392 bR. 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 

 (58,) 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 F! the limit 30725-18 very close to the definitive value found below. For F 2 33937 -99 is 

 supported by ( - 28^ F 2 = (1) 33948 -71 giving F 2 = 33937 85, but the F 2 ( o) is large and 31242 shows 

 a separation with FI of 1865-39 also large. Also (1) 31247 -07 as ( - 8,) F 2 gives F 2 = 31241-64 which 

 makes F 2 (ce) = 32589 -82 and the separation from FI = 1864-64 both improved. On the other hand 

 (-28i)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 = (28,) F, would give 31820-79 and the limit 30724-94, close to the normal 

 value. 31820-18 is then (28,)F 3 (11). With (5) 31483-37 as (28,) F 2 and (In) 31505-49 as (-2S 1 )F S! 

 we get respectively F., = 31494-23 and 94 -63. The mean is entered, and a similar -28, displacement 

 gives F.i as entered. The normal third lines are observed. Probably the F 3 having the same sequent as 

 the Fo adopted should be that given by ( - 26,) F 3 = (4) 34527 64 or F 3 = 34516 37 with * 3 = 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 = (-S,)F,, F, = 29967'22. Moreover 

 the last has links e = 7314-34 to (3) 22652 '88 and u = 4133-20 to (1m) 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 value for the F 2 set. This is supported also by the 

 fact that there are a number of close lines to F 2 . For instance, (2m) 33332 22 and (2) 33330 00 as (38,) F 2 

 give respectively 33348-51 and 6 -29 for F 2 . They are probably all F 2 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 F 2 , with same sequent as in F, and F,, the 

 second as in F 3 . 



m = 12. Note the good agreement the same (- 28,) displaced limit for F 2 . F 2 and same 28, for F, 

 and F 3 . 



m = 13. The two displaced sets give F, = 30167-38, F, = 31283-59. The calculated 

 F, = 30166-40. 



m = 14 to 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 m = 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 are 30238-21, 30297-01, 30345-73, 

 30386 58, 30421 17, 30450 68, 30476 20, 30498 14, 30517 35, 30534 18, 30549 1 1, 30562 32, 30574 08, 

 30584-61, 30594-07, 30602-60, 30610-32. The deviation from the calculated values for F,(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 



