154 



additional phenomenon in comparison with the corresponding 

 reflection in the case of rocksalt, in so far as a maximum intensity 

 now corresponds not only to a glancing angle of 21, as would be 

 expected with regard to the reflection at the potassiumchloride- 

 crystal, but, moreover, to another angle of about 1030'. The maxi- 

 mum is here somewhat feebler than the first mentioned one. 



The cause of this difference is explained by the fact that the 

 atomic weight, and, therefore, the power of emission of sodium- and 

 chlorine-atoms, differ much more than those of potassium- and 

 chlorine-atoms. Indeed, if in the simple cubic space-lattice of fig. 126, 

 in which the black dots are the metal-atoms and the white ones the 

 halogen-atoms, we make sections parallel to (100) or (110), these 

 consecutive sections will all prove to be identical, consisting of equal 

 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 potassiumchloride, 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 the same kind 

 of particles. In the case of sodiumchloride, 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 x ). 



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



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

 1, 3, 5, 7, etc., consisting of metal-atoms, and 2, 4, 6, 8, etc., consisting of chlorine- 

 atoms respectively, and when 5 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) -f- a' cos (nt s.) -f- a cos (nt 2s) -f- a' cos (nt 3z) -f- . . . . , etc. 



If a were equal to a', we should have a maximum for & 2n, 4-n: etc., but for 

 s = 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 = TT, because these oppo- 

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



