Clairaut's Theorem is usually deduced as a consequence of the hypothesis of the original fluidity of the earth, and the near agreement between the numerical values of the earth's ellipticity, deduced independently from measures of arcs of the meridian and from pendulum experiments, is generally considered as a strong confirmation of the hypothesis. Although this theorem is usually studied in connection with the hypothesis just mentioned, it ought to be observed that Laplace, without making any assumption respecting the constitution of the earth, except that it consists of nearly spherical strata of equal density, and that its surface may be regarded as covered by a fluid, has established a connexion between the form of the surface and the variation of gravity, which in the particular case of an oblate spheroid gives directly Clairaut's Theorem. If, however, we merely assume, as a matter of observation, that the earth's surface is a surface of equilibrium, (the trifling irregularities of the surface being neglected), that is to say that it is perpendicular to the direction of gravity, then, independently of any particular hypothesis respecting the state of the interior, or any theory but that of universal gravitation, there exists a necessary connexion between the form of the surface and the variation of gravity along it, so that the one being given the other follows.