This paper provides an analysis of the Hodgskin section of Theories of Surplus Value and the general law section of the first version of Volume III of Capital. It then considers Part III of Volume III, the evolution of Marx's thought and various interpretations of his theory in the light of this analysis. It is suggested that, as late as the 1870s, Marx had hoped to be able to provide a demonstration that the rate of profit must fall. The main conclusions are that (1) Marx's major attempt to show that the rate of profit must fall occurred in the general law section, (2) Part III does not contain a demonstration that the rate of profit must fall and (3) Marx was never able to demonstrate that the rate of profit must fall and he was aware of this. © 2005 Taylor & Francis Group Ltd.