396 Hydrodynamics. 



the body. Sir Isaac Newton supposes, that in a continuous non- 

 elastic fluid, infinitely compressed, the resistances of a sphere 

 and cylinder of equal diameters are equal ; but this appears to 

 be an error in theory as well as in fact. When the motion is 

 slow in water, the fluid may be conceived to be nearly of the 

 nature which Newton supposes; yet the resistances are almost 

 as coincident with theory as when the motion is in air ; thus M. 

 Borda found the resistance of a sphere moving in water to be to 

 that of its greatest circle as 1 to 2,508, and in air the resistances 

 were as 1 to 2,45. The experiments of Dr. Hutton in air give 

 the resistances at a mean as 1 to 2i. 



The reason that experiment gives the ratio of the resistances 

 greater than that of 2 to 1 seems to be this ; in theory it is supposed 

 that the action of every particle of the fluid ceases the instant it 

 makes its impact on the solid ; but this is not actually the case, as 

 we have before observed ; and since the particles, after impact on 

 the sphere, slide along the curved surface, and hence escape with 

 more facility than along the face of the cylinder, the error will 

 be greater in the cylinder; that is, the greater resistance will ex- 

 ceed the theory more than the less. It is also to be observed, 

 that the difference between the resistances of the globe and cyl- 

 inder in water is greater than in air ; and this is directly contrary 

 to what might be inferred from Newton's reasoning, which sup- 

 poses them equal in a continuous fluid, but in the ratio of 1 to 2 

 in a rare fluid. 



505. To determine the relations of v^o r 'fv. space, and time, of a 

 ball moving in a fluid in which it is projected with a given velocity. 



T.etw = the velocity of projection, s the space described 

 in any time t, and v the velocity acquired. Now, by step 4, arti- 

 cle 503, the accelerating force / = ; where s' is the den- 

 sity of the ball, s that of the fluid, and D the diameter of the 

 282. ball. Therefore the general equation v dv = gfds becomes 



and hence 



dv 3s, , 



=: . ds = c d 5, 

 v 8 s' D 



