1901 - 2 .] Lord Kelvin on Molecular Dynamics of a Crystal. 205 
Molecular Dynamics of a Crystal. By Lord Kelvin. 
(With Seven Diagrams.) 
§ 1. The object of this communication is to partially realise the 
hope expressed at the end of my paper of July 1 and July 15, 
1889, on the “Molecular Constitution of Matter”:* — “The mathe- 
matical investigation must be deferred for a future communication, 
when I hope to give it with some further * developments. ” The 
italics are of present date. 
Following the ideas and principles suggested in §§ 14-20 of 
that paper (referred to henceforth for brevity as M. C. M.), let 
us first find the work required to separate all the atoms of a 
homogeneous assemblage of a great number n of molecules to 
infinite distances from one another. Each molecule may he a 
single atom, or it may he a group of i atoms (similar to one 
another or dissimilar, as the case may be) which makes the whole 
assemblage a group of i assemblages, each of n single atoms. 
§ 2. Remove now one molecule from its place in the assemblage 
to an infinite distance, keeping unchanged the configuration of its 
constituent atoms, and keeping unmoved every atom remaining in 
the assemblage. Let W be the work required to do so. This is 
the same for all the molecules within the assemblage, except the 
negligible number of those (§ 30 below) which are within influential 
distance of the surface. Hence -JwW is the total work required to 
separate all the n molecules of the assemblage to infinite distances 
from one another. Add to this n times the work required to 
separate the i atoms of one of the molecules to infinite distances 
from one another, and we have the whole work required to separate 
all the in atoms of the given assemblage. 
Another procedure, sometimes more convenient, is as follows : — 
Remove any one atom from the assemblage, keeping all the others 
unmoved. Let w he the work required to do so, and let 2? o 
denote the sum of the amounts of work required to do this for 
* Proc. Roy. Soc. Edin ., and vol. iii. of Mathematical and Physical 
Papers , art. xcvii. 
