The Plan of the Earth and its Causes. — Gregory. 113 
of fold-mountains is to us a significant question, because there 
is much truth in the phrase, proverbial since its use in 1682 by 
Burnet in his "Theory of the Earth," which describes the 
mountain chains as the "backbones of the continents." The 
first geological attempt to explain the plan of the earth was 
based on this belief. The author of this system was the French 
geologist Elie de Beaumont, whose theory of geomorphogenv 
was stated at length in his "Notice sur les systemes de mon- 
tagnes" (3 vols.: Paris, 1852). This famous theory was 
based on a correlation of the mountain chains by means of their 
orientation. Elie de Beaumont accepts the view that the earth 
consists of a thin rigid crust surrounding a fluid, solidifying in- 
terior. The crust being thin, it necessarily collapses as the in- 
ternal mass contracts. He assumes that these collapses occur 
at intervals of time, and that at these collapses the crust is 
broken along lines of weakness, which are crumpled up into 
mountain chains. He assumes that for practical purposes the 
earth's crust ma)- 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 enclosed by twelve 
equal regular pentagons, possesses an exceptionable degree of 
bilateral symmetry, /. e. it can be cut into exactly similar halves 
in an unusually large number of directions. Sections along 
any of the edges of any of the pentagons and through the 
center of the pentagonal dodecahedron divide it into equal 
and similar halves. So akso 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 penta- 
gonal dodecahedron ma}- therefore be divided by fifteen planes 
of symnietr\-. 
A sphere may be described upon the pentagonal dodecahe- 
dron, so that all the corners (or, to use the correct term, solid 
angles) occur in the surface of the si)here. By joining the cor- 
ners by lines, the sphere is marked off into twelve spherical 
pentagons, ^vhicll i)ossess the same amount of symmetry as the 
plane ])entagons. The lines where these planes of symmetry 
cut the surface of the sphere form a network of spherical tri- 
