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 apparatus 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, strikingly different results, but, in general, they all followed the order given in the table:"
| CASE OF A. G. F. | Time in 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 psychological 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 Lyræ, 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 distance 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 exercised, personal differences are present. In general, these are constant with the same observer, and in astronomy they are usually eliminated in the determination of the zeros. For example, if an ob-
