364 DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



remembered that in the d sequences the oun is not affected by the peculiar triplet 

 modification shown by all elements. In the 20842 set the observed v 2 is 307'68, but 

 the value of the observed v l + v 2 is very nearly normal. This means that the third 

 line does not suffer displacement, but only the middle one 21631. 



If this explanation is correct, the modifications must diminish with increasing 

 order. For instance, in d (2), <J, produces a change in separation of '56, and the new 

 , = 786'45 + '56 = 787'01 as against 787'16 observed. For m = 3 <$ t produces '23, 

 but the possible observation errors in n maximum dn = I'O are now so great that 

 the observed separation of 787'99 is well within the limits of 786'68. So far then as 

 merely numerical agreement goes this explanation would seem very satisfactory, but 

 the changes required are so small that by themselves they can give little confidence. 

 We shall, however, see later how it explains certain effects in the F(o) (p. 368) 

 which depend on the d (l) sequents and, further, how it also explains similar 

 modifications in the other elements of this group. Meanwhile further evidence in 

 its favour may be obtained from linkage considerations. Some examples follow. 

 (Xote. The observation errors in the separations should not exceed about '50.) 



(a) The mesh 



786-03 (1)20714 311-84 



(1)19928 (2)21026 787'36 (4)2181:? 309'47 (1)22123 



789-67 (:?/() 207 18 308-20 



Here with 20714 i/, is normal, v., abnormal, but v t + v 2 = 1097 '87. Our explanation 

 gives 788-51+309-20 = 109771. Thus on the upper set the first and second have 

 the same d sequent, whilst the third has ($i) d. In the lower set, on the other hand, 

 20718 has (S,) d, the same as for the third. 



So also in D 18 . In the first set d has J, in second and third lines, in second set it 

 has 2<5j in second line. 



(6) 



-786-43 (2)23390 788 -77 



(3)24178 308-77 

 (4)22003 789-15 (4)23392 786-03 



i 



311-03 (1)22914 2x786-47 (4)24487 



This is a striking example of persistence of the displacement in linked lines. Of 

 the lines in the second column, the first has the same sequence term as 22603, the 

 next two have the links Vl , v 2 , but the sequent displaced J,. The line 24178 keeps the 

 same displaced sequent as these last, and therefore has a normal i/, to 23392, but the 

 abnormal to 23390. So 24487 keeps this same S l displaced sequent and so shows a 

 normal v , to 24178 and 2*. to 22914. In other words, if the first line is denoted by 

 X, the above sets may be denoted by the following scheme : 



X (?,) 

 X (<?,) 



