506 Proceedings of the Royal Irish Academy. 



what it was a few moBths before in IS'eiif chatel. It was, therefore, sup- 

 posed that there might he some cause for this change, and in order to 

 obtain a certain value for his error, Wolf went in March, 1869, to IN'euf- 

 chatel, and took, jointly with Hirsch, observations with the transit- 

 circle for two days. But, strange to say, they now found almost the same 

 result as that found two years before with the same instruments ; 

 besides, artificial stars had in 1867 given a value for the equation 

 nearly midways between the two results of real transits which com- 

 pleted the confusion : — 



H. - E. W. = - Os-162 + 0^-009 by equator-stars ) in Neiifchatel, 

 = - -067 + -016 ,, artific. „ ] May, June, 1867. 

 = + -056 + -009 „ eqiiator-stars \ in Ziirich, Aug. 1867. 

 = - -139 + -013 ,, „ ,, j in]S^eufcliatel,Marcli,1869.*- 



This was not the first time that such abrupt changes had taken 

 place when the personal equation had been determined at different 

 times with different instruments ; but such a change had generally been 

 explained by one of the observers using a strange instrument. For 

 examplef : — 



Ernest Quetelet -Kam = + 0='60 78 stars, tr. -circle in Leyden, August, 1868. 

 + -IS artificial stars, ,, ,, ,, ,, 



+ "40 transit-instr. in Brussels, September, ,, 

 -|- '16 20 stars, miu'al-circle, Brussels, Sept., ,, 



It was the variation of this equation which made Kaiser doubtful 

 about his time-collimators, which seems strange, as the real transits- 

 differed just as much in their results. Another example is : — 



Jamefalt — Fuss = 4 O^'IO, June 27, July 4, "1 -.o-n -d n „ + 

 -I- -41, July 7-16, j ' + 



Although it was, therefore, nothing new that such strange results 

 should appear in determinations of longitude, still, in the summer of 

 1869, Wolf undertook a series of researches in conjunction with his as- 

 sistant, whereby it was found that the principal cause of the deviations 

 between the cliiferent values was the position of the eye-piece. As is 

 natural, when two persons observe immediately after one another the 

 passages of the same star over the two halves of the system of wires, 

 Hirsch and Wolf had placed the eye-piece midways between the two 

 positions, which were convenient for their eyes; accordingly the eye- 

 piece was for the short-sighted W. too far from the focus, but for H.'s 

 normal sight it was too near this. Wolf derives the following results 

 from all. the observations printed in his "Mittheilungen," page 265 : — 



* R. Wolf, Astronomische Mittheilungen, xxv. (Yierteljabi-sscbrift der Natur- 

 forschenden Gesellschaft in Ziirich, xiv., 1869, page 250). 

 t Annalen der Sternwarte in Leiden, ii., page 169. 



;J; Bestimmung der LangendiiTerenz zwischen PulkoM^a, Helsingfors, Abo, Lo- 

 •wisa imd Wiborg, von J. Kortazzi : St. Petersburg, 1871, pp. 68-9. 



