( 253 ) 



the successive coeflicients of f for the reduced clock rates 



Q — xQB—yQ'—zQy—uQp, 

 according to the new method of interpolation. 



f 

 (i(j may be developed in the following way: 



1 dif 



We have also o = --. ~^j~ where //• = | I t^ I <^^^- 



Hence : 



•^ 1A2/-. A/iAr.\ >^f 



k; = "-^ = 



do;; _ 1 d'lf _ d /I d// A _ ö(j/ _ ^,/ 



therefore the coeflicient of fo in the expression for Oq is equal to the 



coefficient of /g in the expression for oi . 



Let us consider the case that fg = 1 and all the other values of/=0 



then Og = Kq, (Jp = Kp or == Kg , Or = A'/ or =: Kg , etc. The series 

 of the quantities of for that case gives us directly all the coefTicients 



K which are required for the development of Og . In this manner an 

 interpolation was made between the numbers..., 0, 0, 100,0, .. . as 

 many times as there were observations, each time moving the 

 number 100 further over one interval between two successive 

 determinations of the clock correction. 



If this computation is properly arranged, it can be made in a 

 very short time and the accuracy can be tested by the results 

 themselves as the coeflicients are derived twice independently of each 

 other. 



I shall now describe in detail how I have arranged the compu- 

 tation of those coetïieients for a determination of the clock correction. 



According to § 2 of my paper "On interpolation etc." of Dec. 10, 

 1902 we have the relations ; 



. _ _ 9q-\- 9r—^ Qn _ 'Jp + // y — 2 Q,n 



Og — e,i e,)i e„ — r ejii — 



which allow us, once the series of the </ being found,- to deduce the 

 series of the o from the series of the y and Q. 



The series of the </ is determijied by the equations ((') of§ 2 viz. 



_ n Q„^ -\- m Qn n {Q,n — g^) m (Qn — g,) 

 m -\- n 2 (m -|^ n) 2 {in -{- n)^ 



17* 



