Calculation of Series in Spectra. 735 



10791-32 



5462-20 



297 



16233-52 



252013 



3-97 



18753-65 



136585 



4-97 



20119-50 



821-81 



597 



20941-31 



532-37 



6-97 



21473-88 



364-47 



7-97 



21838-35 



261-36 



8-97 



22099-71 





9-97 



The second column contains their successive differences, the 

 third, the denominators ot" the formulae, given by Rydberg's 

 table, which cause these differences, e. y. 



_N N__ 



(2'97) 2 (3-97)' ^ 0iy °' 



The equality of: the decimal parts in the third column 

 shows at a glance that the lines belong to a series which 

 approximately 1'ollows Rydberg's type o£ formula. If, as 

 in the paper referred to, only the 2nd, 3rd, and 4th lines 

 were tested, the Table would enable us at once to determine 

 whereabouts the others should come. For instance, the 

 line after 20119 should be about 822 ahead, the next 532 

 ahead of this, and so on. 



Keally the example is not well chosen to exhibit the 

 advantages of the method, since the series happen to satisfy 

 approximately the Rydberg formula. In a set which does 

 not do this, viz. one in which, in the denominator 

 m-\- fju+ajm, a. is comparatively large, the numbers corre- 

 sponding to /J, in the Rydberg ('97 in the example) would 

 not be exactly the same for all the orders — only approxi- 

 mately so. 



With a numerator 4N all that is necessary is to divide 

 the differences of the wnve-n umbers by 4 and proceed as 

 before. 



In calculating the actual constants I have adopted the 

 following method : — Taking any two successive lines the 

 difference is found. Rydbersps table gives the corre- 

 sponding numbers with this difference. Thus in the above 

 the difference 2519*6 is caused by 6961— 4442. Hence 



16233 = A - 6961 or 18753 = A - 4442. 



The limit A is therefore close to 23194, say 23194 + ?, 

 where f will only be a few units. 



