( 246 ) 



From readings of the hiiroinclcr iiiul the thermometers, dailv means 

 of almospheric |)ressiire, lemperalnre and diiferenee of (emperalure 

 from midnight (o mi(hiigli( iiave heen derived. Let tiie clot'l-c corree- 

 tions at midnight be S, and the mean (hiily rales in tiie intervals 

 between the sneeessive determinations of the (doek eorreetions he Q, 

 in aceonUxnee with the letters ])rc\ionsIy nsed by me. From llie said 

 daily means, the mean valnes of the atmospheric pressnre, of the 

 temperature and of the diflerejiee in temperature were derived for 

 the same inter\als. In the inter})olation these (pianlities correspond 

 with Q, hence I call them Q^', Q"", Q^ ■ For the barometer readings 1 

 used the deviations fi-oni 76 cms. The temperatures »> are those of 

 the upper thermometei'. 



In this paper I shall also u.se the letters S^', S^, >S'' to indicate 

 quantities that can be computed for each ob.servation by taking the 

 sum of the daily means of />, v> and I", to begin willi a certain 

 date, say Jan. 14, J9()3 till midnight of the day for which the 

 clock correction is determined. ^S'^' denotes a value which is -j- 10 for 

 each obserxation of Pannkkokk, and zero for each observation of 

 Bakhuyzkn, and the series (}'' i-elates to the series ^S'^' in the same 

 way as each series Q relates to the series >S' according to the formula 



'^r — '^(1 



Q,i= . Sr and X are two successive ipiantities of the series, 



n 



and ?i is the interval between them exj)ressed in days. 



/v = aS' — .r .s' ' — i/S^ — c,s' —II s'' — _/' 

 must then be considered as a formula for a reduced and compeji- 

 sated clock correction. 



Each of the letters L, S, f represents a series of disci-ete values, 

 one for each observed clock correction, but by means of the inter- 

 polation along the least sinuous line they can also be taken as con- 

 tinuous variable (piantities of which the derivatives of the first and 

 second ordei' also vary coutiuiiously, but of which the derivatives 

 of the third order vary abruptly. To determine such a variable, say 

 S^ , for the instant t^iq-\-T between the epochs q and r of the 

 determinations of the clock correction, we use according to § 4 the 



formula 



D B B D B 



where q is the epoch of the observation which immediately [>recedes /. 

 The coefficients 7'^' e^^ 1'^^ can be derived from the series Q^ if 

 we use the formulae C in § 2 of the previous i)a})er on this 

 method of interpolation. 



Taking the quantities L, S, ƒ in the sense as explained above 



