Pape finds (Astronomische Nachrichten, vol. xliv., p. 179) that the error of a transit observation is composed of two parts: one is constant, and the other depends on the polar distance of the star. Dunkin likewise considers the probable error of a transit observation as depending upon the polar distance of the star, and Wolf's experiments corroborate these results, and show that his own personal equation became larger 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 noticed 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 between 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 personal equation with Argelander (18.223) was alone a case of true physiological personal difference. Let us recall the fact that Bessel and Argelander differed in observations of sudden phenomena only by 08.222, or 08.281; and again, that Bessel observed transits with a chronometer beating half-seconds so much as 08.494 (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 enumeration himself; and again, that, in two nights' observation with Von Lindenau 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 observations were earlier by one second than those observed by his fellow-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
