388 DR. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 



must be possible to raise the limits for D ( oo ) to agree with those calculated from 

 F(oo). That is, to raise that for Ca from. 33981 '85 to 33989'85 and for Sr from 

 31027'25 to 31033*99, or Ca by 8'00 and Sr by 674 or thereabouts. It may probably be 

 possible to find numbers near those which would still make the order differences of 

 Ca and Sr multiples of S, but only by supposing that the successive mantissa- 

 differences in the D series after rising begin to decrease with higher orders, which is 

 against the rule in other cases. This is so far an argument against this way of 

 reconciling the different values of the limits. If however the order differences in the 

 F series behave in a similar manner to that considered above for the D, i.e., by 

 multiples of $ or A, the exactness of the F (oo) found by means of a formula is no 

 longer so close, and the question becomes one of seeing if, when they are made 8 less 

 for Ca and 674 for Sr, it becomes possible to arrange the denominators in the 

 same way. 



If the attempt be made to reduce F ( oo ) by 8 in CaF, a similar objection to that 

 raised above will enter, viz., the successive mantissa-differences after falling begin to 

 rise after m = 5. If however a reduction of about 6 '5 be made, reducing the limit to 

 that found in [II.] for S ( oo ), the order mantissse differ successively within observa- 

 tion limits by 10A 2 , 4A 2 , A 2 , A 3 , 0. Further, in the case of Sr a fall of 675 produces 

 a similar fall and rise in successive denominators. If however be put 1'33, 

 the mantissas differences become within limits 3A 2 , A 2 + 9(5, 16<5, 11$, 4$. If this is 

 justified, it is curious that as in the D series where there are no satellites, the 

 differences proceed by multiples of A 2 the same rule should hold for CaF, where 

 satellites are at least not certain. The difficulty can only be stated and the solution 

 left open. It is possible that the order differences must be compared from the Fj 2 of 

 one line to the F u of the next, for which there is evidence in Ba and Ra. 



Barium. In discussing Ba we start under the disadvantage that the lines 

 belonging to D (2), with the corresponding satellite separations have not been 

 observed, for the ultra-red doublet treated in the discussion on the D series does not 

 seem to belong to the normal D (2). Moreover, the observed lines which are clearly 

 related to the F series are so dispersed by collateral displacements that it is 

 questionable whether it is possible to arrange a series proceeding by an algebraical 

 sequence as in the other cases. The lines exhibited in the table above run on parallel 

 lines with the corresponding lines in Ca and Sr, and are clearly closely related to the 

 successive orders of the series, even if they are not the typical ones themselves. An 

 attempt to obtain a formula from the first three gives a limit = 259067, and gives 

 a value of the wave number for m = 5 of 22729'52 close to the strong line 22706'84. 

 It is 250'05 behind the strong line 22979'57, which indicates that the last is probably 

 the normal F 21 (5), and makes the normal F n (5) about 250 behind. This is in fail- 

 order with the march of the others. We may therefore feel justified in settling that 

 the limit of F^oo) j s near 259067. The F separations are close to 260 and 157, 

 they are therefore based on satellite differences in the D series of 15$ and 9<?; S is so 



