ccxlviii 



WEIGHTS AND MEAN ERRORS. 



embarrassing problem of relative Weight to be solved, which always arises when observations at 

 different places and of widely different orders of merit are to be blended. The criterion for 

 estimating their relative values is clearly to be supplied by the respective probable errors ; but 

 the attainment of these probable errors is environed with obstacles. The probable errors, as 

 determined by the deviation of the individual comparisons from their average, are clearly not 

 available for this purpose, as the first attempt renders very manifest. Cases are not unfrequent 

 in which the mean error, thus determined, is least for the poorest observations ; and in the 

 present discussion it was found that for one observatory the average deviation of the individual 

 comparisons from their mean was both less than the probable error of this mean, as derived 

 from the discussion of the entire series, and than its actual deviation from the truth. 



Nevertheless the investigation of the first-named conventional mean error of observation is a 

 matter of considerable interest, and the results which it furnishes are here appended. They 

 were obtained by reducing the places given by the several comparisons to the corresponding 

 places for the time of their mean, correcting, of course, for differential refraction and differential 

 parallax. For the Santiago equatorial, in which a correction to the adopted value of the 

 revolution of the micrometer- screw, amounting to O."0057 or to about one-half of the last unit 

 employed by Lieutenant Gilliss, was indicated by the solution of the fundamental equations the 

 values have been corrected also for the change in this constant of reduction. On the other hand 

 the observations of one night, (1849, December 12,) were rejected, being evidently affected by 

 some abnormal source of error. The columns headed e show the mean variation of each com- 

 parison from the mean for each date. 



Mean Errors for Comparisons of Mars at Santiago. 



