DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 363 



41951 would correspond to a D 12 , leaving the calculated 47079 as a true Dn (d\. = 0), whilst Di2 is 

 47077 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 the 

 satellite sets show abnormal values in that they are roughly about 2 greater than i/, 

 for the S 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 in 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 /, can therefore be the same within observation errors, but cannot 

 possibly agree with that for the S set. Those for i/ 3 however, 308 '82, 307 '68, cannot 

 be the same without allowing errors larger than d\ = '05. Tf they are to be the 

 same the excessive error is probably in 21766, which is nebulous and would require 

 d\ = '08. Further, in addition to the lines assigned here to the I) 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 D n 

 from m = 1 to m = 7 that there can be little doubt as to the essential correctness of 

 the D H allocation. The limit of the series cannot then be very different from S ( oo). 



(1) Is 788 a real separation -i.e., is it produced by a displacement on S,(oo) by a 

 larger oun multiple in this case of 44|-<5 in place of 44(5 ? 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 b link modified by displacement ? If D ( co ) be as found, i.e., (- <\] S ( oo ), 

 v l will be increased by '09 or 786'45 to 786'54 an inappreciable change. To produce 

 a change of 2 in the value of b or i/j the limit would have to be ( 5(5) 81(03), which 

 gives a value 88'5 above S(oo). But, as a fact, the limit found is quite close to 

 Sj ( oo ). 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 our 

 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 d = 51655-20669 = 30986'20 = N/(l'881350) 2 . A displacement of 

 ! on the denominator 1'881 increases d by 2'06. If the displacement is on the 

 first line of the triplet it must be S lt if on the second +S lt and both give practically 

 the same value 788'51 for the apparent separation in general agreement with the 

 observed value. There is nothing, however, to show whether the displacement should 

 be Si on the d l or +S^ on both d 2 , d s , as the observed 308 '82 is within our assumed 

 error limit, but it is interesting to note that if the oun for i/ 2 be the same as for ^ the 

 true value of v t would be very close to the observed. In this connection it is to be. 



