Early nineteenth century systematists sought to describe what they called the Natural System or the Natural Classification. In the nineteenth century, there was no agreement about the basis of observed patterns of similarity between organisms. What did these systematists think they were doing, when they named taxa, proposed relationships between taxa, and arranged taxa into representational schemes? In this paper I explicate Charles Frederic Girard’s (1822–1895) theory and method of systematics. A student of Louis Agassiz, and subsequently (1850–1858) a collaborator (...) with Spencer Baird, Girard claimed that natural classificatory methods do not presuppose either a special creationist or an evolutionary theory of the natural world. The natural system, in Girard’s view, comprises three distinct ways in which organisms can be related to each other. Girard analyzed these relationships, and justified his classificatory methodology, by appeal to his embryological and physiological work. Girard offers an explicit theoretical answer to the question, what characters are evidence for natural classificatory hypotheses? I show that the challenge of simultaneously depicting the three distinct types of relationship led Girard to add a third dimension to his classificatory diagrams. (shrink)