: chief of which is that it enables any number of observers to make the same identical observation simultaneously, and thus furnish a correct value of the personal equation of each. The method seems to have been tried for this special purpose at Washington, but found not to answer; we, however, found it to succeed perfectly, the personal equations appearing to have the nearly same value with those determined in other modes, but showing much greater uniformity in the separate measures. As the ordinary mode of taking the sun's transit it has further the advantage (a very great one in a tropical climate) of not exposing the observer's eyes to be scorched, or breaking the coloured glasses, a circumstance of continual recurrence even when the aperture has been reduced to an inconvenient degree, and this with no sacrifice, but rather an increase in point of accuracy. "I am aware that the method does not possess any novelty, having been occasionally employed by myself more than 20 years ago, and probably by many others; being also the mode regularly employed by Mr. Carrington in fixing the places of the solar spots; but it is not, I believe, used in any other observatory besides that of Madras as the mode of observing the sun at noon, and therefore it may be useful to bring it to the notice of the directors of observatories." deficiencies already be supplied, and I thus come too late, still I hope that my list may not be quite superfluous, as the estimation of magnitude by a second person may be useful in doubtful instances. In any case, will you kindly accept the intention for the deed? Willingly would I annex, besides, a list of the many errors (nearly 3000) contained in that Catalogue, which I discovered in the course of making my Charts (segments of a 14-foot sphere), but with that also I shall, perhaps, come too late moreover, this catalogue of faults might itself be still faulty, as I have been guided by eye-estimation only. At all events, I shall expect your kind command. A similar catalogue, referring to the Star-Charts of the Berlin Academy, stands equally at your service. Note from the Astronomer Royal to the Editor. "In the last number of the Monthly Notices there is an account of the occultation of Saturn on May 8, as observed at Wimbledon by Mr. Pollock. I do not doubt the perfect accuracy of the description; but I do not clearly understand the tenor of the remarks which follow it. "The phenomena of diffraction are produced as distinctly by the lens of the eye as by the object-glass of a telescope. They are, however, enormously increased by the want of accurate definition in the eye. Very few eyes (especially among those accustomed to look at near objects), perhaps none, see the moon without an enlargement of its diameter to the extent of several minutes of arc. This will easily be perceived upon examining, with the naked eye, the moon at the latest period at which the obscure disk is visible, or 'the young moon with the old moon in her arms,' when it will be seen that the apparent limb of the bright surface belongs to a much larger circle than that of the dark surface. I need not say that this entirely explains the appearance of projection. "The irradiation of the planet has no part in producing the appearance of projection. "The expression, 'projection of a fixed star upon the moon's disk after it should have disappeared behind it,' refers to some supposition with which I am not acquainted. The disappearance occurs, I conceive, exactly at the time at which it ought to occur, but the image of the moon's limb expands at that time so as to cover that of the planet; in the case of yiew with a telescope adjusted to focus, in consequence of diffraction; and in the case of view with the unarmed eye, in consequence principally of the imperfect definition by the eye. "Royal Observatory, Greenwich, Oct. 4, 1859." 482 507 740 910 936 982 List of Star-Magnitudes not included in Baily's edition of Lalande's Histoire Céleste. By M. Hencke. (Extract of a Letter to the Astronomer Royal.) "Will you kindly permit me to annex a list of star-magnitudes, not given in Baily's Lalande's Catalogue: should these No. Mag. No. Mag. No. Mag. No. Mag. 16 8 3321 8 5364 9 7412 8 88 η μ 3605 9 6 5680 8 7561 8 μ 5711 8 μ 7586 9 5876 768 00 00 6 A μ 8 μ 8 pe 1250 4036 78 7 μ 6169 6183 342, 343 List of Star-Magnitudes not included in BAILY's Edition of LALANDE's Histoire Céleste. 343, 344 78 42696 8 μ 8 8 μ μ 42821 8 7 8μ 8 Note from Capt. W. S. Jacob to the Editor. "In my paper on Jupiter's Mass, lately printed in vol. xxviii. of the Society's Memoirs, there occurs a passage which Mr. Airy has pointed out to me as requiring correction. It is at p. 110, 1. 18:- My reason for not adopting Mr. Airy's epoch was, that it was not apparent whether the light-equation was included in it or not.' The portion in italics would read more correctly as follows: that I was not certain of the extent to which the light-equation had been included in it.' "I was aware that the equation had been in some way taken into account, Mr. Airy having distinctly stated the fact in the paper referred to (Mem. R. A. Soc., vol. vi., p. 91); but the term light-equation' has not an invariable meaning, being sometimes taken as the whole interval occupied in the passage of light from the planet to the earth, as, for instance, in Herschel's paper on Saturn in his volume of Cape Results; while at others it means the excess of such interval above a definite minimum, as in Delambre's Tables of Jupiter's Satellites. "Now, in attempting to transform Airy's formulæ so as to suit my purpose, from grades to degrees, and from Greenwich mean time to Madras sidereal time, and