278 Dr. L. Vegard on the X-Ray Spectra 



Now the radius of the surface ring is at any rate approxi- 

 mately determined by the equation (30), and by means of 

 the values previously given to q and n of the surface ring 

 we can easily calculate the radius a and compare its variation 

 with the atomic volume curve. 



Such a comparison would immediately show some striking 

 similarities. 



For chemically related elements (q constant) we find, as a 

 rule, an increase of atomic volume with increase of N in 

 accordance with the variation of a. This increase is in par- 

 ticular very marked for the elements Li, Na, K, Rb, Cs, and 

 Mg, Ca, Sr, Ba. 



If, on the other hand, we consider the elements belonging 

 to the same period we find a marked difference between the 

 variation of the atomic volume and that of the radius. 



Let us, e. //., consider the short period from Ne to Ar. 

 These elements should have the same quant-number of the 

 surface ring ; but the number of electrons should increase 

 from 1 (Na) to 7 (01), and the radius should decrease. Also 

 the atomic volume curve shows at first a rapid decrease ; but 

 it reaches a minimum at the element Al, after which it in- 

 creases quite rapidly to meet the most conspicuous maximum 

 at K. Taking one of the long periods we find a similar 

 variation of the atomic volume and, curiously enough, we find 

 no secondary maximum for Cu and Agas was to be expected. 



When we consider the result of this comparison on the basis 

 of our scheme with regard to the constitution of the surface 

 systems we arrive at the following conclusions : — 



The atomic volume is no doubt greatly influenced by the 

 magnitude of the radius of the surface ring ; but besides it 

 is greatly influenced from other causes, which in certain 

 cases may even more than counterbalance the effect due to 

 change of radius. 



The particular manner in which the atoms are grouped 

 together in the condensed aggregate forms is likely to play 

 an important part in this respect. 



Also the variation of the atomic volume is in favour of 

 of our two fundamental assumptions with regard to the 

 constitution of the surface systems : — 



1. All elements belonging to the same period have the 



same quant-number. 



2. The quant-number increases by one unit when we 



pass from one period to the next one. Also, when 

 we consider the atomic volumes, the best agree- 

 ment is got when the quant-number of the first 

 period is put equal to 1. 



