Mr. A. E. Conrady, Mr. R. Inwards, and Mr. G. J. Newbegin were appointed auditors of the Treasurer's accounts for 1906.

Eighty presents were announced as having been received since the last meeting, including, amongst others :

Abbadia Observatory, Observations, tome 5; and Bordeaux Observatory, Catalogue photographique du ciel, Coordonnées rectilignes, tome 2, presented by the Observatories; Gronnigen. Astrographical Laboratory, Libration of the three inuer large satellites of Jupiter (W. de Sitter), presented by the Laboratory; Ziegler Polar Expedition, Scientific results, presented by the estate of Wm. Ziegler.

Astrographic Chart; 16 charts presented by the Royal Observatory, Greenwich; and 19 charts presented by the French Minister of Public Instruction.

Solar Parallax Papers. No. 6.

Construction of a Standard Catalogue of Photographic Star
Places. By Arthur R. Hinks, M.A.

§ 1. The construction of a standard catalogue of photographic star places along the track of the planet Eros was undertaken in the first instance to provide for the reduction of those series of photographs of the planet which, having a field smaller than 2° square, could not be reduced directly with the étoiles de repère ; and also to provide exact places of the stars which had been used in visual micrometric comparisons with the planet.

It now seems probable that the standard catalogue may have an extended use; for, as will be shown later, it will be possible by its aid to effect very simply the equivalent of a re-reduction of all the published places of the planet to this new system of stars, lying close to the track of the planet, and more nearly equal to it in magnitude than are the étoiles de repère. This should provide a powerful method of searching for systematic errors in the photographic places of the planet and the value of the Solar Parallax derived from them.

§ 2. The published material for the construction of the catalogue was found in the Paris Eros Circulars, Nos. 10 and 11.* The results of an inter-comparison of the work of the different observatories were published in Solar Parallax Papers Nos. 4 and 5 (M.N., vol. lxvi. p. 481, vol. lxvii. p. 70, 1906 June and November). In those papers may be found the following conclusions:

(1) That several series of photographic star places are affected with a magnitude equation of serious amount.

(2) That other series are affected by progressive discordances,

Circular No. 12 appeared after the principal part of the work was
But see later, §§ 11 and 12.

finished.

which are sometimes dependent on variations in the adopted places of the fundamental stars, and sometimes not.

(3) That, in general, the star places published in the Paris Circulars are by no means homogeneous.

(4) And that the adopted form of publication did not permit of a complete inquiry into these matters.

§ 3. In 1906 March I ventured to send to the Directors of the observatories concerned a circular letter, submitting for their consideration the following proposals :

That I should print and distribute a large number of lists of the étoiles de repère.

That they should kindly undertake to fill in upon those sheets, in the spaces provided for the purpose, the deduced photographic places of the repère stars, using a separate list for each plate, so that the results from each individual plate were kept quite distinct.

That they should also fill in, upon other sheets to be provided for the purpose, the lists for each separate plate of the deduced places of the étoiles de comparaison (given in Paris Circulars, Tableau III., either in ledgers or as means, without indication of the plate from which each was derived).

These proposals were very kindly received by the Directors to whom they were addressed. The printed sheets were sent out in 1906 May, and were quickly filled up and returned. My sincere acknowledgments are due to the Directors of the Observatories of Bordeaux, Helsingfors, Northfield, San Fernando, and Toulouse, for the cordiality with which they undertook the troublesome task of filling in upon the printed sheets all the desired information; to the Astronomer Royal, who sent advance sheets of the Greenwich volume containing equivalent information; to the Director of the Pulkowa Observatory, who had previously given me similar material in advance of publication; and to the Director of the Paris Observatory, who furnished advance proofs of the Paris original

measures.

The information thus obtained, added to that already published in full in the Paris Circulars for the étoiles du carré de 20', gave me the completely separated results from a very large number of individual plates covering the path of the planet to 1900 December 31. (The discussion of the material for 1901 is postponed to a later date.)

§ 4. To make this considerable mass of material (about 60,000 star positions) homogeneous, I had first to find a way of reducing all the series to one fundamental system,* and to decide what this system should be.

In paper No. 4 I have given reasons for thinking that no one of those systems of fundamental star places based directly upon the meridian observations is satisfactory for our purpose. I decided to form a provisional system from photographic series which had

See S.P.P. No. 4, § 4, for the system to which each was originally reduced.

been reduced to Loewy's system of meridian places. These series are compared in S.P.P. No. 5, p. 80, Table VI. It is there shown that the results from Greenwich and Paris are in excellent agreement; that the Toulouse places are nearly accordant with them; but that the Catania places differ from Paris in a large and irregular manner. I decided to omit the Catania results for the time, and to base the provisional photographic system of repère stars on a mean of Greenwich, Paris, and Toulouse.

