DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
383 
As supporting the theory of displaced links, the mesh at 2G000 (c 12 and No. 4) is 
interesting. For the link 17256 is easily explained by the displacement in a 
disappearing, and the link 17250 by its continuance to the line 22813. In fact the 
sum of the two links is 2e—'24. From 26000 the link 14929 is not entered as it 
is so small, but there are other examples of this small v in this map and the v 
link appears to be a normal associate with an e mesh. 
Starting from S x there are four separations close to 17264 or e( — S 1 ). The link 
4611'32 is too much out to be introduced on its own account, but it forms part of a 
mesh whose corresponding link is evidently c. It is taken as c( —<h) = 4610'52. A 
displacement somewhere in 42644 producing 3'51 not only makes the long link e 
correct, but with the disappearance of the displacement on the preceding c at the 
same time makes the separation to 26698 a correct u link. The alternative formula 
(No. 15) is on the supposition that the displacement is produced in the c by 2d,. 
Perhaps we should stop at 33345 as the next link 14929, like the one referred to 
above, is 7'70 too small. But the next e link is too small for e( — <b) by about the 
same amount, and the two together have the appearance of a parallel inequality. The 
abnormality however may possibly be due to the fact that the separations are due 
to differences between one line by Eder and Valenta and others by Exner and 
Hasohek. If this be granted the next comes right with e ( — <i,) = 17264'03 with error 
d\ = '07. 
Again starting from S 2 there is a collection of meshes, chiefly of e. They illustrate 
the variations from normal links chiefly in link a. A noticeable peculiarity is that in 
most of these meshes a line is linked by v to one corner, in all cases v being from 3 to 
4 below its normal value. The regular presence of one of these links in each mesh 
would seem to exclude any explanation as a chance grouping. But they further 
exemplify the theory of displaced links in a, 6..., for the defect from the normal 
values of v is not due to themselves but to a concomitant return of a displaced a or b 
to a former value. Thus in 26130 c recurs to its value in 23805. The line 39404 
apparently linked to 45043 by —d ( — <b) really takes the — d link, and the displacements 
in 45043 are annulled. Also 50676 wipes out the same displacements and is 2d above 
39404. The line 26130 is of intensity 8. If the general rule that the strongest lines 
are connected with an e link is satisfied there should be a mesh with a line at 8866, 
which is outside observed limits. The lines on this hexagonal mesh (Nos. 25 to 28) 
appear also in the Y map. From 31921 we get a series of enlarged p links with 
similar displacements ending at 24912 (No. 38) with all the previous displacements 
annulled. In 39404 above there is a similar example of the chain stopping when 
the displacements cut out. 
From 25387 (c 3) the chain passes to a separate map to escape excessive crowding. 
In the next two lines we get two repeated displacements in c links which return to 
normality in the third. The line 58271 is from Handke’s ultra-violet lines and is 
affected with considerable possible observation error. The formulae are continued 
