X CONTENTS. 



short,, the mean motions of the planets undergo no secular varia 

 tion, 122. General law of stability of the system, 123. Gene 

 ral reflexion, 124. No resistance of an ethereal medium, nor 

 any transmission of gravity in time, ib. 



hi. Marvellous powers of Sir Isaac Newton in discussing the subject 

 of disturbing forces, 125. Great superiority to all his successors, 

 ib. Determination of the disturbances arising from a third 

 body s action upon other two, and theirs upon the third and each 

 other, or problem of three bodies, 126. Attraction as the dis 

 tance, alone preserves all motion undisturbed, ib. Produces im 

 mense velocities, 127. The small actual derangement shows the 

 inverse square of the distance not to be much departed from, 128. 



Investigation of the general problem, ib. Case of moving 

 bodies and proportion of masses to forces, 131. Accelerations 

 and retardations at different parts of the orbit : quadrature and 

 syzygies, ib. Different planetary variations deduced by Sir Isaac 

 Newton from the solution, 132. Extraordinary generalization of 

 the problem to precession and tides, ib. Sixty-sixth proposition 

 and its corollaries embrace all that has been done on the subject, 

 134. Error of Laplace, ib. note. 



Attraction under two heads, i. that of spherical ; ii. that of non- 

 spherical bodies. 



i. (SECTION XII. Principia.) Attraction of spherical surfaces, 135. 



Remarkable inferences showing the solidity of the earth, 136. 



Attraction of spheres on particles beyond their surface, 137. 



On particles within their surface, 1 39- Five general theo 

 rems, ib. Corollary comparing corpuscular attraction with cen 

 tripetal forces, 1 40. Peculiarity of the actual law of gravi 

 tation,^. General solution for all other laws of attraction, 141. 

 Reduced to the quadrature of a curvilinear area, ib. Solution 

 of this quadrature, 142. Remarkable result when the force is 

 inversely as the cube, or any higher power of the distance, 144. 



Attraction of spherical segments, ib. 



ii. (SECTION XIII. Principia.^) Attraction of bodies not sphe 

 rical, 145. Proportion of attraction to homologous sides of 

 similar bodies, 146. General theorem for attraction of all bodies 

 as related to the centre of gravity, the force being gravitation, 

 147. Attraction according to any power of the distance in any 

 symmetrical solids, ib. General solution, 148. Laplace s 

 formula for attraction, 149. 



Motions of infinitely small bodies like light, 150. (SECTION XIV. 

 Principia.) Proportion of angles of incidence,, refraction and 

 reflection, ib. Inflection and deflection, 151. Subsequent ex 

 periments on the coloured fringes by flexion, ib. General 

 remark on the perfection of Newton s discoveries, 152. Solution 

 of Descartes focal problem, ib. Newton s optics, ib. Dates 



