Results of Crystal Analysis. 423 



The new measurements will not produce any alteration 

 with regard to the arrangements found for the Y and 

 P atoms ; but the oxygen atoms must be arranged in 

 another way if we are to account For the observed maxima. 



This is clearly seen from the spectrum of the (111) face. 

 The arrangement given in my previous paper gives, for the 

 amplitudes of the (111) face*, 



A» = [2-44+ (-l) n (l'94 + cos na)] cos— • 



n.7r 



which shows that the intensity of the second-order spectrum 

 should vanish independently of the parameter a. 



The second-order spectrum, however, does not vanish, bu 

 is even found to be stronger than that of the first order. 



We must then arrange the oxygen atoms in such a 

 way that the second-order spectrum does not disappear. 

 Following the same line of argument as in the case of 

 zircon f, we find that any tetragonal arrangement of four 

 oxygeu atoms round one Y or one F atom will make 

 the second-order spectrum of (111) disappear, and we are, 

 as in the case of zircon, led to suppose that two oxygen 

 atoms are associated with each P atom and two with each 

 Y atom. The axis of the molecular elements must be 

 perpendicular to the C axis. 



To obtain a tetragonal arrangement, the molecular axis 

 through one of the face-centred lattices of P or Y must be 

 perpendicular to the axis through the other nice-centred 

 lattice of the same element. But with regard to the 

 relative position of the lines through the P atoms to those 

 through the Y atoms, there are, as we saw, two possibilities, 

 which will be apparent by considering the arrangement 

 of lines in a point-plane parallel to the base. If the lines 

 through the Y atoms in this plane were perpendicular to 

 those through the P atoms, we should get an arrangement 

 somewhat different to that of zircon, which would not 

 make the second-order spectrum of (111) disappear. This 

 arrangement, however, would not make the second-order 

 spectrum of this face sufficiently strong as compared with 

 that of the first order. 



There seems, indeed, to be no escape from the assumption 

 that the atoms of xenotime are arranged in a lattice of the 

 zircon type ; and we shall see that a proper choice of the 

 parameters will give a satisfactory agreement between 



* Loe. tit. p. 510, equation (3). 

 t Phil. Mag. xxxii. (1916) p. 77. 



