368 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
they are given clearly by Eder and Valenta as two XX = 2419'41, ’10, so that any 
supposition as to the presence of observation errors is ruled out of court. There is 
therefore a displacement either in the links themselves or in a line 41322'6. 
The other example is from silver, in the AgS (3) linkage, viz., 
31815 
2455-51 
34271 
2461-79 
30846 963-16 31809. 
Here again the two u links deviate from their normal values by equal amounts 3*1. 
Their mean is 2458'66, which is exact. The two lines 31815, 31809 are XX = 3142'82, 
'20 and are clearly displacements by equal amounts in opposite directions from 
3142'51. 
The number of cases similar to the above in which a change in one wave-number 
will make a number of abnormal links all conform to their typical values is extremely 
large. When two such links occur in series—both in the same direction—I refer to 
them as series inequalities; when in parallel, or one additive and the other subtrac¬ 
tive, as parallel inequalities. If one is too large and the other too small by equal 
amounts, it means that when in series, the line between them is displaced from the 
first one, and the third has this displacement annulled. If in parallel it means that 
the third line receives the same displacement over the second that the second received 
over the first. If, however, the two links differ from their normal values by the same 
amount the above changes are reversed. 
In certain cases, especially where D linkages are involved, the nature of the 
displacement would seem obvious — where, for instance, the irregularity can be 
explained by a change from a D n type to a D 12 or vice versd. Thus in the AgD (4) 
linkage the line 33192 is 2620T9 greater than the line 30572. The former depends 
(see No. 7 of the AgD (4) Table) on D 12 . The satellite separation is 2'69 by observation. 
Thus link v + change from D 12 to D n is 2616'61+2'69 = 2619'30, leaving '89 (clX = ’08) 
to be distributed between observations of the two lines and of the satellite separation. 
The first line is p ( — 2A)—s (A) + s—YD 12 (4), the second would then become 
p ( —2A) — s (A) + s ( — A) — VD U (4). A similar explanation is possible for the 
previous example from the AgS (3) linkage. The line 31815 contains—VS (3) in its 
formula. Now VS (3) = 9231'23 = N/(3'446862) 2 , a displacement of —6^ on this 
produces a separation 3'36. So that numerically 34271 is 31815 ( —6<^) +u + ‘22 
(d\ — —'02), and 31809 is 31815 ( — 13^) — 'll (d\ = '01). Such explanation, how¬ 
ever, is not so plausible as in the preceding case, for the S sequences do not seem to 
be so susceptible of small displacements as the D. The most frequently occurring 
irregularities, however, cannot be explained in this way for the P(l) linkages show 
