ALPINE SCULPTURE. 239 



diameter, and let us suppose, in the first instance, the 

 circumference of this circle to remain fixed, and that 

 the elevation was confined to the space within it. The 

 upheaval ^vould 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 re- 

 quired ; for the problem is of such a character as to 

 lender 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 protuberance 

 as a spherical swelling, the length of the arc corre- 

 sponding 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 

 land would be quite absurd, while that the area of the 

 fissures could be one-half or more than one-half that of 

 the land would be in a proportionate degree unthink- 



