Brownian motion　of　particles suspended in　a　fluid　is　studied, and expressions
derived for the particle diff usivity and velocity autocorrelation function. The
theory of thermal noise in a general linear system　is　applied to both the particles
and the　fluid　in　a　n o d　formulation.　This　enables the recent modification of the
Langevin equation to include the effect of fluid inertia to be seen　as　just a
necessary but simple reinterpretation of the original analysis, without intro-
ducing the theory　of　non-Markovian processes.