4 Prof. W. M. Hicks on the 



Ag = 30644, and some other considerations led to the adoption 

 of the latter number. It was completely justified by the- 

 later discussion in [IV. J, the links calculated on the foregoing- 

 data being found to be satisfied with great exactness. 



Taking v= 3815-56, D^oo ) =29465-18 + f, 



D 2 (co ) = 33280*74 + + ^i;, the raantissse are 

 D x (oo) 929298- 32-739 f, 



D 2 (x> ) 815338- 27-273 (jf + rfv), 

 giving 



A = 113960-5-466f+27-27rfv±l = 818, 

 whence 



S = 1406*920+ -012- -067 £ + -336 d»>, 



the + ambiguities being due to uncertainties in final digits 

 when using 7-fig. logarithms with 7-fig. numbers. 



With 20858-97 for D 22 , D 12 is v less, i.e. 17043-41. The 

 mantissa of this satellite is -971410-119-60(1: + v) + 26Sp, 

 and of D n = 17125-54 is 981279 — 120-80 f + 16-9 jt>, where 

 dX='0op in each case, '05 A being in each case K. R.'s 

 estimate of their possible error. The difference of these is 



9872 + 1-1-20 f+ 16-9^!— 26-3^ 2 + 119-6 dv 



= 7{1406-920 + 3-365±-14---171f + 2-41jt? 1 



-3-76jt? 2 + 17-l^} = 7S. 



The difference of the two values of 8 is 



3-365±-15--104f+2-41p 1 -3-76jt? 2 + 16*74^, . (A). 



in which dv is not greater than 0'1. The two values of 8 

 therefore agree within quite easy limits of error, and the two 

 results give no means of obtaining closer approximation. It 

 is from this point that the present discussion starts. For 

 this portion recourse must be had to the other general laws. 

 Now two well-established laws are that in the normal 

 case (1) the mantissa of the extreme satellite of the first line 

 in a D series is a multiple of A, whilst (2) the mantissa 

 of succeeding orders differ from one another by multiples of 

 the oun. But in all the elements of this group the mantissa 

 of D ]2 (2) is decisively not a multiple of A. The only ex- 

 planation that appears to offer is that m = 2 is not the first 

 line, but that a set depending on m = l exists in the far 

 ultra red The evidence for this will be considered below. 

 For our immediate purpose it should be noticed that the two 

 relations above necessitate that the niantiss?e of D lines must 



