442 DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



displacements so analogous to those in X is evidence that the links in question (5640, 

 1864) are of analogous type. We have already seen in X that these separations occur 

 as links, as well as direct displacements on sequences present in the wave-number. 

 Let us determine the F limit required to give a separation in the correct neighbourhood 

 with a displacement 5A 2 . The conditions are that not only must the 5A 2 give the v l 

 but since it must belong to a d(l) sequent, the mantissa of the limit itself shall also 

 be an oun multiple. The result is that the limit should be within close limits of 

 29617 and that then the v l will be close to 5648 one of the most probable values found 

 on p. 431. But this 29617 = F(oo) = d (l) should belong to a D line 50403-27917 

 = 20786. Now there is an observed line (0) 20784'31 (W.) with another at 

 (7)20750-34 (W.) or (7) ...5270 (R.) behind it. Taking 20784'31 its sequent is 

 29618'69 and mantissa 924298 or 11133 above that of 29964'20. Now 6S = 11169 

 and the difference 36 requires a change in wave-number dn = 110 or d\ = '25 A. 

 The line was only read to 'lA so that this error is permissible. The F(oo) is then 

 29617"57. The 5A 2 displacement on this gives 3526616 or a separation 5648'59, 

 and on this it will be found that an extra 2A 2 +5^ gives v 2 = 2810'97 = 2811 say. 

 Further a change of S } on 5A a or 2A. 2 +5S l produces changes in v ly v z respectively of 

 17'88 and 20'00. This accounts for the concomitant value of 563071, and 2831 also 

 observed is due to 5Ai Si, and 2A 2 +6(5 1 precisely those in X. 



The Value of the Oun. The data for the evaluation of the oun are : 



(1) The triplet separations and S(o). The v lt v, 2 are not determinate directly 

 from S lines and consequently no exact values can be obtained from observation. The 

 general argument on p. 433 is in favour of 5371, 2649, or about 3 larger according to 

 limit. These are strongly supported by the set of lines on p. 437, clearly a linked S (l) 

 or an independent S (l) set showing also the displaced S 3 , S 3 by W. and R. 

 respectively. These values point to S = 1787 "0. 



(2) From the F and P series giving definite F(oo)= 29964'20 and/(l); p. 430. 

 The definite result is a limitation of S to one of six alternative values, of which four 

 between 1785'26 ... 87'87 are equally probable, the ambiguity being due to imperfect 

 measurement. This argument is independent of the values of i/,, v 2 . 



(3) The mantissa of the D 13 line 16725 is 25A 2 + ^ and that of the D 23 line 

 22079-34 is 25A 2 . This gives 



A 2 = 3216G-44-l 1 07-l'07d*i+"21p, 



3 

 Here probably 



, or, say. 

 $= 1787'024-05. 



These three determinations are all independent. 



