528 Proceedings of the Royal Irish Academy. 



duration of the luminous impression, we ■will, during this short time,, 

 see the star, not only in its real place, but also in all the places it 

 has occupied during an interval equal to the duration of the luminous 

 impression. 



It does not seem possible that there can be any objection to this ; 

 but in order to account for those errors by vhich the position of the 

 star is anticipated, "W'olf supposes that the transient impression from 

 the place "vvhich the star really occupies in the moment of the second- 

 beat, also may allovr the mind to impute the foUo-sving positions ■^•hich 

 the star occupies during this, to the instantaneous audible second-beat 

 as simultaneous "svith it. This last supposition seems a little difficult 

 to understand. 



As Tve, therefore, cannot fully adopt "WoK's theory, -we must be 

 content to consider the question about the origin of the personal 

 errors, as elucidated in different Tvays by the foregoing. In order tO' 

 give a short review of what we have already said, we may mention 

 among the principal causes producing personal errors : the co-opera- 

 tion of the different senses; the expectation of the regularly returning 

 beats of the clock ; the different velocity of the sensation ; and lastly^ 

 the difference of habit in the mechanical actions. 



Appendix. 



Since the above paper was read before the Royal Irish Academy,. 

 Professor Bakhuyzen kindly sent me some results of observations made- 

 by himself and the assistants at the Leyden Observatory, which con- 

 firm several conclusions arrived at in the foregoing pages. It deserves,. 

 for instance, our attention that observations of Polaris by day and by 

 night have again shown the considerable influence which an eccentric 

 illumination of the wires can exercise over the personal error. That 

 this is the only circumstance through which it is possible to accotmt 

 for the anomalies which so often have appeared in observations with a 

 "broken telescope," has anew been proved by Dr. Yalentiner's and 

 Dr. Becker's observations with the time-coUimator, as the different 

 direction of the motion of the star was found to have very little or na- 

 influence on the personal error. 



Observations have been made in Leyden in order to try whether 

 the observers estimated the transits of bright and faint stars differ- 

 ently. The observations which were taken with the meridian-cii'cle 

 and chronograph gave the following results : 



Stars 3 — 6 magn. Stars 8 — 9 mag^n. 



Valentiner - Becker =- O'-SO (12 stars), - 0'-21 (lo stars), 



Talentiner- H. G. Bakhuvzen = + -13 (34 stars), + -IS (53 stars), 

 Valentiner - E. F. Bakhuyzen = - -16 -0-17 



The difference in the equation Yalentiner-Becker for bright and 

 for faint stars has been confirmed by the zone-observations of stars- 

 between 30^ and 35° northern declination made in Leyden. 



Bri 



s-ht- 



faint 



stars 



-0= 



■09. 



-0 



•do. 



+ 



•01. 



