
Figure 14
Three intersecting lines OX, OY and OZ of three groups of parallel facets or cleavage planes. An arbitrary plane, be it a real or perhaps an only possible one, meets these axes at A, B and C, another at H, K and L, respectively. The fundamental law of crystallography, then, implies that the ratio AO/HO:BO/KO:CO/LO shall be such that small integer values may be found, the socalled indices h, k and l, which satisfy the relation (1/h)(AO/HO):(1/k)(BO/KO):(1/l)(CO/LO). In Miller's view these `indices' are never greater that 6. Posterity was to speak of the `law of rational indices', a law that would take the place of Haüy's `decrescence law' (Miller, 1839, Table I). 