DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
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41951 would correspond to a D 12 , leaving the calculated 47079 as a true D]|(dA = 0), whilst D 12 is 
470/7'38. That 47079 exists is also shown by the u sounder. In the table this arrangement is adopted. 
The line entered for m = 5 is the calculated, as it is so close to the deduced. For m = 6 , 7 they are the 
deduced from the -e- v sounder. The sounders for D 2 , D 3 , m = 4...7, are indicated in Plate 3, fig. 4 . 
The Abnormal Satellite Separations .— The separations of the lines suggested for tlie 
satellite sets show abnormal values in that they are roughly about 2 greater than i/j 
for the b triplets. The difference is real and not due to errors of observation, and we 
shall find a corresponding abnormality in the other elements of the group. Taking 
Baly s maximum error to be d\ = '05, the maximum error 111 n for the D(l) lines 
will range from -21 to '24, or, say, '45 on a difference of two lines. All the D(l) 
readings for v-^ can therefore lie the same within observation errors, but cannot 
possibly agree with that for the S set. Those for v., however, 308'82, 307-68, cannot 
be the same without allowing errors larger than dX = '05. If they are to lie the 
same the excessive error is probably in 21766, which is nebulous and woidd require 
dX = 08. Further, in addition to the lines assigned here to the D series, there are 
a very large number of other lines showing separations of 788. The question arises, 
therefore, as to the origin of this abnormality, and it is important to discuss the 
various possible sources. The formula gives so closely the values of the lines for Dj^ 
from m = 1 to m = 7 that there can be little doubt as to the essential correctness of 
the Dji allocation. The limit of the series cannot then be very different from S ( 00 ). 
( 1 ) Is 788 a real separation— i.e., is it produced by a displacement on Si(oo) by a 
larger oun multiple—in this case of 44iS in place of 44S ? If so the separation would 
be 4-52 greater, or 791 instead of 788, and such an explanation is therefore quite 
inadmissible. 
( 2 ) Is it a 6 link modified by displacement ? If D ( 00 ) be as found, i.e., (- ri,) S ( 00 ), 
will be increased by '09 or 786’45 to 786'54—an inappreciable change. To produce 
a change of 2 in the value of h or vj the limit would have to be (-5^) ( 00 ), which 
gives a value 88-5 above S(go). But, as a fact, the limit found is quite close to 
Sj ( co). This explanation is therefore excluded. 
( 3 ) Are these displacements on the d sequences ? In the normal case the 
d sequences for a given satellite triplet are the same, but are displaced from one 
satellite set to another. Is it possible that the sequences suffer displacement in the 
same triplet also ? Take, for example, the satellite set whose first line is 20669. 
The sequent is = 51655-20669 = 30986-20 = N/(T'881350)h A displacement of 
-(^1 on the denominator 1-881 increases d by 2'06. If the displacement is on the 
first line of the triplet it must be if on the second +(\, and both give practically 
the same value 788'51 for the apparent sepai'ation in general agreement with the 
observed value. There is nothing, however, to show whether the displacement should 
be — on the d-^ or +^i on both d,, dg, as the observed 308'82 is within our assumed 
error limit, but it is interesting to note that if the oun for 1/3 be the same as for the 
true value of p.j would be very close to the observed. In this connection it is to be 
