Brownian motion—zig-zag motion of tiny particles in water—had been known since the late 19th century. Perrin used it by measuring a "sedimentation equilibrium," the balance between gravity pulling particles downward and thermal kicks from molecules pushing them upward. By studying the exponential decrease of particle concentration with height, he showed that the same equation used in kinetic theory of gases also applies in liquids and obtained an independent value of Avogadro’s constant. This strongly confirmed the reality of atoms and molecules, delivering a decisive blow in favor of atomic theory, which was still doubted by some scientists. The work laid foundations for modern nanotechnology, colloid chemistry, and drug-formulation science.

Perrin prepared suspensions of colloidal particles (~1 µm diameter) and quantified their vertical distribution using an ultramicroscope and sequential photography. The particle number density n(h) is predicted to follow n(h)=n(0) exp(−mgh/k_BT), where m is the effective mass, g the gravitational acceleration, and k_B Boltzmann’s constant. By measuring concentration profiles for several particle sizes, he extracted k_B and hence Avogadro’s constant N_A=k_B R/F. The obtained N_A agreed with values derived from gas-law and electrochemical measurements, establishing the discrete molecular nature of energy. Perrin also measured the mean-square displacement of Brownian particles, verifying the Einstein–Smoluchowski relation ⟨x²⟩=2Dt. These achievements provided experimental support for statistical-mechanical links between macroscopic and microscopic descriptions and later underpinned light-scattering techniques and analytical ultracentrifugation theory.

Perrin employed colloidal gamboge and mastic spheres with carefully calibrated densities, using the Siedentopf–Zsigmondy ultramicroscope to count particles layer by layer. He corrected for buoyancy and hydrodynamic interactions to recover the true buoyant mass m_b and verified the barometric law n(h)=n_0 exp(−m_b g h/k_BT) within a few percent over 0.01–0.3 cm. By combining several particle radii he obtained k_B independently of absolute concentration. Time-resolved tracking supplied the diffusion coefficient D, which satisfied the Einstein relation D=k_BT/6π η r, closing consistency among n(h), D, and r. The final N_A=(6.8 ± 0.2)×10²³ mol⁻¹ coincided with Richards’ electrochemical and Rayleigh’s kinetic values, effectively silencing anti-atomists like Ostwald. Perrin’s rigorous control of systematic errors—temperature gradients, convection, van der Waals attractions—set standards for precision colloid physics. His results stimulated Gibbs–Duhem treatments of osmotic pressure, inspired Debye’s light-scattering theory, and foreshadowed Svedberg’s ultracentrifugation analyses. The 1926 Nobel citation thus justly highlights sedimentation equilibrium as an empirical keystone linking statistical mechanics, physical chemistry, and modern soft-matter science.