Marx's conclusions about the falling rate of profit have been analysed exhaustively. Usually this has been done by building models which broadly conform to Marx's views and then showing that his conclusions are either correct or, more frequently, that they can not be sustained. By contrast, this paper examines, both descriptively and analytically, Marx's arguments from the Hodgskin section of Theories of Surplus Value, the General Law section of the recently published Volume 33 of the Collected Works and Chapter 3 of Volume III of Capital. It also gives a new interpretation of Part III of this last work. The main conclusions are first, that Marx had an intrinsic explanation of the falling rate of profit but was unable to give it a satisfactory demonstration and second, that he had a number of subsidiary explanations of which the most important was resource scarcity. The paper closes with an assessment of the pedigree of various currents of Marxian thought on this issue.Financial aid from DGI project SEC 2000-0684 is gratefully accknowledged.