392 THE POPULAR SCIENCE MONTHLY. 



pearances or reappearances of a material object, and. he found that 

 Argelander was later than himself by ! .222. Again, in the obser- 

 vation of the occultations of stars (an instantaneous phenomenon), 

 Argelander was slower than Bessel by 8 .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 dif- 

 ference 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 0*.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) trav- 

 ersed 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 

 diffei*ent personal equation for stars and for the moon. This we now 

 know to have been erroneous, and we shall see that the apparent velo- 

 city 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 equa- 

 tion between observers who were. using the eye-and-ear method. As 

 soon as the chronographic method of registering transits was intro- 

 duced, 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 psy- 

 chologically, although not of capital importance to astronomy. As 



