Dreyer — 'On Astronomical Transit Observations. 523 



eye and ear.* If we suppose that impressions on the eye and ear 

 cannot be compared instantaneously with one another, and that two 

 ohservers take an unequal time to transfer the one impression to the 

 other, there will arise a personal difference or equation, which will he 

 still larger, if one observer begins with seeing and ends by hearing, 

 and the other observer does the reverse. 



There can hardly be any doubt that the explanation here inti- 

 mated, in many cases, especially when the equation is of a consider- 

 able size, is the right one. In the eye-and-ear method the mind is in 

 reality at work in three different ways : hearing, seeing, and count- 

 ing the seconds; perhaps one might say in four ways, considering the 

 expecting of the coming beats of the clock. The longer the interval 

 between the beats, the longer time this expectation will of course 

 take ; and this is perhaps the reason why Bessel's personal error was 

 found half a second smaller, by using a half-second watch, whose 

 single beats were counted, so that he, with this watch, observed 0^'494 

 later than with a clock beating whole seconds, while Struve and 

 Argelander found no such difference.! However, Eessel's very con- 

 siderable error cannot be explained perfectly in this way. Encke has 

 tried to explain it, simply by supposing that Bessel counted a second 

 too early, and this certainly agrees with the decrease of the error by 

 using the half-second clock. | C. Wolf is of the same opinion,^ and 

 he tells us that a few years ago an analogous case occurred at the 

 Observatory in Paris, where an observer noted all the transits one 

 second later than all the others. || But although this proves the 

 possibility of such a mistake, it hardly seems probable that Bessel's 

 personal error should arise from such a very simple cause, and besides, 

 how should we explain personal equations of 0^-5, 0^*6, 0^-7, of which, 

 we have several examples in the eye-and-ear method,^ and how can 

 an observer continually change his way of estimating transits in the 

 course of years (in which case we could not think of a new way of 

 counting the seconds) ? "We have already, in the foregoing, given 

 several examples of such alterations, and the equation Bessel- Struve 

 increased besides, continually, until it reached its maximum 



* Konigsberger Beotaclitungeii, viii.,p. 7. 



t This explanation of Bessel's error has already been suggested by Albrecht 

 (Langendifferenzen, &c., p. 36). Several observers in Leyden observed in 1861 

 and 1862, with two chronometers, one beating single seconds, the other giving 130 

 beats in one minute ; but none of them found any certain variation in their small 

 errors, caused by the use of the latter (Yerslagen, &c., xv., pp. 212 and 217). 

 X Monatsberichte der Berliner Academie, 1858, p. 617. 

 § Annales de I'Observatoire de Paris, Memoires, t. vui., p. 186. 

 II According to Radau (Sur les erreurs personelles, p. 29, Moniteur Scientifique, 

 1866), the said observer, to his great surprise, was convinced of his mistake 

 by observing the disappearance of an artificial star behind a screen, and counting 

 the seconds aloud, while another person (in the moment of the disappearance) gave 

 him a slap on the back. 



" " Main - Kogerson = + 0s-70 (1853). 



Jacob — Sashoo Jengar = + -80 (1858). 

 Quirling - Lucas =+0-67(1868). 



Main -Lucas = + -70 (1868), &c. 



IT Nehus-Wolfers = + 05-73 (1833). 

 Petersen -Madler= + -52(1833). 

 Gerling-Nicolai = + 0-78 (1837). 

 Dunkin - W. EUis = + -84 (1847). 



R. I. A. PKOC, 8ER. II., VOL. II., SCIENCE. 3 G 



