DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



431 



The limit condition is independent of p and can only be modified by in the second 

 decimal place. It gives quite definitely six possible values for S, viz., 1783'52, 1784'39, 

 1785-26, 1786-13, 1787'01, 1787'87 with multiples 512 diminishing by i to 510|. 

 Of these the following can be satisfied by the mantissa difference condition ( 1 ) 

 1783-5 by p = -'8, multiple 70f, not probable. 

 1783'5 by p = I, multiple 70|-, very improbable. 

 The last four by p> '25 < "5, multiple 70^-, equally probable. 

 The others by p>'5<l, multiple 70|-, improbable. 



If WATSON'S readings are really to the nearest unit, p = '5. This probable 

 consideration would largely reduce the limits of uncertainty. It would in conditions 

 (l) exclude the second and with multiple 70j give 1787'0 with p = 0, 178G'l with 

 p = "3, 1785"3 with p = "5. Conditions (3) would then of these give 1787 with p = 0, 

 multiple 440i 178616 with 440f, 1785'27 with 441. All of these have equal 

 probability, but they exclude the 1783 based on HONIGSCHMIUTS' atomic weight. The 

 lowest value 1785'3 would make the atomic weight = 222'1 5 '02, and that of 

 Ra = 226 "15 as compared with HONIGSCHMIDTS' 225 "97. 



Before passing from this series it will be important to get as close an estimate as 

 possible of the two separations. Regarded as oun displacements on the limits they 

 should give some further data for the determination of the oun or, vice versa. The 

 separations given in the sounding operations above are here collected. Errors from 

 WATSON'S, or BALY'S observations will not amount to more than a few decimals at the 

 outside. 



The j/! cluster round 5649, 40, 35 and the v t around 2816. 



In i/j the 49 and 35 differ by 14 and are clearly due to a S t displacement in the 

 limit. We will consider the exceptions in order. In (2) there is an uncertainty 4p. 

 li'p = 1 we get, with other errors close to 35, in this case i/ a = 18"2 + 5p' and a 

 small error in p' brings it to the 16 neighbourhood. In (4) the uncertainty 6p reduces 

 again v a to the 16. In (5) ordinary errors bring v r to the 49 value. In (6) modifi- 

 cation of 10"7 in the middle line brings ^ to 49 and p = "25 brings i/ 2 to 16 or v 1 + v a = 

 normal. In (7) the error allows 35. No. 8 does not seem amenable and may not 



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