10 Prof. W. M. Hicks on the 



either o£ the above lines into the observed regions. Their 

 values e =^(l)(-2A)-p 2 (l)(2A), « = s (1) - « (1) (A), 

 v=s(l)( — &)— s(l) can be calculated from the values of A 

 andy>(l) given above and with the S(co ) =29469'85-f-f are 

 £ = 17252-31, ^ = 1134077, *'=14534'05, with respective 

 changes 10*25, 9" 17, 13"32 per oun-modification. It is shown 

 in [IV.] that each series line is linked to long sets of other 

 lines by these separations, and that successive <?, u or e, v links 

 are very common. If, then, to an unseen line n we observe 

 another at say e + n, it is an indication — though not a proof — 

 that the line n exists. If several such links are found 

 together the evidence is greatly strengthened. When a link 

 is added to a wave-number a it is written after it, if sub- 

 tracted then it is written before it. Thus 2733 . £ = 19987, 

 or £.199^7 = 2733. In the following the calculated values- 

 are given in [ ] and the observed set beneath (with separations 

 from next observed lines as in Table I.) . — 



v, 2733-70. v= [17667-75], 



(4)17675-53(23,16) 3814-84 (21490-37)= (3r) 21499-65 (-^(66,41) 



25223 

 (In) 17927-76 (7,31) 



u, 2733-70. u= [14074-47] ; 6549. u= [1788977]. 



outside obs. (4r) 17890-37 (11, 7) 



e, 2733-7. e = [19986-0]. 



(2) 19988-97(14, 112) 3816 59 C2n) 23805'56 (45, 75) 

 [20240] not obs. 



The v sounding gives a satisfactory complete set if the D 22 

 be really an oun displacement on the D 2 sequent as indicated. 

 The oun on d 2 produces a change of 9'285 and on d x of 9'155. 

 As additional evidence for the D 22 (l), may be added tlie 

 e-tv sounder, i. e., the e sounder for the above set. We find 

 c(l)38746-77±l'5 = 21494-46 + l-5. The next line to this is 

 (1) 38757-29±l"5, which is equivalent to an oun displacement 

 on the sequent, and is the corresponding line linked by e to 

 21504-98. 



The u link is not large enough to reach the D 12 , D n lines. 

 It indicates, however, as is seen, D 22 , This line 17890 is also 

 associated with two lines ahead by e and v links. 



In the e sounding again we get a good indication. There 

 is no observed line, however, corresponding to D n (l).£. 

 The nearest is (2n) 20200'35 (100, 117). Numerically it is 



