Brownian motion states that particles move in a random unpredicted motion (like they dont all more from north to south, or from up to down, they move wherever). Particle theory states that gases consist of particles that are constantly moving in a random direction.
These two theories support each other as particle theory claims that particles are constantly moving in a random motion, and Brownian motion claims that particles move in a random motion.
NOTE: Both of these theories can help explain post 5.5
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