The correct answer is C) Parallax. Parallax is the correction that adjusts the apparent altitude of a celestial body to the equivalent reading at the center of the Earth. This is necessary because the observer's position on the Earth's surface is not at the center of the Earth, so the observed altitude needs to be corrected to account for this difference in position. The other options are incorrect because they do not directly address the issue of converting the observed altitude to the equivalent reading at the Earth's center. Semidiameter is the correction for the angular size of the celestial body, augmentation is the correction for atmospheric refraction, and phase is the correction for the illumination of the celestial body.