heavens where the southern tendency is least discernible, and is nearly quiescent; its proper motion in polar distance may, therefore, be considered as uniform. There is a circumstance that deserves notice, though it may be merely accidental: the stars in the Greenwich catalogue, whose proper motions are south, nearly equal in number those that are north, yet the quantity of southern proper motion exceeds the northern in the proportion of four to one.

I shall at present offer no conjecture on the cause of thèse deviations, but endeavour, by continued observations, more accurately to ascertain the law which they follow. Should the weather prove favourable for observation, I hope before the Society separate for the summer, to be able to give greater accuracy to the numbers here subjoined. Indeed I should not have made so early a communication on the subject, but as the Greenwich observations of 1820 are about to be published, they might without this explanation have appeared erroneous; for I find that during that year the instrument was rather defective from general unsteadiness, than from any perceptible deviation of the telescope. It was not till after the month of Feb. 1821, that the instrument got completely out of repair. It must however be admitted, that the observations of that year ought not to be employed in the determination of such small quantities as form the subject of the present communication.

Horizontal Point of the Circle as found by different Stars observed by direct Vision and Reflection from 11th to 23d March, 1822.

There being no perceptible difference in the results obtained near the zenith and near the horizon, it may be concluded that the instrument has no deviation, either from flexion of the telescope or change of figure.

Appendix to the preceding Paper on the Changes which appear to chave taken place in the Declination of some of the fixed Stars. By J. Pond, Esq. Astron. Royal, FRS. Read Nov. 14, 1822.

THE observations which have been made during the last summer, confirm in a very decided manner the results which formed the subject of my last communication; in which I laid before the Society the nature of the differences that exist between the computed places of the principal Stars of the Greenwich Catalogue, and those deduced from actual observation. It is not my present intention to offer any explanation of the cause of these phænomena, although many obvious conjec tures present themselves, the value of which it will require perhaps many years to determine. It is now my principal object to consider the force of that explanation of the differences in question, which will most readily occur to every astronomer, namely, that the whole may arise either from error committed by the observer, or from defect in the instruments of observation d this objection being the more weighty from the circumstance, that the observations of three distant periods are employed, and that an error in those of either period (but particularly of the two latter) would materially affect the result now under conside ration.

1

I believe that every person, in proportion to his experience in the use of astronomical instruments (even of the most unexcep tionable construction), will be cautious in admitting the accuracy of any results, with whatever care the observations may have been made, which appear to militate against any received theory of astronomy; and I shall have occasion myself to show, from the great discordances between instruments of the highest reputation, that this distrust is but too well founded. More particularly ought our suspicion to be excited, when such anomalies are found to exist, as bear some direct proportion to the zenith distances of the stars observed. In all such cases wei should never hesitate, I think, to ascribe the anomalies to defec tive observation. If therefore in the present instance, any part of the discordances in question can be shown to depend on polar or zenith distances, I shall willingly admit, as to such part of them at least, that they are no otherwise of importance, than as affording data for leading to the detection of some hitherto undiscovered errors. The anomalies, however, that have led me on to this inquiry, and to which alone I attach any importance, are found to depend rather on the right ascensions, than on the

* From the Philosophical Transactions for 1823, Part I,

251 declinations of the stars. Accordingly I found, while collect ing observations to form a catalogue for the present period, that I could more nearly predict the deviation of a star from its com puted place, by knowing its right ascension, than its declination. Now it is not easy to conceive in what way the error of an instrument for measuring declination, fixed in the meridian, can be occasioned by any circumstance depending on the right ascension of a star to be observed.

The general nature of the deviation of the stars from their computed places will be best understood from the annexed tables;* in one of which the principal Stars of the Greenwich Catalogue are arranged according to north polar distance, and in the other, in the order of their right ascensions.

!

- From these tables, it will appear, according to my statement in the former part of this paper, that the general tendency of the deviation is towards the south: that in about one-third part of the heavens in right ascension this southern tendency is very inconsiderable, and would hardly have excited attention: for in this part, stars between the zenith and the pole, appear a very small quantity to the northward; whereas in the remaining, and most considerable portion of the heavens, every star appears to be a considerable quantity to the south of its computed place; and with few exceptions, the more southward stars have greater tendency to deviation than the northern ones.

If we select from the preceding tables those stars which were least frequently observed, at one or all of the three periods, we shall find that they all tend to confirm the foregoing general results; though they must be regarded as doing so, rather by their united effect, than by their weight of evidence when consi dered singly. Stars that have been but seldom observed, give results considerably affected by accidental error of observation; which error is quite of a different nature from that produced by permanent defect in the instrument, and which repetition of observation has no tendency to remove.

