( 252 ) 



small as compared with that depending on other causes which are 

 difficult to account for. But the computation would not become 

 much more difficult if we should assign different weights to the 

 determinations. 



I now use the following thesis for the interpolation with regard 

 to the smallest sinuosity that is proved in § 3 of my previous 

 paper viz.: the partial derivative of the total sinuosity Is of a series 

 of clock corrections with regard to one of the corrections Sq, is 

 equal to twice the abrupt variation which occurs in the derivative 

 of the third order of the interpolation curve near the abscissa g' and 

 the ordinate Sg. Hence according to § 4 



_ = 12 (.„-.„). 



1 apply this relation to the interpolating curve after compen- 

 sation determined b}- the corrections L, and I obtain 



oLcf 

 in case that each part of that curve is represented by an equation : 

 U =Lq^ Gqi-^-C^e -\- En t\ 

 In accordance with the previous paper I have used capitals for the 

 interpolation coefticients belonging to the corrections which are freed 

 from errors. Also the meaning of 2 for this interpolation corre- 

 sponds entirely with that of o used for the interpolation without 

 compensation. 



ö/r ö/x , 7- , ^ • • 



YoY — ^ we may substitute — ^-^ , because L^ -\- /^ is mvari- 



able, hence ^Lq = — ^fq- 



After the substitution of — ^ =— 12 ^q, each relation A — - + -^ = 



O/q ■ ^Jq l^q 



takes the form -. 2q = ^2^ •^*' 



The first member of this relation depends on x, y, z, u and the 

 errors ƒ, and all these quantities occur in it in a linear form: 



B ^ V P f 



If we use the approximate values obtained for x, y, z and u in 



the supposition ƒ = 0, we can compute the expression : 



B ^ V P 



rpg — öq — x6^ —ya^ —zo^ —uo^ . 



1 have made this computation by determining the differences between 



