THE ORBIT OF URANUS. 



169 



A simple glance at the course of the residuals shows (1) that their probahle 

 value is considerably greater than the probable error attributed to tlie equations 

 of condition, being more nearly 0".7 than 0".5, and yet larger in the later years; 

 (2) that during certain periods they are of a systematic character. During the 

 years 1748 to 1753 the observations show a decided positive correction to the 

 theory of a magnitude greater than we can consider probable, amounting to about 

 one-third of a second of time in the mean of Bradley's two observations of 1748 

 and 1753. About 1800 the correction becomes negative, and so continues for 

 20 years Avith an average value of about 1". In 1821 it suddenly becomes 

 positive, and so continues until 1833. From this year forward the residuals are 

 not systematic in character. 



In order to show clearly the general course of the outstanding corrections, they 

 have been divided into groups, generally including about five years each. The 

 mean outstanding correction for each group, taken with respect to the weights 

 indicated by the factors /', is as follows. In tlie column e is shown what the 

 probable error of the residual should be if the weiglits assigned to the several 

 equations were strictly correct, and no systematic errors were present either iu 

 theory or observation. 



