DR. W. M. HICKS; A CRITICAL STUDY OF SPFXTTRAL SERIES. 353 



for different orders within limits of errors, especially in the doublets and differences 

 'I' tin- second and third satellites. Thus we find Cs, 14<J; Ca, 13<J, 83; Sr, 12& for 

 m = 3 and 15<5 for m>3 for first separations, and 8& for all orders in the second ; Ba 

 and Zn show too few for comparison (see discussion below); Cd, 19<J,, 15^, ; Hg is 

 ii regular, Al is anomalous ; In 26$, Tl, 27 <Ji for m = 2, and 28 J, for m>3 ; Se, as 

 amended later, shows 55(5, for m = 4, 6, 7, and 38(J, for m = 5, the lines for m<3 

 Ix-iiig outside region of observation. The evidence points to a normal rule that the 

 differences for the orders beyond the first in any spectrum are the same, but different 

 from in general greater than that of the first. 



The Order Differences. The order differences change very considerably with a 

 change in the value taken for the limit, i.e., in the value given to No doubt with 

 unlimited choice of it would be possible to arrange a set of denominator differences 

 all multiples of the oun within error limits, for a series of values of could be found 

 making the first difference a multiple. Out of these one or two would probably give 

 the second such a multiple. After the second the error limits as a rule come to be 

 very large, in fact larger than half the oun itself, except in case of very high atomic 

 weight. No conclusions could be drawn from any such arrangement. But in the 

 present cases the choice of is bounded by very narrow limits, for the relation 

 D(oo) = S(oo) is supposed to hold, and, as a rule, the values of S() are known 

 with very considerable accuracy, and the possible limits of variation are known. 

 They were given in [I.] and [II.]. Before proceeding to draw general conclusions 

 from Table II., it will be well to consider in more detail the data for the different 

 elements on which the table is based. 



Na. 



Although the readings for NaD are very inexact, the peculiarity of the large 

 depression shown for m = 6, as well as the large recovery afterwards to raantissse 

 close to unity, must be real effects. It is of course possible that NaD, (6) is a 

 collateral from the normal type. If D, (6) be calculated from D.,(6) v, the mantissa 

 becomes '989054, in other words, the D 2 line begins to show the rise to the large 

 final value at m = 6, whilst D, does not do so until m = 7. The D, lines would seem 

 to succumb to the disturbing effects sooner than the D,. It was pointed out in 

 [I., p. 83] that in the Na the D series apparently belongs to the F type, in which 

 the mantissa is '998613. It would almost seem that the peculiar rise shown is due 

 to the fact that it reverts to this F sequence. Here, as we shall see in other cases, 

 the values of the first members of these series appear to be subject to some kind of 

 displacement which affects their (supposedly) normal relations to other lines. If now 

 tin- first mantissa be supposed normally to be this 998G13, it is 9691 above that in 

 tin' modified table, and this is 13A + 32, thus completing the order differences as 

 multiples of A. But in any case the data for Na are of small use for the present 

 purpose, as the errors are so large, and A so small. The arrangement in the table 



VOL. CCXIII. A. 2 Z 



