PKOF. W. H. BRAGG ON X-RAYS AND CRYSTAL STRUCTURE. 259 



Rock salt, diamond, zinc- blende, fluor-spar and other cubic crystals are all built 

 on the same fundamental lattice. In all cases the sines of the angles of the first 

 order spectra of the (100), (110) and (ill) planes are in the ratio 1 : v 2 : \/3/2 ; 

 except by accident, the manner of which will be explained presently. 



The prevailing occurrence of the face-centred form suggests that even in calcite, 

 which is not cubic, the representative points may be conceived of as being placed at 

 the corners and the face-centres of a rhomb of the same form as the calcite crystal 

 itself. Calculating the spacings of various planes on this basis, we find that the 

 corresponding angles of reflection are correct to the minute when determined by 

 experiment. It may be interesting to give part of the calculation. 



Let the side of the rhomb be a. The angles of the rhomb being known, it may 

 easily be calculated that the volume is a 8 x 0*925. Since the specific gravity of the 

 crystal is 2712, the mass in the rhomb is 3 x (T925 x 2712. 



But there are four molecules to each rhomb,* the weight of each being 100 times the 

 weight of the H atom, which is l'64x 10~ 24 gr. 



Hence 



rt 3 xO'925x2712 = 4x I00xl'64x 10' 2 ' 

 or 



a = 6'40xlO- 8 



= 6'40 A.U. 



From this other linear dimensions of the rhomb may be found. For instance, the 

 spacing of the planes parallel to the face is 3 '02 5 A.U., and the reflection of the a 2 

 rhodium ray should occur at an angle given by 



0'614 = 6'05 sin 0. 



Hence = 5 48', and this is exactly verified by experiment. 



It is easy to find the dimensions of the elementary cell of the lattice. The three 

 equal edges join the blunt corner of the rhomb to the middle point of the adjoining 

 faces. The length of each is 4'03 A.U., and the angle between any two, 75 54'. 



In similar ways we may determine the space lattice of any crystal. It is to be 

 remembered that the data on which we depend are the positions of the spectra of the 

 various faces. 



Let us now proceed to consider how we may determine the arrangement of the 

 atoms about the representative point. We now work on an entirely different plan, 

 building in fact on a determination of the relative intensities of the reflections of 

 different order and different sets of planes. As has already been said, measurements 

 of this kind are much more difficult than measurements of position ; and moreover 

 their exact interpretation has been by no means clear. But in many cases we already 

 know so much from considerations of crystal symmetry, and from measurements of 



* ' Roy. Soc. Proc.,' 89, p. 280. 



