SECT. VI. THEORETICAL FORM OF THE EARTH. 43 



SECTION VI. 



Form of the Earth and Planets Figure of a Homogeneous Spheroid in 

 Rotation Figure of a Spheroid of Variable Density Figure of the 

 Earth, supposing it to be an Ellipsoid of Revolution Mensuration of a 

 Degree of the Meridian Compression and Size of the Earth from 

 Degrees of Meridian Figure of Earth from the Pendulum. 



THE theoretical investigation of the figure of the earth 

 and planets is so complicated, that neither the geometry 

 of Newton, nor the refined analysis of La Place, has 

 attained more than an approximation. It is only within 

 a few years that a complete and finite solution of that 

 difficult problem has been accomplished by our distin- 

 guished countryman Mr. Ivory. The investigation has 

 been conducted by successive steps, beginning with a 

 simple case, and then proceeding to the more difficult. 

 But in all, the forces which occasion the revolutions of 

 the earth and planets are omitted, because, by acting 

 equally upon all the particles, they do not disturb their 

 mutual relations. A fluid mass of uniform density, whose 

 particles mutually gravitate to each other, will assume 

 the form of a sphere when at rest. But if the sphere 

 begins to revolve, every particle will describe a circle 

 (N. 116), having its center in the axis of revolution. 

 The planes of all these circles will be parallel to one 

 another and perpendicular to the axis, and the particles 

 will have a tendency to fly from that axis in consequence 

 of the centrifugal force arising from the velocity of rota- 

 tion. The force of gravity is everywhere perpendicular 

 to the surface (N. 117), and tends to the interior of the 

 fluid mass ; whereas the centrifugal force acts perpen- 

 dicularly to the axis of rotation, and is directed to the 

 exterior. And as its intensity diminishes with the dis- 

 tance from the axis of rotation, it decreases from the 

 equator to the poles, where it ceases. Now it is clear 

 that these two forces are in direct opposition to each 

 other in the equator alone, and that gravity is there di- 

 minished by the whole eflect of the centrifugal force, 

 whereas, in every other part of the fluid, the centrifugal 

 force is resolved into two parts, one of which, being per- 

 pendicular to the surface, diminishes the force of grav- 



