DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 435 



comparable. Where W. gives 20438*8, with intensity 4, R.R. give 20446*38 with 

 intensity (0), and a similar effect is shown in the second line of the above triplet (R.B. 

 have not observed so far in the red as 14813). The differences 5 '6, 3 '2 are comparable 

 with the differences shown by the v l 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 R.R.'s 20446'38 is 5633'42 ahead of 14813 

 and is therefore one exact determined value of the F 2 separation. We are justified 

 therefore in taking 20438 as a D n line belonging to the S(oo) = 50400 + . With 

 d = 29964*20-1- ' the calculated D line is therefore 20435'80 + -f' = 20438'8 + *4p 



= 3'0 + *4p + ' 



where ' is small. Hence S (co) = 50403*00 + ^ 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 D n line. With this, S(oo)= 50403'00 + and v } = 5371+di/,, v., =2649 

 + dv a the denominators and values of A 1; A 2 , calculated directly are 1'4751 14, 1*40221)0, 

 1*370130 and 



A! = 72824-2*06^+ 12*571^ = 40|{1787*09-*050^+'31^ 1 } 



A 2 = 32160- 84(^+di/ 1 ) + 11726rfi/ a = 18 {1786'66-'046 (+efo,) + 



The (5 as determined from the A 2 has always been the same as those found from the 

 D and F mantissae, here 1787'015 *062 ( *4p). Hence dv., = '53 correct to the first 

 decimal place and i> 2 = 2649'53+c?^ where dv., < '1 and A 2 = 32166. If the S from A, 

 is the same dv\ = '3 and v l = 5370'7, AI = 72820. Wherever it is different it has 

 always been slightly less than that from A 2 , so that we may regard 53707 as a 

 maximum estimate for i/j. 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 dv lt if S from v l is the same as from i/ 2 . This will at least give maximum 

 values of i/ t . The cases are given for the limit used above and also in the last two 

 columns for that if 20446 is the D u line, that is the limit about 7 larger. 



di>i dv% dv\ di>2 



1787*87-*062 2*5 17 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 Dn. It would make 

 S(oo) = 50410. 



