Mr. Ivorv on the Theory of the Figure of the Earth. 247 



rections : and this is precisely the new condition which, as we 

 have proved, is necessary to the equiHbrium of a homogeneous 

 fluid. It may be observed that, of the two conditions of equi- 

 librium, the one which relates to the attraction of the level 

 strata upon particles within them, which is omitted in the re- 

 ceived theory of fluids, alone determines the figuie of the 

 homogeneous body : and when this is fulfilled, as it is in the 

 figure supposed by Maclaurin, it only remains to compute the 

 attraction, and to adjust the centrifugal force so that the re- 

 sultant of both shall be perpendicular to the surface. What 

 is said of the researches of Maclaurin is equally true of the 

 discoveries of Clairaut, as far as they relate to the figure of the 

 planets. In the first part of his work on the figure of the 

 earth, that excellent geometer has proved that the equilibrium 

 of a mass of fluid cannot be safely deduced from the perpen- 

 dicularity of gravity to the surface, which is the principle of 

 Huyghens; nor from the balancing of the central columns, 

 which is that of Newton ; nor from the hypothesis of Bouguer, 

 whicl'i requires the concurrence of both the i)rinciples just 

 mentioned : and although, in place of these imperfect theories, 

 he has substituted one drawn from more unexceptionable prin- 

 ciples, which is liable to no objection except when there is a 

 mutual attraction between the particles; yet, as the figure of 

 the planets depend upon the very case in which the theory is 

 defective, the main difticulties of the question were left un- 

 touched. In the second part of die work, which contains the 

 author's discoveries relating to the figure of the earth, his in- 

 vestigations are not deduced a priori from his theory of fluids, 

 but from the suj)position of a figure either exactly, or very 

 nearly, an elliptical spheroid. 



If a homogeneous fluid composed of particles endowed with 

 attractive powers be at rest, it will be inequilihrio when it has 

 the figure of a sphere. Conceive that the spherical mass be- 

 gins to revolve upon an axis with a velocity which impresses 

 upon the particles a centrifugal force very small in propor- 

 tion to the attractive energy; the globe will now flatten in 

 some degree at the poles, and become protuberant at the 

 equator. What is the exact form in which die fluid will thus 

 dispose itself? Newton assumetl, but without assigning any 

 reason, that it is an elliptical spheroid of revolution. The dis- 

 covery of Maclaurin verified the supposition of Newton; and 

 as we are now in possession of all the conditions of the equi- 

 iiliriuin of a homogeneous fluid, it is easy to prove that the 

 revolving mass cannot be in equilibrio unless it have the figure 

 which Newton supposed. 



Let as now consider the mnttn- a little diflerently, and with 



rclirence 



