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 
modilication shown by all elements. In the 20842 set the observed is 307‘68, but 
the value of the observed + 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), produces a change in separation of ’56, and the new 
I'l = 786'45 + '56 = 787'01 as against 787‘16 observed. For m = 3 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 tliis 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(go) (p. 368)— 
wliich depend on the d {l) sequents—and, further, how it also explains similar 
modihcations in the other elements of this group. Meanwhile further evidence in 
its favour may be obtained from linkage considerations. Some examples follow. 
{JVote .—The observation errors in the separations should not exceed about ‘50.) 
(rt) The mesh 
786-03 (1) 20714 311-84 
(1) 19928 (2) 21026 787-36 (4) 2181.3 300-47 (1) 22123 
789-67 (3)i) 20718 308-20 
Here with 20714 is normal, Po abnormal, but pi + p 2 = 1097‘87. Our explanation 
gives 788'ol+309‘20 = 1097’71. Thus on the upper set the first and second have 
the same d sequent, whilst the third has d. In the lower set, on the other hand, 
20718 has (dj) d, the same as for the third. 
So also in Dig. In the first set d has in second and third lines, in second set it 
has 2(^1 in second line. 
—786-43 (2) 23390 788-77—| 
(3) 24178 308-77—, 
(4) 22603 789-15 (4) 23392 786-03—1 ; 
i 
'—311-03 (1) 22914 2 x 786-47 (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 j'l, i/g, but the sequent displaced Sy. The line 24178 keeps the 
same displaced sequent as these last, and therefore has a normal Py to 23392, but the 
abnormal to 23390. So 24487 keeps this same dj displaced sequent and so shows a 
normal P 2 to 24178 and 2py 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 (di) +2)'i 
X((ij)+i'i 
X (dj) + p.j 
X 
X (dj) 2pi-\- p.. 
