206 Professor William H. Bragg [June 5, 



When, therefore, we are observing the reflections in the different 

 faces of a crystal in order to obtain data for the determination of its 

 structure, we have more than the values of the angles of reflection 

 to help us : we have also variations of the relative intensities of the 

 spectra. In the case just described we have an example of the 

 effect produced by want of similarity between the planes, which are, 

 however, uniformly spaced. 



In the diamond, on the other hand, we have an example of an 

 effect due to a peculiar arrangement of planes which are otherwise 

 similar. The diamond crystallizes in the form of a tetrahedron. 

 When any of the four faces of such a figure is used to reflect X-rays, 

 it is found that the second order spectrum is missing. The analogous 

 optical effect can be obtained by ruling a grating so that, as com- 

 pared with a regular grating of the usual kind, the first and second, 

 fifth and sixth, ninth and tenth alone are drawn. To put it another 

 way, two are drawn, two left out, two drawn, two left out, and so 

 on. The National Physical Laboratory has ruled a special grating 

 of this kind also for us, and the effect is obvious. The corresponding 

 inference in the case of the diamond is that the planes parallel to 

 any tetrahedral face are spaced in the same way as the lines of the 

 grating. Every plane is three times as far from its neighbour on 

 one side as from its neighbour on the other. There is only one way 

 to arrange the carbon atoms of the crystal so that this may be true. 

 Every atom is at the centre of a regular tetrahedron composed of its 

 four nearest neighbours, an arrangement best realized by the aid of 

 a model. It is a beautifully simple and uniform arrangement, and 

 it is no matter of siu'prise that the symmetry of the diamond is of 

 so high an order. Perhaps we may see also, in the perfect symmetry 

 and consequent effectiveness of the forces which bind each atom to 

 its place, an explanation of the hardness of the crystal. 



Here, then, we have an example of the way in which peculiarities 

 of spacing can be detected. There are other crystals in which want 

 of uniformity both in the spacings and in the effective value of the 

 planes combine to give cases still more complicated. Of these are 

 iron pyrites, calcite, quartz, and many others. It would take too 

 long to explain in detail the method by which the structures of a 

 large number of crystals have already been determined. Yet the 

 work done already is only a fragment of the whole, and it will take 

 no doubt many years, even though our methods improve as we 

 go on, before the structures of the most complicated crystals are 

 satisfactorily determined . 



On this side, then, we see the beginning of a new crystallography 

 which, though it draws freely on the knowledge of the old, yet builds 

 on a firmer foundation since it concerns itself with the actual arrange- 

 ment of the atoms rather than the outward form of the crystal itself. 

 AVe can compare with the internal arrangements we have now dis- 

 covered the external forms which crystals assume in growth, and the 



