DE. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 
37 
in fact, they only observed the triplet S (2), Si (3), 8^(3) of the next and Sj (4)—too 
few to give the series. The triplet S (1) was observed first by Lehmann"^ (more 
accurately later by HeemannI) and the series completed and arranged by Saundees.| 
The first three are only sufficient to determine the constants with a only; in the 
analogous cases of Mg, Ca, and Sr the limits so determined have all come out too 
large. Here it makes the calculated values of wave numbers for Si (4) and Si (5) 
differ from those assigned by Saundees by amounts too large respectively by 71 and 
159—in other words, the limits here, also, are much too large if his allocations are 
correct. If we use his allocation of Si (4) and attempt to find constants for we 
get a formula quite out of line with the others. The first impression is to infer tliat 
Saundees’ allocation of the two last lines is quite wrong, but a closer acquaintance 
with other series gives more caution and suggests another way of meeting the 
difficulty. As a fact, it is difficult to represent all the P series, and especially the 
D series by any modification of the simple formulae hitherto used. In the case of AID 
it seems impossible to do so at all. Further, it will be shown in Part III. that the 
atomic weight term plays a very important part in producing new lines or displacing 
expected ones. 
New lines are produced by the addition (or subtraction) of multiples of the atomic 
weight term to the denominators in the formulm which irresistibly suggest modified 
molecular groupings. The full evidence for this .can only come later when these lines 
are being discussed, but as bearing more especially on this part of the sulqect it will 
be convenient here to show how it enables us to explain why in tlie alkalies 
Pydbeeg’s relations S(oo)=^j)(l) hold while the other P(co) = s(l) does not. 
(F, G of Part I., pp. 75-76.) 
If the first term of a series is modified by the addition of a number to the 
denominator, it may still be possible to represent the series by a formula containing 
am~^ only. If, however, the second be also changed in a similar way, it will in 
general not be possible to do so. We shall require a third term, so that the 
successive changes in the denominator produced by the two alterations may be 
represented. If a change be also made in the third line, it may still be possible to 
retain only because it is an addition to a large number {m large), and it may 
still be possible so to apportion the four formulse constants that the calculated 
results err by amounts less than the observational errors. In general, however, tlie 
limit will be considerably wrong. In Ca and Sr the limit with /3m“^ is certainly very 
nearly the correct value. But, as above mentioned, is not sufficient for Ba. 
Now we have before us the results of the discussion of the alkalies, where it was 
found that if Bydbeeg’s relations {i.e., F, G) are both to hold the jj-sequence must 
have a small term and the s-sequence a term in whicli is of the same 
* ‘Ann. der Phys.’ (4), 8, p. G50 (1902). 
t ‘Ann. der Phys.’ (4), 16, p. 698 (1905). 
X ‘ Astro. Phys. Jour.,’ 28, p. 223. 
