846 



LORD KELVIN. 



§ 20. Except the cases of § 18, the forces with which the strings are 

 stretched are the same for ail the electrions of each case. Hence if we now 

 discard the strings and place the electrions in an atom on a spherical surface 

 concentric with it, its attraction on the electrions towards the centre takes 

 the place of the tension of the string, provicled it is of the proper amount. 

 But it does not secure, as did the strings, against instability relatively 

 to radial displacements, différent for the différent electrions. To secure 



% 6 2 T 



the proper amount of the radial force the condition is — -3-=7 7 ;where 



i dénotes the number of electrions; e the electric quantity on each (and 

 therefore, § 8, ie the electric quantity of vitreous electricity in the atom); 

 r dénotes the radius of the spherical surface on which the electrions 

 lie: a the radius of the atom; and T the tension of the string in the 



e 2 



arrangement of § 17. We have generally T = q~ where q is a nume- 



ric depending on the number and configuration of the electrions found 



in each case by geometry. Hence we have - = iM % for the ratio of 



the radius of the smaller sphère on which the electrions lie to the radius 

 of the atom. For example, take the case of eight electrions at the eight 

 corners of a cube. T is the résultant of seven repulsions, and we easily 



find q = ^^V^ "^"■^^ T f~^) anc ^ nna % ~ = '6756. Dealing similarly 

 with the cases of two, three, four, and six electrions, we have the fol- 



lowinff table of values of ( — ) and -: to which is added a last column 



\&/ a, 



showing values of i 2 — — = 2 — , beins; -4r of the work required to 



D e 1 



remove the electrions to infinité distance. 



