ALPINE SCULPTURE. 239 



the most prominent portions of the protuberance three 

 miles above the sea-level. To fix the ideas, let us con- 

 sider a circular portion of the crust, say one hundred 

 miles in diameter, and let us suppose, in the first in- 

 stance, the circumference of this circle to remain fixed, 

 and that the elevation was confined to the space within 

 it. The upheaval would throw the crust into a state 

 of strain; and, if it were inflexible, the strain must be 

 relieved by fracture. Crevasses would thus intersect 

 the crust. Let us now enquire what proportion the 

 area of these open fissures is likely to bear to the area 

 of the unfissured crust. An approximate answer is all 

 that is here required; for the problem is of such a 

 character as to render minute precision unnecessary. 



No one, I think, would affirm that the area of the 

 fissures would be one-hundredth the area of the land. 

 For let us consider the strain upon a single line drawn 

 over the summit of the protuberance from a point on 

 its rim to a point opposite. Regarding the protuber- 

 ance as a spherical swelling, the length of the arc cor- 

 responding to a chord of 100 miles and a versed sine 

 of 3 miles is 100.24 miles; consequently the surface to 

 reach its new position must stretch 0.24 of a mile, or 

 be broken. A fissure or a number of cracks with this 

 total width would relieve the strain; that is to say, the 

 sum of the widths of all the cracks over the length of 

 100 miles would be 420 yards. If, instead of com- 

 paring the width of the fissures with the length of the 

 lines of tension, we compared their areas with the area 

 of the unfissured land, we should of course find the 

 proportion much less. These considerations will help 

 the imagination to realise what a small ratio the area 

 of the open fissures must bear to the unfissured crust. 

 They enable us to say, for example, that to assume the 

 area of the fissures to be one-tenth of the area of the 



