Wyc'koff — Crystal Structure of Magnesium Oxide. 147 



At oiily one pair of values, u and v equalling % and %, 

 does A become zero. In this particular case the grouping 

 is that of (c). If, however, u and v had values close to, 

 but not equalling % and %, the reflections from such an 

 arrangement would be, with the present methods, indis- 

 tinguishable from those from (o). It is nevertheless 

 not probable as the structure of magnesium oxide since 

 this compound appears to exhibit a higher degree of 

 symmetry than that shown by (e). 



Possible arrangement (f). 

 Plane _(100) _ 



A = Mg j 2cos2 TT nu-\-"ZQos% it oi {ii-\-^) \ -\-0\ 2cos'2 tv nv + 2cos2 tt n 



B = 0. 



In the first order this becomes 



A = and 6 = for all values of u and v. 



Plane (110) 

 When 721=1, 



A =Mg \ cos4 TV u-\- cos 7r(l — 4w) } -f O { cos4 tt ?; + cos 7r(l — 4 v) } , 

 = for all values of ii and v. B = 0. 



Plane (111) 

 When ?2 = 1, 



A = Mg|cos6 ITU -|-3 cos2 7ri^} -j-0{cos6 7r?;-|-3cos2'7r?;}. 



This term has in general a value other than zero and 

 will be large or small depending upon the particular 

 values chosen for u and v. Consequently especially with 

 the present lack of quantitative knowledge about 

 scattering, little difficulty would be experienced in 

 accommodating a structure of this type, differing more or 

 less from (c) according to the particular hypotheses 

 regarding the amount of scattering, to the spectrometer 

 measurements from these three faces. Use must there- 

 fore be made of the results from the Laue photographs. 

 The A term for the amplitude of the reflection in the first 

 order for planes having one odd and two even indices is 

 as follows : ' 



A=Mg{cos27ri/(2m-J-2m^+2m24-l)— cos27ri^.(2m — 2m— 2m2+l) 

 + cos27rw (2mj — 2m — %m^ — 1 ) — cos27ri^ (2^?^2 ~ ^^^i ~ '^^^^ ~ t ) i 

 -|-0{a similar term in -u}, where m, m^, and m^ are 

 integers. 



For the present qualitative purpose the B term need 

 not be considered. It is seen that there will usually be a 



