Series System in the Spectrum of Gold. 5 



be multiples of the oim at least. Usually the oun is so small 

 — or the multiple so large — that no further help to a closer 

 approximation is attainable. In the case of An, however, 

 the oun is so large that the actual multiples could be uniquely 

 determined if the limit were known within about unity 

 (£=1). But in the present case the value of f with our 

 present knowledge may be considerable, and there will 

 necessarily be an ambiguity of a few units. 

 With the above values of A and 8, 



8A+49i8 = 981326±8— ±7-044 % + 2%i'l dv, 

 also mant. of d v =981279- 120*80 f+ 16-9^. 



These are equal within possible errors as they stand, but 

 £ may be so large as to upset the agreement. If the multiple 

 of 8 1 is y larger, 351*7 y must be added, and the condition of 

 equality becomes 



351-7.y.+ 47 + 8 + 73-76f- 16-9^.+ 2347 dv=0. . (B) 



If condition A x 14 be deducted from B the term in dv 

 disappears and 



351-7y + 75*21 ?-50'6jd 1 + 52-6> 2 ± 11 = 0, 

 f=— 4:' 67 y +15 (p having max. values ±1). 



Then iv-=-2±-02--030y--14j» 1 + ; 23j5 s = "2--030y±'4. 



The condition that dv<'\ is thus easily satisfied. 



The results so far arrived at may be stated as follows : — 



i>= 3815-56 + di/ dv<-l 



A = 113960-5-466 f + x x probably < 10 

 o = 1406-91 - -0674 f +- '0123 x 



|= ±1-5-4-674?/ " y = 0, ±1, ±2. j 



It may be noted that if y is as large as 2, f is altered by 9 

 ;and 8 by *6. This would make 8 so different from that 

 determined directly from the atomic weight as to render 

 it improbable, though not impossible (W = 197'20±'07). 

 Certainly y cannot be so large as 3. The only possible limits 

 would then seem to be 



29465-18±l'5, 29469'8'5±1'5, 29474-52 + 1-5, 



with corresponding smaller values. By the preceding con- 

 siderations the choice of the limit has been considerably 

 restricted. 



To arrive at a closer determination, we may attempt to 

 •obtain a more complete allocation of the D series, and have 



>>• (C) 



