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bability e''^^ we may deduce the mean value oitp^,. Let us suppose 

 that all the real clock corrections remain unaltered with the exception 

 of that for the instant q. Then II will be a minimum for Z^ — <fq; 

 and for any other clock correction adopted for the same instant, 

 which differs from this interpolated value by e, II is equal to its 

 least value augmented by 6 /C/ f'. 



Hence the probability of the group of clock corrections contains the 

 factor e-^'^cf" , Avhence follows that the mean value of e, or also 



that of <Pq is equal to , --- „ . Then the mean value of (fq \/K,j is 



constant and e(jiial to ; this constant is called v. 



Hence the 2"'^ power of the mean value of the lirst member of 

 the above relation is : 



Kqv-^ -^(rl--- Kf ^Kf^K- + < + <' + .•.]• 

 The 2"^ member jp^, computed with approximative values of a', //, 2 

 and u is known. I had no direct data for the determination of (.i\ 

 It consists of one part whicli is independent of the mimber of stars 

 observed for the clock cori-ection, and another ])art which is in inverse 

 proportion to this number. For one star observed by Bakhuyzen, the 

 latter part amounts to about 900 and for Pannekoek it is a little 

 less. I wished to avoid a too large value for /i' for fear of exag- 

 gerating the regularity of the clock at the cost of the accuracy of 

 the observations, and therefore I have put for each of those parts 

 of ix' 300, together ii' = 600. 



xVccording to the value given above for S\ we have v"' : (i"- = j? 

 and the mean value of the expression : 



% : i/ic, *+....<+ ^r +<+ ^^ + ^' +••■ ■ 



will be equal to (i. 



With different suppositions for ^, I could derive from this relation 

 the corresponding value ft'. My result was that for Si = V^^ the 

 value of (i- is 592 and therefore I have retained this value of ^i in 

 the further computation. 



The hypothetical expression of the probability was tested in two 

 different ways. 



In the first place I investigated whether indeed r" might be regarded 

 as equal for the different intervals of the period treated. Therefore 

 I have arranged the observations according to their coefficients Kg, 

 and have derived from the lialf with least Kq separately the value 

 of fi' belonging to jï = Vao- The result was (i' = 591. 



