DE. W. M. HICKS: A CRITICAL STUDY OF SPFXTTRAL SERIML J175 



D 13 gives denominator = 31 x 29731 '0, and the latter factor is 



7410-87r' = 82x90'375w a , 

 which is much closer to the probable value of the ouu, and moreover 82 is the correct 



rmiltiple to give 54 x 543'816w 3 for A, + A^ which has been taken as a basis for 3. 

 This value of A is supported by the discussion of the F series below. 



Al. As the order differences are all multiples of A, and there may therefore be 

 some doubt as to the real existence of satellites the values for D, t and D,, are 

 inserted. The denominators for the two only differ by 4<J = 108, or the olwerved by 

 96. As the A differences can only refer to the D n set, it would seem that these 

 should be taken as the normal lines giving 361777 as the value of the oun. 



In. Neither I),, nor D 1:J are exact multiples of A although they are very close to 

 22A. D, 2 is 1722 x 477'1 1, or 1723 x 476'83. If these be taken as multiples of the 

 oun, they give the oun as 362'01 and 36T80 in place of 36T94 of Table I., but the 

 multiples are too large to found any conclusions upon. It would rather seem that 

 there is some displacement from a typical multiple. Using A as given in Table I., 

 viz., 37684, 22A = 829048. So that D w = 22A-7455 and 7455 = 16f$-177. If it 

 is 22A 16(5 exactly, A becomes 8'04 less and the oun 361 '87 lw* in place of 

 36T947. The value of D,.j+165 is therefore inserted. If the typical term were IG& 

 higher, the order differences would run 72<5, 62S, 508, 50<S, in place of 58$, 62<5, &c., 

 and hence more in line with others. 



Tl. Neither the observed nor the supposed collaterals are multiples of A. They 

 are expressed as multiples of S. Although they are large multiples, thir values are 

 quite definite provided we know a priori that the denominators are multiples as 

 a fact. If the multiple be altered by unity, the resultant quotient cannot come 

 within the limiting values of the oun. 



If the normal D,., (2) = 7A = 939078, the order difference over D Ii( (3) would be 

 939078-888643(89) = 5043589, and 33^=134^ = 50495, so that the order 

 difference would come out as usual a close multiple of <V All this group seein to 

 show the same kind of irregularity. 



O. There are three separate series, see data for Table II., differing by multiples of 

 A!, just as iii the order differences. A, is too small to test the multiples of the 

 denominators themselves. 



S. The D(2), D(3) lines for S and Se are beyond observed regions. Sulphur 

 however shows no satellites, and we may surmise therefore in analogy with others 

 that the differences for D (2), D (3), D (4) are like the others multiples of A, or A,. 

 As a fact, D, (4) is a clear multiple of A,, and the surmise is justified so far as A, is 

 concerned. The value of is not very certain. 



Se. Se apparently has satellites, and the order differences are only multiples of S. 

 It should not therefore be expected that D, (4) or D 3 (4) should be a multiple of A,. 

 Nevertheless D! (4) is clearly such a multiple and is entered in the table. 



