730 



SCIENGE. 



[N. S. Vol. VIII. No. 204. 



1885 on ; for 1895 we find e'— e = 0M61 for 

 13 observers in all. The difference — O'.OOl 

 between the mean for ten years and that 

 for the single year 1895 is far less than the 

 probable error about ±0'.002 of the mean 

 for 1895, a decided indication that the 

 quantity 0M6 is obtained with substantial 

 accuracy from the ten years' results, and 

 represents something which arises from a 

 true cause or combination of true causes. 

 A persistent positive sign of the quantities 

 e'— 6 is due, as it seems, to the fact that 

 the chrouographic transits are registered 

 too late, combined with the other fact that 

 the eye-and-ear observations are for some 

 observers too late and for other observers 

 too early. In order, then, to obtain the 

 true time of a series of transits, the chrouo- 

 graphic method, if employed by all the 

 Greenwich observers, would give an average 

 time too late by about 0M6, while the eye- 

 and-ear method would give an average 

 time 0M6 earlier and more nearly correct. 

 We may suppose, for example, that in 1895 

 tlie 13 observers whose eye-and-ear personal 

 equations are discussed in the introduction 

 for that year have observed each a star of 

 the average magnitude of a Greenwich 

 time star, and in a moderate declination 

 near the average declination of time stars, 

 and, reducing the observations in the usual 

 way, have obtained a clock correction by 

 each method, but without the application 

 of the personal equation. The average of 

 the thirteen chronographic clock correc- 

 tions would then be 0M6 too small, while 

 that of the thirteen eye- and- ear clock cor- 

 rections have no common error constant 

 for the thirteen. The standard observer 

 for 1895, Mr. Lewis, obtained by eye and 

 ear a clock correction OMO larger than by 

 chronographic on three nights in that year, 

 and henCe, so far as these three nights show, 

 his eye-and-ear transits are more nearly 

 correct than his average chronographic 

 clock corrections, as we cannot well infer 



that the actual reaction time occupied in 

 the bisection is very far from 0M6. For a 

 series of ten years in all the two-method 

 equation for Mr. Lewis has been 0M39 in 

 the mean or for separate years as follows : 



1885 + 0.06 



1886 + 0.13 



1887 + 0.13 



1888 + 0.19 



1889 + 0.15 

 1890 -f 0.15 



1891 + 0.09 



1892 + 0.19 



1893 + 0.20 

 1895 + 0.10 



ISTo eye-and-ear observations were re- 

 corded for Mr. Lewis in 1894, and the 

 largest difference from the mean, viz. : 

 — .079 for 1885, is not as large as the cor- 

 responding difference —.089 for the chief 

 assistant. Mi', (now Professor) Turner, for 

 the same year. The probable error of a 

 year's determination for Mr. Lewis is 

 ±0'.033 by the sum 0\37 of the ten differ- 

 ences from rhO'.OSl, and by sum of squares 

 the mean error is d=0.047 and the pi-obable 

 error ±0'.031. The important question 

 whether there is in general a variation 

 of personal equation with magnitude has 

 already been tested in a good many ways 

 by various astronomers, with the general 

 result that such variations are far more 

 uniformly exhibited in chronographic tran- 

 sits than in those taken by eye and ear. 

 The investigations of the effect of such a 

 personal equation have been carried on for 

 the following zones of the Catalog der 

 Astronomischen Gesellschaft, already pub- 

 lished : 



Place Obseever 



Zone 1° to 5° Albany Boss 



15° to 20° Berlin Auwers 



20° to 25° Berlin Becker. 



There are various other investigations 

 for chronographic observers which all agree 

 in general with the result of the reaction 



