CONTENTS. XV 



4. The resistance to floating bodies 



a. The phenomenon of emersion 



ft. Waves are excited in the Fluid - - ib. 



y. Strange variations of the resistance as the body 



changes - 370 



CHAPTER V. 



THE MOTION OF A PENDULUM. 



1. Some general considerations - - 240 



2. Motion in vacuo. Newton, xxiv. Note VI. - 372 



3. The properties of a pendulum. Note VI. - 375 



4. Motion in a resisting medium ; modern method of con 



sidering the perturbations of a pendulum ; the New 

 tonian method - 242 



5. Newton s experiments to discover the law of resistance - 252 



CHAPTER VI. 



MOTION OF FLUIDS RUNNING OUT OF SMALL ORIFICES. 



1. Newton s solution of the question, without limiting the 



orifice - - 257 



2. Newton s corollary to deduce the resistance made by a 



fluid to a body moving in it - - - 260 



3. The fallacy of Newton s reasoning How others attempted 



to pursue the investigation. Note VII. -, - 381 



4. The velocity as given by the Equations of Motion. Note 



VII. - 381 



5. The efflux of an elastic fluid through a small orifice 



strange conclusions to be deduced from the formula 



St. Venant and Wantzels experiments. Note VII. - 381 



CHAPTER VII. 



THE MOTION OF WAVES. 



1. General consideration on the nature of Waves - - 266 



2. Waves in air sound - - - 269 



a. The nature of sound deduced from the phenomena. 



Scholium, Prop. L. - 269 



ft. Examination of the case considered by Newton - 27 1 

 y. Velocity of sound Newton s error - 274 



3. The manner in which sound spreads after entering 



through an orifice. Newton, XLII. - 277 



c. The notes sounded by different pipes. Scholium, 



Prop.L. --- . - _ 278 



