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 laud, 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 laud 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, were 
it proved, the fissures would still play the subordinate part 
