228 NEWTON S PRINCIFIA. 



3. Let us now apply this to find the resistance on a sur 

 face of revolution moving in the direction of its axis. Let 

 v be the velocity of the body relative to the fluid. We 

 shall then suppose the fluid in front of the body to be at 

 rest. Take the axis of revolution of the surface as the 

 axis of x, let y be the ordinate and s the arc of the gene 

 rating curve. By what has been already said, the resist 

 ance or pressure on the annulus 2 TT y d s when resolved 

 along the axis will be 



because this latter factor expresses the cosine of the angle 

 the normal makes with the line of motion of the body. 

 Hence the whole resistance will be 



( ~j~ ) dy* 



Let the surface be terminated by a plane perpendicular 

 to the axis of x, the section will be a circle ; let r be its 

 radius. Let y &amp;gt;) . r, and s = &amp;lt;r. r, then the whole resist 

 ance will be 



Thus, assuming merely that the distances of the particles 

 are infinitely greater than their diameters, we learn that 

 in the same fluid the resistance varies as the square of the 

 velocity, and in similar bodies as the square of their 

 radii. 



It is not necessary that all the particles should be of 

 equal size, or at exactly equal distances. It is sufficient 

 that the equal particles be equally scattered in vast num 

 bers throughout the fluid. For as the distances of the 

 particles are supposed indefinitely small, so vast a num 

 ber of particles strike the surface that it will be suffi 

 cient to consider only their average size and distance. 



