DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
411 
The second set is near the end of the observed region, and the fainter Dj line is 
extrapolated by the normal u,, this will introduce a small possible error. The third set 
is wholly outside the observed region and was obtained by sounding. The data are 
as follows, the lines used being regarded as linked by e to the first triplet 36487, .... 
[43801-13] dk 
(1) 36487-03.6 -00 
(1) 29175-186.6(8i) -00 
(1) 39372-7l.» --02 
(1) 39666-49.W -09 
(3) 32351-67.6.h(-8i) -10 
(<1) 24749-35.6.6(Si).®(Si) --04 
[45578-87] dk 
(t».) 38264-77.6 -00 
(1) .30949-88.26 -08 
(1) 41155-14 r(2Si) -03 
(1) 33841-74.6.r(2Si)* -12 
(1) 34126-78.6.?6(-2Si)*- -12 
(1) 26814-18.2e.w(2Si) -03 
[46397-05] 
(1) 39082-95.6 -00 
(<1) 31768-9.3.26 --01 
(<1) 34659-40.6.1) (28i) --07 
The formula obtained from these is 
n = 51045-37-Ny/|m+-898460- 
This was tested to m = 13, with good agreement with the exception of m = 4. 
All are in the ultra-violet and require sounding. As the evidence of the efficacy of 
sounding ah’eady adduced may be regarded as convincing, there is no advantage in 
giving further details of the results, especially as no additional conclusions are based 
on this formula. 
—We are to look for parallel F sets with the same separations as those of the 
D satellites. Starting with the triplet 19880 as an undoubted D satellite triplet it 
was then attempted to determine the others, by picking out those lines of larger 
wave-length whose mantissse differed from that of 19880 by oun multiples. The data 
are contained implicitly in the list on p. 407, independently of the form into which the 
mantissae are there thrown. It is clear that the above condition is satisfied by all 
those which show unsatisfied remainders of the same magnitude as that of 19880 — i.e., 
66 —within error limits of, say, ±6. The selected lines were 19880, 20021, 20041, 
20312, 20500, 20559. We have shown above that the second, third, fifth and sixth 
of these satisfy the capability test for — 3()j displacements on the limits, and have also 
found some evidence that 20312 also belongs to this set, although perhaps with a 
somewhat excessive observation error. It has also appeared that 19880 cannot 
belong to this set, but it has so happened that the satellite separations from it reproduce 
themselves in the F series sufficiently well as to serve for identification. We shall, 
therefore, use this allocation. The selected lines give separations from 19880 
respectively of 140-94, lOFOl, 431-98, 619-41, 679-36. In these 19880 was treated as 
if it were a fifth satellite to 20559 and the notation adopted of Fg, ... Fj series. Such 
series were found, and in what follows I shall chiefliy confine consideration to them 
leaving aside for the present purpose, with one or two exceptions, the very numerous 
other groups which exist. It would not be advisable to suggest a definite notation 
Parallel inequality. 
