by means of Indices of Refraction. 181 



of decimals, and in part to the high, dispersive powers of the 

 prisms employed, which would render it necessary to employ 

 more than two terms in Cauchy's formula to obtain a closer ap- 

 proximation. As the formulae for interpolation would in this 

 way be rendered extremely complicated, it is better, in the case 

 of any series of observations embracing a particular part of the 

 scale, simply to determine the mean of the errors, and to apply 

 this mean with its proper sign to the computed values of the 

 particular wave-length to be determined by the measurement of 

 indices of refraction. If we apply such a correction in the cases 

 of the four series of data and results given above, we find for the 

 corrected values of the wave-lengths the following numerical 

 results : — 



I. 



II. 



III. 



IV. 



656-53 



656-49 



438-67 



438-72 



656-54 



656-61 



438-55 



438-54 



656-38 



656-59 



438-61 



438-57 



656-54 



656-66 



438-55 



438-65 



656-59 



656 75 



438-54 



438-54 



656-62 



• •• 



438-44 



438-49 



the true values being respectively 656-56 and 43856. These 

 results are, I think, sufficient to show that a valuable control for 

 the accuracy of measurements of wave-lengths may be obtained 

 even when prisms of high dispersive power are employed, pro- 

 vided that the intervals taken are not too large. It seems at 

 least probable that a greater degree of precision is attainable in 

 measuring indices in the case of substances of high than in those 

 of low dispersive power, partly because the angular deviations to 

 be measured are larger, and partly because the spectral lines are 

 less crowded together. 



The following example will serve to illustrate the advantage 

 of taking shorter intervals : — 



Lines. 



X. 



Indices. 



X. 



Indices. 



X. 



25 b 



518-63 



1-62459 



• • • 



1-61882 





26 



517-51 



1-62472 



517-61 



1-61895 



517-56 



27/3 



517-07 



1-62479 



• • • 



1-61901 





The data are here also taken from Van der Willigen's measures 

 with the same prisms. 



When the angular distances between three spectral lines are 

 not too great, the angular deviation of the lines may, as I find, 

 be substituted for the indices of refraction in formula? (1), (2), 

 and (3). The differences between the angular deviations are, of 

 course, to be converted into seconds. The following results will 

 show the degree of accuracy attainable by this method, the data 



