Value of the Silver Oun. 303 



can thus obtain $ accurately in terms of f, p l9 p 2 . We know 

 that f must lie between ±12, but this gives far too much 

 latitude for our purpose, and before being of use it is neces- 

 sary to obtain closer limitations to f. For this purpose 

 recourse is had to certain relations which confine the possible 

 values of f within ±2, These will be considered in due 

 course. 



It is convenient to use the letter /it to denote the series of 

 digits in the decimal part of the denominator when VD (m) 

 •or d (m) is thrown into the form N/(d#n.) 2 and no ambiguity 

 will be introduced by using the word mantissa for it — in fact 

 the real mantissa = /j, x 10 ~ 6 . 



The wave number 18291-0122 - -00334/? with the limit 

 30644 is found to give 



^=979595 21— 120'59(f + -00334/?). 



The corresponding //, for D J2 is found by deducting 23 6\ 

 from this. Now S = 4o\ = 421-07 + e where 421-07 is the 

 value already known and e is the small correction it is our 

 object to determine. This gives for D 12 



At = 977174-0G-5-75^-120-59f~-40p, 



whence d 2 (2) = 12373*6888 -f'048* + -00333;? +' 1-0023 £ 

 and 



D ]2 (2) = D(oo)-d 2 (2)=18270-9112--048e--0033p--0023f. 



The difference between this and D 22 (2) gives v, the doublet 

 separation. Thus 



v = 920-4383 + -048 e + -00333^ - 00368 p 2 + -0023 f . 



This is now used to find the value of A. The limits are 

 30644-6000 + {• and 31565-0383 + 1-0023 £ + '048 e + '00333^ 

 — -00368p 2 . These are thrown into the form N/(den.y 2 and 

 •the respective values of fx are 



for Di(w) 891807-06 -30-867 f, 



Pa(oo.) 864020-40- 29-600£-l-417^--0984/) 1 + -K)86/v 



The difference gives 



A = 27786-66-l-267f + 1-417^ + •0984 i ? 1 --J086 i > 2 = 668, 



.-. 5 = 421-0100--0192f + -0214^-H-001o/> 1 --0016/) 2 

 = 421-0700 + ^ ; 



whence e = — •0l>13-"0196£ + -0015^!— 0016j» 2 , 



3 = 421-0()87--i)196£-f0015y> l --0016/> 2 , 

 A = 27786-57-l-293f + -l(^ 1 - i >o). 



Y 2 



