Annus MirabilisEinstein in 1905
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brownian motion

The equation explained

νK6πkP\frac{\nu K}{6 \pi k P}
In wordsThe number of particles in unit volume times the force on one particle, divided by six pi times the friction coefficient of the liquid times the radius of a particle.OverviewHow many particles the force carries across a unit of cross-section in a unit of time: the number in unit volume times the speed each of them takes.Full explanationThe display before gave the speed of one particle under the force. To count how many cross a surface, take the particles that lie within one speed's distance of it: in unit time every particle within that distance passes, and through a cross-section of area 1 that is a volume equal to the speed itself. With ν\nu particles in unit volume, the number passing is ν\nu times the speed. This is the first of the two opposed flows, the one the force drives; the second, the diffusion, is counted in the displays that follow, and dynamic equilibrium is the statement that the two cancel.Every stepv=K6πkPv = \frac{K}{6 \pi k P}The speed one particle takes under the force, from the display before.νv\nu vThe particles crossing a unit of cross-section in a unit of time: those within a distance vv of it, which occupy a volume vv when the cross-section is 1, at ν\nu particles in unit volume.νK6πkP\frac{\nu K}{6 \pi k P}The same with the speed written out. The printed form.Also

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