An Approximate Solution of the Differential Equation of the Ultracentrifuge

Abstract

In determining molecular weights with the ultracentrifuge by the equilibrium method, it is necessary to drive the rotor at relatively high speeds for very long periods of time. It would be a real advantage to be able to deduce molecular weights from the distribution of concentration within a cell placed in a rotor without waiting for equilibrium. The solution of a certain differential equation gives the theoretical distribution within the cell at any time, and a comparison of the experimentally determined concentrations with those deduced from theory should yield molecular weights without waiting for equilibrium. The exact solution of this differential equation is known, but it is not suitable for numerical work. The present paper presents an approximate solution from which numerical results can be obtained with ease.