liU:'.] on Great Advance in Crystallography 688 



es nach Haujs Theorie zur Bildung ebener Krystallflachen notig 

 wiire." The formation of regular stepped faces (of invisibly minute 

 steps, " Treppenstufen ") the lecturer considers to occur only when 

 the grosser units become fixed about their centres of gravity or 

 representative points, with production of a truly solid crystal. 



But now let us pass to the consideration of the internal structure 

 of the grosser or space-lattice units themselves- Their symmetry 

 may be, in simple cases, similar to that of the space-lattice, but in 

 general this will not be so. Whatever the stereometric arrangement 

 of the chemical atoms in the molecule may be, and, if more than 

 one molecule goes to form the space-lattice unit, whatever their 

 mutual arrangement, and therefore, whatever l)e the outer configura- 

 tion of the whole unit, when the crystal is a truly solid one, the 

 force of crystallization (now no longer denied) is adequate to fix 

 each space-lattice unit, not only considered as a point with reference 

 to its neighbours, but as regards its shape and its whole character, 

 parallelwise and sameways orientated with respect to its adjacent 

 fellows, and as close as possible to them. Also if more than one 

 molecule goes to each space-lattice unit, their mutual arrangement is 

 achieved on a definite plan, and is the same for every space-lattice 

 unit ; these constituent molecules of the latter are also as closely 

 packed as possible. The final result is thus to produce an assemblage 

 of chemical atoms, in which not only the demarcation frontier 

 between the space-lattice units disappears, but also that between the 

 constituent molecules in the cases of polymolecular grosser units. 

 We come, ultimately, in consequence, to a structure of atoms, each 

 of which we may represent by a point. 



Now, just as the genius of Frankenheim and Bravais revealed to 

 us the 14 kinds of space-lattices, so Sohncke made us acquainted 

 with 65 regular systems of points, including many of the 32 classes of 

 symmetry, but not all, which von Lang had shown crystals to be capable 

 of possessing. Later the number was brought up to 230 by simulta- 

 neous and wonderfully concordant geometrical researches by Schonflies 

 in r4ermany, von Fedorow in 8t. Petersburg, and Barlow in England, 

 and among these 2;)0 all the 82 crystal classes are represented, and 

 no others. 



Hence, we come to the conclusion that the skeletal framework of 

 crystal structure is the molecular or polymolecular space-lattice, and 

 the detailed ultimate structure the atomic point-system. The latter 

 determines the class of symmetry (which of the 82 classes is exhibited) 

 and therefore governs any hemihedrism or tetartohedrism, as the 

 development of less than full systematic symmetry used to be called. 

 But it is the space-lattice which governs the crystal system, that is, 

 which determines whether the symmetry is cubic, tetragonal, rhombic, 

 monoclinic, triclinic, trigonal, or hexagonal, and which also deter- 

 mines the crystal angles and the disposition of faces in accordance 

 with the law of rational indices, the law which limits the number of 



