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LVII. Researches on the Elementary Law of Hydrodiffusion. 

 By H. F. Weber*. 



AN hypothesis respecting the elementary law according to 

 which hydrodiffusion proceeds was first advanced by A. 

 Fickt twenty-three years since. The great analogy which ex- 

 ists between the process of hydrodiffusion and that of the con- 

 duction of heat in rigid substances induced Fick to assume 

 that the elementary law followed by hydrodiffusion is of the 

 same form as that advanced by Fourier at the commencement 

 of this century for the conduction of heat in rigid substances. 

 According to that assumption, the quantity of salt which, in 

 hydrodiffusion, flows in the direction of diminishing concen- 

 tration through any element of surface in a certain element of 

 time would be proportional to the magnitude of the surface- 

 element considered, the length of the time-element, the value 

 of the negative differential quotient of the concentration at the 

 place of the surface- element in the direction of the current, 

 and, finally, proportional to a constant the value of which de- 

 pends on the nature of the salt-solution in which the hydro- 

 diffusion takes place. This constant, which may be denoted 

 by k, was called by Fick the " diffusion-constant." 



From this elementary law it follows that the diffusion- 

 constant, k, signifies the amount of salt which would pass 

 through the unit of surface during the unit of time if the de- 

 crement of concentration at the place of this unit of surface 

 had invariably the value 1 ; and it follows, further, that the 

 course of the diffusion, in a vessel in which the concentration 

 z at any time t is only a function of a single space-coordinate 

 x y is determined by the partial differential equation 



Fick, in a series of measurements, sought to test the cor- 

 rectness of this hypothetical elementary law by experience. 

 He believed he might conclude from these measurements that 

 hydrodiffusion in fact proceeds according to the defined ele- 

 mentary law ; and he tried to fix the numerical value of the 

 diffusion-constant for aqueous solutions of common salt. Ob- 

 jections have since been repeatedly urged against the method 

 of measurement employed by Fick, — and justly, since his pro- 



* Translated from a separate impression, communicated by the Author, 

 of the memoir communicated to the Zurich Naturforschende Gesellschaft, 

 Nov. 25, 1878. 



t Pog-g. Ann, vol. xciv. 



