Results of Crystal Analysis. 509 



as to increase the weight of the P planes so that the group of 

 P and atoms can balance the heavier Y atoms, and we are 

 led to try to arrange the oxygen atoms tetragonally round 

 the P atoms. 



There are mainly two different arrangements possible : — 



(1) The oxygen atoms are arranged on a line through the 

 P atoms parallel to the tetragonal axis. This would make 

 the spectra of the faces (110) and (100) normal ; but in the 

 case of the face (100) the second order spectrum is nearly 

 as strong as that of the first order, consequently such an 

 arrangement is excluded. 



(2) Four oxygen atoms are arranged in a plane through 

 the P atoms perpendicular to the tetragonal axis. 



In order to keep up the highest symmetry class there will 

 only be two arrangements of this description possible : 



(a) The oxygen atoms are placed on lines through the P 

 atoms which are parallel to the sides of the base ; (b) they 

 are placed on lines through the P atoms which are parallel 

 to the diagonals of the square base of the lattice. 



Let us first consider the first possibility (a), and calculate 

 the intensities for the faces (111) and (110). 



After some reduction we find for the amplitudes, 



(111) A„=(0-47 + (-l)n-22+ cos??a)cos™,l 

 (110) A„=l-69+ cos2rc«, J 



where a is a parameter determining! the distance between 

 P and O. 



In order to explain the disappearance of the three first 

 spectra of (111) we should have to choose a value of a 

 smaller than 25°, because a greater value would make the 

 third order spectrum too strong not to be detected ; and 

 even for a<25° the first order spectrum would probably be 

 too strong to escape detection. Further, we cannot assume 

 a very small value of a, because it would bring the centres 

 of the P and O atoms of the group too close together. 



Finally, a value of a<25° would produce a distribution 

 of intensities of the face (110) which is not in accordance 

 with observations. The observations give for the intensities 

 of the first three orders the relative intensities 100, 58, 25, 

 showing that the intensities of the second and third orders 

 are larger than in the normal spectrum. In other words, 

 the oxygen atoms must be arranged in such a way that 



A!<A 2 <A 3 , 

 while for a<25° the arrangement considered would give 

 A l >A 2 >A 3 . 



