Calculation of Series in Spectra. 567 



uncorrected to vacuo and the International scale. Taking 

 the first two as members of a series, 



«=N/(w 2 -» 1 )=43'510. 

 From the Tables, # = 3*9688 for the first line, and therefore 



*** + N { GF56SS? _ (W? 1 =2 ° 122 ' 7 ' 



which is very close to the real value, and sufficient to indicate 

 precisely the next line of the series, if there is a series. The 

 accuracy of the Tables is, in fact, entirely determined by the 

 accuracy of the Rydberg formula in any individual series. 



Another procedure is as follows : — If two lines are sus- 

 pected to be alternate members of a series, the intermediate 

 one may be found at once. For if n x and ?i s are the two 

 wave numbers, 



^-^= N {i-(.,+2>}' 



where x is the value of m-\-/j, for the first. If ,v = 2//, 



rO/+i) 2 = _ N 



2y + l 4(^3-71,)' 



Writing N/4(;> 3 - //]) = «, y is read from the Tables, and then 

 x = 2y. The intermediate member is then 



Similarly, if n x and n 2 are the wave numbers of two suc- 

 cessive members of a " 4N " series of enhanced or spark- 

 lines, 



" 2 -" 1=4N (i"(.-4ir) 



and 



.i' 2 Q+l) 2 _ 4N 

 2x + 1 u 2 — n i 

 Taking 4N/(n 2 — fli) = «, sc is determined at once. The 

 limit of the series is 



4N 



and the third member is 



"»="' +4N ((^2?-(^Ti?)- 



Other modes of using the Tables will at once su £2'est 



k ; 



