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



and the accuracy of the measurements. Allowing for this, the evidence, with one 



*/ 



exception, hears out what we have already had reason to infer, viz., that the P and 

 D series have about the same value of N, and that that of S is larger. The exception 

 is P'. The mean of N of D', P", D" is 109675 '9, or practically HYDBKKG'S old value 

 obtained from H. We may feel, therefore, reasonable certainty that the actual value 

 for these series is very close to 109675. The N for the two S series are again practi- 

 cally the same about 109725, but there is some uncertainty owing to the top lines 

 having been omitted. The case of P' is exceptional with the large value of 109815. 

 The agreement of the calculated with the observed values is not so good as in the 

 other cases. It must be left at present as an apparent anomaly, but it may be noted 

 that P' is a singlet series, like that of Li, in which a similar case arises. In the 

 alkalies we saw that N for S increased with atomic weight, and if this were the 

 general rule we ought not to expect a large value of N for helium. For this reason 

 He is riot a good test. We shall find better ones when we come to deal with other 

 spectra. 



It is seen that the limits of the S and I.) series for both sets are very closely the 

 same. Also VP'(l) = 2717573 and S'( oo) = 27174-627, whilst VP"(l) = 29221-89 

 and S"( oo) = 29222'G96, so that, as in the other elements, relation (F) is very closely 

 verified. On the other hand again, as in the other cases, relation (G) is only roughly 

 satisfied. VS'(l) = 3 I943'65, VS"(1 ) = 38339'45, which differ from P'(oo) and 

 P"(oo) by 89-44 and 113'9 respectively. 



The two D series run nearly parallel to one another. The differences of corre- 

 sponding wave-numbers are 2044'48, 2045'99, 2046'93, 2047'37, 2047'55, 2047'48, 

 204777, 2047-60, 2047'81, 2048'06, 2048M7, 204779. The two series run down to 

 limits which will be very close to the true values for the last six lines, which give a 

 mean of 2047 '86. Taking this, the values of VD (m) for the two series differ by 

 numbers which are given in the first row of the table below. The denominators of 



o 



VD are m+ - !)96... + ... or m+ I roughly. There are three cases to consider as to the 

 origin of these differences: (l) an alteration in N, the differences will then be 

 8N/(m+ l) a ; (2) an alteration in p, when the differences will be 2N S//./(TO+ I) 3 ; 

 (3) an alteration in a, when they will be 2N 8a/(m+l) 4 . The second, third, and 

 fourth rows give the numerical differences in each of these cases, the first difference 

 being that observed, viz., 3 '38. The fifth row gives the result of dividing successive 

 differences by 2 in other words, making the difference depend on a term A2~'". 



10. 11. 12. 13 



05 -'20 -'31 -07 



04 -02 



