230 



SCIENCE. 



LVoL. II., No. 29. 



in tlie reduction of all the other stars observed. The 

 positions of these secondary stars, therefore, partake 

 of all the errors of the assumed fundamental sys- 

 tem, in addition to the direct errors of observation. 



The following list comprises the most important 

 of the catalogues which have been independently 

 formed; viz., Bessel's Bradley for 17.i5, the various 

 catalogues of Maskelyi>e between 1760 and 1805, 

 Gould's D'Agelet for 1783, Piazzi for 1800, Auwer's 

 Caeciatore for 1S05, Bessel for 1815, a few of the 

 earlier catalogues of Pond, Brinkley for 1824, Bessel 

 for 1823, Struve for 1S25, Bessel for 1827, Struve for 

 18.30, Argelander for 1830, and Pulkova for 1845. 



The important catalogues of secondary stars pub- 

 lished previous to 1865 are comprised in the following 

 table. 



[ Table omiiied.'] 



An analysis of these catalogues reveals four impor- 

 tant facts: — 



First, that a large share of the observations relate 

 to bright stars, at least to stars brighter than the 

 eighth magnitude. 



Second, that in a large number of cases the same 

 star is found in different catalogues, but that no rule 

 is discoverable in the selection. 



Third, that with the exception of the polar cata- 

 logues of Fedorenko, Groombridge, Schwerd, and 

 Garrington, the double-star observations of Struve, 

 and the zone observations of liessel and Argelander, 

 the observations were not arranged with reference to 

 the accomplishment of a definite object. 



Fourth, that each catalogue involves a system of 

 errors peculiar to the observers, to the character of 

 the instrument employed, and to the system of pri- 

 mary stars selected, but that thus far there had been 

 no attempt to reduce the results obtained by differ- 

 ent observers to a homogeneous system. In esti- 

 mating the value of these observations it will be 

 necessary to refer to the researches which have been 

 made subsequent to 186.5. 



The systematic deviations of different catalogues 

 in right ascension inter ne were noticed at an early 

 date by several astronomers; but the first attempt to 

 determine the law of these variations seems to have 

 been made by Safford in a communication to the 

 monthly notices of the Royal astronomical suciety in 

 1861 (xxi. 245), ' On the positions of the Radcliffe 

 catalogue.' I quote the equation derived by Safford, 

 since it appears to be the first published account of 

 a form of investigation almost exclusively followed 

 since that time. It is as follows: — 



Diff. of E. A. (Greenw. 12 Year cat. — Ead.) =; 

 - 0.38^ -I- 0.82s. sin (a -|- 5h. 32 m.). Extending this 

 expression to terms of the second order, it may be 

 put under the form, A = a constant + [m sin a -j- re 

 cos o) + {m' sin 2 a+ n' cos 2 a) +, etc. 



Safford also seems to have been the first to notice 

 the connection between the observed residuals, and 

 the errors in position of the primary stars employed. 

 He remarks, " In investigating the causes which 

 would give rise to such systematic discrepancies, I 

 was struck with the fact that the same or nearly the 

 same variations were apparent in the assumed places 



of the time stars for the years since 1845; that, if the 

 correct positions of the time stars had been .assumed, 

 the resulting positions would have been free from 

 these small errors." That the relation given by Saf- 

 ford should have been observed at all, is the more 

 remarkable, since the primary stars upon which the 

 Radcliffe positions depend are nearly the same as 

 those employed at Greenwich. In reality, the sys- 

 tematic errors of both catalogues have since been 

 found to be considerably greater than is here indi- 

 cated, and the deviation pointed out by Safford is in 

 the nature of a second difference. The speaker has 

 shown {Proc. Amer. acad., 1874, 182) that the weight 

 of the errors of the provisional catalogue assumed, 

 fell between the first and the third quadrants in the 

 Radcliffe observations for 1841-42, on account of 

 the omission of certain clock stars which were used 

 at Greenwich. 



Since the discordances which exist between two 

 catalogues may arise from errors in either one or in 

 both, it is clearly impossible either to determine the 

 nature" of the erorrs, or to assign their true cause, 

 until a fundamental system has been established 

 which is free both from accidental and from periodic 

 errors, — from accidental errors, since a few abnormal 

 differences may easily invalidate the determination 

 of the errors which are really periodic; from periodic 

 errors, because a relative system can only become an 

 absolute one when one of the elements of which it is 

 composed becomes absolute. 



We owe to the researches of Newcomb, published 

 in 1809-70, a homogeneous system of stellar co-ordi- 

 nates in right ascension, which are probably as nearly 

 absolute in tlieir character as it is possible to obtain 

 from the data at present available. He determined 

 the absolute right ascensions of thirty-two stars of 

 the first, second, and third magnitudes, and comxirised 

 between the limits — oO° and + 46° declination. A 

 comparison of the jjlaces of these stars for a given 

 epoch, with the same stars in any catalogue for the 

 sajne epoch, enables us to determine with consider- 

 able precision the system of errors inherent in that 

 catalogue. Several circumstances prevent the exact 

 determination of this relation. Among them maybe 

 mentioned the fact that Newconib's system cannot 

 safely be extended far beyond the limits in decli- 

 nation of the stars -composing the system, that the 

 stars are not symmetrically distributed in declination, 

 and that the system of errors derived from bright 

 stars is probably not the same as that derived from 

 stars of less magnitude. 



To a certain extent all of these objections have 

 been met in the later discussion by Auwers, to which 

 reference will presently be made. The substantial 

 agreement of these two systems, independently deter- 

 mined, furnishes satisfactory evidence that we have 

 at last obtained a foundation system with which it is 

 safe to make comparisons, from which we may draw 

 conclusions with comparative s.afety. When the cata- 

 logues wliich were formed between 1825 and 1865 

 are compared with Newcomb's fundamental system, 

 througli the medium of these thirty-two stars, the 

 following facts are revealed. 



