390 Hydrodynamics. 



This proof supposes that after the body strikes a particle, the 

 action of that particle entirely ceases; whereas the particles, 

 after they are struck, must necessarily diverge, and act upon the 

 particles behind them ; thus causing some difference between 

 theory and experiment. This hypothesis, however, on account 

 of its simplicity, is generally retained, and corrected afterwards 

 by deductions from actual experiments. 



This ratio of the square of the velocity may be otherwise 

 derived, thus. 



It is evident, that the resistance to a plane, moving perpen- 

 dicularly through an infinite fluid, at rest, is equal to the pressure 

 or force of the fluid on the plane at rest, the fluid moving 

 with the same velocity, and in the contrary direction to that of 

 the plane in the former case. But the force of the fluid in mo- 

 tion must be equal to the weight or pressure which generates 

 that motion ; and which, it is known, is equal to the weight or 

 pressure of a column of the fluid, whose base is equal to the 

 plane, and its altitude equal to the height through which a body 

 must fall by the force of gravity, to acquire the velocity of the 

 fluid ; and that altitude is, for the sake of brevity, called the alti- 

 tude due to the velocity. So that if tf denote the surface of the 

 plane, v the velocity, and s the specific gravity of the fluid ; then 



v 2 

 the altitude due to the velocity v being , the whole resistance 



o 



or moving force m, will be 



g being 32,2 feet. And hence, other things being the same, the 

 resistance is as the square of the velocity. 



(4.) If the direction of the motion, instead of being perpen- 

 dicular to the plane, as above supposed, be inclined to it at any 

 angle, then the resistance to the plane in the direction of the 

 motion, as assigned above, will be diminished in the triplicate 

 ratio of radius to the sine of the angle of inclination, or in the 

 ratio of 1 to t 3 , where i is the sine of the inclination. 



