1922] Whitman: Genesis of the Ores of the Cobalt District 289 



span of time at the disposal of the genetic processes operative at 

 Cobalt, have accomplished surprising results. 



The reconciliation of our notions to the idea that diffusion can 

 produce large ore bodies must necessarily center about an analysis 

 of the mechanism of diffusion, and also about a scrutiny of rock 

 media as sites for its operation. Whatever may be the intimate nature 

 of the phenomena their general characters are familiar to everyone. 

 Osmosis may be looked upon as a tendency of water or any solvent 

 to mingle to the maximum with a solute, while diffusion may be looked 

 upon as the reciprocal tendency of a solute to become equally dis- 

 tributed throughout a solvent. R. E. Liesegang 15 has pointed out that 

 a large molecule behaves in a manner intermediate between a colloidal 

 particle and an ion, diffusing with great slowness against gravity, 

 while an ion diffuses with comparative rapidity. It appears that 

 diffusion is roughly inversely proportional to the size of molecules 

 and ions, and that dissociation is proportional to heat and pressure. 

 Soret has also shown that diffusion is proportional to temperature ; 

 while Fick has shown that the rate of diffusion is proportional to con- 

 centration. G. F. Becker, 10 applying Fick's law mathematically, has 

 derived some useful figures showing the distance covered by a diffus- 

 ing salt in a given time. He says : 



In ' ' linear ' ' motion as defined by Fourier the subject of motion, or the 

 ' ' quantity ' ' as Lord Kelvin calls it, varies only in one direction ; in other words, 

 it remains uniform at all points in any one plane at right angles to this direc- 

 tion For quantities obeying the law of diffusion the differential equation is 



— — Tc— t- x- Here v is the quantity, t the time, x the distance from the plane 



dt dx? 



of contact between the subject of diffusion and the medium into which it diffuses, 

 and fc is the " diffusivity " assumed to be constant. The equation may be 

 expressed by the statement that the time rate of change of quality is proportional 



to the space rate of the space rate of change of quality The quality at any 



distance measured perpendicularly to the initial plane is then proportional to the 

 area of the ' ' probability curve ' ' taken between certain limits If the acces- 

 sible tables have the usual form, it is only necessary to write the equation as 

 follows: 



In this equation c represents initial concentration, and q = — = the least 



r 2\Jlct 



laborious method is to assume q at some tabulated even value, find i or t from 

 the first of the above equations and v from the second. 



15 Geologische Diffusionen, p. 5. See also Wolfgang Ostwald, Handbook of 

 colloidal chemistry. 



1 6 Note on computing diffusion, Am. Jour. Sei., ser. 4, vol. 3, art. 25. 



