380 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
The mantissa of (l), using F ( oo) = 30678‘93 + f' is 
9I2207-II2-60^'+IIi9)±‘5 =195 {4677'986--577^'+-05jOi±-002}. 
This requires —’014—a?—‘577^+‘05^ +'002 = 0, or combined with the condition for 
y’(2), — TI2 +'003^ —*086^+■05jOi±‘002 = 0 and can be satisfied within error limits. 
The mantissa of (2) 895149 —II0‘63^'+11^2 which differs from that of f (2) by 
29701-3-37^'+IIj)2-16y = 7 (4243-00--48^ +I-6p-2-3y). 
This requires I'GI-■907x*—■48^+I-6^a —2’3p'=0 easily satisfied for both cases 
within observation errors. 
The mantissa of (3) is 937966 —115-6f'+ 11 ^, 3 , differing from that of/(2) by 72518 
— 8 - 35 ^+1 1 |:> 3 —16^. With ^ = —‘58 and -1-70 this becomes 72523-1... and 72532..., 
or 17A'2+if-^-23... and 17A'2+ifd—24... on their respective values of D'g. The 
amount 23 is perhaps excessive to be covered by the various possible errors but it just 
comes within. It may be noted that 17A'2+ if^ = IGA'sT A 2 . These three data do not 
decisively distingiiish between the two cases. This, however, is not to be unexpected 
because the two arise from a displacement in the sequents in this neighbourhood 
are such that on the limit and 2(li on the sequent are nearly equivalent, and the 
multiples involved 185, 189, 195 are too close to produce contrasts. Incidentally, also, 
the discussion strengthens the allocation of the lines to the displacements given. 
The only further test with our present knowledge is to obtain some independent 
evidence as to the exact value of the limit, and naturally we turn for this to the mean 
of the F and F series. The series however in Kr is not nearly so well developed as in 
X. As has been already seen there are only three sets of observed pairs (m = 2, 3, 4) 
and these give for F ( 00 ) respectively values of 30674-77, ...7'27, ...7-16. Since a 
displacement of produces a change of 2-03 in F ( 00 ) the first may be due to the fact 
that the line taken for F (2) is really (3^j) F (2), when the true mean would be 
30677-81. It is natural to seek further as to the existence of summation lines 
corresponding to our last three examples. The result shows a most remarkable 
agreement. The sets are shown in the following' list together with those obtained 
from the normal F and F. 
m. 
F. 
F ( 00 ). 
P. 
2 
(1) 17321-51 
30677-82 
(44034-13) 
(- 3 ^ 1 ) (2)44028-04 
3 
(In) 23353-84 
30677-27 
( 2 ) 38000-71 
4 
(2n) 26067-66 
30677-16 
(6) 35286-68 
Fi (2) (7A'2) 
( 5 ) 17594-17 
30677-76 
(1) 43761-38 
F, (2) (7A'2) 
Fi(2) (IOA 2 ) 
( 6 ) 17747-14 
30677-73 
(1) 43608-33 
Fi(2) (IOA 2 ) 
F/2) (16A'2 + A2) 
(2) 17972-78 
30677-70 
(1) 43382-63 
Fi(2) (lOA's + As) 
These are remarkably concordant, especially when it is noted that the F (3, 4) are 
diffuse lines and not so susceptible of exact measurement as the others. The mean 
