We apply the differential method of Roscoe (1952) to the problem of finding the viscosity of a suspension of non-colloidal spheres in a power-law matrix. The results are compared with other theories and published experiments, and reasonable agreement is found up to moderate concentrations (phi similar to 0.5) when viscoelasticity and other effects are not important. The Roscoe paper depends on using a "crowding" function in the analysis; here two modified crowding functions are discussed, with a view to explaining the success of the Maron-Pierce formula, which does not reduce to the Einstein form for low concentrations. (C) 2010 Elsevier B.V. All rights reserved.