302 Prof. W. M. Hicks on the 



through uncertainty as to the exact value of the limits of the 

 S and D series. The same method of attack is adopted here, 

 with considerations based on other relations foreshadowed in 

 that paper, and others obtained since, which help to fix the 

 limits more closely. 



Kayser and Runge give four sets for the D series and four 

 for the S series in silver. Taking account of the possible 

 observational errors, the first three sets for D n give a limit 

 30644-60 + 12-2 and the first three for Si give a limit 

 30614'60 + 3'6. Both series formulae reproduce the observed 

 values of the fourth line in their respective series. It is clear 

 that these limits, in so far as their determination depends on 

 the type of formula used, cannot be the same within error 

 limits. As the first S line is frequently difficult to fit in with 

 the series, the limit from the D series would seem the more 

 reliable, and it is taken as the starting point for the new 

 iipproximation. Of the D(2) lines, D n and D 22 have been 

 measured by Fabry and Perot to the third decimal place, and 

 their errors are probably less than *001 A.U. Their values 

 in LA. are 5465*489 and 5209081. In calculating from 

 seven-figure data it is necessary to use 8-fig. logarithms at 

 least, and as the tables at disposal were 9-Hg. the}' were used 

 to their full extent, the data taken to be correct to another 

 place of decimals, and corrections for errors calculated, so 

 that in case better readings are made, the same calculations 

 will hold. Thus the limit for D x is 30644-6000 + f and the 

 wavelengths 5465 4890 + '001^, 5209-0810 + -001y> 2 with 

 p 2 <l. In Rowland's scale * in vacuo these are taken as 

 5467-167 + -001 ;>!, 5210*681 + *001^ 2 . The wave numbers 

 are then found to be 



18291-0122- -00334 p u 1919 1*3495 --00368^. 



The first step is to obtain an exact value of the separation, 

 i. e. the difference of the wave numbers of D 12 and D 22 , 

 whereas Fabry and Perot have only measured D u and D 22 . 

 But the old measures of Kayser and Runge are good, give 

 close values of the oun, and also show quite definitely that 

 the denominator difference which gives the satellite separation 

 is 23^. It is thus possible to calculate D 12 with the same 

 degree of accuracy as the observed values by F. & P. of D n 

 and D 2 2, and thus to deduce the true value of the doublet 

 separation v. The limits of the two D series are then 

 30644-6000 + f, and 30644-6000 + v + f These are then 

 thrown into the form N/d 2 , N/^ 2 , and A = d — d x is 66 8. We 



* Any small uncertainty in reducing to Rowland's scale will have no 

 influence on the result of the present calculations. 



