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part of a series of photographic portraits of the Presidents of the Society, made and presented by Mr. W. Schooling; C. Flammarion, La planète Mars, presented by the author; Barlow and Bryan, Elementary Mathematical Astronomy, presented by Mr. W. T. Lynn; A. Guillemin, Autres Mondes, presented by the author; Catalogue of Proper-motion Stars, by J. G. Porter, presented by the Cincinnati Observatory; Oxford University Observatory, Researches in Stellar Parallax by the aid of Photography, Part 2, presented by the Observatory; H. Gyldén, Nouvelles recherches sur les séries employées dans les théories des Planètes, presented by the author; E. L. Trou velot, Drawing of a portion of the Milky Way, presented by M. Trouvelot (per Mr. A. Marth); Lick Observatory, Photographs of the Moon and Jupiter (enlarged positives on glass), presented by the Observatory; Sydney Observatory, Photographs of portions of the Moon and of the region surrounding Argus (enlargements on paper), presented by Mr. H. C. Russell; Astronomische Gesellschaft, Catalog, Zone +50° bis 55° (Cambridge, Mass.), presented by the Society; Specola Vaticana, Pubblicazioni I. and II., presented by the Observatory; von Kuffner'sche Sternwarte, Publicationen, Band II., presented by the Observatory; J. Bossert, Catalogue de 3950 étoiles (supplément à l'Histoire Céleste de Lalande), presented by the author.

On the Variation of Latitude, as indicated by Recent Observations at the Royal Observatory, Greenwich. By W. G. Thackeray and H. H. Turner, M.A., B.Sc.

The publication of a Star Catalogue at Greenwich has generally been an occasion for discussing the systematic errors of that and of previous catalogues, from comparisons inter se, or with catalogues of other observatories. The last Greenwich Catalogue (Ten-Year, 1880) is, for instance, readily comparable with Stone's Cape Catalogue, 1880, and the comparison has an important bearing on the determination of refraction. It has, indeed, already been made, but the discussion is not quite complete, though it is hoped soon to publish the results. But a somewhat new departure has been made in connection with the Ten-Year Catalogue, in the comparison of the N.P.D.s for different years with the mean. The investigation was, from the nature of the case, limited to those stars which had been well observed at different epochs throughout the ten years; and in practice only those stars were included which had been observed in at least five years out of the ten. For such stars the annual means for N.P.D., formed in the computation sheets during the process of reduction to 1880'0, were compared with the finally adopted result for N.P.D., and the excesses tabulated under the respective years, with a view to the detection of systematic error. Subsidiary arrangements of these quantities were made both in R.A. and N.P.D., and the results are shown in the following tables.

TABLE I.

Excess of Annual Mean N.P.D. over Adopted Result for N.P.D., arranged according to Right Ascension. (The suffixes indicate the number of observations.)

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TABLE II.

Excess of Annual Mean N.P.D. over Adopted Result for N.P.D., arranged according to N.P.D.

-0'125

(The suffixes indicate the number of observations.)

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30

+0'05139 +0'06140 -0°03155

-O'15190

-004-200

- Ο'ΟΙ 140

+0'1193

+ 0·2692

--O'1475

+0·08,06

40

-0'1918

+0'1923

-0·08,9

-O'1330

- 0'20.21

-0.2621

+0.18.26

+0:18:23

+ 02117

+0'08.25

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It is not proposed to make any further comment on these tables as they stand in the present paper, the object of which is to give the results of a line of investigation suggested by the inspection of Table I., which affords sufficient evidence in favour of Mr. Chandler's fourteen-monthly period in latitude to make the present note of immediate interest.

Mr. Thackeray's interpretation of Table I. was as follows:The right ascension of a star is a rough indication of the time of year at which it was observed. We may assume the mean time of observation at Greenwich to be about midway between sunset and 2 A.M., or for our present purpose 10 o'clock P.M.; so that the mean time of observation of the groups oh-6h, 6h-12h, 12h-18h, and 18h-24h would be as follows:

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If, then, the groups in Table I. are arranged consecutively, placing each column in order under the one to the left, we shall have a rough indication of the systematic changes in N P.D. arranged in order of time. There is, of course, the considerable error in this assumption that observations in the group oh-6h in any year were made partly at the beginning and partly at the end of the year, whereas we can only assign them to one of these epochs; but for the particular discussion in question the error thus introduced is not too serious, for Mr. Chandler's period of variation (fourteen months) does not differ very largely from a year, and consequently the phases at the beginning and end of the year would not be very different.

But it is to be remarked that the formation of such large groups as those of six hours-corresponding to nearly a quarter of the whole period-considerably diminishes the apparent amplitude of the wave under discussion. [The theoretical apparent amplitude would become about seven-tenths of the original.] Further, stars observed below the pole must be regarded as having an R.A. differing by twelve hours from their tabular R.A., and Table I. must be corrected accordingly. The original comparison with Mr. Chandler's inequality was, however, made without this correction.

Crediting the group oh-6h, therefore, to the end of the year, we get the chronological variation of N.P.D., as in the following table in the column Q, where in the column C is given the theoretical variation according to Mr. Chandler's paper in the Astronomical Journal, No. 267 :

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TABLE III.

Excess of Mean Annual Mean N.P.D. over Adopted Result for N.P.D., arranged for every 6 of Right Ascension and compared with the Theoretical Variation of Latitude computed from Chandler's Formula (“Astronomical Journal," No. 267).

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This comparison is professedly only rough; but, as it is distinctly favourable to the existence of an inequality such as that of Mr. Chandler's (more especially noticeable when the results are represented in diagrammatic form), a more direct investigation was at once undertaken. A complete examination of all the stars would have involved much labour, and it was, therefore, determined to make some preliminary calculations before definitely embarking on this enterprise.

J. From the theoretical expressions given in Mr. Chandler's paper, above quoted, the epochs of maximum and minimum latitude were calculated. Now, it has long been recognised that there are systematic errors of annual period affecting the Greenwich N.P.D.s, the origin of which is not yet completely understood, but which it is necessary to eliminate carefully for the purposes of the present discussion. This can be done by comparing observations of the same star made (say) in 1880

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