308 Prof. W. M. Hicks on the 



30642*58 and *85 each affected by an uncertainty of *5. 

 This gives £= — 1-89 + *4. 



As lending support to the above considerations but chiefly 

 from its importance in relation to the laws of spectral 

 analysis in general, attention should be drawn to certain 

 other lines in connexion with the first two orders. In 

 general, with doublet separation v and satellite separation a, 

 the D n and D 22 lines are separated by v — <x, the D n , D 22 by 

 v+cr, and their limit means by v. There are also frequently 

 observed lines in which the corresponding separations are all 

 v — a. This is explained as follows. If d 2 , d x be the satellite 

 and main line sequents, d\ is a positive displacement (say 

 x ouns) on d 2 , so that d 2 — d 2 (x$i) — o: If A and B denote 

 the limits B — A = v, then the D n , D 22 lines are respectively 

 A-d 2 (x8 l ), B-d 2 , and the D are A + <*,(* 8^ B + d 2 . The 

 ■corresponding D and D means are A, B and separated 

 by v, whilst the separations of the main D and D lines are 

 respectively v — <r, v + cr. In this new case the summation 

 sequent changes the sign of x as well as of the sequent, and 

 the D lines are A + d 2 { — x Si), B + f? 2 . The D means are 

 A + ^{d 2 ( — .vS 1 ) — d 2 (x o\)} and B and are separated by v — cr, 

 whilst that of the D lines is B — A + d 2 — d 2 ( — #6\) =v — o-, 

 since d 2 *—d 2 (x 6\) =d 2 {— x o\) —d 2 if x is not very large. In 

 the present case we find (2) 59719*32 (3) which differs from 

 the deduced D 22 by 847*27+ or 920*4 — 73*1 + . It is there- 

 fore the representative of this effect for the D(l) set. If we 

 indicate this quality by affixing an asterisk 59719 is 

 D n *(l)=D 11 (-2x23S 1 ). It is clear that D n + D n * = 2D 12 . 



In connexion with m = 2 we find two lines whose relations 

 to D (2) may be shown as follows : — 



Dn 



(10)18291-06 



80622-27 



(1)42953-48 





90032 



92067 



94102 



D 22 



(10)19191-33 



31542-04 



(2)43894-50 



This has the exact appearance of a D set with a \) Y 

 limit of 30622 and separation 920. Bur this limit cannot 

 give the normal separation 920. With the same A the 

 separation would be less, and with any other possible A (i. e. 

 an oun multiple) it could not give exactly the same v. The 

 explanation is that 42953 has for its sequent d 2 (3x8 Y ) where, 

 as before, x denotes the satellite displacement 23 and 43894 

 has the sequent df 2 (2.r§ 1 ), or in other words the correspond- 

 ing seqnents are d 1 {2x8 1 ), d 2 (2x8 l ). 



The existence of S summation series has not been so well 

 established as yet as for the D and F. In Ag, however, we 



