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Why should the story of a woman's role in the development of a scientific theory be written? Is it to celebrate, as some have done, the heroism of a woman's struggle in a man's world? Or is it, rather~to demonstrate that gender is irrelevant to the march of scientific ideas? This book hopes to do neither. Rather, it intends to do justice both to the professional life of a woman in science and to the development of the theory with which she was engaged. Technically, this essay centers on Sophie Germain's analysis of the modes of vibration of elastic surfaces, work which won a competition set by the French Academy of Sciences in 1809. It also evaluates related work on the mathematical theory of elasticity done by men of the Academy. Biographically, it is about a woman who believed in the greatness of science and strove, with some measure of success, to participate in that noble, but wholly male-dominated, enterprise. It explores her failures, analyzes her success, and describes how the members of the Parisian scientific community dealt with her offerings, contributions and demands.