310 



was in the reversed position relatively to the observer, i.e. r and /. 

 In these averages the systematic error is thus eliminated. In this 

 way the mean error of one series was found to be 



WiLDEBOER DlEPERINK H.VKHUYZEN Mean 



0.370 0.296 0.507 0.401 . (V) 



If on the other hand a series in i)Osition ^4 was combined with 



one in B, in which the metre was in the same position with regard 



to the observer, so that the systematic error was not eliminated in 



the mean, the mean error was found to be: 



WiLDEBOER DlEPERINK B.VKHUYZEN Mean 



0.424 0.755 0.768 0.666 . (VI) 



Both the double sets of mean errors (III) and (IV), and (V) and 

 (VI) show clearly, that there is a systematic difference in the results 

 of the series r and /, or with different positions of the metre relatively 

 to the observer. In order to remove the error, therefore, the mean 

 of two corresponding series of observations must always be taken, 

 in which the metre is in different positions with regard to the 

 observer. 



We further computed the mean error from all the series of ob- 

 servations for tiie same portion of the measuring-bar, without regard 

 to the position of the metre or of the observer, in which therefore 

 the influence is present both of the position of the metre and of 

 the observer. First the mean errors were computed for each observer 

 separately. This gave 



WiLDEBOER DlEPERINK Bakhuyzen Mean 



1.222 0.805 0.955 1.009, (VII) 



Finally the results of the series for the same portion of the 

 measuring bar in all positions of the metre and of the observer for 

 all three observers were averaged, and the mean ei-ror determined 

 from the deviations of each of the results, which must therefore 

 contain (1) the influence of the position of the metre (2) the influence 

 of the position of the observer, (3) any other possible influence of 

 the observer. The mean error was then found to be: 



1.002 (VIII) 



The difference of the mean errors (VII) and (IV) shows, that the 

 position of the observer has a marked influence, on the other hand 

 the agreement of the mean errors (VII) and (VIII) shows, that there 

 does not appear to be an influence due to the observer other than 

 that which depends upon the })Osition of the metre and observer. 



We may further conclude from the values found, that if the two 

 systematic errors mentioned are eliminated, the mean error of a 



