Results of Crystal Analysis. 



87 



The spectrum (111), on the other hand, is very much 

 influenced by the position of the oxygen atoms, and will 

 form our main basis for the determination of a x and a 2 . 



The values of f\(n) and f 2 {ii) for the (111) face are given 

 in Table V. for n = l, 2,.. '6. 



Table V. 



n. 

 1 



/.(»)■ 



/»• 



lobs. 



Je. 



1-68 



1'63 — (cos j3 4- cos a 2 ) 



0-80 



100 



2 







-2-00 + (cos2/3 4-cos2a 2 ) 



0-40 



0-30 



3 



-1-63 



1*63 -(cos 30 4-cos3a 2 ) 



0-40 



012 



4 







8-75 4- (cos 4/3 4- cos 4a 2 ) 



1-00 



0-05 



5 



-1-63 



T63 — (cos5j3 + cosoa 2 ) 



005 



0015 



6 







-2-00 4- (cos 6 3 4- cos 6a 2 ) 







0-005 



In column 4 are given the relative intensities observed 

 and in the last column the relative intensities of a normal 

 spectrum. These values are somewhat different from those 

 given by Bragg, because the spectra of the crystals con- 

 sidered usually gives a normal spectrum with relatively 

 stronger maxima of higher order. 



Comparing the values of the last two columns, we see 

 that /3 and a 2 must be given such values that the intensity 

 of the first order spectrum is diminished and that of the 

 third increased. 



Consequently 



/3 + ot 2 

 cos.p + cosa 2 = 2 cos' — --^cos — 



must be positive (I.) 



cos3/3 + cos3« 2 = 2cos3/2(/3 + a 2 ) cos 3/2 (£—«,) 



must be negative (II.) 



As both /3 and a 2 must be less than 7r, condition I. gives 

 that 



+ * 2 <7T. 



As the atoms must have a distance which is of the order 

 of the length d m , neither « 2 nor & can have a very small 

 value. Then we can suppose cos 3/2 (/S — a 2 ) positive, and 

 from condition (II.) we get 



^ </3 + a 2 <7T. 



