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ROYAL SOCIETY OF CANADA 



The determination of the systematic error, ease (c) above, due to the 

 asymmetric position of the nucleus of the star image within the slit 

 opening, which evidently affects all the lines on a plate, is a more diffi- 

 cult matter. Probably the best that can be done is to obtain the probable 

 error of a plate from all the plates in a series by treating the residuals 

 from the velocity of each plate; but the question is complicated by the 

 fact that this velocity is also affected by the accidental errors of measure- 

 ment. Moreover, the number of plates in a series, 10 and 6 respectively 

 in dispersions (1) and (2) is not large enough to give a wholly trust- 

 worthy value of probable systematic error. Nevertheless, the relative 

 values for different slit widths will certainly give some indication as to 

 whether systematic displacement is more liable to occur when the slit is 

 widened. 



It has not seemed necessary here to tabulate the separate measures, 

 but only to give the probable errors in kilometres per second for each 

 slit width at each dispersion. 



PROBABLE ERROR 



Fol" convenience of reference and comparison the values obtained in 

 the previous investigation using the measures of the same three lines 

 will be given and it will be seen that they agree fairly closely with the 

 above in the relation of slit width to probable errors. Any differences 

 which are specially noticeable in the errors for slit width 0.076 mm. are 

 probably due to the different ratios of focal lengths of collimator 

 and camera in the two instruments. 



