402 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
We can now use this series to test the question as to the existence of parallel 
series depending on (+ 2^i) D ( oo). This does not mean that the sequences must be the 
same in each. In fact it is to be expected that there may be a concomitant change 
in them also, but they can only diflPer by a few multiples of the oun. The important 
point to notice is that for large values of m, the effects of such differences become 
negligible and the observed separations from the standard D should approximate to 
±21‘25, which is that due to 2 ^^ on the limit. It will not be necessary to go into 
such a full discussion as in the standard series with D (oo), except for the first three 
sets, where the evidence for changed sequence terms with displaced limits is conclusive 
and important. The lists and sounders are given in the same table as for the 
standard series, in the first and third columns respectively. The considerations adduced 
enable us to feel that the ground is safe in recognising that parallel series depending 
on displacements on the limit D (oo) = S ( oo) really exist. The evidence does not 
depend on a single numerical coincidence of a line, or of a line found by sounding, but 
on the fact that these numerical coincidences appear for so many sounding links in 
all the 15 sets tested. This is not affected by the high probability that several of the 
sounded lines are chance coincidences. This result then gives more confidence to the 
method partially applied above, in the application of the law that the D sequences 
must have mantissse which differ by multiples of the oun from multiples of Aa, or in 
other words must be themselves multiples of the oun. This method consisted in 
testing certain lines to see whether by using the displaced limits (y^i) D(oo). —-now 
seen to really exist—-the above relation holds. 
The evidence seems to show that the typical lines—D ( oo) = S ( oo)—for m = 1 
have been much affected by displacement effects, and tlurt consequently the intensities 
of the normal lines themselves are much diminished. Although this is some 
disadvantage, it will be well to attempt here to get some insight into the complete 
satellite system for the first two orders. 
We have seen that 19989 belongs to this normal set with a mantissa = 8 OA 2 and 
that 20581 satisfies the condition necessary for a Dj line with this. The difference of 
their mantissa (see below) is 29|-^. If they are of the Dja, types, as is indicated 
by the fact that the first belongs to a doublet and the second stands by itself, a triplet 
satellite set should be expected whose first line D 13 is separated from the Dia by about 
three-fifths that of Dja from Its mantissa should therefore be about 18^ = Aa less. 
This would mean a line about 19623 forming the first line of a triplet. No line is 
observed here. There are, however, lines at (l) 19602‘66 and ( 3 ) 19632’44 of which 
19602 passes the suitability test for a normal D line, and the other does not. The 
mantissa of 19602 is fOAa— i.e., 19^ behind that of 19989 and rather too large. On 
the other hand the problematic 19623 may be too weak, in which case the corresponding 
Oa, D 3 lines which should be stronger might be observable. The Da line should be 
about 21400. We do find this, in fact, with triplets of a kind. The whole set of these 
lines can then be arranged as follows :— 
