392 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
a mean of 73-56. But 32048 is also (S)F 3 . This is not a mere list coincidence. As a fact ( 8 ) F 3 and 
(58j) Pi are very nearly equal, and if both existed would show as a double line too close to have been 
resolved. The second line has a separation 1864-23 to ( 2 ) 33962-43, and its deduced Fi makes with the 
calculated El the limit 30725-18 very close to the definitive value found below. For F 2 33937-99 is 
supported by (- 2Si) F 2 = (1) 33948-71 giving F 2 = 33937-85, but the F 2 ( 00 ) is large and 31242 shows 
a separation with Fi of 1865-39 also large. Also (1) 31247-07 as (-Si)F 2 gives F 2 = 31241-64 which 
makes F 2 (oc) = 32589-82 and the separation from Fi = 1864-64 both improved. On the other hand 
(- 2 Si)F 2 = (4) 31253-32 gives F 2 = 31242-46 precisely the line observed. These small differences 
depend partly on observation errors and sequence or satellite displacements. In the case of F 3 and F 3 the 
equally and oppositely displaced lines give the same mean as the lines calculated from them. 
m = 9. There seem considerable displacements in the sequences here. The calculated values for the 
first lines are 29632-80 and 31817-72. They are not observed, but the corresponding F 3 , F 3 lines are. 
There are two near observed lines ( 1 ) 29629-10 and ( 2 ) 31820-18 which give the mean 30724-64, which 
is small, but (1) 31810-86 = (2S^) F^ would give 31820-79 and the limit 30724-94, close to the normal 
value. 31820-18 is then ( 2 Si)F 2 (ll). With (5) 31483-37 as ( 28 JF 2 and (l?i) 31505-49 as (- 2 Si)F 2 
we get respectively Fj = 31494-23 and 94-63. The mean is entered, and a similar -28^ displacement 
gives Fo as entered. The normal third lines are observed. Probably the F 3 having the same sequent as 
the Fj adopted should be that given by (-28j)F3 = (4) 34527-64 or F 3 = 34516-37 with — 830-83. 
m =10. The allocation seems satisfactory. The limits also are very close to the correct, but the 
different triplet separations show that the successive sequents suffer displacement, but the same in each 
F, F. 
m = 11 . The calculated F^ is 29966-21. With ( 1 ) 29982-13 = (-Sj)F^, F^ = 29967-22. Moreover 
the last has links e = 7314-34 to (3) 22652-88 and m = 4133-20 to (Dr) 25854-02 in very striking 
agreement. The value as calculated with normal e is entered. With the lines as entered it is seen that 
the means of the corresponding separations for the two series are both normal, although the individuals 
are abnormal. This shows that both corresponding lines have the same limit, and the same sequent, but 
that the latter shows a displacement from the normal rmlue for the F 2 set. This is supported also by the 
fact that there are a number of close lines to Fj. For instance, ( 2 ?i) 33332-22 and ( 2 ) 33330-00 as (38^) Fj 
give respectively 33348-51 and 6-29 for Fg. They are probably all Fg lines showing sequence displace¬ 
ments. The first gives the triplet separations 1865-14, 828-42 and limit 32589-77, the second 1862-92, 
830-64 and limit 32588-66. In other words, the first gives Fg, with same sequent as in Fj and F^, the 
second as in Fg. 
771 = 12 . Note the good agreement—the same (- 28i) displaced limit for Fg. Fg and same 25i for F^ 
and F3. 
771 = 13. The two displaced sets give F^ = 30167-38, Fj = 31283-59. The calculated 
Fi = 30166-40. 
m = 14 D 30. It is remarkable how the series seems to persist to high order. It may be said that 
this is only apparently so, because in this region the spectrum is so crowded with lines that it is neces¬ 
sarily possible to select sets near the calculated values. But in truth the reason of the crowding is 
because of the series. The F and F lines crowd up together on either side of the three limits, and at the 
same time there are different sets of limits depending on the 28^ displacements. The spectrum has not 
been examined beyond tti = 30, and from 14 to 30 the list indicates an allocation without further specifi¬ 
cation. There is, however, much evidence not adduced here to indicate actual cases where sequence 
displacement occurs. The calculated values for F^ from m = 14 to 30 az’e 30238-21, 30297-01, 30345-73, 
30386-58, 30421-17, 30450-68, 30476-20, 30498-14, 30517-35, 30534-18, 30549-11, 30562-32, 30574-08, 
30584-61,30594-07,30602-60,30610-32. The deviation from the calculated values for Fj(29) and 
Fj(29), which, however, gives the correct limit, shows that the sequent /(29) receives a large displace¬ 
ment value, so large indeed as to totally alter its mantissa. The set must be doubtful. The whole set 
