There is now major concern about the extent of the world's endowment of conventional oil resources and the North American supply of natural gas. This paper presents the details of the parabolic projection technique for the interpretation of geological assessments of undiscovered resources of conventional oil and gas in terms of production-time curves. The object is to present the methodology that was devised over the last decade in sufficient detail to allow this type of projection to be used and interpreted readily by others. Specific examples of its application are taken from some recent papers.The examples include a projection of the Mean Value for the world's conventional oil resources published by the U.S. Geological Survey in 2000, the techniques devised for dealing with the Reserves Addition and the problem posed by the existence of idle capacity in the global oil system, and the 'plateau peak' now likely in Canadian natural gas production. The procedure used to calculate these special cases is presented along with the results in graphical form.