Dreyer — Oil Astronomical Transit Observations. 495 



that their probable errors of a transit over one "wire are respectively 

 a' and a". We find then — 



A = 



a + a' 



As the probable error in a single wii'e-transit, for experienced ob- 

 servers, generally amounts to nearly the same quantity, we may in 

 the above formula introduce a = -J-^a' + a") instead of a' and a". We 

 have then — 



A = afl^ 

 yj n ' 



and accordingly (as there is no reason "why E should be dependent on 

 the number of "wires) — 



\ yj nj 



W is here the probable error, which appears from the accordance 

 bet"ween the results of different stars. From this "we, therefore, find 

 the probable uncertainty in a personal equation, arising from the ob- 

 server's passing from one star to another — 



£ ^ \W'--a'. 

 n 



If "wc, for instance, from the observations given in the Report on 

 "the determination of the difi:erence of longitude between Berlin and 

 Lund, compute the value of SJ, we may either deduce W from the de- 

 viations of the single values of the equation between the observers 

 (Yalentiner and Backlund) from the average value for one night, or 

 we may put all the observations, made on different nights, together, 

 and deduce 77^ from their accordance with the mean of them all. In 

 the former way I find as mean of four nights' results — 



JF= 0^-068 and ^ = 0^-0o3 ; 



and in the latter way — 



JF= 0^-066 and^= 0'-050. 



Dr. Albrecht has, in his above-quoted book, computed JE fi'om a 

 number of observations ; we have computed it fi'om several others, and 

 find that chronograpluc observations, on an average, give aboiit 0''"04 

 as the value for jE, whether we compute IF in one or the other of the 

 above-mentioned ways. As the eye-and-ear method is now-a-days 

 very seldom used for determinations of longitude, it does not furnish 

 us with such rich materials for the calculation of £ as the chrono- 



