J. F. ENCKE ON THE METHOD OF LEAST SQUARES. 353 



because the errors are distributed equally on both sides of 0. If 

 we put here 



h A = t, 

 then 



By partial integration we find the general integral 



The first part disappears for the limit as well as oo ^ because 



with the latter e~^=—^ will, in the development of the series 



always produce higher powers of t in the denominator than 

 those which are in the numerator ; consequently, 



2 2 ' 



or 



kb>) = I (^' - ^) yt(«-2); ^(» + -0 = i (^ + 1) ^(«)^ 



By the continuation of this operation we shall aiTive, accord- 

 ing as n is even or odd, either to k^^^ or to k^^^l but the former 

 is, according to (5.), 



and for the latter we find, by a glance at the formula 



h a/ TT' 



Hence we have at once the following values 



;fc(o) = 1, 



* -Ah*' 



(8) 3.5.7 



16A« ' h? y/ 1: 



