1901 - 2 .] Lord Kelvin on Molecular Dynamics of a Crystal. 209 
In the two parallel nets at distances k from middle : 6 
each equal to x /(k 2 + ?’ 1 2 ); 6, Ji^ + rf); 12, J(« 2 + rf); 
1 2, + rf) ; 6 , J^ + rf); 12, J(# + r*); 6 , J^ + rf). 
In the two parallel nets at distances 2k from middle : the 
same as (B) altered by taking 2/c everywhere in place of k . 
In the two parallel nets at distances 3 k from centre : the 
same as (A) altered by taking *J(9k 2 + q 2 \ sJ(9K 2 + qf), etc., in 
place of q v q 2 , etc. 
In nets at distances on each side greater than 3k : distances of 
atoms from A, found as above, according to the cycle of atomic 
configuration described in (e) of § 6. 
§ 8. By geometry we find 
— A ; # 2 — V3* = 1‘732a ; q 3 =2\; q±= n /7a = 2 , 646a ; q 5 = 3a : I 
= ViA= '577a ; r 2 = 2\AA— 1 '154a ; r s =V|A = 1*527a; r 4 = VV-A = 2’082a ; H4). 
= 4ViA = 2*308A; r 6 = VV 9 A = 2'517a ; r 7 = 5V|A = 2’887A. J 
§ 9. Denoting now, for assemblage I., distances from atom A of 
its nearest neighbours, its next-nearests, its next-next-nearests, etc., 
by Dj, D 2 , D 3 , etc., and their numbers by j v j 2 , j z , etc., we find 
by §§ 7, 8 for distances up to 2A, for use in § 12 below, 
Dj = A, D 2 = 1-414 A, D 3 = 1*732 A, D 4 = 2A, 
ii = 12 >i 2 = 6 ; is= 18 ; J* = Q - 
§ 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 f-^/f-A, 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 x\/§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, 
+ V), n/(tV 2 + ^ 2 ). etc (5). 
The remaining one of the four nearests is on a net at distance 
l^f- A from our “middle plane,” having one of its atoms om the 
PROC. ROY. SOC. EDIN. — VOL. A XIV. 
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