THE PREDECESSORS OF PASTEUR 5 



balance themselves at the eight angles of a cube, and that 

 a molecule of carbonate of iron could displace without 

 disturbance at one of these angles a molecule of calcium 

 carbonate of an entirely different configuration. But 

 a new theory in order to be useful and fruitful does not 

 need to have a solid foundation. It is enough that it 

 should be sufficiently well founded to give a new point 

 of view, one which allows the investigator to see things 

 the other way around, and it even happens that some 

 inexact theories may claim an active part in progress. 

 The progress which the very original researches of 

 Mitscherlich brought about was incontestible. 



Some years later, M. Delafosse, a pupil of Haiiy, 

 studying another phenomenon than isomorphism, that 

 of the hemihedron, advanced a step farther. The 

 beautiful geometrical laws stated by Haiiy were some- 

 times found lacking. They required, for example, that, 

 since the eight angles of a cube are identical from a 

 physical point of view, every natural modification which 

 acts on the one should also act on the other, for why 

 should there be any choice? If one of them is inter- 

 sected by a plane and is truncated, this truncation, what- 

 ever it is, must be repeated eight times. But it some- 

 times happens that only four of the angles of a cube bear 

 planes, and these are placed in such a way that no two 

 of them are ever at the extremities of the same edge of 

 the cube. The ensemble of these four faces prolonged in 

 the imagination form a tetrahedron. This is the case 

 with boracite which crystallizes in the cubic system. 

 Quartz likewise forms hexagonal prisms (Fig. 1) and the 

 twelve angles at its two bases are physically identical. 

 Nevertheless, it often happens that only six of these 

 angles, situated for example alternately above and below 

 the lateral edges, are intersected by facets which, joined 

 together, would form a rhombohedron with six faces. 



