-( 



266 Investigation of Stability of Dr. A . W. Stewart 9 s Atom. 

 is always negative for values of r greater than a, and 



JL . 1 



(a- 6(1 — e))~ (a-6(l + e)) 2 



/ 46*6— 4«6e \ 



" ~ \(a-6(l-e)j 2 (a-6il + e))V ' 



since & > a, the above is negative. 



Hence whole quantity in bracket in first equation is 

 negative and the equilibrium condition is impossible. Here 

 again the inner ring would decompose spontaneously when 

 the above configuration was reached. 



Summary and Conclusion. 



(1) Conditions for the equilibrium and stability of Dr. 

 Stewart's atom are obtained. They are then applied to 

 several special cases among the simplest atoms. 



(2) It is found that in each case tried, equilibrium cannot 

 be maintained indefinitely for the inner ring of negative 

 electrons, even in the entire absence of external perturbing 

 forces. Thus, on the atomic theory considered, instability is 

 placed to the account of those elements which are found to 

 be the least unstable in reality. 



(3) Dr. Stewart adds a note to his description of the atom 

 to the effect that it is not of material consequence to his 

 theory if the relative positions of the inner ring of negatives 

 and the ring of positives are interchanged, or even if these 

 positives and negatives form a kind of double-star system. 

 The equations obtained will still hold (due attention being- 

 paid to sign) for the former alternative arrangement. The 

 inner ring (in this case the positives) would still break up, 

 and this arrangement seems more unlikely than the original 

 one, since a copious supply of separate positive electrons 

 would be continuously given off. Such an effect has not, up 

 to the present, been observed. 



(4) The author hopes to investigate the second alternative 

 given above at some future time. The success of Dr. 

 Stewart's atom in explaining chemical phenomena makes it 

 reasonable to hope that, by some such modification as that 

 mentioned, the atom may be made more amenable to ordinary 

 dynamics and more successful in explaining physical 

 phenomena. 



Physical Department, 

 University College, Nottingham, 

 May 12th, 1919. 



i 



