856 



LORD KELVIN. 



§ 35. For the preseut let us think only of the octopolar electric 

 aeolotropy discovered by Haùy in the cubic class of crystals. The quartet 

 of electrions at the four corners of a tetrahedron présents itself readily 

 as possessing intrinsically the symmetrical octo-polar quality which is 

 realized in the natural crystal. If we imagine an assemblage of atoms 

 in simple cubic order each containing an equilateral quartet of elec- 

 trions, ail similarly oriented with their four faces perpendicular to the 

 four diagonals of each structural cube, we have exactly the required 

 aeolotropy; but the equilibrium of the electrions ail similarly oriented 

 would probably be unstable; and we must look to a less simple assem- 

 blage in order to have stability with similar orientation of ail the elec- 

 trionic quartets. 



§ 36. This, I believe, we have in the doubled equilateral homoge- 

 neous assemblage of points described in § 69 of my paper on „Moïecular 

 Constitution of Matter" republished from the Transactions of the Royal 

 Society of Edinhiirgh for 1889 in volume III of my „Collected Maihe- 

 matical and Physical Papers' 1 (p. 126); which may be described as 

 follows for an assemblage of equal and similar globes. Beginuing with 

 an equilateral homogeneous assemblage of points, A, make another 

 similar assemblage of points, B, by placing a B in the centre of each 

 of the similarly oriented quartets of the assemblage of Â's. It will be 

 found that every A is at the centre of an oppositely oriented quartet of 

 the B's. To understand this, let A l A 2 A s A^ be an equilateral quartet 

 of the A's; and imagine A 2 A 3 A^ placed on a horizontal glass plate ') 

 with A x above it. Let Bi be at the centre of A Y A 2 A 3 A k and let 

 B x B 2 B 3 7? 4 be a quartet of the B\s- similarly oriented to Ai A 2 A, A A . 

 We see that B 2 B 3 /i 4 lie below the glass plate, and that the quartet 

 Bi B 2 B 3 B k has none of the A' s at its centre. But the vertically opposite 

 quartet B Y B' 2 B\ B\ contains A l within it; and it is oppositely 

 orientée! to the quartet Ai A 2 A ?> A k . Thus we see that, while the half 

 of ail the quartets of As which are oriented oppositely to Ai A 2 A 3 A k 

 are void of B's, the half of the quartets of B's oppositely oriented to 

 Ai A 2 A 3 A k have each an A within it, while the other half of the 

 quartets of the B's are ail voici of Al s. 



2 ) Parallel glass plates are useful auxiliaires for graphie construction and 

 illustrative models in the molecular theory of crystals. 



