Results of Crystal Analysis. 515 



choice of the parameter can give the right intensities for the 

 spectra (001) and (111). 



The amplitudes are determined by the following expressions: 



(001) A„=r375+ cos?i«, . . .1 



7171 



(111) A„ = (1-375+ cos w/J) cos—, ! 



0-i-ftri 



4 c 



(4) 



where I is the distance from the Ti atom to one of its oxygen 

 atoms. 



It follows from the lattice that l/c<\ or /3<7r, and 

 et<4z7r. Let the smallest value of a which gives the right 

 intensities of (001) be a , then the amplitudes of (001) will 

 be unaltered if we interchange « by the values : 



2tt— a , 2TT + a , 47T — a . 



Which of these is the right one must be determined from 

 the (111) spectrum. 



The right value of a is very nearly equal to 60°, and from 

 (111) we find « = 27r-a = 300° and £ = 75°. 



Table IV. gives the calculated and observed intensities 

 for the two faces. 



Table IV. 



/3=75°. 



(001). 



(HI). 



leal. 



lobs. 



leal. 



lobs. 



100 



7-6 

 0-5 

 08 



100 

 6 



1-5 

 1-4 



100 







23 



9 



100 

 



66 

 11 



The calculated and observed values agree as well as can 

 be expected, and we have no doubt found the right lattice 

 for anatase with the right symmetry properties. 



Also in the case of anatase the tetragonal structure is 

 produced by the oxygen atoms. 



The molecular element must require much more space in 

 the direction of its axis than in a direction perpendicular to 

 it. As all molecular axes are parallel to the tetragonal axis, 



