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CHAPTER XXI. 



THE MOVEMENTS OF THE PLANETS. 



The System op the World. 



an extended application of the laws of gravitation demon- 

 strated by newton's ' principia ' and 'system op the world.' 



Table of Contents. 



Prop. 

 I. The gravitation of a body in motion in free space tends to 



draw other bodies in the same direction. 

 II. A rotating sphere tends to revolve surrounding bodies. 



III. The ratio of the revolving to the direct force is inversely as 



the distance. 



IV. The revolving force is haversely as the cube of the distance. 



V. The velocities of motion are as the square roots of the ratio of 



the revolving to the direct force. 

 VI. The velocities of revolution are as the square roots of the 

 revolving force, 

 VII. Vis-inertias being the cause of gi-avitation, the moon must have 

 both an orbital and an apparent motion. 

 VIII. The centrifugal force of astral gravitation increases as the 

 square of the A'elocity of revolution. 

 IX. The direct force of the Sun's gra^dtation acts as a retardmg force, 



opposing its revolving force, along the orbits of the planets. 

 X. The direct force of the Sun's gravitation tends to retard the Sun's 

 axial rotation more than the revolution of the planets round 

 the Sun. 

 XI. The retarding action indicated by the foregoing proposition is 

 apparent as regards the axial rotation of the Sun, and also as 

 regards the axial rotation of the Earth and of the planets 

 Saturn and Mars. 

 XII. The ratio which vis-inertise bears to the Sun's gravitation is as 

 the square of the distance from the Sun, 



XIII. That which it bears to the revolving force is as the cube of the 



distance. 



XIV. The ratio which the vis-inertiee of the planets bears to the com- 



bined action of the direct and revolving forces of the Sun's 



