Results of Crystal Analysis. 425 



order. If, however, we let the values of k decrease some- 

 what less rapidly, we get a very satisfactory agreement 

 between the amplitudes calculated from the lattice and 

 those calculated from observations. In the present cas > 

 we have put 



h = 1-00, k 2 = 2/5, k 3 = 1/7, k± = 1/12. 



When we are going to compare the amplitudes in 

 Table VII., we must remember that only in the cas^ of 

 the faces (111), (110)., and (001) was the reflexion obtained 

 from a fairly plane crystal surface. In the case of (100) 

 u nd (101) we had to measure the reflexion from edges, and 

 as a consequence the intensity measurements will be less 

 accurate. Usually we find in such cases that the intensity 

 of the first order is found too weak, which is also in agree- 

 ment with our figures. Thus we arrive at the conclusion, 

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

 zircon type. 



The dimensions of the elementary lattice are the same as 

 oiven in paper III. Table V. p. 516. We have only to add 

 the distances from the central atom of a molecular element 

 to one of its oxygen atoms. The distance Zy from the 

 Y atom to one of its oxygen atoms will be 



Z Y = a \/2^:= 2-55x10"* cm. 



And the corresponding distance for the P atoms will be 



h = a\Z2* 2 = l'42xl0- 8 cm. 



Thus, in a " molecular element " the distance from the 

 central atom to one of the two oxygen atoms is much 

 greater in the case of yttrium than in the case of phos- 

 phorus, similar to the case of zircon. 



§ 8. The fact that the lattice of xenotime is of the same 

 type as that of zircon will have far-reaching consequences 

 with regard to the question between chemical constitution 

 and crystal structure. 



From the fact that in zircon we might associate oxygen 

 atoms with each Zr atom, and two oxygen atoms with two 

 Si atoms, we were led to suppose that the zircon mineral 

 had to be considered as a dioxide, Zr0 2 Si0 2 . 



And in a similar way we were from the structure led to 

 regard rutile as (Ti0 2 ) 2 and kassiterite as (Sn0 2 ) 2 . 



Now, however, we have found that the atoms of xenotime 

 (YP0 4 ), in spite of the difference of valency of the elements, 



