430 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
representatives for m =3, 4 is not surprising as their limit displaced values are 
certainly observed and the change is in full agreement with what takes place in the 
other elements. 
We shall assume in what follows that the preceding allocation is correct, in other 
words the limit is 29964‘20 + ^, the line for m = 2 is 15846 + 2‘5p, and that the series 
belongs to the F type. In that case the mantissa of the limit and of the sequent are 
both multiples of the oun. These mantissse are respectively 913165 —31‘92^ and 
787174 +246p —987^. As both are oun multiples, so must be their difference. This 
difference is 
125991-246» + 68f = 70|-(l787l0-3-49p +•97 f) 
( 1 ) 
= 70f (l78075-3-49p + -97^) 
In which if Watson is correct to nearest unit p is equally probable between +'5. 
It is very unfortunate that here we have to deal with two uncertainties not 
generally met with, viz., on the one hand the uncertainty as to the real value of the 
atomic weight, and on the other the magnitude of the possible observation error in the 
o 
fundamental wave-length, which Watson has only measured to the nearest Angstrom. 
If this had been '\, i.e., p> — iFe above result would show that since 8 lies between 
1789 and 1783, the multiple must be 70|- without any doubt, and consequently ^ in 
the neighbourhood of 1787. The value of ^ is so small, that its term will not affect our 
present reasoning. We have, however, to allow for this uncertainty and a value of 
p = —'7 makes the second multiple = 70fx 1783’2 with a possible S. In this case the 
first multiple gives 70|-x 1789'55, or S just on the improbable limit and it might be 
excluded. The result, therefore, is 
Equally possible, ^<‘5>—'5, multiple =702- and § between 1785’3 and 1788. 
Improbable, but perhaps possible, p = —7, multiple may be 7Of and ^ = 1783‘1. 
Very improbable, p =1, multiple 70^ and S = 1783’6. 
But also the limit and sequent mantissae must also be oun multiples, now 
913165-31-92^ = 512 (l783-52--062^) 
= 511 (l787-016--062^) 
787174+ 246p-98-7f= 44l|-(1782-95+ ’55^--22^) 
= 4401-(1787-00 +-55p--22f) 
( 2 ) 
It might occur to the reader that the last should be a multiple of Aa. But if the 
series is the analogue of the 1864XF, to which the foregoing argument has pointed, 
it should have a line of order m = 1 {n about = 3260). This should show M (As). 
