250 Mr. Tredgold on a new Theory of the Resistance 



4. The vacancy left by the motion of the body is filled by 

 the motion of the fluid ; but, with a loss of the force necessary 

 to maintain an equilibrium among the parts of the fluid, equi- 

 valent to the force producing this motion in the fluid. The 

 increase of resistance from this cause has been termed the 

 minus pressure of the fluid. 



5. The sum of the direct resistance, and that due to the de- 

 ficiency of equilibrium, called the minus pressure, is the total 

 resistance when the friction is neglected. 



6. If fluids were devoid of friction they would be perfectly 

 elastic, differing only in the degree of compression produced 

 by a given force ; hence, in considering the effect of collision 

 on a fluid, it must be esteemed an elastic body. The coherence 

 and friction of natural fluids render their elasticity in a slight 

 degree imperfect, but not sufficiently so to interfere with the 

 application of rules founded on its perfect elasticity in most 

 of the cases occurring in practice. The total want of elasti- 

 city is incompatible with the very nature of a fluid. 



7. If a body moving with an uniform velocity in a straight line 

 AB, Plate IV. fig. 1 . impinge on a filament of a fluid in which 

 it moves, with a part of its surface inclined in any manner to the 

 direction of the motion, the fluid will be reflected, and the di- 

 rection of the resultant of the impingeing and reflecting forces 

 will be perpendicular to the surface, and equal to the pressure 

 of a column of the fluid capable of producing the actual ve- 

 locity of the body. For the fluid being elastic, the restoration 

 of figure produces the reflecting force, and the force in a di- 

 rection perpendicular to the surface is only half that which 

 would arise from the collision of a non-elastic body. 



•8. Of the direct Resistance. — Let v be the difference between 

 the velocity of the fluid and that of the body, when estimated 

 in the direction of the motion ; g = the space described in a 

 second by the velocity due to the force of gravity in vacuo = 

 32£ feet ; a = the angle the portion of the surface, on which 

 the filament of fluid strikes, makes with the direction of the 

 motion: and h = the height of the column of fluid equal to 

 the direct resistance. The velocity of the body is to that of 

 the surface in a direction perpendicular to itself; or in the di- 

 rection of the resultant as v : v sin a ; and " n = the co- 



lumn of fluid whose weight would be equivalent to the per- 

 pendicular pressure. This pressure reduced to the direction 



of the motion is h = v *" — , the forces perpendicular to the 



direction of the motion being supposed to mutually balance 

 one another. 



9. Of 



