ISO THE EVOLUTION OF 



to the sphere. By the action of centrifugal force, every 

 part exerts an outward pull on the mass, a pull directed 

 from the axis of rotation. Yielding to these pulls, the 

 figure ceases to be spherical and becomes a spheroid the 

 form of an orange flattened along its axis of rotation. 

 This is the actual form of the Earth. The spheroid is 

 therefore a figure of equilibrium of the rotating mass, and, 

 if the speed of rotation is not excessive, it is a figure of 

 stable equilibrium, for it again tends to reassume its form 

 after being disturbed. As the speed of rotation is in- 

 creased, the centrifugal forces increase, and a further 

 flattening is the result, but for a time the stable spheroidal 

 form is retained. The section through the equator 

 remains a circle, and every section through the axis of 

 rotation is an ellipse of the same form. The laws regu- 

 lating the spheroidal form of a mass of rotating fluid were 

 investigated by Maclaurin about the year 1 750. 



We have supposed the liquid to be initially at rest, and 

 have assumed that a rotation is impressed upon it after it 

 has acquired a spherical form, the sphere passing in con- 

 sequence of the rotation into the spheroid. If, however, 

 the different portions of the liquid are not initially at rest, 

 the mass may, under simple conditions, though it need 

 not under more complicated ones, assume the form of the 

 rotating spheroid directly, and it is more natural to regard 

 the spheroid as having been formed in this way. In 

 the time of Laplace the spheroid was the only figure of 

 equilibrium known for a mass of rotating fluid, and the 

 spheroidal form was naturally adopted by him as the 

 initial state of the nebula of his hypothesis. Since then, 

 however, other possible forms of equilibrium have been 

 discovered, and these are connected with Maclaurin's 

 spheroid in a very interesting manner. 



We have left the spheroidal nebula rotating with 



