214 
Proceedings of Poyal Society of Edinburgh. [sess. 
in contact with it, repulsion at distance between centres less than 
£ and attraction at any distance between £ and I. 
Assemblage I. 
Assemblage II. 
Distances be- 
tween centres 
of nearest 
atoms for 
maximum and 
minimum 
values of w. 
Maximum and 
minimum 
values of w. 
Densities. 
Distances be- 
tween centres 
of nearest 
atoms for 
maximum and 
minimum 
values of w. 
Maximum and 
minimum 
values of w. 
| 
Densities. 
Law of Force according to Curve 1. 
1*16 
8 ’28 (max.) 
’904 
1-00 
11-52 (max.) 
•652 
1-23 
1 5 ’22 (min.) 
•759 
1-10 
*76 (min.) 
•490 
1-61 
14 ’76 (max.) 
•338 
1-61 
4*92 (max.) 
•158 
Law of Force according to Curve 2. 
1-00 
11’58 (max.) 
1-414 
1-00 
12 ‘36 (max.) 
•652 
1-07 
3 ’78 (min.) 
1-146 
1-15 
0*16 (min.) 
•433 
1*22 
10 ’44 (max.) 
•774 
1-53 
5 - 20 (max.) 
•184 
1"28 
9 ’36 (min.) 
•671 
1-53 
15*60 (max.) 
•393 
§ 16. To interpret these results, suppose all the atoms of the 
assemblage to be subjected to guidance constraining them either 
to the equilateral homogeneousness of assemblage I., or to the 
diatomic homogeneousness of assemblage II., with each atom of 
one constituent assemblage at the centre of an equilateral quartet 
of the other constituent assemblage. It is easy to construct 
ideally mechanism by which this may be done ; and we need not 
occupy our minds with it at present. It is enough to know that 
it can be done. If the system, subject to the prescribed constrain- 
ing guidance, be left to itself at any given density, the condition 
for equilibrium without extraneous force is that w is either a 
maximum or a minimum ; the equilibrium is stable when w is a 
maximum, unstable when a minimum. It is interesting to see the 
two stable equilibriums of assemblage I. according to law of force 
1, and the three according to law of force 2; and the two stable 
equilibriums for assemblage II. with each of these laws of force. 
§ 17. But we must not forget that it is only with the specified 