If the deviations of those stars that have been imperfectly observed, were attributable either to error of observation, or defect in the instruments, the deviation would either follow no law at all, or some law depending upon zenith distance: but the facts we have seen to be at variance with either of these hypotheses. Not however to rest satisfied with these considerations drawn from the general tendency of all the stars without exception, let us select some striking examples of deviation, in parti cular groups of stars, on which we might be satisfied to rest the issue of this question. Of these groups I have marked five, in the table of stars, arranged according to north-polar distance, each of which we will take the pains to consider more attentively.

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1. There are six stars in my Catalogue north of y Draconis,

• These are necessarily omitted in this work; see note to p. 248.

of which three are found to the north, and three to the south of their computed places. These inequalities may appear at first sight to be wholly accidental; but if we pay attention to the right ascension, we shall find that the three which appear to the northward, are situated in that part of the heavens as to right ascension where the southern deviation is the least perceptible, and that the three which appear to the southward, are in that part as to right ascension where the southern deviation is the greatest. But of these six stars there are two, a Cassiopeiæ, and Ursa Majoris, which deserve further consideration. These two stars are within less than one degree of each other in polar distance, and consequently pass over the meridian at nearly the same altitude. The observations of Bradley on the stars north of the zenith are not so numerous as could be wished; but each of the two stars in question was observed by him about five times towards the year 1758; that is 60 years from the date of my catalogue of 1813. I have carefully recomputed the predicted places of these stars, and I find a Cassiopeia not less than 15" to the south of its predicted place, and y Ursa Majoris half a second to the north. Now I am quite at a loss to conceive how this difference in so small an arc can arise from error of observation, and I can only attribute it to that cause, whatever it may be, which seems so generally to depend not on the polar distance, but on the right ascension of the star.

2. The second group which I shall consider, contains the stars a Arietis, Arcturus, and Aldebaran, comprehended within an are of about six degrees and a half. Of these three, Arcturus alone has yet been observed by reflection; but from the present very perfect state of the Greenwich circle, which the method of reflection has enabled me to ascertain, it cannot be doubted that the places of the two other stars are well determined. In Arcturus the southern deviation is nearly insensible, but in the two other stars it is very considerable, being in each not less than 1.5". Now these three stars, but particularly the two latter, are among those that have been most assiduously observed by Bradley and myself, at each of the three periods. Let us suppose then, if it be possible, that the whole of these deviations arise from error of observation; or, in other words, that no systematic deviation has really taken place in the stars, but that their proper motions are uniform. Then we must admit that the mural quadrant and the mural circle have at each period given the polar distance of Arcturus correct, or at least subject to the same constant error; and as this star has been observed at each period, at all times of the day, and at all seasons of the year, the observations may be considered as perfectly exempt from accidental error. It will I believe be readily conceded that both instruments are so far perfect, that if the error be either nothing, or a given quantity at one point of the arc, the errors

This has been confirmed by subsequent observation.

must be very nearly indeed the same within a moderate distance, as within 15 degrees, for instance, of that point. Upon this supposition, how can we possibly reconcile the great errors that must have been committed in stars, adjacent as to polar dist ance, but of opposite right ascensions? I do not wish to press these remarks, in order to obtain greater confidence than they deserve, for observations which can never be regarded with too much suspicion; but the arguments I have used appear to me to follow logically from the data before us, and strongly to indicate the probability that some cause purely astronomical has, at least, some share in producing these unexpected deviations.

3. The third group, a Herculis, a Pegasi, and Regulus, is still more remarkable, being comprehended within two degrees of declination, and two of the stars, a Herculis and Pegasi,* being within half a degree of each other. In this group a Pegasi is at least 3" south of its predicted place, whereas the other two stars have not deviated much more than 0.5′′ to the south.

4. a Orionis, a Serpentis, and Procyon, furnish an example equally striking, they being within less than 2° of declination from each other; a Serpentis is exactly in its predicted place, while a Orionis and Procyon are each of them at least 2′′ to the south.

5. Rigel, Spica Virginis, and Sirius, are not contained within so short an arc as the former groups, nor are their places so well determined, on account of their proximity to the horizon; but they afford another instance of the inequality of southern devia tion, in stars having nearly the same polar distance, but opposite right ascensions.

But leaving the considerations suggested by these groups of stars, let us examine more minutely the different hypotheses that may be formed on the supposition, that the whole of these devia tions depends on error of observation caused by some defect in the instruments employed: this investigation becomes the more necessary, as it does not appear that Dr. Brinkley, with his instrument at Dublin, has met with similar discordances. Admitting the accuracy of the observations of Bradley to form the ground-work of this inquiry, there are then two distinct hypotheses, that may be formed by those, who are inclined to maintain, that the proper motions of the stars are uniform; and that the discordances in question have their source, not in any astronomical cause, but in some erroneous system of observation. Of the observations from which the catalogues of 1813 and of the present year have been computed, we may suppose the one or the other to be erroneous. Let us consider the consequences of each hypothesis.

Let us first suppose the error to be in the observations of 1813.

The lunar nutation of a Pegasi was nearly a mininium at each period.