Resistance of Fluids. 397 



q 



putting c for - . The correct integral of this is log. u log. r, or 



8 S 7 D 



log. - = c s. Or putting e = 2,718281828, the number whose 

 hyp. log. is 1, then - = e cs , and the velocity 



The velocity v at any time being the e~ cs part of the first 

 velocity, the velocity lost in any time will be the 1 e~ cs 



part, or the e ^ part of the first velocity. 



(1.) If a globe, for example, be projected with any velocity 

 in a medium of the same density with itself, and it describe a 

 space equal to 3 D or 3 of its diameters ; then s = 3 D, and 



3 s J5_ ^ 



~ SS'D ~~ SD' 



therefore c s = f , and the velocity lost is 



c 08 1 __ 2,08 

 e cs ~ 3,08 ' 



or nearly f of the projectile velocity. 



(2.) If an iron ball of two inches diameter were projected with 

 a velocity of 1200 feet per second ; to find the velocity lost after 

 moving through any space, as 500 feet of air ; we should have 



D = T \ = i, u = 1200, s = 500, s' = 71, s = 0,0012 ; 

 and therefore 



and 



__ 3 ss _ 3.0,0012.500 _ 3.12.500.3.6 _ 81 



" 8 s' D " ~8 . 7 . ~ 8 . 22 . 10000~~ " 440' 



1200 

 v - - = 998 feet per second ; 



having lost 202 feet, or nearly 1 of its first velocity. 



