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^) 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 differ 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 ( o ) = S ( ) 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 mantissas which differ by multiples of the oun from multiples of A 2 , 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 (ySi) D(o) now 

 seen to really exist the above relation holds. 



The evidence seems to show that the typical lines D ( oo ) = S ( ) for m = I 

 have been much affected by displacement effects, and that 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 = 80A a and 

 that 20581 satisfies the condition necessary for a D[ line with this. The difference of 

 their mantissa (see below) is 29^8. If they are of the D^, D n 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 D 12 by about 

 three-fifths that of D ia from D n . Its mantissa should therefore be about I8S = A 2 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 79A 2 -S, i.e., 19<J behind that of 19989 and rather too large. On 

 the other hand the problematic 19623 may be too weak, in which case the corresponding 

 D 2 , D 3 lines which should be stronger might be observable. The D 2 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 : 



