I'i;. \V. M. HICKS: \ riMTK'AI. STI IV OF M'KCTKAI, SKI: IKS. 339 



Tin- Lilt' i is the Principal series, and the difference between the wave numbers of its 

 first line and of its limit gives the limit of the other two. Of the other two series, 

 < int- shows a Zeeman effect of the same nature as that in the Principal. This is called 

 the Sharp series or (by KAYSER and RUNOE) the 2nd associated series. The third 

 series is called the Diffuse or the 1st associated series. It has in fact a negative 

 kind of criterion. The preceding definitions apply to the three series in all elements, 

 including such elements as Li, He, and others which show singlet series. When 

 doublets and triplets appear, we have a simple physical criterion for the Principal 

 series in that it is that series in which the doublets or triplets converge with increasing 

 order. This criterion can be applied even when the 1st line has not been observed. 

 In certain elements the constant separations are shown between satellites. In these 

 < MSOS the series is certainly a D-series, at least in those recognised up to the present 

 but further knowledge may show that in certain cases such satellites may appear in 

 other seri s. If, passing beyond the mere physical appearance of the series or their 

 visible arrangement in the spectrum, we attempt to represent their wave numbers by 

 formulae of the recognised types, we have further criteria for the Principal and Sharp, 

 viz., that the 1st line of the Principal may also, very nearly at least, be calculated 

 from the formula for the Sharp or vice versd and that the denominators in their 

 formulae differ, roughly indeed but sufficiently closely for use as a criterion, by 

 a number not far from '5. But when an attempt is made to deal in the same way 

 with a line of the diffuse series, no general type of formula has, at least as yet, been 

 found. In the alkali metals, as was seen in [I.] all the D-series take a positive value 

 for at in other words, the fractional parts of the denominators decrease with 

 increasing order, and the general conclusion might be drawn that this was a common 

 feature of all diffuse series. But the opposite occurs in the triplet spectra of the 

 2nd group of elements, whilst a similar rule of a positive value of a recurs in the 

 3rd group. This suggests that the series giving doublets have a positive and triplets 

 <x negative, but this is contradicted by the triplet series of O, S and Se, which behave 

 in the same way as the doublets of Groups 1 and 3. The question naturally arises, 

 is there a typical D-sequence with a positive, and the diffuse series in the 2nd group 

 do not really belong to this type, or is there no actual D-sequence, i.e., no regular 

 type, of formula to which the D-series conform. The difficulty of finding formulae to 

 accurately represent any particular D-series would point to the latter supposition, 

 a supposition also which is strengthened when we study comparatively the series of 

 numerical values of the denominators found directly from observations as is done 

 below. In the case of the alkalies the formulas given in [I.] (as well as those in l/m 3 ) 

 do not reproduce well the high orders and are probably only within the limits of error 

 because the lines are so diffuse that the observation errors are very large. In fact 

 one of the few excessive deviations found in [I.] was that of NaD (6), in which it is 



* K.g., in ScS., see Appendix I. 

 2x2 



