132 TRANSACTIONS. 1906-7. 



a moment. Starting with the earth as a molten mass, we have a 

 sphere as the result of the action of gravity. If vfe revolve the 

 sphere we obtain an oblate spheroid, with flattened poles — 

 orange-shaped, the shorter axis being the one of revolution. 



The angular velocity of rotation being uniform and constant 

 the whole body would be in stable equilibrium. If now any force 

 or forces are brought into play to disturb this equilibrium strains 

 and stresses are set up, and a counter tendency to relieve these 

 strains is called forth to restore equilibrium. It is at this juncture 

 that the property of the tetrahedron comes into play. Taking 

 as our principal disturbing force of our supposed liquid or molten 

 spheroid of revolution, that of dissipation of heat or cooling pro- 

 cess, we find that the crust or shell of the earth tries to adjust itself 

 to the stresses set up by the contracting body, and does so by the 

 line of least resistance, that is, by spreading the stresses over the 

 greatest surface, with the result, that the tendency of the surface 

 of the earth is to assume the tetrahedral form, i.e., of an eciuilateral 

 pyramid. Or one may say that the contracting earth changes 

 into that form whereby the original superficial area is maintained. 

 For equal surfaces the volumes of the sphere and tetrahedron are 

 to each other as 1:.55; and for equal volumes the surfaces are as 

 1:.1.45. 



Neither the theory nor its advocates gives us a four-cornered 

 earth, its original condition and axial rotation would prevent that, 

 but the theory does claim that the tendency however slight or 

 great in effect, must be towards shaj)ing the surface into that of a 

 tetrahedron, or tetrahedroid, the latter having curved surfaces 

 or edges. If a complete transformation from the sphere to the 

 tetrahedron took place, which is of course impossible, we would 

 have, taking the axis of the earth co-incident with an axis of the 

 tetrahedron through one of its apices, a north polar sea, which is 

 the case; three great equatorial oceans; a south polar land cap, 

 which too is the case; and there would be six grand mountain 

 ranges, three diverging from the south pole, corresponding to 

 three edges of the tetrahedron, and the other three encircling the 

 northern hemisphere, being along the remaining three edges of 

 the pyramid. 



In the tetrahedron every corner has a surface opposite to it, so 

 that for the earth this would mean that land and water are anti- 

 podal, which is fairly well represented in the actual conditions. 

 Another result would be that land masses would be broad in the 



