to have the Properties of Polonium or Radium. — 533 
f£§12. Going back to fig. 1, alter to make the two circles 
touch one another in e; and for simplicity suppose the two 
atoms held fixed in this position ; ¢ is unstable in the central 
position, but if disturbed ever so little to either side it will 
vibrate between the two; and by giving out etherial waves 
will come to rest in either of the atoms at the point in the 
line joining the two centres at which the attractions on the 
electrion are equal and opposite. The distance @ of this 
point from either centre is given by the equation 
Ce aa 
ror (2r—«)” 
where m denotes the quantity of vitreous electricity belonging 
to each atom. ‘This is a cubic equation of which one root is 
«=r: its greatest root does not belong to this problem: and 
its least root is y=7(3— V5)/2=°382r, which is the required 
distance of the position of stable equilibrium from the centre 
of atom in which the electrion rests. 
§ 13. Considering now the @ rays of Radium, look to 
fig. 2. We have 2¢ of resinous electricity and je of vitreous : 
requiring fe of vitreous for neutralization. The simplest 
way of applying this, which has also the advantage of con- 
verting into stability the instability of the electrions of fig. 2, 
is to take an atom of very large radius endowed with vitreous 
electricity to an amount e, and place it concentric with the 
smaller atom shown in fig. 2. This addition gives us a non- 
electrified combination of two atoms and two electrions all 
in stable positions with the electrions slightly inside the 
boundary of the smaller atom as shown in fig. 2. For 
brevity denote by A the smaller atom and by B the larger : 
and by R the radius of the larger. 
§ 14. The larger is R/r, the smaller are the distances of the 
two electrions from the boundary of A inwards ; and the 
smaller and the narrower is the range of their stability ; and 
: Sel tiie (ait | 
the more nearly correct is the estimate g,? 2 §8 for the 
Y 
energy of the explosion, when an explosion takes place. By 
making 7 small enough we may make the explosive energy 
as great as observation shows it to be. 
§ 15. Thus in $$10, 13 we have two un-electrified mole- 
cules, which, if put together in any substance, would give it 
the a, 8 properties of Radium. There are many other plans, 
some no doubt very much simpler than the combination of 
these two now suggested, for a combination of atoms to give 
the properties of Radium. it is indeed easy enough to 
design a single atom possessing vitreous electricity in a fixed 
