  There were yet further dimensions to Perrin's experiments. In his 1905 paper, Einstein had derived expressions for the mean displacement and rotation of Brownian particles as a function of time on the basis of the kinetic theory. Perrin was able to show how these predictions were borne out by his observations of the particles. He, in effect, showed that propositions basic to the kinetic theory, such as the independence of orthogonal components of the velocity of particles and the equi-partition of energy amongst their degrees of freedom, were satisfied by the Brownian particles. What is more, it was again possible to calculate values for N from the experimentally determined mean displacements and rotations, and in both cases the measured values were within a few percent of 68 × 1022.