Rev. 0. Fisher — On the Formation of Mountains. 255 



is proportional to tlie part of the stratum on. which it stands, in that 

 case the height of each ridge will 2 kme. 



If we do not consider each ridge formed out of, or even propor- 

 tional to, the part on which it stands (which will be more general 

 and probably more in accordance with nature), we have, 



5* i| A. ■J^ = / A; ('. 

 taking for i] its average value, which we will call h. 



^ l\h = Ike. 

 but S X=: I. 



.*. h z=2 k e a.s before, 



1 /7> 



and if the compression be thrown into — of the datum line 



m 



h = 2 k m e. 

 which gives this rule to estimate the average height of the mountains. 

 Multiply together the thickness of the layer before its compression, 

 the number of times which the datum line contains the widtli of the 

 disturbed area, and the coefficient of expansion ; and twice this pro- 

 duct will give the average height of the mountains. 



If a uniform deposit were laid down upon the datum line before 

 the expansion occurred, as in the case contemplated by Capt. Hutton, 

 we should get a very similar result, except that the surface contour 

 line would not coincide with the upper line of the expanded layer, 

 but would run at a nearly uniform distance from it, so that the 

 formulse already investigated would still be applicable, except that 

 the heights would have to be measured from a new datum line, viz. 

 the upper surface of the deposit. When the deposit had reached its 

 utmost extent, this would be the sea-level, and if such depressions 

 as b, b, were formed, they would probably be seas. 



Let us apply our rule to the mountains which would be formed 

 by the expansion of the layer of rock with the data suggested by 

 Captain Hutton. In this case I is the length of the arc, which geo- 

 metrically is sufficiently nearly a straight line, and mechanically is 

 strictly horizontal, for it is at every point in the direction of the 

 compressing force, and also at right angles to the force of gravita- 

 tion. We will suppose the ridge or ridges to be formed along the 

 whole of the base line or arc. 



Let us take for our instance the fourth column of the table. Here 

 e = 0-001 and m = 1. But h is unknown. 



The average height of the mountains will therefore be 2 x 0-001 

 X thickness of the heated layer, or 0-002 x thickness of heated layer. 

 It is of course independent of the length of the arc. 



I will not presume to guess the thickness of rock which would in 

 the manner supposed be heated by 200° F. But whatever assump- 

 tion be made, the average height of such corrugations as I have 

 assumed would be each of them (were they few or many) ten five- 

 thousandths of that thickness, that is about ten feet high for every 

 mile thick of rock raised 200° F. 



Were the corrugations supposed of a curvilinear contour they 

 would be not quite so high. We see then that the elevations which 

 could be produced by such heating and expansion would be quite 



