Scottish botanist and palaeobotanist Robert Brown published for private distribution in London at the press of Richard Taylor a small number of copies of his 16-page pamphlet entitled A Brief Account of Microscopical Observations Made in the Months of June, July, and August 1827, on the Particles Contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic bodies.
While studying pollen, Brown observed particles within the grains in a state of constant motion. He extended his observations to both dead and inorganic matter, and found that such motion was not restricted to live pollen but could be observed in any substance ground fine enough to be suspended in water. In 1879 William Ramsay explained that Brownian motion is due to the impact on particles of the molecules in the surrounding fluid, an explanation proved in 1908 by Jean Perrin. Brown's observations also inspired Einstein's 1905 paper Ueber die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendieren Teilchen, which gave a theory of Brownian motion based on the kinetic theory of gases.
The seemingly random movement of particles suspended in a liquid or gas or the mathematical model used to describe such random movements is often called particle theory.
"The mathematical model of Brownian motion has several real-world applications. An often quoted example is stock market fluctuations.
"Brownian motion is among the simplest continuous-time stochastic processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem). This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience rather than the accuracy of the models that motivates their use" (Wikipedia article on Brownian motion).
Hook & Norman, The Haskell F. Norman Library of Science and Medicine (1991) no. 353.
♦ You can download a PDF of the original private printing of Brown's paper at this link.