Smoluchowski 's theory of Brownian motion starts from the same premise as that of Einstein and derives the same probability distribution ρ (x, t) for the displacement of a Brownian particle along the x in time t. He therefore gets the same expression for the mean squared displacement: E [ ( Δ Δ x ) 2 ] . However, when he relates it to a particle of mass m moving at a velocity u which is the result of a frictional force governed by Stokes's law, he finds E [ ( Δ Δ x ) 2 ] = 2 D t = t 32 81 m u 2 π π μ μ a = t 64 27 1 2 m u 2 3 π π μ μ a , where μ is the viscosity coefficient, and a is the radius of the particle. Associating the kinetic energy m u 2 / 2 with the thermal energy RT / N, the expression for the mean squared displacement is 64/27 times that found by Einstein. The fraction 27/64 was commented on by Arnold Sommerfeld in his necrology on Smoluchowski: "The numerical coefficient of Einstein, which differs from Smoluchowski by 27/64 can only be put in doubt."