DISCOVERY BY MEANS OF INFERENCE. 601 



one of the first to infer that minerals might be arranged 

 according to their mathematical forms, and to construct 

 such an arrangement. Walleriue, about the year 1774, 

 seems to have been the first to discover the idea of deri- 

 vative forms of crystals, by truncations of angles and edges. 

 Werner, at the same time, had a similar idea ; but it 

 was Kome de Lisle who extended the idea to all crystal- 

 line bodies. Bergmann in 1773 concluded that a hexa- 

 gonal prism might be built up of solid rhombs on the 

 planes of a rhombic nucleus. The theory of decrements 

 explained why a series of forms occur in crystals of the 

 same kind, while all apparently intermediate forms are 

 rigorously excluded, by showing that there must exist 

 regular numerical relations between the rows of mole- 

 cules in the different planes of the crystal, in order to 

 produce a regular shape. 



The idea of reference to crystalline axes, and thereby 

 to arrange all crystalline forms into systems, was another 

 valuable discovery by inference ; and appears to have been 

 first made by Weiss, in the year 1809, and afterwards 

 extensively applied by Mohs. It was Fuchs who, in 

 1815, inferred the idea of isomorphism; speaking of 

 gehlenite, he said, ' I hold the oxide of iron, not for an 

 essential part of this genus, but truly as a vicarious 

 element, replacing so much lime.' 



Most of our great geological ideas have been arrived 

 at by means of inference. Sir Charles Lyell, for instance, 

 by studying the fact that the river Ganges yearly conveys 

 to the ocean as much earth as would form sixty of the 

 great pyramids of Egypt, was enabled to infer that the 

 ordinary slow causes now in operation upon the earth 

 would account for the immense geological changes that 

 have occurred, without having recourse to the less reason- 

 able theory of sudden catastrophes. 



