Dreyer — Oil Adronoinical Transit Observations. 493 



■difficult to say whetlier these instriiments answer their purpose per- 

 fectly. Each single one of them must of course be most carefully 

 examined, in order that constant errors in its results may be detected, 

 -and their causes done away with. When this has been done (as in the 

 ■case of C. "Wolf's apparatus), there is no reason for not relying upon 

 the exactness of the results obtained with it, within a reasonable de- 

 gree. And several of these instruments have, by a careful construction 

 of all the details, furnished us with results which agree extremely 

 well. Kaiser, for instance, found, with his first instrument, the pro- 

 bable error in a single determination (that is, by a single wire transit) 

 = + 0'"081, from the results of four observers,* while Wolf's apparatus 

 gives the probable error of a double observation over one wire 

 = ± 0^'038.f The possibility of the existence of constant errors in the 

 results is certainly not excluded by this, nor by another control which has 

 been tried by comparing the results of artificial transits with those of 

 real ones. We give the following examples here : — 



Apparatus- stars = 0''"035 Plantamour and Hirsch. 



"02 Albrecht and Yan Hennekeler. 



-004 Albrecht and Valentiner. 



"03 Tietjen and Valentiner. 



-002 Biicklund and Valentiner. 



All these differences are within the degree of exactness possible to 

 be attained, as we shall see presently. But artificial stars have not 

 always agreed so well with the real ones as in the determinations of 

 personal equations which we have just quoted. There appeared, for 

 instance, during the determination of the difference of longitude 

 between Leyden and Brussels, in 1868, a perfect discordance between 

 the transit instruments and the time-collimator ; but the observations 

 with the former instrument differed just as much, inter se, and there 

 can hardly be any doubt that a special cause of variation in the per- 

 sonal equations has influenced the observations. | The mistrust in 

 his own apparatus which Kaiser, by this, was led to express, § was 

 therefore apparently unfounded, and the results furnished by time- 

 collimators may be considered as very fairly representing the true 

 errors of the observer. 



After having considered the accuracy of artificial transits, it is 

 natural to test the degree of exactness which may be attained in de- 

 terminations of personal differences by means of simultaneous observa- 



difference of longitude between Wasldngton and Havanna, 1870, page 13), but we 

 do not know of any published observations taken with it, A proposal of Dr. E. 

 Kayser's (Astron. Nachrichten, No. 1665) seems perfectly impracticable. 



* Verslagenen MededeHngen, xv., 1863, page 207- 



t Annales de 1' Observatoire Imperial de Paris, t. viii., page 178. 



X We shall further on consider this circumstance fully. 



§ Annalen der Stemwarte in Leiden, ii., page 153, 



3E2 



