( 254 ) 

 which for the first and the hist epochs a and z become: 



<ja — Qy. H ^ — gz = (iv H ~ — 



where ii and v refer to the interx^als at both ends. 



In the example given here, also one of the latter relations occurs, 

 i. e. that for the observations of January 20, 1903. The successive 

 intervals with the values of Q belonging to them are here: 



3 6 10 . . . (/, m, n, o) 



7b . . . (Q) 



The line separates what precedes this observation and what follows. 

 As a first approximation for the quantities </ I have adopted 



3 3 



+"7, 



100 , 



m -{- n 



, only three of tliese values differ from zero, namely 



I _ 



flu ^^^ ; ; ^iii i ƒ/(/ ^^^^ siw ^'» ' 9r —— ", " ^'1* 



^ m -\- I n -\- 



In my example: Q,,, = -|- 33 ; Q„ ^ — 12 ; / = 3, ?/i := 3, n = 8, 

 o r= 3 ; hence <fj> = + 17 ; ^^^ = + 21 ; g,- = — 3. With these three 

 values begins the annexed scheme, in whicli the successive corrections 

 of the g are computed, (see p. 255 sq.) 



Annexed to this paper is a table (II) (p. 256 sq.) containing the 

 coefficients 100 /v for this computation; under the heading "Sum of 

 tlie squares . . . ." have been given the sums of the «(piares of the 

 coefficients for each date, and to the first and second approximations 

 the values of 100 ip which belong to the observations. 



Each equation of errors is reduced to the form : 



.... < /o + K,' f, MK, + ^)f,i + Kfr + Kl /; + .... = ^, 



where ^ = — , is constant for all equations, and must be deter- 



12 X n^ 



mined in order to enable a solution. 



In the relation : 



which is independent of the hypothesis of the probability of a group 

 of clock corrections, the quantities ƒ represent real errors of observa- 

 tion, of which the mean value is fi. The error of interpolation g)q 

 in the interpolation with regard to the least sinuosity, i. e. the 

 difference between the real clock correction A/ and the interpolated 



correction for the same instant is ^. From the expression of pro- 



Kg 



