462 DR. W. M. HICKS : A CEITICAL 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--0029p, 



85 -4080- "0029 (p, -p.) 

 5881-8958 = 16996'6140--0029p 2 



265 -3518- -0029 (p,-p 3 ) 



5944-8344 = 16816-6702--0029jo 3 



(1) 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(o), and the 

 separation 8 5 "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 + 



Its mantissa = 858133'15--085 (p 1 -p 2 )-29' 



Difference from F t = 2492-85... 

 Now 



9A 2 + 5f<$= 2492-504 + 9-311o;, x < '2 



I I *T~t ("*(-* 



9'Bllx = '35--085 (pi-p,)-'H7 



x= 



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 

 F! series that ( is probably within '33 also p^p^ will not numerically be greater 

 than 4. Hence x = '038 036 0042 = '038 '04 



A, = 267738'04 

 S= 14'4705-0009 



(2) Separation = 265'3518. Limit = 31586'8298 + +'0029 (j9,-jo 3 ) 



Mantissa = 863408'31-'085 (fr-pa) -29'498 



Difference from F, = 7778'01-'085 (p^-pj) -'368^ 

 Now 



29A 2 + f ? = 777777 + 29'05z 

 therefore 



29'05a; = '23--085 fa-pJ-'SGSg 



x= '008 --0029(^-^3) -'01 26^= '008-016 

 A,= 267708016 



