In 1906 Smoluchowski published a one-dimensional model to describe a particle undergoing Brownian motion. The model assumes collisions with M ≫ m where M is the test particle's mass and m the mass of one of the individual particles composing the fluid. It is assumed that the particle collisions are confined to one dimension and that it is equally probable for the test particle to be hit from the left as from the right. It is also assumed that every collision always imparts the same magnitude of Δ V. If N R is the number of collisions from the right and N L the number of collisions from the left then after N collisions the particle's velocity will have changed by Δ V (2 N R − N). The multiplicity is then simply given by: ( N N R ) = N ! N R ! ( N − − N R ) ! and the total number of possible states is given by 2. Therefore, the probability of the particle being hit from the right N R times is: P N ( N R ) = N ! 2 N N R ! ( N − − N R ) !