462 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
Amongst the sets of F series given (p. 452) two, in addition to F (l) itself have been 
measured to the required degree of accuracy. They are those showing separations of 
85 and 265. Under these conditions 
Mantissa of 31852-1816+ ^ = 855630-30-29-130^ 
Wave-numbers of 5852-4870 = 17082-0220 —-0029jOi 
85-4080- 0029 (pi-Pa) 
5881-8958 = 16996-6140--0029jO2 
265-3518- 0029 (Pi-Pg) 
5944-8344 = 16816-6702--0029jO3 
(l) Separation = 85-41.—This is the same within error limits as occurs in the D series, 
but the corresponding F series shows v increasing to 87-57 W or 87-41 B at m = 5, 
which means additional displacements either in F(oo) or the sequences. As the 85 
agrees in both the F (l) and D series this will not happen in the F(co), and the 
separation 85-41 will be due only to the actual separation in 31851. The limit of the 
F series in question is therefore 31852-4170 — 85-4080 = 31765-8336-I-A 
Its mantissa = 858133-15 —-085 (^i—pa) —29-247^ 
Difference from F^ = 2492-85... 
Now 
9A2-l-5f ^ = 2492-504-h 9-31 Icc, x < '2 
Hence 
9-311ic = -35--085 {p^-p^)--l\7i 
x= -038--009(j9i-p2)-'0126^ 
The important point to notice is that with our preliminary limit of uncertainty 
(.X <-2), the oun multiple cannot be any other than that used, so that the second 
approximation is quite definite. It has already been seen in the discussion of the 
Fi series that ^ is probably within ±-33 also Pi—p 2 will not numerically be greater 
than 4. Hence x = -038 ±036 ±0042 = -038 ±-04 
A 2 = 267-738±-04 
S = 14-4705±-0009 
( 2 ) Separation = 265-3518.— Limit = 31586-8298+ ^+-0029 (pt—jOs) 
Mantissa = 863408-31 --085 {p.-ps) -29-498^^ 
Difference from Fj = 7778-01 —-085 {pi—ps) —-368^ 
Now 
29A2 + <i = 7777-77 + 29-05X 
29-05X = -23--085 {pi-p3)-'S6S^ 
x= ■008--0029 {p,-p^)--0l26i = -008±-016 
Aj = 267-708±016 
therefore 
