WycTioff — Crystal Structure of Magnesium Oxide. 149 



With thirty-two molecules associated with the niiit 

 cube, the first reflections observed from the (100) and 

 (110) faces correspond with the fourth order. Third 

 order reflections from planes having indices that are all 

 odd are found in the Laue photographs. 



Plane 100: 



A=Mg{16cos2 7r^zz^ + 16cos2 7r7i (w+|-)J + term. 



7i — 9 — 



A -, Q,r =Mg { 32 cos4 7r2<;j4-0{ 32 cos47ry;=0 when u=\,v =f. 



Plane 110: 



A = Mg 1 8cos2 TT ni<-|-8 + 8cos2 tt n (w+i) + 8cos tt ?i} -f-0 term. 



A^^Yo^=M^{16+cos4 7rw!- +0{16+cos4 7rv'f. 

 This term also equals zero when u^^\^ and v = ^. 



Plane 111: _ 



A=:Mgj8cos6 7rm<+24cos2 7rfm} +0 {a similar term in ^ }. 



The problem in this case is to determine whether there 

 are values for u and v such that A, for n = l and n = 2, 

 is practically zero ; the intensity of reflection when n=^?> 

 must be appreciably less than when n = ^. An approxi- 

 mate solution can be given graphically ; a more exact one 

 could, however, onl}^ be made if quantitative measure- 

 ments of scattering were available. The intensity of 

 reflection (or the amplitude) for all values of u and v 

 when n has a particular value can be represented by a 

 three dimensional figure. Certain ^4so-t^'s" of such a 

 figure obtained when n = l are given in figure 3. 



The curves enclosing region n = l of figure 4 are 

 obtained by plotting those values of u and v which give a 

 certain small amplitude (as may be determined with the 

 aid of figure 3) on either side of zero (arbitrarily chosen 

 for this representation as +50 and -50). All points 

 lying within this region then will satisfy the experimental 

 requirement that no first order is observable. The 

 regions n^2 similarly enclose all values of u and v for 

 which the second order will be negligible. The condition 

 that the amplitude shall be very large in the fourth order 

 is fulfilled within the areas defined by the curves n = 4. 

 These three conditions are satisfied only in the regions 

 about u = ^4^ or % and v = y^^ or y^. It will be observed 

 that when u=^y^ and i; = ^ the arrangement is identical 

 with that of (c) ; small deviations from these values could 

 not, however, be detected by the experimental means 



