183 



CHAPTER III. 



THE MOTION OF A PARTICLE IN A RESISTING MEDIUM. 



1 . The object and mode of conducting the enquiry. 



2. When the resistance varies as the velocity. 



a. Rectilinear motion. 



0. Curvilinear motion. Section I. 



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



a. Rectilinear motion. 



p. Curvilinear motion. Section IT. 



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



square of the velocity, and the motion is rectilinear. Section HE. 



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. 



6. The motion of a particle in a resisting medium round a centre of 



force. 



o. The method used by Newton. 



. The method supplied by the Planetary Theory. Section IV. 



1. PART of the theory of the motion of a body in a resist 

 ing medium is contained in the first four sections of the 

 second book. The manner in which a medium resists the 

 motion of a body moving in it is not the subject of this 

 inquiry. It manifestly depends on a great many circum 

 stances which we shall presently consider. At present we 

 shall assume that the changes of resistance throughout 

 the motion depend only on the changes of velocity. Again, 

 the resistance will greatly depend on the form of the body, 

 and will change, therefore, as the body during its motion 

 opposes different faces to the resistance of the fluid. If 

 the resultant of the resistances on the several parts of the 



N 4 



