510 



SCIENCE 



[N. S. Vol. XXXI. No. 796 



ical denudation per unit area may not have 

 changed considerably, but the most rigid uni- 

 f ormitarian would not maintain that the total 

 area of exposed massive rocks has been con- 

 stant. The inference seems unavoidable that 

 sodium accumulation is an asymptotic process 

 which progressed more rapidly (though pos- 

 sibly not with greater intensity) in the dis- 

 tant past and will come substantially to an 

 end when a certain very finite layer of surface 

 material has been exhausted. It seems worth 

 while to attempt some rough estimates based 

 on this conception of the saltness of the ocean. 

 There is a great deal of evidence for the 

 elder Dana's generalization as to the perma- 

 nence of continental areas. Dana would have 

 been the last to assert absolute invariability 

 of the land area but, just as it seems less 

 hazardous to assume a uniform areal rate of 

 decomposition than any uncertain or fanciful 

 variation of that rate, so it seems safest for 

 the present purpose to suppose the total area 

 constant. 



The simplest law compatible with the con- 

 ditions set forth is that the proportionate de- 

 crease in the sodium-producing exposures of 

 massive rocks has been constant. This is of 

 course the familiar compound-interest law. 

 In other words the hypothesis proposed is that 

 the area of exposed sodium-bearing rocks can 

 be represented approximately by the descend- 

 ing exponential which is so characteristic (in 

 Mr. Walcott's words) of cases in which " an 

 entity is subject to gradual extinction or ab- 

 sorption." 



If 4 is the total constant land area and y 

 the exposure of sodium-bearing rocks when the 

 ocean had an age of t years while c is a certain 

 constant to be determined from limiting con- 

 ditions, then the hypothesis to be examined is 



i^Ae-t^o 



< = c log A/y. 



Suppose the total sodium content of the 

 ocean at time f to be iV and let my be the 

 increment of N in any one year. Then m 

 being constant 



N=: I mydt = Amc{l — y/A). 

 Jo 



Here N is pretty well known, and so is A, or 



at least its present value, while m and the value 

 of y for the present time are known to a cer- 

 tain degree of approximation. Hence c can 

 be found. If i were infinite, y would become 

 zero, and therefore Amc represents the total 

 sodium which can possibly be supplied to the 

 ocean if the hypothesis fits the case. From 

 this total it is easy to compute the thickness 

 of the layer of average massive rock which 

 would yield it. 



Mr. Joly's assumption expressed in this no- 

 tation is that, subject to minor corrections,' 

 the age t would be given by N/my. His data 

 are 



iV = 14,694 X lO"- and my — 155.42 X 10' 

 tonnes (or metric tons) and I shall adopt the 

 same values in order to obtain strictly 

 comparable results. The ratio N/my is 

 94.544 X 10'. 



A careful study of the areas of exposure of 

 the principal geological formations was made 

 by the late distinguished physical geographer 

 Lieutenant-General Alexis von TiUo. This 

 includes the Archean and the younger erup- 

 tives, the results being expressed in hundredths 

 of the total surveyed area. The following is 

 an extract from von TiUo's table.* 



Continent Archean 



Europe 20.6 



Asia 17.7 



Africa 18.4 



Oceaniea 20.0 



North America 27.2 



South America .... 18.7 

 Mean ; . 20.3 



The most recent geological map of North 

 America (compiled by Mr. Bailey Willis) 

 shows that the relative area of exposed feld- 

 spathic rocks on this continent is not so large 

 as was supposed when von Tillo wrote, and, 

 though I have made no minute measurements, 

 this exposure as now mapped seems not to ex- 

 ceed 25 per cent. With this emendation von 

 TiUo's table shows a truly remarkable uni- 



' Especially for marine denudation and uncer- 

 tainty in the volume of the ocean. 



* Gomptes Rendus, Paris, Vol. 114, 1892, pp. 246, 

 967. 



