NEWTON S PRINCIPIA. 353 



regard to the motion of the fluid behind the plane, we 

 shall have the normal pressure given as before by 



//= C + g f&amp;gt;z Jpu 2 ; 



by reasoning as above, the resolved part of the pressure 

 along the axis will be 



The difference of these two pressures will be 



v 2 cos 3 p A ; 



thus the resistance to a cylinder moving in the direction 

 of the axis is independent of the inclination of the posterior 

 end, and varies as the cube of the cosine of the inclination 

 of the anterior end to the perpendicular section of the 

 cylinder. 



In determining the pressure on a curved surface, it is 

 usual to consider each element of the front as the oblique 

 end of a cylinder whose axis is parallel to the direction of 

 motion; the corresponding element of the back of the 

 body being the other oblique end of the cylinder. By 

 integration, therefore, the whole pressure may be found. 

 It also appears that the resistance depends only on the 

 form of the front, and not at all on that of the back of 

 the body. The suppositions on which this result is 

 founded, are 



1. That the velocity of the particles behind the body is 

 the same as that of the general velocity of the fluid. 



2. That the velocity along any element of the front is 

 equal to the resolved part of the general velocity of the 

 fluid along the plane of the element. 



Throughout these investigations the motion of the fluid 

 has been supposed steady. No applications of these re 

 sults to any other case can be regarded otherwise than as 

 an approximation. The relative velocity of the body 



A A 



