THE PERSONAL EQUATION. 39 i 



tance, as he was a diligent and useful assistant to me in other respects, 

 I parted with him." 



But time has its revenges, and Kinnebrook's observations are now 

 used as well as Maskelyne's {see " Annales de l'Observatoire de Paris ; 

 Memoires," iii., p. 307), and they are probably about as free from acci- 

 dental errors as his. 



In 1822 Bessel examined this subject, and we find in the Konigs- 

 berg observations of that year an account of quite extended experi- 

 ments on personal equation. 



Bessel, after quoting from Maskelyne's own report (see extract 

 above), considers the subject at some length. He calls attention to 

 the fact that the accidental errors in an eye-and-ear observation cer- 

 tainly do not exceed two-tenths of a second, and that a careful con- 

 sideration of the observations of Maskelyne and his assistant shows 

 that there may be an " involuntary constant difference " between the 

 estimations of various observers which far surpasses the limits of pos- 

 sible accidental error. 



In 1819 Bessel made a visit to the Seeberg Observatory, where he 

 observed, on two nights, transits with Von Lindenau and Encke. 

 These observations showed no personal equation between these three 

 celebrated astronomers. In 1820 Dr. Walbeck and Bessel made sev- 

 eral sets of observations at Konigsberg, for the purpose of determining 

 their relative personal equation, and the results of their work are 

 given below : 



s. 

 1820, December 16th and 17th, Walbeck later than Bessel 1.045 



" 17th and 19th, " " " " 0.985 



" 19th and 20th, " " " " 1.010 



" 20th and 22d, " " n " 1.025 



Mean 1.041 



Bessel says that this great difference was evident from the second 

 day, and that no pains was spared by either of them to observe care- 

 fully ; and that at the end of the series each was confident that it would 

 have been impossible for him to observe differently, by so much even 

 as a tenth of a second. Here, then, was an enormous difference one 

 almost incredible. To test the reality of the phenomenon, Bessel com- 

 pared with Argelander, and found that Argelander was later than he 

 by 1 9 .223. 



Bessel remarks that neither Walbeck nor Argelander had observed 

 as much as he had with the transit-instrument, and he therefore used 

 all opportunities for comparing his work with that of Struve, of 

 Dorpat. He found that in 1814 Struve was later than himself by 

 0\044 ; in 1821, by 8 .799 ; in 1823, by 1 9 .021. Bessel now determined 

 to arrive at some conclusion by studying this phenomenon under dif- 

 ferent aspects. 



To this end Argelander and himself noted the times of 78 disap- 



