314 . Prof. W. D. Harkins on the 



number 16 or less the condition for bigb abundance of an 

 atomic species, and presumably therefore the condition 



ESSENTIAL FOR A HIGH ORDER OF STABILITY, IS THAT THE RATIO 



total number of negative nuclear electrons /AT ,-n. 



— — j - x — ^-rp -, p— or (N/P) SHALL 



total number or positive nuclear electrons v ' 



BE equal to 0*5, or in the most stable light nuclei one 

 negative electron is equal to two positive electrons in 

 combining power. 



Before considering further the data concerning the 

 abundance of the various atomic species, it will be well to 

 consider the general relations which exist between the 

 values of the functions N/P and some other variable. 

 PI. XII. fig. 1 represents this function on the Y-axis, and the 

 value of P (atomic weight or number of positive electrons) 

 on the X-axis. It indicates that in no atomic species is 

 N/P less than 0'5. This ratio increases with increasing- 

 values of P, and therefore with increasing values of M, or in 

 the language of hypothesis as the nucleus becomes more 



POSITIVE WITH REFERENCE TO ITS NET CONTENT OF POSITIVE 

 ELECTRICITY, IT BECOMES MORE NEGATIVE WITH REFERENCE 

 TO ITS RELATIVE CONTENT OF NEGATIVE ELECTRONS (N/P). 



Thus while an increase of net positiveness alone (with N/P 

 constant) would cause the nucleus to become unstable, the 

 stability may be maintained by opposing this change by an 

 increase in relative negativeness, 



Isotopic Numbers. — An inspection of fig. 1 (PL XII.) 

 reveals the fact that all of the pure atomic species represented 

 fall either upon one of a set of 54 rectangular hvperbolas, or 

 upon the X-axis itself, the latter representing a value of 0*5 

 for N/P. To this latter, the lower asymptote of all of the 

 hyperbolas, the number zero will be attached, while the 

 hyperbolas, as may be seen, have been numbered beginning 

 with 1 for that closest to the asymptotes, up to 54, the 

 hyperbola upon which uranium of atomic weight 238 is plotted. 

 The numbers thus obtained, which vary * from to 54. 

 will be designated as the isotopic numbers of the atomic 

 species. It will be shown that the stability and composition 

 of atom nuclei are related in an important way to this 

 number, while there is no such relation to the atomic 

 weight. Thus the atomic number classifies the atomic 

 species, the atomic weight merely serves to index them. 



The three isotopes of magnesium may be listed as 

 Mg 12 24 , 12! 25 , and 12 2 26 . It will be seen that the isotopic 



* Another plot will show that — 1 is the isotopic number of hydrogen 

 and of helium of mass 3. 