The three observatories were given equal weight. A photographic place depending on 1 or 2 plates was given weight 1; on 3 to 6 plates, weight 2; and on 7 or more, weight 3. There would have been little advantage in adopting a more elaborate system of weights, since the real comparative weight of a result from one and from two plates depends very much upon the consideration whether or not the two plates are upon the same centre, and reduced with the same selection of fundamental stars.

We will call this system the System P.Ph. (provisional photographic).

The rôle of system P. Ph. is temporary. It serves to detect and eliminate systematic deviations between different observatories. It will be judged by the eventual degree of accordance between the reduced results when they are brought together for formation of the mean standard places. If this is satisfactory, we may consider that the system P.Ph. has played its part, and it may be allowed to disappear. We need not give, therefore, in this paper, the adopted places of the repère stars in the P.Ph. system, but may proceed at once to examine its use, and the effects of its use.

§ 5. The system P.Ph. is used as follows:

:

We take differences between the places of the repère stars derived from a single plate, and their places in the system P.Ph. The mean of these differences, in the sense P.Ph.-plate, applied as a correction to the plate places of the repère stars, makes them conform on the average to the system P.Ph.

The same correction applied to all other star places deduced from this plate should reduce them equally to the system P.Ph., provided that there is no systematic discontinuity between repère stars and other stars.

The application of this correction produces in a general kind of way the same effect upon the star places as a re-reduction of the plate to the system P.Ph.; it leaves the results rougher in detail than a complete re-reduction, but nearly without those systematic errors which have been called Progressive discordances in S.P.P. No. 5, Tables VI. and VII.

§ 6. Corrections to be applied to individual plates were obtained in this way for the whole of the plates made at Bordeaux, Helsingfors, Northfield, San Fernando, and Toulouse. The following summary will give an idea of the size and distribution of these corrections.

The above figures show that the reduction to a system P.Ph. is by no means superfluous.

The fact that the mean correction for an entire series often differs considerably from zero may no doubt be attributed to divergence in the methods of combining and weighting the meridian results for the adopted repère star places.

The variations from plate to plate must be due partly to these divergences, and partly to the roughness of the meridian places compared with the smoothed system P.Ph.

Plate corrections for Catania, Greenwich, and Paris were not derived, because the separated results for each plate were not at the time available.* It seems certain, however, that it would have been superfluous to apply the process to the Greenwich and Paris series, which agree exceedingly well, and have preponderating weight in the formation of the system P.Ph. The absence of plate corrections for Catania is to be regretted, since large divergences occur in this series. (See S.P.P. No. 5, p. 84.)

§ 7. Corrections for Magnitude Equation in the San Fernando and Toulouse Series.-It was shown in S.P.P. No. 5, p. 78, that the Toulouse results have a large and nearly linear magnitude

The separated results for the Greenwich plates have since been com municated to me in proof, by the kindness of the Astronomer Royal.

equation in declination (but none in right ascension). This result has been confirmed by M. Baillaud, Director of the Toulouse Observatory, but he has not succeeded in discovering the cause of (For this information I am indebted to M. Baillaud.)

it.

It was shown in the same place that the San Fernando right ascensions and declinations were both affected by a considerable non-linear magnitude equation. No further light has been thrown on the cause of this error. Corrections were obtained by plotting the results for successive magnitude groups (loc. cit.), and drawing the best possible smooth curves through them. The quantities derived from these curves were adjusted to allow for the fact that a general mean correction for stars of all magnitudes resulted from the application of the plate corrections of Table I.: the quantity o" 03 was subtracted from the Toulouse corrections, and 08007, 0" 08 from the respective San Fernando corrections. The final magnitude corrections applicable to Toulouse and San Fernando are given in condensed form in the following table :

Table II.

Adopted Corrections for Magnitude Equation.

(

38. Collection of material for formation of catalogue.-The individual star places published in Paris Circulars 10-12, or communicated to me in manuscript upon the printed forms sent out from Cambridge, were entered on catalogue cards, differently coloured for each observatory. These will be referred to as "detail cards.'

The plate corrections and the magnitude equation corrections were applied on the detail cards, and "observatory means" were formed.

Whenever a star had been observed at more than one observatory, a summary card" was added to the card catalogue on which the observatory means were collected, and the final weighted mean taken.