
Figure 16
The deduction of the three cubic kinds of lattice according to William Barlow. The packing of white and black spaces, (a), is used in thought as a rack for white and black atoms. Barlow first fills the black spaces of the first, the third and fifth rows of the first layer of the rack, the front layer, and then the second and fourth rows of the white spaces of the second layer. The third layer is filled like the front one, the fourth like the second etc. This results in (b). In a second approach, he fills all the spaces of (a) with atoms of the corresponding color; this leads to (c). He concludes by filling only one kind of the spaces of (a), which gives (d) (Barlow, 1883a,b). Packing (b) represents the bodycentered cubic lattice (an envelope of 8 black atoms surrounds 1 white atom), (c) the normal cubic lattice (envelope 6) and (d) the facecentered cubic lattice (envelope 12). 