16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5G 



being 23 per cent. He too was impressed by the smallness of the variation 

 in the relative areas of Archean exposures. 



If the present continental area were the mean land area von Tillo's 

 data would give at once y/A = 0.23, but since the land now stands at a 

 high level the true value of A is smaller than the actual area and the 

 quantity 0.23 must be modified accordingly. 



The greater part of the area of massive rocks lies at a considerable dis- 

 tance from the sea, so that a partial submergence would diminish the con- 

 tinental area much more in proportion than the exposure of feldspathic 

 rocks. In order to include, if possible, the true mean value of the land 

 area, I shall take y/A first at three-tenths and again at one-fourth ; the 

 latter exceeding the 0.23 derived from von Tillo's data by a proportion 

 relatively trifling while, closely enough, 0.3 = 0.23/0.8, the denominator 

 representing the mean taken from Mr. Schuchert's memoir. 



With these data the results are as follows : 



y/A 0.30 0.30 0.25 0.25 



N 10-ymy 144.2 99.5 144.2 99.5 



c/10" 61.80 42.64 48.07 33.17 



Amc lOiY/7 lOA^/7 43V/3 4AV3 



t/lO" 74.4 51.3 66.6 46.0 



Here the second line gives the ages on Mr. Joly's hypothesis in millions 

 of years, and the last that computed from the logarithmic relation. The 

 fourth line gives the ultimate amount of oceanic sodium calculable from 

 the equations, and inferentially the thickness which Clarke's shell may 

 reach, 10/7 or 4/3 of its present value. With the larger fraction this 

 shell, now measuring 2050 feet, would ultimately attain a thickness of 

 2930 feet, or if it were all piled onto our continents, 2.2 miles. The 

 difference between this estimate of the ultimate size of Clarke's shell and 

 its present dimensions represents a volume 2-| times as great as that of 

 the present continents above sea level. Such, then, on this rather extreme 

 assumption, would be the volume of massive rock, still fresh, but doomed 

 to eventual decomposition. Thus the hypothesis leaves an ample margin 

 for future igneous effusions and epeirogenic uplifts without putting an 

 excessive strain upon the imagination. 



Of the ages computed, the greatest, 74 million years, is the most 

 valuable. It is indisputable that the process of rock decomposition is an 

 asymptotic one and at least roughly represented by the simple exponential, 

 while every effort has been made to select for the first computation the 

 highest reasonable values for N/my and y/A. All the estimates would be 

 greatly reduced if a primitive salinity of the sea or the former existence 

 of land areas in the great oceanic basins were assumed. Those who do not 

 feel obliged to accept either of these hypotheses may perhaps agree in my 



