Results of Crystal Analysis. 517 



from the measured glancing-angle and the known wave- 

 length. If V is the volume of the elementary cell, M and p 

 molecular weight and density, n the number of molecules in 

 the cell, N the number of molecules in a gramme-molecule 

 (61*5 x 10 22 ), we have the relation : 



If we knew p and n and had measured V, we might 

 find M. As the glancing-angle can be found with a very 

 great accuracy, the reflexion of Pontgen rays from crystals 

 might furnish us with a valuable and accurate method of 

 determining the atomic weight of an element which had 

 entered into combination with elements of known atomic 

 weight. 



If we only want ordinary relative values of the atomic 

 weight, the accuracy mainly depends on the accuracy of the 

 glancing-angle, and not on the number N. To fix the 

 idea, let us suppose that we have two cubic crystals, one 

 of which we take as a standard. Let the glancing-angle of 

 the cube faces be and 0, then 



M = M M / S iDfl \ 8 



p p n \ sin 6 ) 



Summary. 



(1) The crystalline structure of xenotime Y(P0 4 ) and 

 anatase (Ti0 2 ) has been determined. 



(2) The lattice of xenotime is not of the zircon type ; the 

 difference, however, is only due to a different arrangement 

 of the oxygen atoms. In xenotime they are arranged in 

 groups of four round each P atom, while in zircon both Zr 

 and Si have essentially the same relation to the oxygen 

 atoms. The lattice gives the constitution formulae Y(P0 4 ) 

 and Zr0 2 Si0 2 for xenotime and zircon respectively. 



(3) In spite of the different arrangement of the oxygen 

 atoms, which accounts for the chemical differences, the 

 lattice also accounts for the crystallographic similarity of 

 the two substances. Both possess the right symmetry, and 

 in both cases the same relative number of oxygen atoms are 

 arranged in planes perpendicular to the tetragonal axis, and 

 will expand the lattice perpendicular to this axis to the same 

 extent and make the ratio c/a smaller than unity and almost 

 equal for both crystals. 



(4) We can imagine the lattice of anatase to be derived 