taking the lightequation in its first sense, I found a wide difference between the observed and computed places of the satellite; and though this was reduced by adopting Delambre's sense, the difference 7 μ was still large enough to leave room for doubt. This might arise from some error in my computation; but as no such error could be readily detected, and as there was no one on whom I could thoroughly depend to repeat the computation, it seemed better to adopt an independent epoch, of the meaning of which I could be quite certain, than to lose time in trying to hunt up my error, or in a reference to Mr. Airy himself, the reductions having been made in Madras. "P. S. I regret to have to indicate the following errata, which have been discovered in my papers :— 347, 348 ASTRONOMER ROYAL: Corrections of the Elements of the Moon's Orbit. Corrections of the Elements of the Moon's Orbit, deduced from the Lunar Observations made at the Royal Observatory of Greenwich from 1750 to 1851. Being an extension of a preceding Memoir entitled "Corrections of the Elements of the Moon's Orbit, deduced from the Lunar Observations made at the Royal Observatory of Greenwich from 1750 to 1830." By G. B. Airy, Esq., M.A., Astronomer Royal. The author commences with a statement of the reasons which induced him to continue the reduction of the Greenwich Lunar Observations subsequent to 1830, on the same plan as that pursued in the great work on the reductions from 1750 to 1830; and he at the same time mentions the circumstances which led him to fix upon 1851 as the final year which would be distinguished by the system of reduction hitherto employed. In the year 1836 some changes were made in the system of observations, and very important changes in the system of daily reductions. The elements in these were varied from time to time as the observations seemed to indicate, and the tabular comparisons were made with Burckhardt's Tables, then employed in the computations of the Nautical Almanac. Thus there were inconsistencies of reduction which it was desirable to remove, and tables of inferior character had been employed, which it was desirable to replace by tabular calculations made on the same theoretical elements as those of the preceding reductions. An occasion for recommencing the work, and a reason for fixing a definite limit, were alone wanting. "The occasion and the reason," says the author, 66 were supplied by Mr. Adams' discovery of the error in Burckhardt's Tables of the Moon's Parallax, and his corrections to that element published in the Nautical Almanac for 1856. Astronomers cannot be too grateful to Mr. Adams for that investigation; not only because it corrects a very important error in the construction and numerical values of the Parallax Tables, but also because it brings together the investigations founded on different theories and different observations, shows their precise agreement when correctly treated, and finally establishes the whole doctrine of Lunar Parallax on a firm basis. Nothing has been done which has aided so much the daily reductions of lunar observations." The author was enabled to use the parallax as corrected by Mr. Adams from the beginning of 1852. This circumstance alone was sufficient to induce him to fix on the end of 1851 as the definitive limit of the proposed reductions. He was further prompted to adopt this resolution by the probability which existed of the speedy publication of Hansen's Lunar Tables, and their employment in the computations of the Nautical Almanac. The proposal of the author having met with the approval of the Board of Visitors of the Observatory and of the Lords Commissioners of the Admiralty, the computations were commenced in the beginning of 1856, and were finally brought to a close in the summer of the present year. 349, 350 Before investigating the results which form the object of his paper, the author gives a statement of the groups in years into which he has divided the period (1750-1851) over which his observations extend, with the range of longitude of the moon's node corresponding to each group. It is worthy of remark that the materials of the last of these groups (1847-1851) consist solely of observations with the altazimuth.* After giving the forms of the expressions for the comparison of the moon's observed places in longitude and in ecliptic polar distance with the corresponding tabular places, the author exhibits the equations depending on the new groups with the corresponding values of the unknown quantities, and combining the latter with the results of his former memoir (Mem. Ast. Soc. vol. xvii.) he obtains the definitive value of each unknown quantity. By means of these corrected values he then determines the most important corrections of elements and inequalities. We now proceed to give the principal results of this important paper. I. Correction of Moon's Epoch of Longitude and Mean Motion. The correction to Damoiseau's mean motion for one year is +o" 596. Damoiseau's epoch is very nearly correct for 1806. The difference between these numbers and those in the former memoir arises principally from the change made by Professor Hansen in the equations of long period. II. Correction of the Equation depending on the Elliptic form of the Earth. This inequality has for its argument the mean place of the moon's node. The corrections being applied its entire value is found to be, + 6:41 × sin longitude of moon's node Correction of the principal coefficient of the Equation of the The corrected value of the coefficient of the sine of mean anomaly when the true longitude is expressed in a function of the mean longitude, as in Damoiseau's form, is: |