In the middle of the last century, the German physiologist Fick applied the principles of heat conduction to various examples of diffusion in animals. He observed that the velocity at which a substance diffused through a given cross sectional area, its diffusive flux (J), was related to the concentration gradient of that substance (dC/dX), in the following manner:

where D is the Diffusion coefficient (in cm2 per sec); the negative sign convention indicates diffusion occurs from regions of higher C to those of lower C. Integrating this expression for diffusion from a region of high concentration to one of lower concentration, produces the following relationship:

Thus, in the cgs system, a deltaC measured in M (mol per l or mmol per cm3) over a distance of 1 cm, with a Diffusion Coefficient in cm2 per sec, would produce a flux with units of (mol per cm2) per sec. Redefining the terms and solving for the substance's velocity (V) of diffusion produces:

where P is the Permeability Coefficient of the substance being measured (the Diffusion Coefficient per unit X), and A is the effective cross-sectional area of the region over which diffusion occurs. This is the usual form of the Fick Equation.