442 
DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
displacements so analogous to those in X is evidence that the links in question (5640, 
1864) are of analogous type. We have already seen in X that these separations occur 
as links, as well as direct displacements on sequences present in the wave-numher. 
Let us determine the F limit required to give a separation in the correct neighbourhood 
with a displacement bA.j. The conditions are that not only must the 5 A, give the v-^ 
hut since it must belong to a c?(l) sequent, the mantissa of the limit itself shall also 
he an oun multiple. The result is that the limit should be within close limits of 
29617 and that then the i/j will be close to 5648 one of the most probable values found 
on p. 431. But this 29617 = F(oo) = cZ (l) should belong to a D line 50403 — 27917 
= 20786. Now there is an observed line (O) 20784‘31 (W.) with another at 
(7) 20750'34 (W.) or (7) ...52‘70 (R.) behind it. Taking 20784’31 its sequent is 
29618’69 and mantissa 924298 or 11133 above that of 29964'20. Now 6|-^ = 11169 
and the difference 36 requires a change in wave-number dn — ITO or dX = — ’25A. 
The line was only read to ’lA so that this error is permissible. The F(oo) is then 
29617’57. The — 5 A 2 displacement on this gives 35266'16 or a separation 5648'59, 
and on this it will be found that an extra 2A2-t-5(5i gives V 2 = 2810'97 = 2811 say. 
Further a change of on 5 A 2 or 2A2-t-5^i produces changes in i/j, 1/2 respectively of 
17'88 and 20'00. This accounts for the concomitant value of 563071, and 2831 also 
observed is due to 5Ai —^ 1 , and 2 A 2 + 6 ^i precisely those in X. 
The Value of the Oun. —The data for the evaluation of the oun are :— 
( 1 ) The triplet separations and S(oo). The rj, v.^ are not determinable directly 
from S lines and consequently no exact values can be obtained from observation. The 
general argument on p. 433 is in favour of 5371, 2649, or about 3 larger according to 
limit. These are strongly supported by the set of lines on p. 437, clearly a linked S (l) 
or an independent S (l) set showing also the displaced So, S 3 by W. and R. 
respectively. These values point to (5 = 1787‘0. 
( 2 ) From the F and F series giving definite F(c»)=: 29964'20 and p. 430. 
The definite result is a limitation of S to one of six alternative values, of which four 
between 1785'26 ... 87'87 are equally probable, the ambiguity being due to imperfect 
measurement. This argument is independent of the values of i/^, V 2 . 
( 3 ) The mantissa of the D 13 line 16725 is 25A2 + (li and that of the D 23 line 
22079'34 is 25 X 3 . This gives 
, A 2 = 32166-44-r07£-l-07cZri+-21p, 
^= 1787‘024--059^--059(71/1+-012^9. 
Here probably 
f<-5, dv^K'l, p<-5, or, say. 
^ = 1787-024 + -05. 
These three determinations are all independent. 
