PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



101 



RAYLEIGH'S interferential measurements allow us to compare some of these lines with 

 what may be considered their actual values, and the comparison shows that the 

 degree of accuracy is not nearly so high as that estimated by R. and P. The lines are 

 given in the following list, together with the estimates of error by R. and P. : 



If R. and P.'s measurements are correct as a set they ought to show a constant ratio 

 to the corresponding ones of RAYLEIGH, but a glance at the differences shows that 

 this is by no means the case. With so large a number of lines for comparison as 

 seven, it would seem legitimate to deduce what this ratio (k) should be for the whole 

 of R. and P.'s scale, and thus to correct these seven at least. I have done this, 

 making the mean square value of (correct-actual) least, treating first all observations 

 as of equal value, and secondly as weighted according to R. and P.'s estimates. In 

 both cases the result is the same, viz., k = 1 '000033. If, as might possibly seem 

 preferable, the ratio of difference to wave-length is to be a minimum, then 

 k = 1 '000030. On these suppositions we obtain the following corrections to apply to 

 R. and P.'s lines to bring them into their true positions on their scale : 



The List I. actual errors a minimum appears the better, in view of the fact that 

 some of the corrections are within R. and P.'s estimates, and that they are generally 

 smaller than in II. It would, perhaps, have been advisable to use these corrected 

 values in determining N by least squares, but the ^work had been done before 



