Molecular Dynamics of a Crystal. 143 



§ 9. Denoting now, for assemblage I., distances from atom 

 A of its nearest neighbours, its next-nearests, its next-next- 

 nearests, etc., by D ls D 2 , D 3 , etc., and their numbers by 

 jujtojsy e tc., we find by §§ 7, 8 for distances up to 2X, for 

 use in § 12 below, 



Di=X, ' D 2 =1414X, D 3 =1-732X, D 4 =&c, 

 ii=12j t / 2 = 6; is = 18; i 4 =6. 



§ 10. Look back now to § 5, and proceed similarly in 

 respect to assemblage II., to find distances from any atom A 

 to a limited number of its neighbours. Consider first only 

 the neighbours forming with A a single equilateral assemblage: 

 we have the same set of distances as we had in § 9. Consider 

 next the neighbours which belong to the other equilateral 

 assemblage. Of these, the four nearest (being the corners of 

 a tetrahedron having A at its centre) are each at distance 

 | */§X, and these are A's nearest neighbours of all the double 

 assemblage II. Three of these four are situated in a net 

 whose plane is at the distance J n/§ A, on one side of our 

 " middle plane " through A, and having one of its atoms on 

 either of the guide lines b or c. The distances from A of all 

 the atoms in this net are, according to fig. 2, 



Si-fof+rfi, vW+ftf), etc. . . . (5). 



The remaining one of the four nearests is on a net at 

 distance § %/§X from our " middle plane," having one of its 

 atoms on the guide line through A. The distances from A 

 of all the atoms in this net are, according to fig. 1, 



iV§X, V(iV + ft 2 )>'/ft" 2 + ? 2 2 ),etc. . . (6). 



All the other atoms of the equilateral assemblage to which 

 A does not belong lie in nets at successive distances k, 2k, 3k, 

 etc.. beyond the two nets we have already considered on the twa 

 sides of our '"middle plane " ; the atoms of each net placed 

 of course according to the cvclical law described in (e) 

 of § 6. 



§11. Working out for the double assemblage II. for A's 

 nearest neighbours according to § 10, we find four nearest 

 neighbours at equal distances f -v/|A. = '613X : twelve next- 

 nearests at equal distances X ; and twelve next-next-nearests at 

 equal distances v/yx=l"173X. These suffice for § 12 below. 

 It is easy and tedious, and not at present useful, to work out 

 for D 4 , D 5 , D 6 , etc. 



