pearances or reappearances of a material object, and. he found that Argelander was later than himself by 08.222. Again, in the observation of the occultations of stars (an instantaneous phenomenon), Argelander was slower than Bessel by 08.281. Here was some light: for it was now evident that not only had each astronomer a different habit of estimating time, but that this habit was only constant so long as the same phenomenon was observed; that a personal equation for transit observations would not serve for observations of occultations.
Bessel next investigated the question whether there was any difference in his own absolute personal equation in observations with a clock beating whole seconds, or with a chronometer beating half-seconds; he found that he observed 08.494 later when the clock beat half-seconds than when it beat whole seconds, while Argelander and Struve did not change their habits in this regard.
Bessel's whole investigation is very complete, especially when we consider that it was the first published research on a subject which had escaped attention until his time. The principal points established were:
1. A personal equation subsists in general between two observers.
2. For limited periods of time this equation is probably constant between two observers for the same class of work.
3. The absolute personal equation of any one observer varies with the class of observation; i. e., from transit observations to sudden phenomena like occultations.
4. The rapidity with which the star (in transit observations) traversed the field of the telescope had no influence on Bessel's personal equation.
Bessel does not seem to have supposed that there would be any different personal equation for stars and for the moon. This we now know to have been erroneous, and we shall see that the apparent velocity with which a star moves through the field of the telescope is also held by some observers to have an influence on the magnitude of their personal equation.
All of the preceding results referred simply to the personal equation between observers who were. using the eye-and-ear method. As soon as the chronographic method of registering transits was introduced, it was seen that the personal equation became smaller. This is undoubtedly due to the smaller amount of work which the brain has to perform; the phenomena to be appreciated are, in this latter case, far more simple than in the former, and the effect of this is shown in the amount of personal difference.
We must now give a brief account of the ordinary methods for determining the amount of the relative personal equations of various observers, in order that we may proceed to the determination of the absolute equation, which is of great interest physiologically and psychologically, although not of capital importance to astronomy. As
