842 



LORD KELVIN. 



tion of A draws the electrion from the centre of À ; at first very slightly, 

 but farther and farther as the distance between the atoms is diminished. 

 What will be the position of the electrion when the distance between 

 the centres is, as in fig. 4, 2#'? Without calcul ation we see that tlie 

 electrion would be in equilibrium if placed at the point in which the 



Fig. 4. Fg. 5. 



ce' = 1 C'C = 2 CE = '38 C'C=Ï8$ CE = Q-m 



surface of Â is eut by the line of centres; but the equilibrium would 

 be obviously unstable,, and a simple calculation *) shows that the stable 

 position actually taken by the electrion is *38 oc from C , when the 

 distance between the centres is 2& (fig. 4). If the distance between the 

 centres is now diminished from %a! to 1\89#' (û& being now supposed 

 to be anything less than '89x) the electrion cornes gradually to 

 distance "63#' from C (fig. 5); its equilibrium there becomes unstable; 



') Denoting by ^ the distance between the centres, and by X the force on 

 E when its distance from C is x\ we have 



1 X 



Hence for equilibrium — j-= — — „ . This is a cubic for x of which the 



{£ — x) a 



proper root (the smallest root) for the case Ç = 2 a' is '38 a'. The formula for 

 X has a minimum value when Ç — x = a! 2, which makes 



-a- 



Hence the value of x for equilibrium coincides with the value of X, a minimum, 

 and the equilibrium becomes unstable, when ^ is diminished to — - — oî = l'890<a:' 



u 



\$ 2 



For this, the value of x is a' = "63 « '. 



