CONTEMPORARY ADVANCES IN PHYSICS 395 



an abstraction, like a coordinate-frame, or the network of meridians 

 and circles of latitude which intersect upon a map. It is usually con- 

 ceived as a network of three sets of parallel planes, the planes of any 

 set following one another at even intervals of spacing. For conveni- 

 ence of drawing, each plane is sketched as a network of two sets of 

 parallel lines (Fig. 1). The intersections of three planes are the 



Fig. 1 — A space-lattice. Intersections of three lines are lattice-points. 



lattice- points; the intersections of two planes are axes of the lattice. 

 Axes of the lattice run in three directions, and along each there is a 

 constant spacing from one lattice-point to the next. The three may 

 be at right angles to one another, and the spacings along all three may 

 be the same, in which case the lattice is cubic; but this need not be the 

 case. All these ideas are required to make definite the notion of 

 regularity of arrangement which as I have mentioned is the distinction 

 of a crystal. They will probably become clearer in what follows. 



Around each lattice-point a particle is placed. I say around rather 

 than at, for it is desirable to think of the particles as rather bulky, 

 each containing a lattice-point at some definite place within itself, and 

 filling an appreciable part of the space extending from that point to 

 its neighbors. Moreover it is desirable to think of them as quite ir- 

 regularly-shaped objects, not as spheres, the way they are drawn in 

 Fig. 2. Some crystals do have such properties that the picture of 

 spherical particles is nearly adequate; but usually, if we were to assume 

 that the particle has the full and complete symmetry of the sphere, 

 we should be restricting the model to such an extent that it could not 

 be adapted to the properties of the actual crystals. The observations 



