NEWTON S PRINCIPIA. 227 



axis with a uniform velocity v in a medium, and let us 

 suppose that the particles of the fluid are perfectly elastic. 

 They will then rebound with the same velocity relatively 

 to the cylinder as that with which they struck it. There 

 fore the cylinder, on striking each particle, gives it a velocity 

 twice its own, and in moving forwards a length half its 

 axis communicates a motion to the particles which is to 

 the whole motion of the cylinder as the density of the 

 medium to the density of the cylinder. Hence the cy 

 linder meets a resistance which is to the force by which its 

 whole motion may be taken away in the time in which it 

 describes half its axis as the density of the medium is to 

 the density of the cylinder. If / be the length of the axis, 



the time of describing the half axis will be -, and the ac 

 celerating force that would generate a velocity v in this 



2 u 2 



time is -j- ; hence the moving force, which is the re 

 sistance, is 



2Av*p, 



where A is the area of the base, and p the density of the 

 fluid. 



Next, let us suppose the particles perfectly inelastic; 

 they will not be reflected, and the cylinder will merely 

 communicate its own simple velocity to the particles it 

 strikes against. The resistance is therefore only half as 

 great as before, that is 



Resistance = A v 2 p. 



Thirdly. If the particles be imperfectly elastic, the par 

 ticles will rebound from the cylinder with a less velocity 

 than if they were elastic, and a greater velocity than if 

 they were inelastic ; hence 



Resistance = x A v 2 p, 

 where * is some quantity lying between 1 and 2, 



Q 2 



