354 J. F. ENCKE ON THE METHOD OF LEAST SQUARES. 



If these values be substituted in the above formula, we have on 

 the left side of the equation ^A;(") 



1.3.5 ....(w-1) 



for n even 

 n odd 



1 n/1.3 



_ 1 ''/ 1.2.3...1 (n-l) 

 ~ h - V Vt 



consequently, if we multiply both sides by g, and then leave on 



the left side -^ = r standing alone, we then obtain the following 



values : 



r, , q /I5 7r-81 



f e /945 7r - 128^ 



or in numbers, — 



r = 0-845347 • ^. |l ± "-v^^T"/ 



r = 0-674489.. ,|l±—;;,^^| 



r, 0-4971991 

 >•= 0-577190. S3 |l±-;7^} 



r, , 0-5507191 

 r = 0-512502. s,|l±—^;r^J> 



r 0- 63 5 5 08 "1 



r = 0-465553. s,jl±—^^^^| 



f, 0-755776 1 

 r = 0-429497. e,|l±^;^^^^| 



where e is the arithmetical mean of all the errors without re- 

 garding their signs ; £3 is the square root of the arithmetical 



