The Plan of the Earth and its Causes. — Gregory. 115 
only be applied to a symmetrical world ;* in a dodecahedron the 
opposite faces are always similar and parallel ; in Elie de Beau- 
mont's network the antipodal areas are always similar. But, as 
we have seen, the fundamental fact in the plan of the world is 
that opposite areas are dissimilar. In crystallographic language 
the lithosphere is hemihedral, not holohedral ; and no scheme 
based on a holohedral form will serve. It is the recognition of 
this principle that led to the next great advance. 
THE TETRAHEDRAL THEORY. 
Elie de Beaumont's scheme is now mainly of historic inter- 
est, though Lefort's recent map of the Nivemais shows that it is 
still used as a working hypothesis by some French geologists. 
But Elie de Beaumont's theory marked an epoch in this sub- 
ject, for it led to the system of Mr. Lowthian Green, which far 
better meets the requirements of the case. 
This system was founded in 1875, by Mr. Lowthian Green, 
in a work which was neglected or ridiculed at the time of its 
appearance. Like his predecessor, Green assumes that the 
earth is a spheroid based on a regular geometrical figure. He 
adopted as his base the apparently hopelessly unsuitable figure 
of the tetrahedron, which is contained within four equal similar 
triangles. This form, with its four faces, six sharp edges and 
four solid corners, does not conform to the ordinary conception 
of the figure of the globe. Any comparison between them looks 
ridiculous. But if we place a three-sided pyramid on each 
face of the tetrahedron, its proportions are nearer those of a 
globe ; and if these pyramids had elastic sides so that they could 
be blown out and the faces thus made curved, then the tetrahe- 
dron would become spheroidal and even spherical. Converse- 
ly, if a hollow sphere be gradually exhausted of air, the ex- 
ternal pressure may force in the shell at four mutually equi- 
distant points, and, by the flattening of these four faces, make 
it tend towards a tetrahedral fonu. Now the tetrahedral the- 
ory does not regard the world as a regular tetrahedron with 
four plane faces ; it considers that the lithosphere has been sub- 
jected to a slight tetrahedral deformation, to an extent indeed 
only faintly (if at all) indicated by geodetic measurements, but 
•This objection applies also to various later modifications of Elic de Beau- 
mont's principle, such as those of Owen ; or to the more than local acceptance 
of the diaclases of Daubree, or orthogonal cross-folds of Bertrand. 
