DE. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 
431 
The limit condition is independent oi‘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 ^ to 510f. 
Of these the following can be satisfied by the mantissa difference condition {I) 
1783‘5 hy p = —’8, multiple 70|-, not probable. 
1783‘5 byp = 1, multiple 70|-, very improbable. 
The last four byp> —■25<'5, multiple 70^, equally probable. 
The others byp>'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 70|- give 1787'0 with p = 0, I786‘l with 
p = '3, 1785‘3 with p = '5. Conditions (3) would tlien of these give 1787 with p = 0, 
multiple 4405 -, 1786T6 with 440f, 1785‘27 with 441. All of these have equal 
probability, but they exclude the 1783 based on Honigschmidts’ atomic weight. The 
lowest value 1785’3 would make the atomic weight = 222T5 + ‘02, and that of 
Pta = 22615 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. 
F. 
F. 
1 . 
5649 •71 , T Q , 7 
35-7 J +1 + 
2816 + 3/- l-9i? 
9. 
10 . 
5649-6 
50•9 + dv 
2795 + 4^j 
2 . 
40 • 6 + 4jj + du 
14 • 2 + 5/ - 4jp 
11 . 
55 • 2 + - du 
3. 
48 • 31 + de - dv 
14-9 
. 12 . 
Zb-m + dv 
2802 -l+de- dv 
16 • 0 - + dv 
13. 
36-6 
33-0 
4. 
48•6 + du 
22 + 6 » 
5. 
52•8 + dv 
17-4 
6 . 
59 • 7 + de - du 
793-6 + 6 i) 
7. 
40 • 4 + 6 p + dv 
8 . 
42•0 + dv 
The cluster round 5649, 40, 35 and the 1/3 around 2816. 
In the 49 and 35 differ by 14 and are clearly due to a dj displacement in the 
limit. We will consider the exceptions in order. In ( 2 ) there is an uncertainty 4p. 
Ifp = —1 we get, with other errors close to 35, in this case 1 / 3 = 18’2 + 5p' and a 
small error in p' brings it to the 16 neighbourhood. In (4) the uncertainty 6 p reduces 
again to the 16. In (5) ordinary errors bring to the 49 value. In ( 6 ) modifi¬ 
cation of 107 in the middle line brings to 49 and p = '25 brings to 16 or V]^ + V 2 = 
normal. In (7) the error allows 35. No. 8 does not seem amenable and may not 
VOL. CCXX.-A, 3 N 
