process of reduction to the standard system by means of the stars in the 20' square will avoid the systematic effects of all these untoward circumstances, and will give a result equivalent to, though not so smooth as, a complete re-reduction. The standard system will also be indispensable for the reduction of the micrometric comparisons of the planet. In Paris Circulars 8 and 9 Monsieur Loewy published a list of stars used in these comparisons, and desired that they should be measured on the photographs whenever possible. As a result of this, the standard catalogue contains good places of a very large majority of these stars, and provides almost completely for the reduction of most of the micrometer series. The only serious difficulty may be found in reducing the observations made at Washington and Yerkes Observatories, where they used some stars so faint that they are not found on the ordinary photographs. These stars were all marked on charts sent to Professor Perrine for use in selecting his comparison stars, and he has succeeded in finding and measuring a large part of them on the Crossley plates. We have therefore reason to hope that this standard photographic system of stars may provide, directly or indirectly, for the complete reduction of the Eros observations of 1900 on a homogeneous system. The extension of the system to the early months of 1901 is making excellent progress. § 20. As before, the additional assistance required in this work has been provided by a grant from the Government Grant Fund of the Royal Society. Acknowledgments are also due to Miss Julia Bell, Girton College, who has continued to perform a great part of the computations; and to S. E. Bowd, who has made the card catalogue and assisted efficiently in all parts of the work. Cambridge Observatory: Note on the Position of the Sun's Axis of Rotation, as deduced from Greenwich Sun-spot Measures 1886-1901. Papers of the I.U.S.R. Computing Bureau, No. I. By H. H. Turner, D.Sc., F.R.S., Savilian Professor. 1. The present note is to be regarded rather as a statement of problems than as a solution of them. A discussion of the Greenwich sun-spot measures was begun a few years ago, as a necessary preliminary to computations in connection with the International Union for Solar Research; and it is being continued as the work of the Computing Bureau, of which the writer was asked to take charge. But the resources of this Bureau are at present very slender, and the time of the Director is much occupied with the printing of the Astrographic Catalogue, so that it may be some time before a definitive discussion is completed. Meanwhile the following provisional statement may be of interest; it has been drawn up in response to one or two inquiries for information. Another note will shortly be presented, dealing with the velocity of rotation. 2. The material used is taken from the Greenwich sun-spot ledgers, 1886-1901 inclusive. Later publications, especially the welcome volume of "photoheliographic results, 1874-1885," which has just been issued, will allow of a considerable extension of the discussion; but these were not available when the following computations were commenced. The discussion was confined to spot groups which were seen for a period of ten days at least; and no notice is taken in what follows of the identity of recurring groups. The longitude and latitude on each day were compared with the mean values given in the ledgers; and the differences were tabulated under each 10° of distance from central meridian, so as to show the motions in latitude and longitude. The spots were further grouped according to their latitudes, in groups to 10°, 10° to 15°, 15° to 20°, 20° to 25°, and over 25°, N. and S. latitudes being kept separate. 3. When we have a set of mean residuals for each 10° of longitude, various methods may be proposed for deducing the mean drift from the series. Take, for instance, the following series of mean residuals in latitude for spots in N. latitudes o° to 10° in the month of October (all years combined). Differences of method would turn chiefly upon the relative weights to be assigned to the outer and inner residuals. The outer give better intervals for measuring the motion; but, on the other hand, they are affected by larger errors, owing to foreshortening, and possibly to optical distortion. We shall do no harm by making two separate determinations of drift from outer and inner groups and comparing the results. If we reject the outermost groups (80° to 90°) as too much foreshortened, and take the mean of the next three, we get results for +65° and - 65°, a difference of 130° in longitude. The next three groups will give us mean values for +35° and -35°, a difference of 70°. 4. A drift in longitude may be taken to increase steadily with the time, and hence the differences for ±65° should be to those for ±35° in the ratio of 13 to 7. Thus, if the above figures had related to longitudes, the mean drift per 10° would have been (-0.38 -0°40)/13 -0°060 from the outer groups and (-0°24 -0°22)/7= -0°066 from the inner groups. The 5. The same might be true of a drift in latitude if it were a physical drift; but if it is an apparent drift, due to a faulty determination of the Sun's axis, these formule will not apply. error due to a wrongly assumed axis is of the form k sin (0+65°) – k sin (0-65°)=2k cos sin 65° in one case, and (similarly) 2k cos sin 35° in the other. The ratio is thus sin 65°/sin 35° = 1*58 instead of 65/35 = 1.86. 6. To take the latitude first: if we have adopted a wrong axis, the effect will be a spurious latitude drift, varying in amount as we go round the Sun during the year. The drift will in fact be, roughly, similar to the Sun's drift in declination, if for a moment we regard the equator as an erroneous determination of the ecliptic: it will be northwards at one time of year and southwards six months later, with no drift midway. Hence, if we arrange the results according to the time of year, they will form a cycle. The results for latitude were accordingly collected in months, each spot being assigned to the calendar month in which it appeared on the central meridian ; and the mean drifts between the meridians above specified are given in Tables I. and II., which require no further explanation. The unit in the table is oo1, and the figures are differences between the mean residual at +65° and that at 65°. The row of figures at the top represents solar latitude. TABLE II. Latitude drift between +35° and -35° in each month (of the years 1886-1901). Multiplying the coefficients A and B by cosec 65° for Table I., and cosec 35° for Table II., we get the error of the Sun's axis, which we may now express (as Carrington does) in minutes of arc. The separate determinations are given in Table III. Excluding, at any rate in the first instance, the outside groups (for latitudes above 20°), we can now analyse the remaining 6 columns in each table harmonically, to find an expression of the form A sin+B cos + C, where = 0 for the middle of January. TABLE III. Quantities representing the Errors of the Sun's adopted axis. Inspection of Table III. suggests the following conclusions: (a) The determinations from meridians ±65° and ±35° are satisfactorily accordant. Thus the Sun's disc may be treated as free from distortion for the purpose in view. (b) The adopted axis is sensibly in error for the period under discussion. (c) The different zones give sensibly different values for the error, zones - 20° to - 15° and -15° to -10° being specially discordant. But the results seem really to fall into three groups: The conclusion (c) was not altogether unexpected, for an inspection of Carrington's material had indicated something of the kind. The material is given on pp. 240-242 of his volume Observations of Solar Spots (published in 1863 by Williams & Norgate); and if it is divided into four groups according to the latitude of the spots, we get approximately for his X and Y— |