151 



f.n-li i-h/onnc-ntom thus falling midway between two consecutive 

 >m7<//-atum>. and vice versa. 



llu (littnvnt behaviour with respect to the reflection at (111) 

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

 o! 7\ 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 v. 

 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 = 

 i ,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 . a i s about = 1,13, we can conclude that 

 sin 3> ( Kci) 



this is the same for-j : -=- ; and it is easily calculated from 



"(Nad) d(KCl) 



the molecular weights M x and M 2 (74,6 and 5<?.j) of both salts and 

 from their densities s t and s 2 (i ,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 3.35, and j.ooc.M. 

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

 however known. For the absolute weight of a hydrogen-atom is / ,64 x 

 10~~ 24 gram, that of a mol sodium-chloride therefore 95,94 X 10 24 

 gram. The number of molecules NaCl in the cube with its edge of 



58 5 

 ' 

 /\ i \j 



10 24 atoms. On every edge of the cube there are as a consequence: 



3 00 

 7,07 x 10 8 atoms, their mutual distance therefore being ~~\f\ 



1 ,U I X 1 V 



c.M. = 2,8 x /o~~ 8 c.M. 



The spacing of the layers parallel to (110) or (111) is then easily 

 calculated from this number, while that of the consecutive layers 

 of KCl parallel to (100), is of course 3,15 x 10~ 8 c.M. etc. 



26. The cases of sodium-, and potassium-chloride, discussed more 

 in detail, may give an idea of the general method of reasoning 

 followed by Bragg to try to find out the internal structure of crys- 

 talline substances. The study of the relative intensities of the spectra 

 of the first, second, third order, etc., and of other peculiarities of 



3,00 c.M. is therefore ' 24 = 0,610 x 10 24 , or 1,22 x 



