150 



numbers of metal- and halogen-atoms. But if we make sections 

 in a direction perpendicular to a trigonal axis of the space-lattice, 

 we have layers of metal-atoms alone, alternating with layers con- 

 sisting only of halogen-atoms. In the case of potassium-chloride, where 

 K and Cl with respect to their secondary emission behave almost 

 identically, the result of the interference of the reflected rays is 

 nearly the same as when all layers are built up by same the kind 

 of particles. In the case of sodium-chloride, however, this is no longer 

 the case ; here the result of the interference of rays coming from the 

 layers 1, 3, 5, 7, etc., will be different from that of the waves coming 

 from the alternating layers 2, 4, 6, 8, etc. The latter will of course 

 have a phase opposite to that of the first series; but as their ampli- 

 tudes are different, they will not completely counterbalance each 

 other, and a second maximum, as mentioned above, is therefore 

 observed here v ). 



The structure of both salts is therefore much the same: both 

 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 c/z/onwe-space-lattice is shifted 

 over a distance of half the cubic-edge of the w^a/-space-lattice, 



1) When a and a' are the amplitudes of the waves reflected by the planes 

 /, 3, 5, 7, etc. consisting of metal-atoms, and 2, 4, 6, 8, etc. consisting of chlorine- 

 atoms respectively, and when & is the phase-difference produced by the reflection 

 at two consecutive layers of the whole parallel set, the resulting amplitude A produ- 

 ced by the interference, may be represented by an equation of the form: 



A = a cos(nt) -\- a' cos (nt s) + a cos (nt 2) + a' cos (nt 3i) -f . . . .etc. 



If a were equal to a', we should have a maximum for f, = 2it, 4-x etc., but for 

 = TT, the value of A would become zero, because every two consecutive terms 

 of the sum would counterbalance each other, their phases being exactly opposite . 

 When a and a' are however not equal, there will besides the maxima mentioned 

 in the preceding case, also be some feebler ones for e = it, because these oppo- 

 sitely directed vibrations now no longer counterbalance each other, their intensities 

 being different. This is the analytical expression for what is said here. If the conse- 

 cutive 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 1 : 3, we 

 should have: 



A = acos(nt) + a'cos(nt z) -f- acos(nt Js) + a'cos(nt 4^) + 

 + acos(nt 2s) + etc. 



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

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

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

 is the case observed in zinc-sulphide. 



