The third installment (July 1821) was a short "postscript" in which Fresnel announced that he had found, by a "mechanical solution", a formula for the reflectivity of the p component, which predicted that the reflectivity was zero at the Brewster angle. So polarization by reflection had been accounted for—but with the proviso that the direction of vibration in Fresnel's model was perpendicular to the plane of polarization as defined by Malus. (On the ensuing controversy, see Plane of polarization.) The technology of the time did not allow the s and p reflectivities to be measured accurately enough to test Fresnel's formulae at arbitrary angles of incidence. But the formulae could be rewritten in terms of what we now call the reflection coefficient : the signed ratio of the reflected amplitude to the incident amplitude. Then, if the plane of polarization of the incident ray was at 45° to the plane of incidence, the tangent of the corresponding angle for the reflected ray was obtainable from the ratio of the two reflection coefficients, and this angle could be measured. Fresnel had measured it for a range of angles of incidence, for glass and water, and the agreement between the calculated and measured angles was better than 1.5° in all cases.