DR. W. i\r. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 4(55 
All independent datum is necessary to fix the value of which at present we know 
cannot be greater than a few units. In the other gases this is obtainable by the 
conditions that the mantissa of/(l) is a multiple of Ag and that of F ( oo) of The 
value of F (l) is known with great exactness, probably to within less than ‘001 A. 
Priest gives X = 5852 4862, Meissner ‘4875, B.M.M. ‘488. They all agree within 
001 of 487 so that the wave-number of F (l) is 17082'0242-f-'0029jo with p within 
±1. But here we have to answer the question whether our first F line 17082 is 
really the first of the series. If this F series—a very marked and definite one— 
belongs to the 1864XF type it has its first line for m = 1 in the ultra-red (calculated 
n = —8168 62X = 12242) and far beyond the reach of any sounders. This un¬ 
certainty will therefore have to be kept in mind. The mantissa of 17082 must in any 
case be a multiple of and may be of A 2 (if it is the first F line). In addition the 
D set 20551 may belong to that D satellite set with M (Ag), or since the j/j separation 
is modified, differ from a multiple of Ag by a few ouns only. We have then 
Mantissa F (00) = 855630‘30-29‘130f = M((ij) and possibly M (A 2 ) 
„ ■ / (1) = 725012‘36-92‘2^57f-‘2675p = M(cii) and possibly M (A 2 ). 
The term in p will not affect our immediate purpose and may be omitted. There is 
evidence for ‘33. Also A 2 = 267‘708-0124^+.'r with x < ‘002. We find 
27 O 8 A 2 = 724953‘26-33‘58f-92708a;, 2708a; <5‘4 
3196 A 2 = 855594‘77-39‘63f+3i9G^r, 3196 .t<6‘4 
Hence 
Mantissa of F (00) = 3196A2-t35‘5-M0‘5f—3196a; 
„ / = 2708A2+59‘10-58‘68^-2708a-. 
A first definite result is that 20551 is not a D line of the M (A 2 ) type. Its mantissa 
must differ from such by at least 7 or 8 ouns. The coefficient of f is so large that 
the actual oun multiple cannot be uniquely decided. Further f cannot follow the A 2 
multiple law unless f be of the order 1, or three times our estimated limit of variation. 
We cannot say that it is impossible. If however this F line is the first of the series 
then ^ must be of this magnitude. It is seen that no further definite and certain 
information can be obtained. It will however be of some interest to follow out the 
assumption that its mantissa is a M (Ao). In this case put l-f^ where now ^ is 
small,' and 
•42-2708a--58‘68f-‘2675j-j = 0 
The uncertainties in fare now ‘42 +5‘4 —59f ±’26 = 0, or f < ‘1. 
Ao = 267-6957-‘0124f+a;. ' 
In conclusion some reference is necessary to the series due to Rossi.* These 
Log. cit. 
