380 
DR. W. M. HICKvS: A CRITICAL STUDY OF SPECTRAL SERIES. 
displacements adopted for the purpose of indicating their modified values. The 
formulae given in the AgPj list agree very closely with the observed values and 
depend, as is seen, on ( — 3d) displacements of e and d displacements in u and v. In the 
AgP 2 list our displacement convention has been departed from in No. 13 and 
dependent lines by assuming a displacement 3<b in p ( — 2 A). This makes the link 
3777 cut out a former e link and reduces the formula to two terms. 3777‘52 is as 
far as it can be from an e link displacement, and the suggested formula only gives 
a dX = —'07 error. From 28600 a long v link 2621 'll = v ( — 2d)—'40 connects to the 
whole succeeding P 2 lines through 31221. Some doubt might be felt as to its reality, 
but it is accompanied by an enlarged u link = u( — d) + '15, which suggests a parallel 
inequality. The formula for 31221 gives dX = —'02. It may be simplified to s ( — A) 
-p ( — 2A)(d), givin g dX = — '13 possibly within observation limits. But if so, the error 
dn is such that it entirely upsets the parallel inequalities in the succeeding mesh. It 
is, therefore, not adopted, although the line 30214 has the analogous form s( — A)— p 
(-3A )(S) with dX = — '12. Further, this error makes the parallel link 2461'04 into 
2459'62, i.e., would replace u ( — $) — '05 by one as far as possible from a displacement 
value. 
The double mesh from 31221 is noticeable for the great modification in the links. 
They are, however, examples of parallel inequality which demand with each link some 
displacement continued for each case. In the table it is supposed to be ( — 3d) on the 
b link. It is possibly, however, (d x ) on the p ( —2A) term. From 30415 the list 
passes from (i.) to (iv.) and is continued to the strong line 34446. 
The D linkages. I have not been able to find any links attached to D (2) or D (3). 
They exist, however, for D(4) and D(5). 
AgD (4). D n (4) = 26235'29, D 21 (4) = 27153'03, VD X = 4409'31, VD 2 = 4412*01, 
giving satellite difference 2'70, but the measures are not very accurate, especially that 
of Dj. There is a considerable linkage in which no cycles appear. It contains, how¬ 
ever, the line 29084, referred to under the P linkage, as connecting with lines in it. It 
is itself a clear D line, as the linked mesh in the map shows. In order to test the 
links into the P map lines, the formulae have been calculated up to the strong line 
38234 (see AgP (iii.)). The modifications of many links would seem to point to dis¬ 
placements producing about 1'5. • For instance in the first eleven links there are three 
examples, viz., the links below Nos. 1, 4, and 9. It is possible that they occur in the 
d sequence and not in the links themselves. For this reason and because the actual 
D (4) lines may be considerably in error, displacements have not been introduced into 
the formulae, and errors up to dX = '1 or '2 have been admitted, whilst changes from 
the satellite sequence d 2 to the chief line sequence d 1 have been allowed. But as a 
fact there does not seem to be much demand for these displacements either in D (4) 
or D(5), and the linkages are distinguished from those for the P and S linkages by 
their absence. In No. 2 there is an example of a link acting as a pure displacement 
so that the three lines (A) D (4), D (4), ( —A) D (4) exist. The link after No. 6 has 
