44 THEORETICAL F011M 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 Newton, nor the 

 refined analysis of La Place, has attained more than an approxima- 

 tion. The solution of that difficult problem has been accomplished 

 by our distinguished 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. 117), 

 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 consequence of the centrifugal force arising from the 

 velocity of rotation. The force of gravity is everywhere perpen- 

 dicular to the surface (N. 118), 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 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 diminished 

 by the whole effect of the centrifugal force, whereas, in every 

 other part of the fluid, the centrifugal force is resolved into two 

 parts, one of which, being perpendicular to the surface, diminishes 



