88 PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



(which involves a particular value of N). This gives a better agreement, and clearly 

 brings 7931 into the series. If we employ RYDBERG'S formula, 



n = 13458-N/(m+-99667) 2 , 

 with errors Q Q _^ _ 4 _ 13 _ u ^ 



clearly the limit is too low. PASCHEN has pointed out that 27065 '6 and 27215 are 

 respectively V?! (2) ^ VS (2) and VP 2 (2) ^ VS (2). How closely this is the case may 

 be illustrated by calculating these values with the limits of errors. VPj (2) and 

 VP 2 (2) are 10286'84 and 10305'59, with possible errors 173. Using the calculated 

 limits of the D series (Table I.) and PASCHEN'S value of S (2), the value of VS(2) is 

 13980-163"82, giving respectively from the above relations 3693'32 + 5'5 and 

 3674'575'5. The wave - numbers of the actual lines are 3694'02'14 and 

 3673"74'27. Still it is a single agreement, and might possibly be fortuitous. The 

 measurements of wave differences are much more reliable than those of actual wave- 

 lengths. Now the difference for the two lines in question gives v = 20'28'41, with 

 PASCHKN'S estimates of his errors. The difference for Pj (2) and P 2 (2) is 1875 '36, 

 which is decidedly against the conclusion. In favour of it, on the other hand, is the 

 fact that a similar relation shows itself under Na. There is another unallotted pair, 

 4642-35 II. ('50 S.) and 4638'6 II., with a separation 17'404'5 dX, where dX denotes 

 the wave-length difference error of observation. The first has a wave-number about 

 P(oo)-VD(2), viz., 21534-92 4-5 (/A. as against 215327. It is difficult to see 

 where a doublet with v about 17 to 20 could come in unless the D series was a 

 satellite one, in which case the first series here considered should be a doublet one. If 

 so, however, it would have been seen by PASCHEN, who separated much closer lines in 

 the ultra-red Na spectrum. The other lines left over are 4829 R, 4808 L. D., and 4767 E. 

 Na. The lines observed in Na not belonging to the regular series are much more 

 numerous than in the other elements. The following is the list : 



23391-3 P. A, (3) 5532-7 S. 1 B : (5) 4660'2 S. "1 

 23361-0 P. 17 K.H. J '0 K.H. J 



22084-2 P. A a (3) 5528-21 S. A, (5) 4633"! K.H. 



22056-9 P. 7-1 J K.H. A 2 (5) 4629'4 K.H. 



F (3) 18459-5 P. G, (3) 5100 LE. Ej (5) 4629'5 S. 



F (4) 12677-6 P. 4975'0 S. 1 - E 2 (5) 4625'5 S. 



G! (2) 7418-3 S. B, (4) 6'1 K.H. J E, (6) G, (4) 4472'5 S. 



G 2 (2) 7410 S. B 2 (4) 4973-0 K.H. A, (6) O'O LE. 



A, (2) 7377-4 S. A, (4) 4918'4 S. A, (7) 4372 S. 

 A 2 (2) 7369-48. A 2 (4) 4914'0 S. 



B, (3) 5675-92 K.B. E t (4) 4913'5 K.H. 

 B 3 (3) 5670-40 K.E. E 2 (4) 4910-1 K.H. 



4820 LE. 

 4730 LE. 



