S Prof. W. M. Hicks on the 



Let us take at first those data which depend directly on 

 observed lines and do not require displacements for their 

 interpretation. They are D 22 (2) and the whole set for m = 3. 

 Their means point quite definitely to limits in the vicinity of 

 29469 and 33285. In many portions of the Au spark 

 spectrum the lines are excessively crowded, so that in those 

 regions mere coincidences have little value, as evidence. 

 Fortunately, however, in these particular instances this is 

 not the case. This is indicated by showing in brackets on 

 the right of the lines the separation from the next observed 

 lines on either side. In all the examples they are large, so 

 that the combined evidence is convincing that the limits are 

 close to the values given. It is striking, also, how closely 

 they approximate to the second of the set of alternative 

 values obtained above from quite independent considerations. 

 It corresponds to putting y = — 1 in the data under C, and 

 makes them : 



(C) 



The formula for D n , re-calculated with the new limit, is 



w = 29469-85 — N/{m + '964130 + -033168/>»} 2 . 



It gives for m = 4. . . 10 wave-numbers of 25034*05, 26393*42, 

 27212-05, 27742-76, 28106*24, 28366*01, 28551*06. The 

 question of the existence of lines corresponding to m = l is 

 of special importance for the reason mentioned above. 

 Values extrapolated by the formula for m = 1 rarely show 

 any close agreement with observation, especially when, as 

 now, they should occur in the far ultra red. In this case 

 the law that the extreme satellite of the first line has its 

 mantissa a multiple of A should give a very close approxi- 

 mate value for D 12 and D 22 . This mantissa must be greater 

 than that of D(2), and it is natural to take for the first 

 experiment the multiple just larger — in this case 9 A — and 

 then seek for evidence as to its existence or not. 

 The value of 9 A is 1*025370+ 9 x. This gives 



D 12 = 2733-70-f£-'237.r, 

 D 22 = 6549*06 + £ - *237.r. 





e= 



= ±1-5 + 4-674 







-\ 





A = 



= 113935 + x 











8 = 



= 1406*60 + -0123 



V 





> 



I) 



(00) = 



= 26469'85 + £ 



f= 



±i 



5 1 



\\ 



(oo ) = 



= 30285-41 + f. 







1 

 1 



-J 



