November 35, 1898.] 



SCIENCE. 



729 



graph, and completed his zone about a 

 dozen j'ears ago. Other observers decided 

 for themselves whether or not to employ 

 the chronograph, with the general result 

 that with it the zone would be rather more 

 accurate on the surface, and without it 

 would be rather more promptlj' completed. 

 When I say rather more accurate on the 

 surface I mean that chronographic regis- 

 tration appears to be especially liable to a 

 peculiar form of personal equation, viz.: 

 a variation of the time of transit and, con- 

 sequentlj', of the resulting right ascension, 

 when the star is fainter than the ordinary 

 stars observed for clock correction. This 

 matter was pointed out originally as es- 

 sential to be investigated, but has not yet 

 been fuUj' cleared up. So far as chrono- 

 graphic observations are concerned, there 

 seems to be no doubt that the effect 

 of faintness upon the time of transit is to 

 delay the reaction or registration very gen- 

 erally, if not absolutely without exception. 

 But, on the other hand, there are several 

 observers, Argelander, Bauschinger, Deich- 

 miiller, Copeland and Borgen, for whom 

 stars near, but below the limit of easy ob- 

 servation, with the instrument employed, 

 are observed by Bradley's method earlier 

 than brighter stars, while the same ob- 

 servers note the transit of stars near this 

 limit, but above it, quite normally. This 

 feature of his own observations was de- 

 tected by Argelander himself, and con- 

 firmed by Auwers in his careful discussion 

 of his own Berlin -zone, in which the Bonn 

 observations are taken into account. 



As the phenomenon detected by Arge- 

 lander in his own observations was referred 

 to a psychical cause, it is likely that other 

 observers might become aware of a similar 

 phenomenon in their own observations, if it 

 were not that the diffei-ences are trifling 

 and liable to mislead the investigator who 

 shall attempt to reproduce them, as is suffi- 

 ciently apparent when the attempt is made 



to introduce a strict logical order into the 

 statements already j)ublished. 



Personal equation is a subject so different 

 in its causes from the ordinary instrumental 

 peculiarities which manifest themselves in 

 results that the causes of it, which are psy- 

 chical, are entirely liable to be mistakea 

 and thus obscured, and entirely tru.stworthy 

 results are liable to be rejected as abnormal, 

 because they do not agree with groundless 

 hypotheses. Suspicion has been expressed, 

 for example, that Nyren's latitude observa- 

 tions, with the prime vertical transit of the 

 Pulkova Observatory, are liable to an 

 equation of a personal nature depending 

 upon the magnitude of the star observed. 

 The suspicion was based upon the theory 

 that the chronographic and ej'e-andear 

 methods have some elements in common, 

 which rendered them equally liable to such 

 a form of personal equation, while the fact 

 is that the general phenomena of personal 

 equation by eye and ear are due to the 

 cause detected by Bessel, viz.: the ' Zeit- 

 verschiebung,'or displacement of time, which 

 arises when the attempt is made to add an 

 impression on the sense of hearing to one 

 at exactly the same instant on the sense of 

 sight. In the chronographic method of 

 registration the time required is in normal 

 instances positive — that is, the ' reaction ' 

 time of the psychologists. The two methods 

 of observing transits are psychically differ- 

 ent, and the general result for ordinary time 

 stars is that the average chronographic ob- 

 server produces transits about as much later 

 than the average eye-and-ear observer as is 

 required for a simple reaction. The amount 

 is 0.1G2 at Greenwich for the ten j'ears 1885 

 to 1890, inclusive, and 1890 to 1894, inclu- 

 sive, with trifling fluctuations (see my paper 

 in No.425 of the Astronomical Journal). Since 

 writing that I have received the introduc- 

 tion to the Greenwich Astronomical Obser- 

 vations for the year 1895, which gives a re- 

 sult almost identical with the years from 



