( 2-12 ) 



cessive points wliifli Jiro well doliiied by observations this curve 



satisticsan equation of the third degree Si = Sq-^g(, T -\- c,, T^ + e,, T^, 



where 7'=/ — q and q<it<^r, and has moreover the properties 



(IS (PS 



that besides S also -- and -— are continuous, while at the ends of 

 db dr 



this curve — is zero ; these data appeared to be sufiicient for a 



<Jf- 



detuiite determination of such an interpolating curve. 



In the same paper in § 3 1 lui\e referred to the })roblem ofconi- 

 })ensation for the case that the results of the observations .S' are 

 alfected with errors. 



Now T shall describe how that problem was solved and I shall 

 apply this method of compensation to the corrections and the rates 

 of the clock HonwC 17 diu-ing the ])eriod .Ian. 14, 1903— Jan. 14, 1904. 



For the sake of the compensation 1 have used instead of the 

 supposition on which my interpolation was based, another hypo- 

 thesis which covers more, and foi- this purpose I have accepted that the 

 probability of a grouj) of corrections S is proportional to c.-'h, 

 wdiere the factor / is iiulepeiulent of the intervals between the obser- 

 vations; the original coiulition of minimum is a result of this hypo- 

 thesis, if we acce[)l as interpolated for the time t that value which 

 (considered as result of observation) makes the expression e—'^s as 

 large as possible. 



As formerly I have called the erroi- of observation in .S',/ : f,j and 

 the real clock correction L,,, so that L,, — S^ — ƒ;, meanwhile, 

 I venture to use the same letters A, aiul L,, in the sense of most 

 probable values of the errors and measured quantities, although 

 there is naturally a dilferonce between the latter (piautities and the 

 real values. 



As soon as we have to do with errors of observation we must 

 substitute //. for /.^ in the expression for the probability of a group. 



The probability that the errors fa,--- /,„ /'/> />•,--- f~. I'e- 

 spectively, occur in the observations, must in those cases where 

 the continuity of the observed quantity agrees Avitli the hypothesis 



made above, be proportional to the i)roduct of d andc^ 'v ; 



in the latter expression /i,/ I'epreseuts the value of the mean error 

 in Sj. The system of errors of greatest probability satisfies the 

 condition : 



1 Is—f-\- Va -^'-^1 = minimum, 



f*9 



