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XLV. Atomic Frequency and Atomic Number. — Frequency 

 Formulce with Empirical Constants. By H. Stanley 

 Allen, M.A., D.Sc, University of London, King's College*. 



§ 1. Introduction. 



A RELATION between the characteristic frequency of 

 .ljL an element in the solid state and the atomic number 

 is to be expected on theoretical grounds. In a paper 

 communicated to the Royal Society the author has sought 

 to establish such a relation, and it will be convenient to 

 summarize briefly the conclusions already reached. 



1. If N denote Moseley's atomic number for an element 



and v the characteristic frequency deduced from 

 determinations of the specific heat in the solid state, 

 simple relations are found to hold between the values 

 of the product Nv for different elements. 



2. For 26 metals it is found that the product can be 



expressed in the form 



Nv = nv A , 



where n is a whole number and v A a constant having 

 the value 21*3 x 10 12 sec. -1 (approximately). 



3. The same rule is obeyed in the case of certain non- 



metallic elements. 



4. Similar results are found when the characteristic 



frequency is calculated from the elastic constants of 

 the solid by Debye's formula. The value of the 

 " frequency number," n, thus obtained is not in all 

 cases the same as that deduced from the specific heat. 



5. Application of the theory of probability shows that 



there is but a small chance of the product approaching 

 so nearly to integral multiples of a constant frequency 

 by a mere accident. 



6. It is found that the atomic numbers of Moseley give 



better agreement with the proposed relation than do 

 the atomic ordinals of Rydberg. 



7. The empirical results have been discussed from the 



standpoint of the Quantum Theory, and it may be 

 suggested that the integer n is related to the number 

 of electrons concerned in determining the crystalline 

 space-lattice of the element in the solid state. 



In the present communication an attempt is made to 

 extend these results by considering other methods of deter- 

 mining the characteristic frequency. 



* Communicated by the Author. 



