the Weight of Continents and Mountains. 263 



In § 8 I build up out of these six harmonics an isolated 

 equatorial continent. The nature of the elevation is exhib- 

 ited in Plate xx, fig. 5, in the curve marked "represen- 

 tation ;" no notice need be now taken of the dotted curve. 

 This curve exhibits a belt of elevation of about 15° of latitude, 

 in semi-breadth, and the rest of the spheroid is, approximately, 

 spherical. This kind of elevation requires the second as one 

 of its harmonic constituents, and this harmonic means ellipticity 

 of the whole globe. Now, it may perhaps be fairly contended 

 that on the earth we have no such continent as would require 

 a perceptible second harmonic constituent. I therefore give, 

 in Plate xx, fig. 5, a second curve which represents an equato- 

 rial belt of elevation counterbalanced by a pair of polar conti- 

 nents in sudi a manner that there is no second harmonic 



I have not attempted to trace the curves of equal stress- 

 difference arising from these two kinds of elevation, but I 

 believe that they will consist of a series of much elongated 

 ovals, whose longer sides are approximately parallel with the 

 surface of the globe, drawn about the maximum point in the 

 interior of the sphere at the equator. The surfaces of equal 

 stress-difference in the solid figure will thus be a number of 

 flattened tubular surfaces one within the other. 



At the equator, however, the law of variation of stress-differ- 

 ence is easy to evaluate, and Plate xx, fig. 6, shows the resnlls 

 graphically, the vertical ordinate's representing stress-uiflcr- 

 ence, and the horizontal the depths below the surface. The 

 upper curve in Plate xx, fig. 6, corresponds with the "repre- 

 sentation curve " of Plate xx, fig. 5, and the lower curve with 

 the case where there is no second harmonic constituent. 



The central stress-difference, which may be observed in the 

 upper curve, results entirely from the presence of the second 

 harmonic constituent in the corresponding equatorial belt of 

 elevation. 



The maximum stress-differences in these two cases occur at 

 about 660 and 590 miles from the surface respectively. 



We now come to perhaps the most difficult question with 

 regard to the whole subject — namely, how to apply these 

 results most justly to the case of the earth. 



The question to a great extent turns on the magnitude and 

 extent of the superficial inequalities in the earth. As the 

 investigation deals with the larger inequalities, it will be 

 proper to suppose the more accentuated features of ridges, 

 peaks and holes to be smoothed out. 



The stresses caused in the earth by deficiency of matter over 

 the sea-beds are the same as though the seas were replaced by 

 a layer of rock, having everywhere the thickness of about jf.fyf 

 or nearly T 4 T of the actual depths of sea. 



