How did James Clerk Maxwell describe the distribution of molecular speeds in a gas?

In 1859, Scottish physicist James Clerk Maxwell described the distribution of molecular speeds in a gas using probabilistic arguments. Rather than assuming all molecules move at a uniform speed, Maxwell recognized that in a kinetic-molecular system, molecules travel in arbitrary directions at speeds distributed randomly about an average determined by the gas temperature.12

This work, known as the Maxwell-Boltzmann distribution, provides a statistical description of how velocities—and later, energies—are distributed among the molecules of a classical gas. The distribution function implies that while individual molecular speeds vary, the collective behavior of the gas follows predictable statistical patterns, provided that quantum-mechanical effects are not significant. This foundational concept remains a cornerstone of statistical physics.12