THE MOLECULAR TACTICS OF A CRYSTAL _LORD KELVIN_ London HENRY FROWDE OXFORD UNIVERSITY PRESS WAREHOUSE AMEN CORNER, E.C. [Illustration] New York MACMILLAN & CO., 66 FIFTH AVENUE THE MOLECULAR TACTICS OF A CRYSTAL BY LORD KELVIN, P.R.S. PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF GLASGOW AND FELLOW OF PETERHOUSE, CAMBRIDGE _Being the Second ROBERT BOYLE LECTURE, delivered before the Oxford University Junior Scientific Club on Tuesday, May 16, 1893_ WITH TWENTY ILLUSTRATIONS Oxford AT THE CLARENDON PRESS 1894 Oxford PRINTED AT THE CLARENDON PRESS BY HORACE HART, PRINTER TO THE UNIVERSITY ON THE MOLECULAR TACTICS OF A CRYSTAL By LORD KELVIN, P.R.S. § 1. My subject this evening is not the physical properties of crystals, not even their dynamics; it is merely the geometry of the structure--the arrangement of the molecules in the constitution of a crystal. Every crystal is a homogeneous assemblage of small bodies or molecules. The converse proposition is scarcely true, unless in a very extended sense of the term crystal (§ 20 below). I can best explain a homogeneous assemblage of molecules by asking you to think of a homogeneous assemblage of people. To be homogeneous every person of the assemblage must be equal and similar to every other: they must be seated in rows or standing in rows in a perfectly similar manner. Each person, except those on the borders of the assemblage, must have a neighbour on one side and an equi-distant neighbour on the other: a neighbour on the left front and an equi-distant neighbour behind on the right, a neighbour on the right front and an equi-distant neighbour behind on the left. His two neighbours in front and his two neighbours behind are members of two rows equal and similar to the rows consisting of himself and his right-hand and left-hand neighbours, and their neighbours’ neighbours indefinitely to right and left. In particular cases the nearest of the front and rear neighbours may be right in front and right in rear; but we must not confine our attention to the rectangularly grouped assemblages thus constituted. Now let there be equal and similar assemblages on floors above and below that which we have been considering, and let there be any indefinitely great number of floors at equal distances from one another above and below. Think of any one person on any intermediate floor and of his nearest neighbours on the floors above and below. These three persons must be exactly in one line; this, in virtue of the homogeneousness of the assemblages on the three floors, will secure that every person on the intermediate floor is exactly in line with his nearest neighbours above and below. The same condition of alignment must be fulfilled by every three consecutive floors, and we thus have a homogeneous assemblage of people in three dimensions of space. In particular cases every person’s