of the Stability of Dr. A. W. Stewart's Atom. 251 



following limitations, facts, and assumptions are used in the 

 investigation : — 



(1) The case considered is that in which all the inner 

 negative electrons are in a single ring, similarly the 

 positives in a single ring and the cometary electrons 

 in a single ellipse. This would probably be the case 

 for the atoms of simplest structure and lowest atomic 

 weight. 



(2) Since the presence of elliptical orbits requires that 

 the law of force should be that of " inverse squares/' 

 this law will be used as the foundation of the 

 investigation. 



(3) The total number of negative electrons in the atom is 



equal to the atomic number of that atom. 



(4) The number of cometary or valency electrons is as 

 given in the following table : — 



Group in Periodic System . 







1 l 2 3 4 



1 



5 

 5 



-3 



+ 5 



6 

 6 



+ 6 



7 



7 



+ 7 



8 



No. of Valency Electrons... 









 



12:3,4 



-flt+2 +3 +4 

 -7 -6 -5 -4 



~ 1 



Valency 



The theory is developed generally and conditions for 

 equilibrium and stability are obtained. These conditions are 

 then applied to special cases on the assumptions (3) and (4 ) 

 given above. 



Conditions for Equilibrium* 



Let no. of positive corpuscles in ring = ^"> 



no. of negative electrons in inner ring =>*, 

 no. of negative electrons in outer ellipse —n u 



then N = /i + -»i, 



radius of inner ring of negatives =a, 



radius of positive ring =r, 



major semi axis of ellipse =b, 



and eccentricicy of ellipse =e. 



Consider the equilibrium of an electron in the inner ring. 

 It is in equilibrium if the net force due to the attractions 

 and repulsions of the other components of the atom is equal 

 and opposite to the centrifugal force on the electron. 



