Mr. Tredgold on the Theory of Hydro-dynamics. 113 



Prop. 2. — The quantity of motion impressed on a fluid by 

 a body moving in it must be estimated in a direction perpen- 

 dicular to the resisted surface, whatever may be the direction 

 of the motion of the body. 



The resistance on a surface is composed of the force which 

 moves the fluid in the direction of its motion, and the re- 

 sistance to reflection ; the resultant of these forces is perpen- 

 dicular to the surface; but the whole action to displace the 

 fluid being measured by the resultant, the velocity of displace- 

 ment must be estimated in the same direction : hence the quan- 

 tity of motion impressed being in the direction of the resultant 

 is perpendicular to the surface. 



Prop. 3. — The direct velocity of a body is to the velocity of 

 any part of that body in a direction perpendicular to its sur- 

 face as the radius is to the sine of the angle of inclination of 

 the surface to the direction of its motion. 



Let A b represent the direction and velocity of the plane, 

 and draw Ae perpendicular to the plane, and be parallel to 



the plane, then Ae is the velocity in a direction perpendicular 

 to the plane; and A b is to Ae as the radius is to the sine 

 ofBAC. 



Prop. 4. — If a plane surface moves with an equable velocity 

 in a fluid, the height of a column of that fluid which would 

 generate the velocity of the plane, in a direction perpendi- 

 cular to its surface is half the height of a column equal to the 

 pressure on that surface. 



For, the velocities of the forces of incidence and reflec- 

 tion being unaltered, the pressure in the direction of the re- 

 sultant must be double to produce the same quantity of mo- 

 tion. 



Prop. 5. — The height of a column of fluid equivalent to 

 the direct resistance of a plane surface moving in it, varies di- 

 rectly as the square of the velocity and as the cube of the sine 

 of the plane's inclination to the direction of the motion; or as 



v 1 sin 3 a 

 32 r3 ' 



Vol. 68. No. 340. 



Aug. 1826. 



Let 



