THE PLAN OF THE EARTH AND ITS CAUSES. 373 



lines of weakness, which are crumpled up into mountain chains. He 

 assumes that for practical purposes the earth's crust may be taken as 

 homogeneous; hence that the fractures of the crust would be regularly 

 distributed, and those of successive periods would cross one another 

 along the lines of a regular symmetrical network. 



Among the regular simple geometrical forms that known as the 

 pentagonal dodecahedron, which is inclosed by twelve equal regular 

 pentagons, possesses an exceptionable degree of bilateral symmetry, 

 i. e., it can be cut into exactly similar halves in an unusually large 

 number of directions. Sections along any of the edges ot any of the 

 pentagons and through the center of the pentagonal dodeeahedrou 

 divide it into equal and similar halves. So, also, do sections from the 

 center of the pentagons to any of the angles, and likewise sections 

 across the pentagons from alternate angles. Each face of a pentagonal 

 dodecahedron may therefore be divided by fifteen planes of symmetry. 



A sphere may be described upon the pentagonal dodecahedron, so 

 that all the corners (or, to use the correct term, solid angles) occur in 

 the surface of the sphere. By joining the corners by lines the sphere 

 is marked off into twelve spherical pentagons, which possess the same 

 amount of symmetry as the plane pentagons. The lines where these 

 planes of symmetry cut the surface of the sphere form a network of 

 spherical triangles. Such a network FJie de Beaumont called his 

 pentagonal network, and he used it in the following way: He studied 

 the mountain ranges of the world, and by elaborate calculations showed 

 their relative directions at a few localities which he chose as centers of 

 comparison. He found that many mountain ranges have the same 

 orientation and that others cross the first set at definite regular angles. 

 The directions of the different sets of mountain ranges coincide with 

 the lines of his pentagonal network, lillie de Beaumont claimed that 

 the mountains whose directions are parallel 1 were formed at the same 

 date. Successive mountain-forming movements raised chains parallel 

 to different edges of the network, and thus the intersecting mountain 

 lines of the world, and consequently the forms of the continents, were 

 determined. 



Elie de Beaumont had no difficulty in pointing out striking coinci- 

 dences between important geographical lines and his pentagonal net- 

 work. Thus the Mediterranean volcanic axis, passing through the 

 Grecian archipelago, Etna, and Teneriffe, is parallel to the Alpine 

 chain and at right angles to the circle through Etna, Vesuvius, Ice- 

 land, and the Sandwich Isles. He was able to show a close geometrical 

 relationship between those lines and the line of the Andes, with the 

 pentagon that covers Europe. That the earth is traversed by great 

 intersecting lines is undeniable. E. g., Daubree showed that the valley 

 system of northern France follows a line of rectangular fractures, which 



1 For explanation and justification of this use of the word "parallel," see Hopkins, 

 "Presid. Address, Geol. Soc," Quart. Jour. Geol. Soc., Vol. IX, p. xxix. 



