08 OUTLINES OF NATURAL PHILOSOPHY. 



If c is opposed to w, then the force is m a 2 (v -j- c)*. 

 and if v 0, the force = m a 2 c 2 . The plane, 

 therefore moving against a fluid at rest, with the 

 velocity c, suffers the same impulse as if the fluid 

 were to move with the velocity c, and the plane to 

 remain at rest. 



Hence the resistance of a fluid to a body in motion, 

 is the same with the percussion of a fluid moving 

 with the same velocity against the body at rest. 



Though this conclusion seems to be supported by 

 very sound reasoning, yet, in fact, the resistance is 

 less than the percussion, the velocity being in both 

 cases the same, in the proportion of 5 to 6, DON 

 JUAN, in his Examen Maritime, makes the difference 

 much greater. It arises, no doubt, from the action 

 of the fluid on the hinder part of the moving body, 

 by which the resistance is in some degree counter- 

 acted. It appears, however, to be only the abso- 

 lute quantities, and not the ratios of the resistan- 

 ces, that are thus affected ; the resistances being as 

 the squares of the velocities. 



In the reasoning on which this proposition is found- 

 ed, we have supposed the only resistance to arise 

 from the inertia of the particles. There is, how- 

 ever, another arising from the cohesion of these 

 particles, which must be proportional to the quan- 

 tity of that cohesion overcome in a given time, that 

 is, to the velocity simply. This resistance is only 

 perceived in slow motions, and is small in respect 

 of the other, except in fluids of much viscidity. 



COULOMB 



