14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 56 



jDresses the decay of velocity of -a body moving in a resisting medium ; or 

 the gradual extinction of light in an absorbing medium; the loss of 

 electricity or of heat by radiation from a conductor; the decay of radio- 

 activity, and an endless number of similar phenomena. Whenever the loss 

 of an entity during any instant is simply proportional to the amount of 

 the entity then present, the process must be expressed by the exponential. 

 It does not follow that the decomposition of feldspathic rocks is ac- 

 curately represented by a single exponential term. Were the whole history 

 of these rocks known it might very probably appear that the process is 

 complex and should be expressed in some such manner as 

 y_^4g-f/c_^^4^g-*/ci^ .... 



one term expressing, for example, the decay of albitc; another tbat of 

 anorthite, etc. 



There is no close analogy between the asymptotic diminution of the 

 area of those feldspathic rocks which are subject to erosion and the process 

 of refrigeration of a globe or that of the diffusion of solutions, although 

 these also are asymptotic. In the diffusion of solutions the molecular 

 flow across a plane during an instant of time is proportional to the differ- 

 ence of concentration of the two thin layers divided by the plane. If one 

 of them is devoid of solute, the process commences at immense speed ; but 

 it soon becomes very slow because the layers tend to acquire the same 

 concentration.^ Beneatli areas in which there is no erosion, such as the 

 ocean floor or lake bottoms, decomposition by diffusion is probably in 

 progress; but the amount of sodium tbus contributed to tbe rivers or the 

 sea must be negligible in comparison with that yielded by denudation.^ 



At present it appears useless to speculate on sodium accumulation as 

 represented by a series of exponential terms, nor can I think it needful. 

 Precisely as a cubic mile of granite may be regarded as isotropic because 

 the mass is so large compared with that of the single seolotropic grains of 

 which it is composed, so local inequalities of chemical denudation disap- 

 pear in the average of innumerable diversities. There must be some 

 descending exponential whicli will fairly represent the process and the 

 problem reduces to making a judicious selection of constants. 



The earlier portion of this paper is devoted to a discussion of the value 

 of N/my, or the ratio expressing the earth's age on ^fr. Joly's hypothesis, 

 and limiting values have been found for it. To compute the age on the 

 exponential hypothesis it only remains to find a value of y/A for the 

 present time. From ]Mr. Charles Schuchert's valuable memoir on paleo- 



^ For examples of the extreme slowness of diffusion see Amer. Jour. Sci., vol. 3, 1897, p. 27. For 

 definition of the process, see Everett's c. g. s. system of units, 1902, p. 151. 



^ Although the hyiserbola is an asymptotic curve, its equation would not express the course of the 

 extraction of sodium from the outer shell of massive rocks, for that would imply that this shell 

 would in time yield an infinite quantity of the metal. 



