382 DK. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



It is clear that these lines also show satellites. Also, it is curious that the first 

 sets of triplets apparently have the lines corresponding to the second separation 

 displaced below those forming the first. Thus in Ca the second set (giving i/ 2 = 13'5) 

 have not been observed, in Sr the two ( Vl = 101, i> 2 = 60) are separated by a gap of 

 143, and a similar effect will be found later in Ba. Owing to this fact, the formulae 

 constants are calculated from the 2nd, 3rd, and 4th sets. They give for F n 



Ca 28934-93-N/(m + '' 



Sr 27612'37-N/(m + '875560 + 



37-N/( 



m / ' 

 100548V 



\ m 



These give the following values of O C : 



m. 2. 6. 7. 



Ca . . . -1'18 '18 '22 

 Sr . . . '42 '05 '02 



The agreement is good, except for m = 2, and in this case the agreement is sufficient 

 to show that the allocation for m = 2 is correct. 



The limits are close to those of VD U (2), which is not known with great exactness 

 because the values of S ( oo ) or D ( oo ) given in [II.] for the second group are subject 

 to possible errors of some units. With formulae in ] /m the values ofD(oo) = S(oo) 

 are given [II., p. 36] as 33994'85 for Ca and 31037'27 for Sr, whilst with formulae in 

 1/m 2 , the respective limits are 33983'45, 31027'64. The values of VD n deduced 

 from these are- respectively 28939'93, 27615'65 with 1/m and 28928'53, 27606'02 

 with 1/m 2 . The limits, therefore, found above for F n ( oo ) lie each between their 

 corresponding values as deduced from the D series direct. Assuming that the F ( oo ) 

 are more accurate, the values of D (oo) deduced from them are 33989 '8 5 for Ca and 

 3 1033 '99 for Sr, in both cases close to the mean of those in [II.]. If the series 

 depend on formulae sequences, these limits may be taken as close to the correct 

 values. If, however, the different orders proceed by multiples of S or A in the way 

 illustrated in Table II. for the D series, the limits may require modification by a 

 few units. 



As the separations of the F series depend on the separations of the satellites of the 

 first lines of the D series, and these depend on displacements by definite multiples 

 of S, as given in Table II., it is possible to calculate the values of the former with 

 extreme accuracy. Table II. gives 13(5 and 8S as the multiples in question for both 

 the elements Ca and Sr. Using the values of S and of the denominators of D n there 

 given, the separations in question calculate out to 22'49, 13'75 for Ca and 100'34, 

 62 '01 for Sr. These may be regarded as exact to the 2nd decimal place and 

 independent of any possible variation of 



