Programs such as Bacon, Abacus, Coper, Kepler and others are designed to find functional relationships of scientific significance in numerical data without relying on the deep domain knowledge scientists normally bring to bear in analytic work. Whether these systems actually perform as intended is an open question, however. To date, they have been supported only by anecdotal evidence-reports that a desirable answer has been found in one or more hand-selected and often artificial cases. In this paper, I describe a function-finding algorithm which differs radically from previous candidates in three respects. First, it concentrates rather on reliable identification of a few functional forms than on heuristic search of an infinite space of potential relations. Second, it introduces the use of distinction, significance and lack of fit -- three general concepts of value in evaluating apparent functional relationships. Finally, and crucially, the algorithm has been tested prospectively on an extensive collection of real scientific data sets. Though I claim much less than previous investigators about the power of my approach, these claims may be considered-to a degree quite unfamiliar in function-finding research-as conclusively proven.