THE PERSONAL EQUATION. 397 



pressing upon the key, unseen by the subject, I could at the same time 

 close the circuit and produce a clear and distinct sound, upon hearing 

 which he made a response registered as before. I connected my ap- 

 paratus with the key-board of a piano-forte in such a way that I was 

 able to introduce an exercise of judgment in the comparison of two 

 tones differing in pitch much or little, as I chose. . . . With different 

 persons, as many as 2,000 individual trials have been made, and the 

 errors of experiment eliminated as far as possible by averages. . . . 

 As was anticipated, different individuals furnished, in some cases, stri- 

 kingly different results, but, in general, they all followed the order 

 given in the table : " 



CASE OF A. G. F. Time iu seconds. 



Response to appearance of a white card 0.292 



" " " " an electric spark (in the dark) 203 



" " sound 138 



" " touch on the forehead 107 



" " " " " hand 117 



" when required to decide between white and red 443 



" " " " " " tones C and E 335 



" " " " " " C and C above (octave) 428 



One cannot but be struck with the additional time required when 

 the phenomenon to be observed becomes even slightly more complex. 

 This is evidently not entirely a physiological effect, but is truly psy- 

 chological in part. Just what bearing this has on the question of the 

 cause of personal equation it would be difficult to say : at the same 

 time we must admit that the slightest additional exercise of judgment 

 requires additional time. This is forcibly shown by the smallness of 

 chronographic personal equation as compared to eye-and-ear-equation. 



Let us now consider personal equation in things other than the 

 estimation of time. We stated that the distance of one star, north or 

 south of another, was usually measured directly; i. e., by graduated 

 circles for large distances, and with micrometers for small ones. Prof. 

 Coffin, now Superintendent of the American Ephemeris, has shown 

 that in his own case, and in the case of two other observers, at the 

 United States Naval Observatory of Washington, a marked personal 

 difference appears in the observations of a Lyrae, and one or two other 

 stars which pass near the zenith of Washington, depending on the 

 direction in which the observer faced, whether north or south. It is 

 plain that a star near the zenith may be observed as a south star or as a 

 north star, and it appears that each position gives a different polar dis- 

 tance to the star: the difference of polar distance is small but constant. 



In reading microscopes, and, in short, in performing any operation 

 where the senses are strained to appreciate small differences of time, 

 space, or position, and particularly where the judgment has to be ex- 

 ercised, personal differences are present. In general, these are con- 

 stant with the same observer, and in astronomy they are usually 

 eliminated in the determination of the zeros. For example, if an ob- 



