DR. W. M. HICKS : A CRITICAL STUDY OF SPECT1CAL SEKLES. 407 



As a final result the evidence would seem conclusive that D(oo) for Au is 

 29465'187, that A = 81* = 1139Gl31'5y, and that the satellite separation is 

 produced by 28^. 



Summary. 



It must be confessed that much of the foregoing discussion is of a problematical 

 nature, and that, in fact, some of the suggestions offered are incompatible with one 

 another. This is no objection in a preliminary search for general principles, as the 

 raising of questions is only next in importance to answering them. Nevertheless, 

 some results appear to be well established and others to have considerable evidence in 

 their favour. Amongst the first are 



(1) The dependence of the spectrum of an element on its oun, a quantity 

 proportional to the square of its atomic weight and which prolwbly does not differ 

 from S 1 = 90'4725M> 3 by more than '01310 2 where w denotes one-hundredth of the 

 atomic weight ; 



(2) The direct dependence of the ordinary doublet and triplet separations on 

 multiples of the oun ; 



(3) A similar dependence of the satellite separations in the Diffuse or the 1st 

 associated series on multiples of the same quantity ; 



(4) The existence of collateral displacement, whereby new lines are formed by the 

 addition or subtraction of multiples of the oun. Until, however, the laws which 

 govern the formation of collaterals are more fully known, it is not safe to assume that 

 any displacement indicated by mere numerical coincidence corresponds to the physical 

 change such collateral indicates. Nevertheless, many cases of clear displacement of 

 this kind, involving considerable multiples of A, especially in the F series, are given 

 which serve to give more accurate values of the oun. 



The conditions which govern the various multiples of the oun which enter in the 

 various separations have not been determined. It is probable, however, that the 

 multiple for the doublet, or first two of a triplet, in the two sub-groups of the 

 n th group of elements contain 2/H-l and 2w + 2 respectively as factors. 



It is probable that the mantissa of the normal first line of the Diffuse series, the 

 last satellite, when such exists, being considered as the normal, is a multiple of A, 

 and it is possible that its magnitude has some general relation of approximation to 

 that of the corresponding F series, which again may depend directly on a group 



constant. 



It is possible that the wave numbers of the lines in the Diffuse and F series may 

 not depend directly on a mathematical function of the order m of the line, and it is 

 probable that this is the case when there are no satellites, the differences now being 

 multiples of the A themselves. 



In the discussion of the material it has been attempted to keep the mind as free as 



