In ultracentrifugation, the concentration gradient of mono-disperse samples obtained by sedimentation velocity experiments is described by Gehatia's equation which holds several parameters including the sedimentation and diffusion constants. Once these two constants are known, the molecular weight follows from the Svedberg equation. A least squares method has been developed to derive the transport constants from the refractive index gradient curves. The method employs a mathematical model based on Gehatia's theory. A main feature of the model is the application of two sets of intermediate parameters via which the transport coefficients are much casier calculated than along a direct way. Furthermore some difficult to observe quantities cancel out. The square residues are minimised numerically. The potential errors introduced by this numerical minimalisation are shown to be unimportant compared to the unavoidable experimental errors.
Grievink, J., Houterman, R. T. B., & de Groot, K. (1974). Protein molecular weight computation from sedimentation velocity data. Analytical biochemistry, 57(1), 137-156. https://doi.org/10.1016/0003-2697(74)90060-8