DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
49 
those found when the series is determined from the first three lines only, and 
consequently with the term in m~'^ only. In only nine lines out of the whole 
known were compared {m — 2 ... 9 and 12). In all there appear only foiii" exceptions 
to the rule that the calculated values of N are constant in any one series after tlie 
first. They occur in Ca, Sr, In, and Tl. In Ca for m = 3 the numljer is 1 11458+ 8'5 
instead of 111406±4. In Sr for m = 3 the number is 111779+ ? This triplet is 
interesting as having been missed in K. and R.’s first list of the Sr spectrum and as 
having been calculated by Rydberg. The other two exceptions are for In and Tl, 
in which the values appear to go in two steps, viz., for In 109348, 109348, 
109390‘3 ± 22‘6, 109390, with the two last equal to either within limits of error. If 
^ be taken to be —1 they may, however, all be brought to 109343 by allowing the 
maximum observational eri'ors, hut this is scarcely permissible. In Tl w = 2, 3 give 
109088, m — 5, 6 109200, m = 6 either value, whilst m = 4 gives 108671. The last 
is the case mentioned on p. 39, where there is a large error between calculated and 
observed, and in which a transcription error is suggested. If the value given by the 
original formula is used, the value for N becomes 109134. Here also, with a small 
change in the limit, the value of N may l^e made the same, but only at the expense 
of allowing maximum errors. It is probable the two last cases correspond to a 
real change. It is to be noted that, mercury excepted, all the elements of Group II. 
show a greater value than Rydberg’s constant 109675, whilst those of Group III. 
show a less value. The generality of the rule is striking, but a further discussion 
must be postponed until the atomic weight terms are considered. It does not, of 
course, affect the question of the atomic volume terms considered above, as the 
reasoning there is based on the first terms of the series, in which N retains the normal 
value. It may be noted that this change of N gives the ratio = '21520 for all 
the elements, and explains why the rule to deduct W(l—always failed for the 
elements of large atomic weight. 
The Principal Series. —No principal series were known in the 2nd and 3rd group 
of elements until Paschex^' discovered those of Zn, Cd, Al, Tl and suggested certain 
lines in those of Mg, Ca, and Hg. Those for the first four were clear and definite, 
and little doubt could be felt as to the correctness of their identification as a whole. 
The same certainty cannot be felt as to those for Mg and Ca, and, in fact, I give 
below certain considerations which tend to throw doubt on some of them. The first 
definite observations of the HgP are due to Milner,! who gave the lines of orders 
5 to 16. For 5 to 8 he gave values for Pj and Pg but, as later work of Paschen has 
shown, lie allocated the Pg lines to the real P^ and his Pj lines do not come into the 
direct line of the series, although it is possible they may be collaterals. Since then 
PaschenJ has published a long list of lines observed by Wiedmann, and has attempted 
* ‘ Zur Kenntnis ultraroter Linienspectra,” ‘Ann. der Phys.,’ 29 (1909). 
t “The Series Spectrum of Mercury,” ‘Phil, Mag-.,’ XX. (1910). 
t ‘ Ann. d. Phys.’ (4), .35. 
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