138 



are eliminated. Thus the good observations of 1859 give the e a 

 equal to 89' only, while in those of 1843-8 the e a attains the great 

 value of 8731'. 



The values of/ 2 given by the observations of the three stars accord 

 very well, considering the different circumstances under which they 

 were obtained. It will be seen also that little effect is produced on 

 the mean result by using these different methods of reduction. 



In the account of the American Coast Survey of 1856, and at 

 pages 307-8, will be found a formula by which the probable error is 

 deduced from the differences from the mean alone, the probable error 



or P=0*845347 , where e represents the error of a single 



observation. 



I have tested this in the case of three stars in which n was equal to 

 6, 10, and 156, respectively, and the probable error deduced was a 

 little greater in the first two cases, and a very little smaller in the last. 



