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/{^(m)}^ where N is 
Rydberg’s constant and (p (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 v^ay on the order 
w, 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 
^ 1 , the quantity d — 4(5i is of such frequent recurrence that it is useful to treat it as 
one datum. The oun is acc\irately proportional to the square of the atomic weight, 
and is given by (5 = (361‘8±'l) (w/lOO)^ where w denotes the atomic w'eight. 
In the case of doublet or triplet series, the corresponding separations between them 
are due to different limits whose mantissse differ by amounts A or Aj, Ag (say). In 
aU cases these are found to be integral multiples of the oun. For triplets A^ : Aa is 
always somewhat greater than 2. 
In the case of D series where satellites occur, the separations of the latter are due 
to difierences in their d sequences. The mantissae 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 Ag. The only known exceptions are found in Sr, Cd which 
show the multiple law, Sr in djs and Cd in du instead of in djg. In both these cases 
also the Zeeman pattern is abnormal. As the main lines D^ (and in triplets Djg 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 
