Variable inner radius variation of P with S

Differentiating equation (8.72) with respect to S, keeping R and t constant, and substituting back for P dP. gives  

Three distinct methods are therefore available for calculating the mass distribution of particles in suspension for a series of sector-shaped tubes filled to a series of levels. First, the mass fraction of particles larger than a known diameter may be calculated from equation (8.77) and the distribution function determined from the slope of the cumulative mass deposited against S. Secondly, the distribution function may be calculated directly in terms of the first and second derivatives of the fraction sedimented with respect to the length of the column of suspension centrifuged by use of equation (8.77). Thirdly, from the sedimentation -time curve at a series of levels, the distribution functions may be calculated by the use of equation (8.77). 

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