137 



these three methods, I requested my assistant, Mr. Morton, to ob- 

 serve three stars, selected from among those which present only 

 average difficulties, a very great number of times, so that the measures 

 should be sufficiently numerous to eliminate all one-sided errors. 



The observations of Position only have been used ; but these have 

 been dealt with in the three different methods above described, that 

 is, the final result and its probable error and weight have been ob- 

 tained by each of the three modes. The results are here subjoined, 

 and the errors and their squares are given in full as to two of the 

 stars, together with the whole computation ; and it is to be hoped 

 that this may not only prove interesting to observers of double stars, 

 but may throw some light on the curious mathematical question in- 

 volved in the inquiry which is the subject of the above remarks. 



Among the stars selected as above mentioned for the trial of the 

 three methods, was 2 Comae Berenices, or S 1596. Now this star 

 had been very frequently observed during the six years from 1843 to 

 1848, at the time of the Parallax investigation, to which reference 

 has been already made. The comparison then made between the 

 mean of all the measures of position obtained and the value of the 

 angle of position given by Struve, gave reason to believe either that 

 the angle had not altered during a period of sixteen years, or at least 

 that it had altered very little. The observations of 1859 fully con- 

 firmed this opinion. Rejecting from the observations of 1843-8 those 

 made on two nights, when less than 6 measures were obtained, the 

 result of 1859 differs only 8' from that of 1843-8. I was thus 

 enabled, for the purposes of this inquiry, to treat these observations 

 of 1843-8, 156 in number, as if they had all been made within an 

 interval of time not greater than about two months. Now these 

 observations had been made by three different observers, and while 

 the results of separate nights were very discordant, the probable 

 errors derived from the partial values of nights, the results of which 

 differed greatly from the general mean, were as remarkably small ; 

 on the other hand, the observations of the same star in 1859, 215 in 

 number, were by one observer only, and the results of different nights 

 agree very closely. The applications of the three methods to the 

 early and late observations of this star therefore illustrate yery 

 strikingly the effect produced by discordancy in the values obtained 

 on different nights, when the peculiarities of the object observed 



