Cn.vp. XXT.] CONTENTS OF CHAP. XXI. 



225 



Phop. 

 XXVII. To apply Proposition XXV. to the upheaval of the ocean 

 round the equatorial regions, by the action of the Earth's 

 rotation. 

 XXVIII. A planet continuously acted on by any motive force, 

 tending to carry it onwards in its orbit, excepting the 

 Sun's revolving force, could not remain in the solar 

 system. 

 XXIX. Objects free to move on the surface of a rotating sphere 

 T\ill have a relative motion along the surface if the 

 direct be greater than the revolving force of the sphere. 

 XXX, If the revolving be greater than the direct force of the 



sphere, nothing can rest loosely on its surface. 

 XXXI. • Within the limits of the atmosphere, the normal force of 

 astral gravitation and the Earth's revolving force are 

 together less than the direct force. 

 XXXII. At some distance from the Earth its direct force must be 

 brought into equilibrium, as regards the normal and 

 centrifugal forces of astral gravitation. 



XXXIII. An indefinite number of these lines of equilibrium may be 



formed. 



XXXIV, The effective action of the Earth's revolving force depends 



on the proximity and power of other centres of rotation. 

 XXXV. To determine the motion of a body acted on by revolving 

 forces from different centres of rotation, 

 Seo. 1. — The action of two equal forces rotating in oppo- 

 site directions. 

 -The action of two equal forces rotating in the 

 same direction. 

 3. — Unequal forces rotating in opposite directions. 

 4. — Action on the Moon of the revolving forces of 

 the Sun and Earth if rotating in tlie same plane. 

 Sec. 5. — Effect of the inclination of the planes of rotation. 

 Sec. 6. — Newton's demonstrations of the laws of gravita- 

 tion harmonise necessarily with the theory of 

 vis-inertise. 

 XXXVI. To apply Propositions XXXIV. and XXXV. to the dis- 

 turbing action of the Earth's rotation as regards the 

 orbital motion of the Moon round the Sun. 

 XXXVII. To apply Propositions XXXIV. and XXXV. to the dis- 

 turbing action of Neptune on the orbital motion of its 

 satellites. 

 XXXVIII. To determine the interaction of revolving: forces. 



Sec. 2. 



Sec. 

 Sec. 



