The Collaborative International Dictionary of English v.0.48:

Brownian \Brown"i*an\, a.
   Pertaining to Dr. Robert Brown, who first demonstrated (about
   1827) the commonness of the motion described below.
   [1913 Webster]

   Brownian motion, Brownian movement, the peculiar, rapid,
      vibratory movement exhibited by the microscopic particles
      of substances when suspended in water or other fluids.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Brownian movement
    n 1: the random motion of small particles suspended in a gas or
         liquid [syn: Brownian movement, Brownian motion,
         pedesis]