the Spectrum of Copper. 459 



the S x (4) has a limit 1*94:0; larger than the others. If there- 

 fore 37169 is the true summation line for observed S 2 (4), 

 its limit should also be 4*94 x larger. This is clearly indicated 

 with w=l making the normal S x (co) = 31523*41. This is a 

 remarkable agreement supporting the previous reasoning of 

 S 1 (oo)=31536-29-12-46^±2 = 31523-83 + 2 with x = 1. 

 The set S 2 (4), S 2 (4) give an intermediate limit which, how- 

 ever, is explained by taking 37410 as the normal S 2 (4), not 

 displaced as is the S 2 (4). The mean would therefore be 

 ix i 4-94 = 2'47 greater than the true, or S 2 (oo ) =31770*79 

 + 1*7 giving S] (co) =31522*35 + 1*7, the same as the others 

 within error limits. There appears no S 2 (2) but a line 

 observed by McLennan X = 1925 or n = 51931*8 + 13 in 

 which all values within ±13 are equally probable is linked 

 to it. In fact e . 51931*8+13 = 50932*0+13 as S,(2) gives 

 :S 2 (co) =31766*68 + 6*5 = 31771*92 so far as the wave length 

 is known. The evidence from the combined difference and 

 summation lines, considering normal lines alone, is thus 

 quite decisive in making S^co ) quite close to 31523*48. 



The D material is not so definite although it supports this 

 value. The sets under D n (3), D 22 (3) give 31524*17 + 1; 

 ..21*56+3-4. Also the doubtful D n (5j is related to a 

 D n (5) which gives D^oo ) = 31522*39 + *8. But in m = 2 the 

 lines XX2276, 2263 as the summation D n , D 2 2 in the table 

 give Dj (co ) = 31537*59+*5. There is however a set con- 

 nected by the z^-link to Di 2 , D22 which agrees with the others. 

 The general agreement in favour of S x (co)= 31523 shows 

 that the lines XX = 2276, 2263 cannot be the D(2) set. Their 

 separation as a Dn, D22 set should be 248*44 + 6*60 = 255*04. 

 It is 254*13+2 as observed. If they represent ( — 5 f 8) D, 

 the separation should be 5|x*06 = *35 larger or 255*39 

 which the observation errors allow, and the normal D set be 

 5fx4*94 = 28*41 less for D n and 5f X 4*99 = 28*70 less for 

 D22. The means then become 14*20 and 14*35 less or 

 31523'39, 31771*31 agreeing with the others. They may 

 therefore be this displaced set, but they must not be used for 

 deducing the limit. 



The result is that the limit is within a few decimals of 

 31523*4. The closest limits of variation are those given by 

 m = 3, viz. S!(co) = 3152348 in which the possible error is 

 + *7 but the actual error, judging from the combined results, 

 is probably much less and about '02. The same value is also 

 given by certain p (1) — /, p(l)-\-f combinations considered 

 below (p. 465). For one of these sets — /(4) — the observa- 

 tion errors are small and give S : (co ) = 3 1523*475. In taking- 

 then the limit as 31523*48 + £ the value of f will not be more 

 than a few decimals. Using this as limit and the accurate 



2H2 



