contestants, Denis Poisson and Germain. Then Poisson was elected to the Academy, thus becoming a judge instead of a contestant, and leaving Germain as the only entrant to the competition. In 1809 Germain began work. Legendre assisted by giving her equations, references, and current research. She submitted her paper early in the fall of 1811 and did not win the prize. The judging commission felt that "the true equations of the movement were not established", even though "the experiments presented ingenious results". Lagrange was able to use Germain's work to derive an equation that was "correct under special assumptions". Subsequent attempts for the Prize The contest was extended by two years, and Germain decided to try again for the prize. At first Legendre continued to offer support, but then he refused all help. Germain's anonymous 1813 submission was still littered with mathematical errors, especially involving double integrals, and it received only an honorable mention because "the fundamental base of the theory [of elastic surfaces] was not established". The contest was extended once more, and Germain began work on her third attempt. This time she consulted with Poisson. In 1814 he published his own work on elasticity and did not acknowledge Germain's help (although he had worked with her on the subject and, as a judge on the Academy commission, had had access to her work). Germain submitted her third paper, "", under her own name, and on 8 January 1816 she became the first woman to win a prize from the Paris Academy of Sciences. She did not appear at the ceremony to receive her award. Although Germain had at last been awarded the , the Academy was still not fully satisfied. Germain had derived the correct differential equation (a special case of the Kirchhoff–Love equation), but her method did not predict experimental results with great accuracy, as she had relied on an incorrect equation from Euler, which led to incorrect boundary conditions. Here is Germain's final equation for the vibration of a plane lamina: where N2 is a constant. After winning the Academy contest, she was still not able to attend its sessions because of the Academy's tradition of excluding women other than the wives of members. Seven years later this situation was transformed, when she made friends with Joseph Fourier, a secretary of the Academy, who obtained tickets to the sessions for her. Later work in elasticity Germain