1822.] Difference in the Specific Gravity of Bodies, 41|!^^ 



•of a cylinder or prism with its flat face perpendicular to the 

 direction of motion. 



Now let X = the diameter of the sphere, and also of the prism 

 of the fluid, which is to be equal to the weight of the sphere. 



h = the height of the last prism. 



V = the velocity acquired by a body falling through h. 



B = the specific gravity of the body. 



f = that of the fluid. t 



c = 3,1416 ; and 



g = 16-pV = the space a body falls through in one second. 



Then the content of the sphere will be ^, and that of a prism of 

 the fluid of the height the body falls from, to acquire its 



c x^ h 



greatest velocity, will be — ^? which would be equal to the re- 

 sistance, if the surface were A flat, and perpendicular to the 

 direction of the fall, but the sphere has only half that resistance. 



Hence <^^:f^ = ^, and ^ = -^,= -ir/. 



6 4x2' 4B -/ 16 ^B/ 



What will be the diameter of a sphere of lead to fall at the rate 

 of one foot per second after it has attained its maximum. In 

 this case, t; = 1, and A = ^ = ^|- inches = ^V = "ISyS. 



B= 11, specific gravity of lead. 



f =. -00119, that of air (water being 1). 



B - / = -99881 . X = '^--!-^ ''rr'^ = 0000152 inches 



*^ 4 X 10-99881 



nearly. The maximum velocity of the same sphere in water will 

 be obtained by putting, instead of//, -. Hence we get 3 tJ^y* 



-J] =z 0329 feet per second, and 



16 X 16 X -000001266 x (11 - 

 ___ 



1*974 feet = per minute. 



If the sphere were of a specific gravity of 2, about that of earthy 

 matter, by which water is sometimes rendered muddy, its uniform 

 velocity v/ould be -6414 feet per minute. TJie falling of various 

 precipitates in chemical experiments must depend upon their 

 specific gravity, and the size of the. particles ; data might be 

 obtained from an experiment by observing the time in which 

 bodies are falHng, the diameters and specific gravities being 

 known, in order to find the magnitude of particles of other mat- 

 ter, the time of falling and their specific gravities being known. 



Very small shot of a given size might be made to fall in a long 

 glass tube filled with water, and the time of falHng observed ; 

 from this data, if the time of any other matter falling be given, 

 the height fallen from and specific gravities being known, the 

 size of the particles may be found. The unequal times for the 



