Bev. 0. Fisher — On the Formation of Mountains. 253 



In like manner let a, /3, be similar areas for the lower datum 

 level CD. Then the space included between the curved lines 

 (which we will call the " contour" lines) must be equal to 

 AhCd = iZ (1 4- e). 

 It is also evidently equal to 



^ jB Ci) + « + a + &c. + yS + /S + &c. 

 — h — h — &c. — a — a — &c. 

 or, denoting the sums of the quantities of the same sort by the 

 symbol X, we get 



kl{l^e) =kl+X[a)- X[b) + 5'(/3)-^(a). 

 :,kle = X{a)-X{h)-\-X{m-X{a). (1). 



Let us now suppose that the crushed and contorted mass is solely 

 supported by the superheated rocks below, which, but for the attach- 

 ments dit AG and B D, would be absolutely true ; and must be very 

 nearly true in any case. We may treat the superheated rocks as a 

 fluid, and apply the conditions of statical equilibrium. 



The mass which is supposed thus to float, the fluid being allowed 

 to have free access to every part, was in hydrostatic equilibrium 

 before its expansion and consequent disturbance ; that is, its surface 

 would then have been at the same level as the surface of the fluid. 

 (This is the same as the supposition that we made at the commence- 

 ment, p. 250.) It is therefore evident that, upon the expansion of 

 A B CD, or h I, into hi (1 -\- e), the part which would float above the 

 surface, would be equal to the additional volume arising from the 

 expansion, because the specific gravities will be inversely propor- 

 tional to the volumes, or (since we are considering the thickness to be 

 nnity) to the areas. 



Hence hie = ^ (a). 



Also, since the specific gravity of the expanded mass is supposed 

 everywhere to be less than that of the fluid beneath it, its surface 

 would be everywhere above the surface of the fluid, unless it was. 

 tinder constraint, or in other words we should have 



S{b)=o. _ , 



Hence, if such hollows as b, h, extend below the datum line, it can 

 only be under constraint, and since there is more freedom for the 

 rocks to be contorted upwards than downwards, we may consider it 

 most probable that there will be no such hollows below A B. How- 

 ever, for the present, we will suppose them to exist, but that the 

 fluid has not access to them. Then, applying the conditions of 

 hydrostatic equilibrium, we get, putting p and a for the densities 

 before and after expansion, the former being that of the fluid, and 

 observing that 



p _ l-\- e 



kl {l ^ e) a = kip — X (a) p + 'X {^) p 

 = — ^ (a) + 5 i,Q). 



