DE. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 465 



An 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 A 2 and that of F ( co) of S } . 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 + '0029p withp 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= 8168'62A = 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 (A,), or since the /, separation 

 is modified, differ from a multiple of A 2 by a few ouns only. We have then 



Mantissa F ( <) = 855630'30-29'130 = M(^) and possibly M (A,) 



/ (1) = 725012'36-92'257^- '2675p = M(^,) and possibly M (A,). 



The term in p will not affect our immediate purpose and may be omitted. There is 

 evidence for < '33. Also A, = 267708-0124+.r with x < '002. We find 



2708A, = 724953'26-33'58f +2708,r, 2708.r < 5'4 



3196A 3 = 85559477-39'63+3196.r, 

 Hence 



Mantissa of F( oo ) = 319GA, + 35'5 + 10 



2 + 59'10-58'68^-2708.r. 



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 is so large that 

 the actual oun multiple cannot be uniquely decided. Further / cannot follow the A 2 

 multiple law unless 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(A 2 ). In this case put = 1 + ^ where now is 



small, and 



> 42-2708cc-58 1 68^- > 2675jp = 



The uncertainties in are now 425 > 4-59'26 = 0, or < '1. 



A 2 = 267'6957- > 0124+aj. 



In conclusion some reference is necessary to the series due to Rossi.* These 



* LOG. cit. 

 3 R 2 



