24 



PASTEUR: THE HISTORY OF A MIND 



tetrahedrons which can be derived from a cube by 

 hemihedrism are identical and could fit into one another. 

 The two tetrahedrons represented in Fig. 4, passing 

 through opposite vertices of the cube, have the same 

 angles and edges; it is only necessary to reverse the 

 first in order to make it fit over the second: they are 

 superposable, to speak in geometrical parlance. The 

 same thing is true for the different rhombohedrons 

 derived from the hexagonal prism. It is quite otherwise 

 for the hemihedrons of the 

 tartrates. The tetrahedron 

 which one obtains by pro- 

 longing and joining the hemi- 

 hedral facets which a right- 

 handed crystal of tartrate 

 bears, is not superposable on 

 the tetrahedron obtained in 

 the same way from the left- 

 handed tartrate. Their faces, it is true, are equal two by 

 two, but they are not arranged in the same order in re- 

 spect to the vertices. 



Fundamentally, the difference amounts to this, that 

 the tetrahedron of the cube has several planes of 

 symmetry, to the right and left of which the elements 

 are regularly distributed. If one imagines a reflect- 

 ing surface passing through any given edge of the 

 tetrahedron and the center of the opposite edge, the 

 image of the rear half in this mirror coincides with that 

 of the forward half, and inversely: in more general 

 terms, the object is superposable on its image in a mirror. 

 We shall say that in this case there is superposable 

 hemihedrism. The hemihedrism of the tartrates gives, 

 on the contrary, tetrahedrons which have no plane 

 of symmetry, w r hich are not superposable oh their image, 

 and when we reflect upon it we see that "all material 



FIG. 5. 



Right tartrate. Left tartrate. 



