20 



MINERALOGY 



number. Both the parameters and the indices can be expressed 

 in whole numbers, 0, or oo . It has been 'the experience in the past 

 that, with few exceptions, these numbers are small, rarely larger 

 than 9. In Fig. 23, the sheet of molecules lying in the axial plane 

 cob is represented. Possible planes intersecting this sheet at right 

 angles are represented by aa, dd, ee, etc., each of which intersects 



g 



FIG. 23. 



the axis b at greater distances; let all these possible faces be 

 moved up towards o until they intersect the axis c at unit distance, 

 or the diameter of one molecule ; they will now be represented by 

 the dotted lines a' a', d'd', e'e', etc. The ratio of the intercepts of the 

 plane a'a' on the axes c and b is as 1 : 1 ; of d'd', 1 : 2 ; of e'e', 1 : 3 ; of 

 f'f , 1:7; of g'g', 1 : oo . Thus the parameters are all whole num- 

 bers and the ratios are rational quantities. Theoretically it would 

 be possible for a face to occur with an intercept greater than any 

 indicated, but actually they are very rarely observed. 



The distance between neighboring molecules lying in the plane 

 of any face will increase with the intercept, except when the plane 

 becomes parallel to an axis. The molecules in the plane aa are 

 much nearer each other than the molecules in the plane ee ; mole- 

 cules have the tendency to crowd together as closely as possible. It 

 follows therefore that those faces will appear the more often on crys- 

 tals in which the molecules are the nearest. In Fig. 23, the cube 

 face hh and rhombic dodecahedron aa will occur the more often, as 



