Molecular Dynamics of a Crystal. 147 



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 constraining 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, 



A 



'semblage I. Assemblage II. 





Distances be- 

 tween centres 

 of nearest 

 atoms for 

 maximum and 

 minimum 

 values of to. 



ilaximumand 



minimum 

 Talues of w. 



Densities. 



Distances be- 

 tween centres 

 of nearest 

 atoms for 

 maximum and 

 minimum 

 values of w. 



A[aximum and 



minimum 



values of w. 



Densities. 





Law of Force according to Curve 1. 





116 

 1-23 

 1-61 



828 (max.) -904 



522 (min.) -759 



1476 (max.) -338 



1-00 

 1-10 

 1-61 



1L52 (max.) 



"76 (min.) 



4-92 (max.) 



•652 

 ■490 



•158 



Law of Force according to Curve 2. 



1-00 

 1-07 

 1-22 

 1-28 

 1-53 



11 '58 (max.) 

 3-78 (min.) 



10-44 (max.) 

 9-36 (min.) 



15-60 (max.) 



1-414 



1146 



•774 



•671 



•393 



100 

 1-15 

 1-53 



1236 (max.) 

 0-16 (min.) 

 520 (max.) 



•652 

 •433 

 •184 



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 

 -table equilibriums for assemblage II. with each of these laws 

 of force. 



§ 17. But we must not forget that it is only with the 

 specified constraining guidance (§ 16) that we are sure of 

 these equilibriums being stable. It is quite certain, however, 

 that without guidance the monatomic assemblage would be 

 stable for the small density corresponding to the point m of 



L2 



