THE PERSONAL EQUATION. 395 



Pape finds (Astronomische Nachrichten, vol. xliv., p. 179) that the 

 error of a transit observation is composed of two parts : one is con- 

 stant, and the other depends on the polar distance of the star. Dunkin 

 likewise considers the probable error of a transit observation as depend- 

 ing upon the polar distance of the star, and Wolf's experiments cor- 

 roborate these results, and show that his own personal equation became 

 lai-ger as the velocity of the star increased. It is evident that this 

 rule must be held true only within limits, and probably these limits 

 are not very far apart. Wolf further made experiments to determine 

 whether the position of the observer affected his personal equation, 

 and he concluded that, for his own case, there was no effect due to 

 this cause. It is probable that most astronomers would differ with 

 Wolf in this respect : observers of double stars, especially, have no- 

 ticed a constant influence in their measures due to the position of the 

 head. 



After having recited the results of his experiments, M. Wolf comes 

 to the consideration of the really important question, " What is the 

 origin of the phenomenon known as personal equation?" Before he 

 discusses this, he considers the remarkable personal differences be- 

 tween Bessel and other astronomers which we have noticed, showing 

 that this is undoubtedly the largest personal equation on record, and 

 expressing his opinion that it was really due to an erroneous counting 

 of the whole seconds, and that the fractional part of his enormous pex - - 

 sonal equation with Argelander (1V223) was alone a case of true physi- 

 ological personal difference. Let us recall the fact that Bessel and 

 Argelander differed in observations of sudden phenomena only by 

 0\222, or 3 .281 ; and again, that Bessel observed transits with a chro- 

 nometer beating half-seconds so much as 8 .494 (nearly a whole beat) 

 later than with a clock beating seconds ; and it seems impossible to 

 avoid Wolf's conclusion that Bessel counted his seconds differently 

 from other observers. The only thing which militates against this 

 theory is, that Bessel must have examined this question of enumera- 

 tion himself; and again, that, in two nights' observation with Von Lin- 

 denau and Encke, he found no signs of personal equation. Encke, 

 however, in speaking of this large personal equation of Bessel's, says 

 that there is no doubt that he had a different method of counting the 

 strokes of the clock from other observers. M. Wolf, too, mentions 

 the case of an assistant at the Paris Observatory, whose transit ob- 

 servations were earlier by one second than those observed by his fel- 

 low-assistants (Bessel's habit), but, in this case, a few experiments on 

 artificial transits sufficed to show him that his habit was wrong, and 

 led him to change it. 



The opinion of most astronomers has been, that personal equation 

 is not purely a physiological phenomenon, but likewise a psychological. 

 The time required for the sound of the clock to reach the observer's 

 brain, and the time required for the light to pass from the image of 



