472 



NATURE 



[Sept. 13, 1883 



of arranging a scheme of observations by which, through the co- 

 operation of astronomers in different parts of the world, it has 

 been possible to accomplish the most important piece of astro- 

 nomical work of modern times. With a feasible plan of opera- 

 tions, undertaken with entire unity of purpose on the part of the 

 observers to whom the several divisions of the labour were 

 assigned, this great work is now approaching completion. 

 While it is yet too early to speak with confidence concerning 

 the definitive results which the discussion of all the observations 

 is expected to show, we may with profit consider the object 

 sought in the undertaking, the general plan of the work, the 

 difficulties which have been encountered, and the probable bear- 

 ing which the execution of the present work will have upon the 

 volution of a problem concerning which we now know absolutely 

 n ithing with certainty, — a problem of which what we call 

 universal gravitation is only one element, if, indeed, it be an 

 element, — a problem which reaches fa.rtb.er than all others into 

 the mysteries of the universe, — the motion of the solar and the 

 sidereal systems in space. 



Our first inquiry will be with respect to the condition of the 

 question of stellar positions at the time when this proposal was 

 made by the Gestllschafl in 1865. All the observations which had 

 been madeuotothis timepo: sess one of tw o distinct characteri-tics. 

 A portion of them were made without direct reference to any 

 assumed system of stellar coordinates as a base ; but by far the 

 larger part are differential in their character. This remark 

 holds more especially with reference to right ascensions. Nearly 

 all of the observations of the brighter stars made 1 revious to 

 about iS30were referred to the origin from which stellar co- 

 ordinates are reckoned by corresponding observations of the sun ; 

 but since that date it has been the custom to select a sufficient 

 number of reference stars, symmetrically distributed both in 

 right ascension and declination, and whose coordinates were 

 supposed to be well known. The unequalled Pulkowa observa- 

 tions for the epoch 1S45, form, I believe, the only exception to 

 this statement. From the assumed system of primary stnrs are 

 derived the clock errors and instrumental constants which are 

 employed in the reduction of all the other stars observed. The 

 positions of these secondary stars, therefore, partake of all the 

 errors of the assumed fundamental sjstem, in addition to the 

 direct errors of observation. 



The following list comprises the most important of the cata- 

 logues which have been independently formed: viz. Bessel's 

 Bradley for 1755, the various catalogues of Maskelyne between 

 1766 and 1805, Gould's d'Agelet for 17S3, Piazzi for 1800, 

 Auwer's Caccialore for 1S05, Bessel for 1S15, a feu of the earlier 

 catalogues of Pond, Brinkley for 1S24, Bessel for 1S25, Struve 

 for 1825, Bessel for 1S27, Struve for 1830, Argelander for 1830, 

 and Pulkowa for 1845. 



An analysis of these catalogues reveals four important 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 catalogues of 

 Fedorenko, Groombridge, Schwerd, and Carrington, the double- 

 star observations of Struve, and the zone observations of Bessel 

 and Argelander, the observations were not arranged with refer- 

 ence to the accomplishment of a definite object. 



Fourth, that each catalogue involves a system of errors pecu- 

 liar to the observers, to the character of the instruments em- 

 ployed, and to the system of primary stars selected, bnt that thus 

 far there had been no attempt to reduce the results obtained by 

 different observers to a homogeneous system. In estimating the 

 value of these observations it will be necessary to refer to the 

 re.-earches which have been made subsequent to 1865. 



The systematic deviations of different catalogues in right 

 ascension inter se were noticed at an early date by several astro- 

 nomers; but the first attempt to determine the law of these 

 variations seems to have been made by Safford in a communica- 

 tion to the Monthly Notices of the Royal Astronomical Society 

 in 1861 (xxi. 245), on the positions of the Radcliffe catalogue. 

 1 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 R.A. (Greenw. 12 Year Cat.--Rad.) = - 038s. + 

 032s. sin (a + 5I1. 32m.). Extending this expression to terms 

 of the second order, it may be put under the form A = a con- 

 stant + (m sin a + n cos a) + (/«' sin 2 a + n' cos 2 a) + , &c. 



Safford also seems to have been the first to notice the connec- 

 tion 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 discrepan- 

 cies, 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 s'nee 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 

 Safford 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 systematic errors of r oth catalogues have since been found 

 to be considerably greater than is here indicated, and the devia- 

 tion pointed out by Safford is in the nature of a second differ- 

 ence. The speaker has shown (Proc. Amcr. Acad. 1874, 182) 

 that the weight of the errors of the provisional catalogue as- 

 sumed fell between the first and the third quadrants in the Rad- 

 cliffe 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 im- 

 possible either to determine the nature of the errors 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 ove to the researches of Newcomb, published in 1869-70, 

 a homogeneous system of stellar coordinates in right ascension, 

 which are probably as nearly absolute in their character as it is 

 1 1 sible to obtain from the data at present availal le. He deter- 

 mined the absolute right ascensions of thirty-two stars of the 

 fir t, secoi d, and third magnitudes, and comprised between the 

 limits -30° and +46° declination. A comparison of the places 

 of these stars for a given epoch with the same stars in any cata- 

 logue for the same 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 may be mentioned the fact that New- 

 comb's system cannot safely be extended far beyond the limits 

 in declination 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 discus'ion by Auwers, to which reference will presently 

 be made. The substantial agreement of these two systems, 

 independently determined, 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 safety. When the catalogues which were 

 formed between 1825 and 1865 are compared with New-comb's 

 fundamental system, through the medium of these thirty-two 

 stars, the following facts are revealed : — 



a. The only catalogues in which there is freedom from both 

 accidental and periodic errors are Argelander's Abo catalogue 

 for 1S30 and the Pulkowa catalogue for 1S45. ^ )ne > s reminded 

 in this connection of the remark of Pond, that "we can hardly 

 obtain a better test of our power of predicting the future posi- 

 tion* of stars than by trying by the same formula how accurately 

 we can interpolate for the past. In a variety of papers which I 

 have submitted to the Royal Society I have endeavoured to 

 show that with us the experiment entirely fails." 



i. During this interval the constant differences between the 

 earlier catalogues and Newcomb's system vary between + 01 7s. 

 lor Pond, 1820, and -o - iqs. for Pond, 1830; and for later 

 catalogues between + C07S. for Cambridge, i860, and +o'02s. 

 tor Greenwich, 1S60. 



c. All the ri;;ht ascensions determined at English observatories, 

 and especially those which depend upon the positions published 

 by the British Nautical Almanac, are too large in the region of 

 five hours, and too small in the region of eighteen hours. The 

 general tendency of the constant part of the deviation from 

 Newcomb's system is to neutralise the periodic errors in the 

 region of five hours, and to augment them in the region of 

 eighteen hours, « here, in the case of a few catalogues, the error 

 becomes as great as o"ios., — a quantity which can be readily 



