August 24, 18S3.] 



SCIENCE. 



■2:n 



a. The only catalogues in wliicli there is freedom 

 from botli accidental an<l periodic errors are Arye- 

 hiuder's Abo catalogue for 1S:!0, and the Pulkova 

 catalogue for 1S45. One Is reminded, in this connec- 

 nection, of the remark of Poiul, that " we can hardly 

 obtain a better test of our power of predicting the 

 future positions of stars than by trying by the same 

 formula how accurately we can interpolate for the 

 past. In a variety of papers wliich I have submitted 

 to tlie Koyal society, I have endeavored to show, that, 

 with us, the experiment entirely fails." 



h. During this interval the constant differences be- 

 tneen the earlier catalogues and Newcomb's system 

 vary between +0.17* for Pond, 1820; and —0.10" for 

 Pond, 1830: and for later catalogues, between +0.07" 

 for Cambridge, ISOO; and +.02* for Greenwich, 1800. 



c. All the right ascensions determined at English 

 observatories, and especially those which depend upon 

 the positions published by the British Nautical al- 

 manac, are too large in the region of five hours, and 

 too small in the region of eighteen hours. The gen- 

 eral tendency of the constant part of the deviation 

 from Newcomb's system is to neutralize the periodic 

 errors in the region of five hours, and to augment 

 them in the region of eighteen hours, where, in the 

 case of a few catalogues, the error becomes as great 

 as 0.10', — a quantity which can be readily detected 

 from the observations of two or three evenings with 

 an indifferent instrument, if it relates to a single star. 



The right ascensions determined at French observa- 

 tories exhibit systematic errors, which follow nearly 

 the same law as those which characterize English 

 observations. 



Distinctively German observations are nearly free 

 from systematic errors. As far as they exist at all, 

 their tendency is to neutralize the errors inherent in 

 distinctively English and French observations. 



d. In the case of several catalogues, residual errors 

 of considerable magnitude rem.ain after the syste- 

 matic errors depending upon the right ascensions 

 have been allowed for. These errors are found to 

 be functions of the declination of the stars observed, 

 and without doubt have jH)me connection with the 

 form of the pivots of the instrument with which the 

 observations were m.ade. This statement holds true, 

 especially with respect to the observations at Paris, 

 Melbourne, and Brussels, between 1858 and 1871; 

 and to the Washington observations between 1858 

 and 1801. 



e. The systematic errors which exist in observations 

 previous to 1805 follow tlie same law, and have nearly 

 the same magnitude, as the errors of the same class 

 which are inherent in the national ephemerides of 

 the country in which they were made. 



The British Nautical almanac .and the Connaisance 

 des temps are largely responsible for the perpetua- 

 tion of this class of errors. For a few years before 

 and after 1800, the ephemerides of the Nautical 

 almanac were based upon the observations of Pond, 

 whidi contain large periodic errors. It is found that 

 the errors of this system have been transferred with- 

 out sensible diminution to every catalogue in which 

 the obsen'atious depend upon Nautical almanac clock 



stars. At English observatories it has been the cus- 

 tom to correct the positions of the fundamental stars 

 by the observations of each successive year; but this 

 has produced no sensible effect on the diminution of 

 the periodic errors, which belong to the fundamental 

 system. The periodic errors of the American ephem- 

 ecis fidlow nearly the same law as the errors of the 

 Nautical almanac, but their magnitude is somewhat 

 reduced. The error of equinox is also less. 



Wolfer's Tab. rer/., upon which the Berliner jahr- 

 buch is based, has no well-defined systematic errow; 

 and the correction for equinox is nearly the same in 

 amount as in the American ephemeris, but with the 

 opposite sign. The accidental errors seem to be 

 rather larger than in the system of tlie American 

 ephemeris. 



/. A general estimate may be formed of the rela- 

 tive magnitudes of the errors of secondary catalogues 

 by comparing the average error for each star of the 

 primary catalogue. The numbers given below rep- 

 resent the average deviation for each star, expressed 

 in hundredths of seconds, after the various catalogues 

 have been reduced to a common equinox. 



Averaife 

 error for 

 each star. 



li'Agclct (Gould) 



C':ipe of Good Uopu (llonderson) 



Gruenwicli 



Greenwicli 



t'iipc* of Good Hope 

 Ifcidcllirc .... 

 Grtenwich . . . 

 Binsel . . / . . 



Gillid 



Madras (Taylor) 



Capu of Good Hope (Fallows) . 



n.-iacirae 



iiiagh 



zzl 



Pi 



Bcssel's Bradley 



1830 

 1S4.5 

 18+5 

 13G0 



lisa 

 ]8S:i 



18.111 



1871 



1S87 



1846-52 



18.10 



1856 



1860 



1840 



1823 



1830 



1840 



1K,10 



1830 



1845 



1840 



18U0 



1755 



180O 



1750 



It is obvious from these relations, that previous to 

 about 1825 the magnitude of the accidental errors of 

 observation, combined with the errors of reduction, 

 prevent any definite conclusions with respect to the 

 periodic errors inherent in these early observations. 

 It is probable, aUo, that early observations of stars 

 of the eighth and ninth magnitudes are subject to a 

 class of errors peculiar to themselves, the nature of 

 which it is now well-nigh impossible to determine. 



The systematic errors in declination which belong 

 to the various secondary catalogues named are even 

 more marked than those in right ascension. The 

 experience of Pond in is:!;j is the experience of 

 every astronomer who has attempted to compare 

 observations of the same star made at different times, 

 under different circumstances, with different ' in- 



