NEWTON S PRINCIPIA. 221 



CHAPTER IV. 



THE MOTION OF FLUIDS, AND THE RESISTANCE TO BODIES 

 MOVING IN THEM. SECTION VII. 



1. Newton s investigation of the law of resistance to similar bodies. 



2. The manner in which the resistance depends on the form of the body. 



Newton, xxxiv. & xxxv. 



3. Their resistance when the body is a surface of revolution. 



4. The surface of least resistance, its properties and form. Scholium, 



Prop, xxxiv. 



5. The law of resistance deduced from experiment. Prop. xl. and 



Scholium. 



1. SUPPOSE we have two systems of an equal number of 

 particles similarly placed, and proportional each to each 

 both in density and volume. Let them begin to move, 

 the particles of one system amongst themselves, and those 

 of the other amongst themselves, with like motions and in 

 proportional times. If no action ever took place between 

 the particles, by the first law of motion the similarity 

 between the systems will always exist. It is also clear 

 that any collisions or reflexions among the particles will 

 not affect this similarity of motion ; if any collision occur 

 in one system an exactly similar collision will occur in the 

 other ; similar changes of motion will be thereby produced 

 in the two systems. 



Next, suppose the particles attract or repel each other 

 with accelerating forces, which are as the squares of the 

 velocities directly and the diameters inversely of the cor 

 responding particles in the two systems. Consider two 

 homologous particles, one in each system, the attractions 



