The same memoir contained Fresnel's first attempt at the biaxial velocity law. For calcite, if we interchange the equatorial and polar radii of Huygens's oblate spheroid while preserving the polar direction, we obtain a prolate spheroid touching the sphere at the equator. A plane through the center/origin cuts this prolate spheroid in an ellipse whose major and minor semi-axes give the magnitudes of the extraordinary and ordinary ray velocities in the direction normal to the plane, and (said Fresnel) the directions of their respective vibrations. The direction of the optic axis is the normal to the plane for which the ellipse of intersection reduces to a circle. So, for the biaxial case, Fresnel simply replaced the prolate spheroid with a triaxial ellipsoid, which was to be sectioned by a plane in the same way. In general there would be two planes passing through the center of the ellipsoid and cutting it in a circle, and the normals to these planes would give two optic axes. From the geometry, Fresnel deduced Biot's sine law (with the ray velocities replaced by their reciprocals).