DR. W. M. HICKS: A CRITICAL STUDY OF SRECTRAL SERIES. 
39 
to work upon until we can get some evidence as to wliat the limit really is. The 
constants determined for the three elements in this way are given in the following 
scheme. Values for Ba are also given on the supposition that A 2 is subtracted in the 
same way as for Sr. 
For 
Mg . . n = 39754-31-N/{m+1-379975-•067249m-'}' add 5 A 2 for m ^ 1, 
Ca . . = 33981-96-N/{m+l-572477--094220m-'}' „ 5 A 2 
Sr . . - 31027-58-N/{m + l-640373--097552m-'}' „ A^ 
Ba . . w = 28619-23-N/{m+l-692912--084616w-'}' „ As 
In the following Table II. a comparison of the calculated values with the observed 
is given. The first column under the element gives tlie maximum permissible error 
and the second the difference between calculated and observed. The tliird column, 
under Mg, Ca, Sr, gives the same difference when the lines are calculated from the 
formula in ^m~^. Under Eu no estimates of observational errors are available, and 
the two columns refer to the two series referred to in the text below and in 
Appendix I. In all cases the deviations are only given for the first lines of a doublet 
or triplet. 
It will be seen that the only real deviations from observed values greater than the 
possible are for TTS (4) and CaS(5). In the case of TIS (4) the doublet separations 
given by the observed values is too small by 1-5, and the calculated value corrects 
this. The whole of the calculated values agree so closely with the observed as to 
-make it certain that the error must be in the observed. The observed is 2665-67—a 
transcription error of 2665-76 would bring the two sets in agreement. As to the case 
of CaS(5) the line 3181-40 also gives an incorrect separation which the calculated 
corrects. It has an observed accuracy of -03 A.U., and the calculated differs by 
15 times this amount. It should be noticed, however, that its intensity is higher 
than we should expect, viz., 4 as against 1 for S(5). Moreover it is an enhanced 
line and therefore does not belong to the S-series. It is probable, therefore, that it 
hides the true S line, which should be about 3181-00 and of less intensity. 
A curious point is that in In the 83 lines appear to be more persistent than the S^. 
Kayser and Bunge give a line 2200-0 as 83 ( 8 ), with possible error "30. The 
calculated, however, deviates by more than 5 times this from the observed, and as 
the formula reproduces the other lines with good accuracy it is probable that 2200 is 
wrongly assigned to 8 , or should be 2201 - 6 . 
Connection of a and jx .—The study of the alkalies led to the result that the denomi¬ 
nator of the p-sequence can be tlirown into the form 7 )z + l—W (l—-f g( l — 
where W is the atomic weight term, and k is a constant which is about -21520, the 
only exception was for Cs for which a slight modification was required. It is 
important to see whether a similar relationship holds for the analogous sequences in 
the elements now under consideration. In the alkalies W is one-half the difference 
