DR. W. M. HICKS : A CRITICAL STUDY OF .SPECTRAL SERIES. 467 



The formulae calculated from the first three lines of each series give 



n = 24104'67-N/{m+ -973110 + '016932/m} 3 

 n = 24104M8 -N/{m+ '987215 + '014948/m} a 



The O C values for these are given in the above list before the wave-numbers. 

 They are larger than we should expect the observation errors to be. If, however, the 

 limit be reduced by '40 and p., a. calculated from the first two, the O C for m = 4 

 is '04 and zero for all the others, m = 5... 8. For m = 9, using L.D. 23 168 3 167 

 as the observed for the first of the pair the O C is '2. The agreement for all is 

 therefore exceedingly close except for m = 4. The calculated wave-number for this is 

 19677 '50 which makes the separation 16672 and more in step with the others. The 

 uncertainty in the limit 24104'67 must therefore be very small. 



The doublet separations show a tendency to converge with increasing order, but this 

 is clearly due to the fact that the constant separation must be taken between the 

 strong first line and the weak second. After m = 3 the weak is not seen and the 

 observed separation is not the true one but that between the first and the second 

 strong one. The separation in the second series is somewhat larger than in the first, 

 that for the first being 167'17 and for the second 168'2504 (mean for m = 2, 3). 

 These require limit mantissa? changes of 7354 in the first where 308^<5 = 7354'!, and 

 of 4779176 extra for the other where 3(5= 46'41. The separation 173 between 

 the four satellites in the first doublet must be due to displacement in the sequent. It 

 requires a mantissa change of 209 and 14^5 = 209 - H. 



These considerations point strongly to the conclusion that the series are of the 

 F type. Fortunately, owing to the fact that the first line of the first series has been 

 very accurately measured by B.M.M., as A = 8495'380 I.A., it is possible to test if the 

 mantissa of/(2) is M (A 2 ). Taking the observation error as '00 Ip, the wave-number 

 is 11767'8680 + '0014p. Its mantissa with limit 24105'0731+ (the I measure of 

 4'2700 E.) is 



981622'48-120'87ffl7p = 3667 {267'6910- '03296+ '00005^} = 3667A, 



within the uncertainty of 



The first line of the second series has not been measured so exactly. Its 

 \ = 8418'38-'02p; n = 11875'50 + '028p ; mantissa = 13092- l'56+3'52p larger 

 than the other. Now 49 A 2 7^ = 13091 '8. Hence if the two limits are the same 

 24104'89 (i.e., put = -'19), the mantissa is larger by 49A 2 -7c$ 1 + '51 + 3'42p. It is 

 satisfied by p = '14 or d\ '002. But it is possible that these F are due to 

 independent groups, i.e., that the sequence of the second series also depends 

 on a whole multiple of A a . This cannot happen unless the two limits are 

 different, which in fact seems to be the general rule. If the limit is displaced 

 by y$i, f is 3'6l7//44'25 = '082y, and the mantissa difference from 49A 2 is now 



8 B 3 



