DR. W. M. HICKS: A ClilTICAL STUDY OF SPECTRAL SERIES. 371 



suggested scheme of actual lines may therefore be represented as follows where 

 D n , D H stand for the normal type, and D,,(m) = D n (m) (-55J,) :- 



D., (4), D 13 (4) 



( + ^)D U (5), D u (5) 



( + <*)D U (G), D w (6) 



( + 2J)D n (7), 



D n (8) 



The order (4) of the first line is so large that the error limits are too wide for absolute 

 certainty. In fact better agreement on the whole for the satellites would be 

 obtained by taking the difference as 56^, i.e., 4<? u , <J U being specially associated with 

 this group (see p. 331). The line 6269'28 is separated from G2G6'36 by 6'44, and is 

 therefore possibly the lateral ( + 2<S) D,, (5). 



The table shows of course the known essential difference between the liehaviour of 

 the elements of Group 2 and that of Groups 1, 3, G, signified by the signs of a in the 

 formula. It consists in the fact that in Group 2 the orders are formed in succession 

 by the addition of multiples, whilst in the others it is by subtraction, with the 

 exception that Cu and Ag of Group 1 are additive. But there are certain other 

 features which appear between the different sub-groups when higher orders are 

 looked at. The alkalies all show a gradually decreasing decrement with a sudden 

 dive. Na then shows a sudden rise continued for several lines, and Cs has a similar 

 indication. Cu and Ag with only a few lines observed show decreasing incrementa 

 The alkaline earths show decreasing increments and a sudden dive (Mg excepted). 

 The Zn sub-group shows decreasing increments and then a sudden ascent. The Al 

 Sub-group 3 show decreasing decrements (Sc decreasing increments). ( ) with S and 

 Se show decreasing increments. In fact, were it not for the very clear behaviour of 

 Zn, Cd, and Hg, the evidence would rather point to the conclusion that in each 

 group, the low melting-point sub-group show subtraction (at positive) and the high 

 melting-point addition (a negative). If this series depends on a formula sequence, it 

 is difficult to see how it can be any simple algebraic one the mantissa would rather 

 seem to depend on a term similar to sin ma or tan ma. In the detailed discussion 

 above, however, it is seen how these changes of direction can be explained by lateral 

 displacements. It is noticeable that where the irregularity observed in the first lines 

 as compared with the others in the satellite differences appears, a similar irregularity 

 exists also in connection with the first order differences. This is evident especially in 

 the alkalies, where the first differences are so close to exact multiples of A or & as to 

 cause the conviction that they really are so. 



3 B 2 



