352 



infinite distance from the small plane, and that the normal 

 velocity of the fluid over the surface of the plane is zero. 

 Having thus found the motion, we can then substitute 

 for v in the equation above, and find the difference 

 of pressures on the two parts of the plane. It is mani 

 fest that the solution in this case must contain discon 

 tinuous functions. 



If the front of the plane be inclined to the direction of 

 the motion of the fluid, one of the two suppositions on 

 which the theory is built fails. We can no longer regard 

 the velocity in front of the plane as zero. It is necessary 

 to substitute another assumption. The theory supposes 

 that the velocity in front of the plane will be equal to the 

 general velocity of the fluid resolved in the direction of the 

 plane. Let &amp;lt;p be the angle a normal to the plane makes 

 with the general direction of motion. Then the velocity 

 of the particles of the fluid in contact with the front will 

 be v sin &amp;lt;p, and the normal pressure will be given by 



Let us regard this plane as the oblique front of a cylin 

 der moving in the direction of its axis. Let B be the area 

 of a perpendicular section, then the area A of the front 



T) 



will be - , and the normal pressure will therefore be 

 cos &amp;lt;p 



- ; resolving this along the axis, the pressure will be 



come, B being supposed very small, 



pE = (C + gpz-^pv* sin 2 &amp;lt;p)B. 



Let be the angle a normal to the oblique posterior 

 plane of the cylinder makes with the general direction of 

 the motion. Then, retaining the former supposition in 



