254 Ret\ 0. Fisher — On the Formation of Mountains. 



But we have shown that 



kle = -^ {a) ^ X [b) + ^ {^) - -X (a). 

 hle=Xia) - X{b). 



Hence, if the mass was under such constraint as to admit of the 

 hollows 6, 6, existing below the datum level, the above relation would 

 subsist between the areas of section of the mountains and of these 

 basins. The datum level will be, on Captain Button's hypothesis, 

 a surface buried beneath new deposits. 



But if the mass was not under such constraint as to form these, 

 hollows, so that as already shown 5* (&) = o, then we should have 

 as before 



k le = X («). 



This I consider a very important result. The above considera- 

 tions give us the further information. 



X (a) = X (/3). 



That is to say, the sum of the areas which dip down into the 

 superheated rocks will equal the sum of the areas in which the 

 superheated rocks rise up into the synclinals. This is another 

 important conclusion. 



I will proceed to consider the more simple case in which the sur- 

 face of the contour of all the masses, be their form what they may, 

 is above the datum level. (See Woodcut 3). 



For further simplicity let us consider the sections of the ridges to 

 form isosceles triangles. It is likely that for the same area X («), 

 the average height of the ridges, will be slightly greater for such 

 triangles than for curves, and the length of contours will not be 

 very different in the two cases. 



It is easily seen that if any number n of triangular ridges be 

 formed all along the datum line, and each triangle out of the ex- 

 pansion of the part of the stratum on which it stands (i.e. a = base 

 y. k e), and if X be the base of any triangle and r) its height, 

 since I \i] =:\k e, 

 V = 2ke. 

 This shows that if each ridge is formed out of the part of tho' 

 stratum on which it stands, the height of the ridge, so long as we 

 can suppose a triangle to represent it, will be nearly the same, 

 whatever be the width of its base (unless the base be very narrow). 



If under the same suppositions we conceive the whole disturbance 



1th 

 thrown into — of the datum line, and that the- area of each triangle 

 m 



