Annus MirabilisEinstein in 1905
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brownian motion

The equation explained

−D∂(μν)∂xGramm-D \frac{\partial (\mu \nu)}{\partial x} \quad \text{Gramm}
In wordsMinus the diffusion coefficient times how steeply the mass of one particle times the number of particles in unit volume changes along the column, in grams.OverviewThe second of the two opposed processes: diffusion carries matter from where the suspended substance is crowded to where it is not, and the grams crossing a unit of cross-section each second are the diffusion coefficient times the steepness of the fall in mass per unit volume.Full explanationThe paper calls DD the diffusion coefficient of the suspended substance and μ\mu the mass of one particle, and writes down what passes per unit of time by diffusion in grams. The product μν\mu \nu is the mass of suspended substance in unit volume, so this is Fick's law in its usual shape, a flow proportional to how steeply the concentration falls. The minus sign says the flow runs from the crowded side to the empty one: where μν\mu \nu grows with xx, the flow is towards smaller xx. The paper does not derive the law here; it is the definition of the diffusion coefficient, and the value of DD for suspended spheres is what the section is about to compute.Every stepμν\mu \nuThe mass of suspended substance in unit volume: the mass of one particle times the number of them in it.∂(μν)∂x\frac{\partial (\mu \nu)}{\partial x}How steeply that mass per unit volume changes along the column.−D∂(μν)∂x- D \frac{\partial (\mu \nu)}{\partial x}The grams crossing a unit of cross-section in a unit of time, proportional to that steepness, with the sign making the flow run towards the emptier side. The printed form.Also

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