PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 87 



K. The K lines to be accounted for are the following : 



27215-0 P. 4829 R 



27065-6 P. 4808-8 L.D. 



F 15165-8 P. 4767 R 



F 11028-0 P. 4642-35 K. 

 F 9590 B. -5 S. 



F 8908 B. 



F 8500 B. 4638-6 R 

 F 7931-8 S. 



The lines marked with F form one series. The constants calculated from the first 

 three (third inexact) give 



13522-81 -N/(m+ "907393 +m~ l x '21 1692). 

 This reproduces the lines with the following values of obs. calc. : 



w 3 4 5 6 7 89 10 



000 22-5 14-9 -27 



The lines corresponding to in = 8.9 would be 8232"9, 8059'6, which lie below 

 BERGMANN'S lowest region of observation and SAUNDERS' upper limit. PASOHEN'S 

 two observations are good, BERGMANN'S may quite possibly err to the amount 

 indicated.* There can be no doubt about the series the formula is only doubtful in 

 so far as the third line from which it is determined may be several units out. The 

 value of the wave-number of D (2) is by PASCHEN'S observation 8496 '63 + '36. The 

 limit of the D series is 2196(5-826-64 (see Table I.). Hence the value of VD (2) 

 is 21966-826'64-8492-63-36 = 13474'197. The most probable value is 

 21972 8492 = 13480. The limit of the series as found is so close to this that there 

 is some justification in taking it to be exactly so. If this be assumed, there are 

 three reliable data to go upon, viz., PASCHEN'S two lines and the limit. These give 

 the formula 



n = l:3480-N/(m+-966367 + m~ 1 x '071808) 2 , 



giving the following values of obs. calc. : 



-10 +4 -3'8 -22 



The agreement is much better for BERGMANN'S lines, but the last is too far out to 

 allow 7931'8 to be included in the series, nor can this be set down to uncertainty in 

 the constants if the supposition of limit = VD (2) is exact for the kind of formula. 

 If it be remembered that, so far as the matter has been yet considered, the value of 

 P(oo) is never exactly VS(l), and that a similar cause for the apparent difference 

 may occur here, we may still hold that in fact the limit is the true VD (2), but that 

 the first formula is the most correct to use with the actual form of the formula 



* E.g., in the lines 27215 and 27065 his diligences from PASCHEX were - 11G and 1C. 





