Abstract: A detailed derivation of the window factor analysis methodology is presented, showing how quantification of a single species can be achieved. The method takes advantage of the fact that each component lies in a specific region along the evolutionary axis, called the 'window'. For comparative and illustrative purposes the method was applied to the flow injection analysis data of Gemperline and Hamilton (Ibid., 1989, 3, 455). Window factor anal. (WFA) is a self-modeling method for extracting the concentration profiles of individual components from evolutionary processes such as flow injection, chromatography, titrations and reaction kinetics. The method takes advantage of the fact that each component lies in a specific region along the evolutionary axis, called the 'window'. Theoretical equations are derived. The method is used to extract the concentration profiles and spectra of seven bismuth species from data obtained by Gemperline and Hamilton, who injected bismuth perchlorate into a flowing stream of hydrochloric acid.