CONTENTS. Xlll 



Page 



1. Solution of the question ; defect in the application to 

 physical questions. Newton, xxi. xxn. c. - -172 



2. First application measurements of heights. Note II. 320 

 Second application form of our atmosphere, the zo 

 diacal light not part of the sun s atmosphere. Note II. - 322 



CHAPTER II. 



THE FIGURE OF THE EARTH. 



1. Newton s calculation of the ellipticity of the earth; its 



defects - -177 



2. An accurate investigation of the ellipticity on the supposi 



tion that the earth is homogeneous ; the form thus 



found proved to be stable - - 178 



Note III. - - - - 324 



3. Newton s calculation of the law of variation of gravity - 179 



4. Newton s application of his theory to the planet Jupiter - 181 



5. The figure of the earth considered as heterogeneous, Clai- 



raut and Laplace s results. Note IV. - - 328 



a. The form of the strata - - 328 



/3. The law of variation of gravity - 329 



6. The law of density in the interior of the earth. Note IV. 330 



7. Whether the interior of the earth is solid or fluid. Note IV. 333 



8. Measures to determine by observation the ellipticity of the 



earth s surface. Note IV. - 337 



o. Measurement of degrees - - 337 



(3. Observations on the pendulum - - - 338 



y. Astronomical observations - 341 



CHAPTER III. 



THE MOTION OF A PARTICLE IN A RESISTING MEDIUM. 



1. The object and mode of conducting the inquiry - - 183 



2. When the resistance varies as the velocity - 186 



a. Rectilinear motion - - ib. 



/3. Curvilinear motion. Section I. - - ib. 



3. When the resistance varies as the square of the velocity - 196 



a. Rectilinear motion , - ib. 



/3. Curvilinear motion. Section II. - - ib. 



4. When the resistance varies partly as the velocity and partly 



as the square of the velocity, and the motion is 

 rectilinear. Section III. ,- 205 



5. When the resistance varies as any power of the velocity and 



the motion is rectilinear consideration of an 

 analytical difficulty in the solution the terminal 

 velocity and instances - - - 210 



