DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
435 
comparable. Where W. gives 20438'8, with intensity 4 , R.E. give 20446’38 with 
intensity (O), and a similar effect is shown in the second line of the above triplet (14.14. 
have not observed so far in the red as 14813). The differences 5 ’ 6 , 3'2 are comparable 
with the differences shown by the sets roughly estimated above, say 5371, 5374 , and 
would seem to be due to the same effect, although this would not go with the 
explanation there suggested. Further Id.K.’s 20446-38 is 5633-4±2 ahead of 14813 
and is therefore one exact determined value of the Fa separation. We are justified 
therefore in taking 20438 as a line belonging to the S(oo) = 50400 + ^. With 
d = 29964'204-^' the calculated D line is therefore 20435-80 + ^—^' = 20438-8+ ‘ 4 ^ 
^ = 3-0+ - 4 p + ^' 
where is small. Hence S (co) = 50403-00+ f where ^ is small and equal to ^'±- 4 . 
A reliable value of this limit has thus been obtained. The measure of its reliability is 
that of two assumptions (l) that the 5649 (or 34) series studied at the beginning of 
the discussion of this element is an F type analogous to the 1864 of X, and ( 2 ) that 
20438* is a Du line. With this, S(oo)= 50403-00 + ^ and ^ b2,7l + dv^, i/ 2=2649 
+ dv 2 the denominators and values of Ai, A 2 , calculated directly are 1-475114, 1-402290, 
1-370130 and 
Ai = 72824-2-06^+ 12-571di.i = 40|{l787-09--050^+ -^Idv^} 
A 2 = 32160- -84 (^+di^i) + ll'726(i.2= 18 {1786-66--046 {i+dv,) + -Qb\dv.^^. 
The d as determined from the Aa has always been the same as those found from the 
D and F mantissm, here 1787-015--062 (^--4p). Hence dv.^ = -53 correct to the first 
decimal place and v.^ = 2649-53 + dj/2 where dv^ < -f and A2 = 32166. If the 8 from A^ 
is the same dv^ =--3 and = 5370-7, Aj = 72820. Wherever it is different it has 
always Ijeen slightly less than that from A 2 , so that we may regard 5370-7 as a 
maximum estimate for p^. It may be a few decimals smaller, but we have no direct 
means from observed lines to determine it more closely. 
A similar treatment with the four equally probable values of S are appended. Also 
changes in dp^, if S from p^ is the same as from p. 2 . Tliis will at least give maximum 
values of p^. The cases are given for the limit used above and also in the last two 
columns for that if 20446 is the Du line, that is the limit about 7 larger. 
dpi 
di'2 
di>i 
dv2 
1787-87--062^ 
2'5 
1-7 
3-5 
2-5 
1787-01- 
- -3 
•5 
•9 
1 
1786-13- 
-3 
- -8 
-2 
- -3 
1785-26 
-6 
-2-1 
-5 
-2 
* Possibly not so certain. 20446 gives one of the normal 5633 to 14818. Its weak intensity may be 
due, as in the other gases, to the presence of displacements and so may be Du. It would make 
S ( 00 ) = 50410. 
