﻿1068 Mr. R. Hargreaves on Atomic Systems 



§ 2. We may for shortness use the term ion for "positive 

 electron," leaving the unqualified word for the negative 

 electron : the mobility of the latter would suggest an inter- 

 change of terms if it were feasible. 



The feature that the outer ring contains the more massive 

 ions contributes to stability through the protection afforded 

 to the mobile electrons. In part this is due to actual 

 screening, but the main defence lies in the fact that near 

 each electron are two ions, so that external action on the 

 former calls into play a strong counter-action from the 

 latter. 



The angular velocity in the orbit is known when the central 

 force has been found, whether we are dealing with the double 

 ring or a single ring with core ; but in the former case the 

 adjustment of radii requires a preliminary calculation. In 

 each case tabulation is needed when the number n in a ring 

 is small, and an asymptotic formula can be used when n is 

 not small. For the double ring when the adjustment of 

 radii has been made, the angular velocity is given by 



??2 1 &) 2 a 1 3 = Ne' 2 , (ii. a) 



where e is the standard charge and N a number tabulated 

 below. An asymptotic formula (cf. § 13) is 



N ='44l7i + -424^- 1 + # . . (ii./,) 



which is of service from n = 10 upwards. 



For a multiple core +ne, and a ring of n electrons the 

 formula is 



m 2 co 2 a z = N c e 2 , (iii.a) 



where 



N c = -98n--36646>2log 10 n + -02182n- 1 ... (iii. b) 



is an asymptotic formula. The calculations required for N" 

 are more serious than for N c , but the asymptotic formula 

 simpler. 



The value of n for which N c becomes negative lies beyond 

 the range of n required for application to atoms. N c /n is at 

 first greater than N/n, is not much different for n about 30, 

 and then diminishes much more rapidly than N/w as n is 

 increased. As (ii.a) and (iii.a) have the inertias m x and ??? 2 

 respectively it is clear that the numerical relations connecting 

 to and a are very different, and must involve corresponding 

 differences of interpretation. 



