  Perrin's observations revealed that the density distribution of Brownian particles decreased exponentially with height. He was able to explain this quantitatively by appeal to Newtonian mechanics and statistics. Because of the decrease in their density with height, more particles per second strike a unit area of the lower surface of a thin horizontal layer in the liquid than will strike a unit area of the upper surface. As a result there will be a net pressure directed upwards. Perrin was able to derive a value for the pressure in terms of the number of particles per unit volume, their mass and the mean of the squares of their velocities. Equilibrium is reached when the upwards force due to the pressure is equal to the weight of the particles arising from the excess of the density of the material of the particles over that of the suspending liquid. The resulting equation, when integrated, showed the density of the particle distribution to vary exponentially with height and also enabled Perrin to calculate a value for the mean kinetic energy of the Brownian particles from the measured variation in density of the particle distribution. It transpired that the mean kinetic energy depended only on temperature and was independent of the material of the particles, their size and the density of the liquid in which the particles were suspended.