Still water looks different through a microscope
A speck of dust is heavier than water, so we expect it to fall and remain on the bottom. Look at a sufficiently small suspended grain through a microscope, however, and it keeps wandering. Jean Perrin used this restless motion in experiments reported in 1908 and 1909. By counting visible grains, he could estimate how many invisible molecules make up a familiar quantity of matter.
The wandering is Brownian motion, named after Robert Brown’s observations. Water molecules continually strike the grain from different sides. For a large object, the many tiny pushes almost cancel at the scale we notice. A small grain receives an uneven succession of pushes large enough to move it visibly. Even water at a uniform temperature contains this incessant molecular activity.
He first had to make the grains comparable
A jar containing grains of many sizes gives a confusing mixture. Large grains settle differently from small ones, and they experience different amounts of visible wandering. Perrin prepared emulsions of materials such as gamboge and mastic, then separated them to obtain batches with closely similar grain sizes. The preparation made a quantitative comparison possible.
He also needed the grain density and size. Gravity pulls a grain downward, but the surrounding water pushes upward through buoyancy. The effective downward force therefore depends on the excess of the grain’s density over that of the liquid. A small error in radius matters greatly because the grain’s volume grows with the cube of its radius.
Only after controlling these properties did a count at one height become meaningfully comparable with a count at another. Under the microscope, focusing selected a thin horizontal slice. Repeating the counts reduced the noise caused by grains entering and leaving that slice during observation.
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Gravity and thermal motion set a height distribution
Gravity favours the bottom of the preparation. Thermal motion spreads grains upward as well as sideways. Once the suspension reaches sedimentation equilibrium, these tendencies balance: the average concentration at each height stays steady even though individual grains continue to move. Equilibrium describes a stable distribution of activity.
The prediction is quite specific. For equal grains at a fixed temperature, raising the observation layer by the same distance should reduce the average concentration by the same factor. A sequence might have half as many grains at each successive level. The size of the height step depends on temperature and the buoyancy-corrected weight of a grain.
From that measured decrease, Perrin could infer the thermal energy associated with one particle. Comparing this microscopic energy scale with the independently known gas constant gave Avogadro’s number, the number of entities in a mole. A visible grain contained an enormous number of molecules, yet it followed the same statistical rule as one much smaller particle.
The random walks offered another route
Einstein and Smoluchowski had developed theories of Brownian motion that connected diffusion with thermal energy and viscous resistance. The useful measurement was a grain’s displacement over a stated time interval. Tracing every bend of its path was unnecessary. Many displacements, collected under the same conditions, could be compared statistically.
The time dependence gives an intuitive test. Wait four times as long, and the typical distance from the starting point grows only about twofold. The grain repeatedly changes direction, so its progress is much slower than a steady journey at one speed. A single long excursion is unreliable; the average over many observations is the quantity the theory predicts.
The mean squared displacement grows in proportion to elapsed time for ordinary diffusion. Perrin’s group changed grain sizes and liquids and compared the inferred molecular counts. Agreement with the sedimentation measurements strengthened the molecular explanation, because one method used the final distribution and the other used motion over time.
The experiments also taught a practical caution: a nearby wall slows a grain’s movement. Perrin discussed how measurements farther from the walls changed the inferred value. His historical values were approximate and do not equal the modern exact definition of Avogadro’s constant. The persuasive result was that several different measurements approached the same molecular scale.
A molecular picture became experimentally tangible
The 1926 Physics Prize recognized Perrin’s work on the discontinuous structure of matter, especially sedimentation equilibrium. The experiments gave the idea of molecules a measurable consequence in ordinary liquids. One could prepare a suspension, wait, focus the microscope at a new height, and ask whether the count matched the molecular prediction. The invisible structure of water had become accessible through the behaviour of visible grains.
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