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: