DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 337 



enable a specialist judgment to be formed on it, the communication has unfortunately 

 become very lengthy. The mass of detail will perhaps be rather dreary to the 

 general reader not specially interested in this line of study. It is apt also to hide by 

 its amount and complexity the general conclusions arrived at. I propose therefore to 

 give a slight general survey of these conclusions before giving the evidence. 



As is well known the wave-numbers of series lines depend on four types of 

 sequences p (m), s (m), d (m), f(m), and that in any one series they depend on the 

 differences between one sequent of one type and the successive terms of the sequence 

 of another type. These sequences are all of the form N/{0(m)} 2 , where N is 

 RYDBERG'S constant and $ (m) is of the form m + fraction, the fraction being, as a rule, 

 determinable as a decimal to six significant figures. Our aim is to discover the 

 properties of these functions. The fractional part depends in some way on the order 

 m, although whether it can be considered a definite function of m in the ordinary 

 sense is doubtful.* This fractional part will be referred to as the mantissa, and in 

 dealing with it, it will be regarded as multiplied by 10", i.e., as if the decimal point 

 were removed. 



The Oun. It is foundt that in each element a constant quantity particular to each 

 element plays a fundamental part in the constitution of the sequences. This is called 

 the oun. The d and f sequences depend in definite ways on multiples of this 

 quantity, whilst it also enters into the constitution of the p and s. Its determination 

 is therefore for each element a matter of the first importance. Denoting its value by 

 S lt the quantity S = 4^ is of such frequent recurrence that it is useful to treat it as 

 one datum. The oun is accurately proportional to the square of the atomic weight, 

 and is given by = (361'8"l) (w/100) 2 , where w denotes the atomic weight. 



In the case of doublet or triplet series, the corresponding separations between them 

 are due to different limits whose mantissas differ by amounts A or A 15 A 2 (say). In 

 all cases these are found to be integral multiples of the oun. For triplets A l : A 3 is 

 always somewhat greater than 2. 



In the case of D series where satellites occur, the separations of the latter are due 

 to differences in their d sequences. The mantissse of these latter again differ by 

 quantities which are multiples of the oun, and in the case of triplets they appear in 

 normal types to be very close to the ratio 5 : 3. 



The d Sequence. In the normal type the sequent of the extreme satellite has its 

 mantissa a multiple of A 2 . The only known exceptions are found in Sr, Cd which 

 show the multiple law, Sr in d i2 and Cd in d n instead of in d n . In both these cases 

 also the Zeeman pattern is abnormal. As the main lines D n (and in triplets Dj., also) 

 have their mantissse greater than that of the outer satellite by multiples of the oun, 

 it follows that all the d sequences for the first order have mantissse multiples of the 

 oun. It is probable that this is true for all orders of m, but the data are not 



* ' Astro. J.,' 44, p. 229, see also [III., p. 339]. 

 t [III.], also 'Proc. R. S.,' A, 91 (1915). 

 3 A 2 



