BIRTH AND AFFINITIES OF CRYSTALS 131 



calcite is the only one which possesses this power of bringing 

 down sodium nitrate in parallel position upon itself. Yet calcite 

 is by no means the one which most nearly resembles sodium 

 nitrate in form ; in fact, it differs from it in angle more than any 

 of the other carbonates. It is clear then that some other 

 criterion than equality of angle must be applied. On comparing 

 the molecular volumes, however, it is found that calcite is the 

 only one mineral in this group which possesses a molecular 

 volume nearly equal to that of sodium nitrate. A reason why this 

 equality of molecular volume should be essential for a parallel 

 growth to take place is made evident from the following 

 considerations. 



In order that two structures of particles may fit together it 



>— f— f— > + "*> 



- 1 1 ' 



Fig- 3- 



Fig. 4. 



is necessary not only that the arrangement of the particles should 

 be the same in both, but also that the spacing of the particles 

 should be identical. Consider, for example, a cubic structure 

 consisting of particles arranged as in fig. 3. The particles 

 are situated at the corners of a series of equal cubic cells. Let 

 fig. 4 be a similar structure, but smaller in dimensions. Both 3 

 and 4 are cubic structures, and will yield crystals having the 

 same angles ; but they will not fit together, because the cubic 

 cells of 3 are larger than those of 4. If the structures are to 

 be identical they must be made up of cells whose volume is 

 the same. 



Now the specific gravities, or relative weights of equal 

 volumes, of the two crystals will depend both upon the intrinsic 



