Dreyer — On Astronomical Transit Observations. 527 



the other two) when the outer ones appeared with reg'ular intervals ; 

 and it was only sharply defined, if these latter flashed up at irregular 

 intervals. But if the steadily shining star had been caused to dis- 

 appear at the moment when the others appeared, they were all seen 

 in a straight line. 



WoK explains these phenomena in the right way, I think, when 

 lie says, that by the irregular sudden appearance of the outer stars, 

 the eye, taken by surprise, is principally occupied with them for a 

 moment, and in the meantime ceases to observe the central one, which 

 •can only be seen again after that moment, at a time when it has 

 moved in advance. This last impression seems now to the mind to be 

 simultaneous with the sudden appearance of the other two stars. 

 J3ut if they appear at regular intervals, the mind is prepared for their 

 appearance, and the observation of the motion of the steadily luminous 

 star is not perfectly interrupted during the sudden impression. While 

 this lasts, the observer will therefore see all the places which the star 

 has occupied, and it depends now entirely on his individuality as to 

 which place he will select out of this series, and consider simultaneous 

 with the sudden appearance of the outer stars. To conclude, from 

 the sign of Wolf's personal error, he selected the place which was 

 reached by the central star at the end of the sudden impression. But 

 when the eye begins to see the flashing sparks, it retains all the posi- 

 t;ions which the central star successively occupied during a space of 

 lime equal to the duration of a luminous impression ; it is, therefore, 

 ^Iso possible that an observer imputes the position of the star in the 

 moment of the flashing up to some point in this "parcours anterieur." 

 Lastly, if we abolish the steady illumination of the central star, it is 

 not possible to see a series of its positions during the sudden impres- 

 sion, and the personal error is done away with, at least for an antici- 

 3)ating observer.*' 



Such impressions on the senses, which, to the mind, seem to last for 

 rsome little time (although their duration in reality is extremely short), 

 m^ust, according to the above, be of gi-eat importance as the sources of 

 personal errors. Wolf tries on these experiments to found a theory 

 for all kinds of personal equations in transit-observations, without 

 being quite successful, as far as we can see. He remarks that the 

 ^bove explanation of personal errors, in case of our perceiving the 

 seconds by the eye, cannot without alteration be applied to the eye- 

 ^nd-ear method, as a considerable difference between the duration of 

 perceptions by the eye and by the ear has been found by his own 

 direct researches, as well as by those of Helmholtz and Emsmann. 

 If we perceive the seconds by the ear, the impression will certainly 

 last for an extremely short time (less than O^'Ol), but owing to the 



* Hartmann has found something similar by his apparatus (Grimert's Archiv. 

 fiir Mathematik, xxxi., p. 17). If he placed a scale in the telescope and before the 

 ■observation remarked at which division the star should be at the second-beat, he 

 often fancied when he concentrated his attention on the motion of the star, that he 

 saw it a little in advance of its real position. He oftener saw it in. the right place 

 when he was tired. 



