CONTENTS. XI 



of the publication of Lectiones Opticae, Principia, and Optics, 

 ib. note. 



General conclusions from the Newtonian discoveries relating to 

 attraction, 153. Universal prevalence of gravitation., ib. 

 Further proof of this from Herschel s discoveries in double 

 stars, 154. Those observed by Cassini, ib. Not understood 

 till the elder Herschel s time, ib. Their revolutions round each 

 other and periods, 155. Apparently follow the law of sesqui- 

 plicate proportion, ib. note. 



Three other important applications of the Newtonian theory of 

 attraction, ib. 



1. To find the weights of bodies at the sun and different planets, ib. 



2. To find the masses of the heavenly bodies, and their densities, 

 156. Singular confirmation of the Newtonian theory by Lap 

 lace s calculation on Jupiter derived from different sources, 157. 



3. Application of the theory to the figures of the heavenly bodies, 

 ib. The earth s figure as determined by Newton, ib. Of 

 Jupiter, compared with observations, 158. Measurements 

 and pendulum experiments show the earth not to be homo 

 geneous, ib. Newton s computation respecting the earth s figure, 

 on the supposition of its being homogeneous, 159- His frac 

 tion for the excess of the quotient diameter, J^, still used as 

 accurate, ib. Remarks upon the wonderful completeness of the 

 theory at its first establishment deduced from hence, ib. No 

 improvements whatever upon that theory since his time, nor any 

 defect found in its proofs, 160. Note on structure of the 

 Earth, l6l. 



II. 



Introductory remark, 162. Resistance of media in all motions 

 except those of the heavenly bodies, ib. Resistance of air, ib. 

 Water, ib. Pressure and motion of fluids, ib. Hydrostatics, 

 Hydraulics, Pneumatics, ib. 



Arrangement of the Second Book of the Principia under five 

 heads. 



I. Motion of bodies in media which resist in different proportions 



to the velocity. 



i. Where the resistance is as the velocity. (Section I. Prin 

 cipia.} 



ii. Where the resistance is as the square of the velocity. 

 (Section II. Principia.} 



iii. Where the resistance is partly in one proportion to the 

 velocity, partly in another. (Section 111. Principia.} 



II. Spiral motion in resisting media. (Section IV. Principia.) 



III. Motion of pendulums in resisting media. (Section V. Prin 



cipia.} 



