155 



systems consist of two interpenetrating cubic face-centred space- 

 lattices, the one of which is built up by chlorine-, the other by metal- 

 atoms, and so intercalated that the cA/onw^-space-lattice is shifted 

 over a distance of half the cubic-edge of the metal- space-lattice, 

 each chlorine-atom thus falling midway between two consecutive 

 metal-atoms, and vice versa. 



The different behaviour with respect to the reflection at (111) 

 is fully explained by the difference of atomic weights in the case 

 of K and Cl, and of Na and Cl. 



However, there is again further evidence as to the correctness 

 of these conclusions. In comparing the behaviour of both crystals 

 with respect to the reflection at the same face, let us say at (100) 

 or (110), it is obvious that they are similar, but, as it were, 



executed "on a different scale". This scale is governed by a constant 

 proportion in so far, as the sines of the corresponding glancing 

 angles on the same faces of KCl and NaCl prove to be nearly 

 1,12. The explanation of this fact is very simple indeed: it is caused 

 by the difference in magnitude of the distances d between correspon- 

 ding consecutive layers in both crystals. If, therefore, it be observed 



that the ratio - V {NaCl) is .about = /,/?, we can conclude that 



this is the same for -, : -^ ; and it is easily calculated from 



"(Nad) "(KCl) 



the molecular weights M 1 and M z (74,6 and 5^,5) of both salts, and 

 from their densities s l and s 2 (1,99 and 2,17), that this ratio is almost 

 exactly the same as that of the edges of two cubes, each of which 

 contains one mol of the salts; these edges are j,J5, and 3,00 cm. 

 respectively. The number of molecules present in such a cube is, 

 however, known : for the absolute weight of a hydrogen-atom is 1,64. x 

 1024 gram, that of a mol sodiumchloride therefore: 95,94 X 10 24 



being different. This is the analytical expression for what is said in the above. If the 

 consecutive layers of different atoms did not follow each other in equal distances, 

 but e. g. in such a way that every layer of the one kind of atoms divided the 

 distances d of two consecutive identical layers of the other kind in a ratio of 

 I : 3, we should have: 



A = acos(nt) -\- a'cos(nt Js) -f- a cos(nt t) -j- a'cos(nt |) -f- 

 -f- acos(nt 2) + ...... etc. 



Now there will be a maximum for e = 2-n, and a feebler one for = 4it. The 

 two first vibrations of the series will be : a cos (nt) and a' cos (nt w) ; they are oppo- 

 sitely directed, but do not nullify each other, because a and a' are different. This 

 is observed in the case of zinc- sulphide. 



