( 259 ) 



In the secontl place 1 have investigated vvhetiier also for intervals 

 of longer duration, the constancy of r' remains the same. In tliat 

 case I could deri\'e v^ from the total sinuosity //, of the real clock 

 corrections. 



If we imagine that from the series of those clock corrections one 

 is dropped, wliich deviates from the interpolated value by y„, 

 then //, is diminished by 6 Kg (p^'. 59 times we caji drop succes- 

 sively one observation from the 61 observations at our disposal, and 

 thus each time diminish the total sinuosity of the remaining clock 

 corrections by 6 /t ^^ At the end //^ is zero and hence Ii may be 

 considered as consisting of 59 parts, each of a mean value of 6 i;". 

 Hence the mean value of II is 354 ^'^ 



From tlie reduced rates Q—x Q^ -y Q^—z QV—uQP i deduced 

 the total sinuosity of the clock corrections L-\-f and obtained 

 /z_,_/=8756. 



In my previous paper on this interpolation it is demonstrated that 

 if the errors ƒ and the clock corrections expressed by I are independent 

 of eacli other 1 ij^f^Ij^-\-If. Instead of the formula derived there: 

 /^=:S'6e„(/;— ƒ,) I now write" //■=:^6/;(^„—f„0=2'6/>/ 



and substitute for öq its value expressed in terms of the errors /'. 

 In this way we get : 



/ƒ = ^ 6 /; [. . . /v; ./; + K'^f, + K, j\ + K\ fr + K\ /; . . .] 



In the 2°'^ member occur under ^ many products of real errors. 

 The mean value of these terms is zero. I omit them, substitute ft* 

 for the square of each error and find as mean value for If G ^^ 2 Kg. 



The computation of -5" K,j yielded 1.39. 



In this way I have found the following relation between v and n -. 

 8756 = 354 r* + 8,34 jx* 



whence, if ii'^ is equal to 600, r^ = 11, which result is in good 

 harmony with the value first found for ^. 



The set of equations by which the most probable errors are 

 connected is readily solved, if we use as a first approximation 



fq = 0.45 — . After I had found by the substitution of these 



Kg -f - JV 



values that the 2"^^ member required still another correction Aj i|?, I used 



A,ip„ 



0.80 as a correction for the first approximation. 



Kg 4- jf ^ ^ 



When computed according to the em[)irical formula 

 _ 0.45 rpg + 0.80 A, ^g 



