54 



Procccdinf/s of the Royal Irish Academy. 



spectrum. There are also uiue pairs with a similar separation for each single 



P^^^-~ /4ffl a 3a 6a « a 2a 



VT' 4' T' T' 6' 7' T ^'' 9y 

 The peculiar character of the separation which has heen repeated in the lines 

 2917"14 and 3063'21 appears worthy of remark. Two similar lines are of 

 coiu'se inadequate for the establishing of a series. 



There are 603 lines which break up into three components. Owing to 

 want of space, Table YI, containing these, ha.s been left out ; but I shall be 

 pleased to give a copy of the results to anyone who specially desires it. 

 These include many lines with the same separations; and on that account 

 the probability of finding a series should be greater. However, as there is 

 only one interval corresponding to each line, and in addition there is a range 

 of possible error, it will be seen that the number of lines to be considered as 

 having the same separation is in general too large, and the search among 

 those for the lines forming a series becomes one of enormous difficulty. The 

 work connected with this is extremely tedious, and again and again meets 

 with no success. I have sought for series among the Knes whose separations 

 are approximately given by 0-72, 0-85, 0-97, 1-09, 1-17, 1-29, 1-82, 2-02, and 

 2-12. Each of the formulae given by Eunge* was tried. Only in two eases 

 where the separations are approximately 2-02 and 1-29 was there a partial 

 success. In those cases the series formula used was 

 10' _ - I ~ -,: 

 X 'III- ri<} 



where «, h, c are constants, and m represents the whole numljers taken in 

 order. The following table arives the results. 



Table VII. 



A (calculated) A(obserTed)j Z.E. 



9 



3 



Used to determine \ 

 constants. . 



3537-64 

 3155-71 



1-98 

 2-00 



10, 10 

 3. 4 



_ 



4 



( 



2S94-55 



2-05 



1, 2 



~~ 



5 



2765-31 



2765-40 



2-11 



2, 3 



- 0-09 



2 



3 



Fsed to determine ) 

 constants. '. 



3127-67 

 3044-85 



1-27 

 i-29 



20, 25 

 7, 7 



- 



4 



( 



2980-S8 



1-29 



5, 3 



— 



5 



2946-06 



2946-00 



1-31 



S, 10 



+ 0-06 



6 



292.5-SS 



2926-1 



- 



1 + (Tables) 



- 0-22 



* 0. Eunge, " On the harmonic series of lines in the spee&a of the elements." Eep. Brit. As=o 

 1888, 576-577. 



