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 accidental errors as his.
In 1822 Bessel examined this subject, and we find in the Königsberg observations of that year an account of quite extended experiments 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 certainly do not exceed two-tenths of a second, and that a careful consideration 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 possible 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 several sets of observations at Königsberg, for the purpose of determining their relative personal equation, and the results of their work are given below:
| 1820, December 16th and 17th, Walbeck later than Bessel | 1.045 |
| "17th and 19th,"""" | 0.985 |
| "19th and 20th,"""" | 1.010 |
| " 20th and 22d,"""" | 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 carefully; 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 compared with Argelander, and found that Argelander was later than he by 18.223.
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 08.044; in 1821, by 08.799; in 1823, by 18.021. Bessel now determined to arrive at some conclusion by studying this phenomenon under different aspects.
To this end Argelander and himself noted the times of 78 disap-
