50 THEORETICAL FORM OF THE EARTH. [SECT. vi. 



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 New- 

 ton, 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 distinguished countryman Mr. Ivory. 

 The investigation has been conducted by successive steps, be- 

 ginning 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 mu- 

 tual relations. Afluid 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 centre 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 conse- 

 quence of the centrifugal force arising from the velocity of 

 rotation. 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 perpendicularly to 

 the axis of rotation, and is directed to the exterior. And, as 

 its intensity diminishes with the distance from the axis of 



