Resistance of Fluids. 395 



If a leaden ball, for example, one inch in diameter descend 

 in water, and in air of the usual density at the earth's surface, the 



specific gravities of these bodies being 11,3, 1, 0,00122, res- 



s / s 



pectively, since f of an inch is fa or O? 11 ? f a f ot > ~ ^e- 



comes 10,3 in the case of water, and 



11,8-0,00122 = 926 ^ 

 0,00122 



in the case of air, we shall have 



v = V 2 X 32,2 X 0,11 X 10,3 = 8,54 



nearly, for the greatest velocity the ball can acquire per second 

 in water ; and 



V/2 X 32,2 X 0,11 X 926 = 256 

 nearly, for the greatest velocity in air. 



But if the globe were only one hundredth of an inch in diam- 

 eter, the greatest velocities would be only T V of the above re- 

 sults, or 0,85 of a foot in water, and 25,6 in air ; and if the ball 

 were still further diminished, the greatest velocity would be di- 

 minished also, in the subduplicate ratio of the diameter of the 

 ball. This is well illustrated in the fall of rain. The different 

 sized drops descend with different degrees of rapidity, but all so 

 gently as to cause no injury. Were this fluid so constituted as 

 to allow the drops to form in larger masses, or were the air much 

 less dense, tender vegetables would suffer by the shock, as they 

 sometimes do in fact by the more rapid descent of hail. 



504. It appears from the third step of the preceding article, 

 that the resistance to the motion of a cylinder moving in the 

 direction of its axis is double that of a globe of the same diame- 

 ter ; and in experiments with bodies that move slowly, this will 

 nearly hold true in water, but still more nearly in air ; because 

 its particles move more freely than those of water, and less dis- 

 turb each other's motions ; but when the motion is more rapid, 

 considerable aberrations will occur, both from the mutual dis- 

 turbance of the particles, and from the fluid not flowing in so fast 

 behind as the body moves forward ; in the air also, a new cause 

 of deviation will arise, from the condensation of the fluid before 



