ALPINE SCULPTURE. 183 



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 corresponding to a chord of 

 100 miles and a versed sine of three 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 num- 

 ber 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 

 comparing 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 imagina- 

 tion to realize what a small ratio the area of the open fis- 

 sures 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 unthinkable. If we suppose the 

 elevation to be due to the shrinking or subsidence of the 

 land all round our assumed circle, we arrive equally at the 

 conclusion that the area of the open fissures would be 

 altogether insignificant as compared with that of the un- 

 fissured crust. 



To those who have seen them from a commanding eleva- 

 tion, it is needless to say that the Alps themselves bear no 

 sort of resemblance to the picture which this theory pre- 

 sents to us. Instead of deep cracks with approximately 

 vertical walls, we have ridges running into peaks, and 

 gradually sloping to form valleys. Instead of a fissured 

 crust, we. have a state of things closely resembling the sur- 

 face of the ocean when agitated by a 'storm. The valleys, 

 instead of being much narrower than the ridges, occupy 

 the greater space. A plaster cast of the Alps turned up- 

 side down, so as to invert the elevations and depressions, 

 would exhibit blunter and broader mountains, with 

 narrower valleys between them, than the present ones. The 

 valleys that exist cannot, I think, with any correctness of 

 language be called fissures. It may be urged that they 

 originated in fissures: but even this is unproved, and, wriv 

 it proved, the fissures would still play the subordinate part 



