Resis tance of Fluids. 387 



To illustrate this by an example, let it be required to find 

 the time in which air of double the atmospheric density, confin- 

 ed in a cubical vessel, each of whose sides is 12 feet, will expand 

 into the atmosphere through an opening of one tenth of an inch 

 in diameter, so as to be reduced to the common density. The 

 above formula gives by substitution, 



2 X 12 3 



t =. - - X an arc whose tang, is 1, 

 0,007854 X 1338 



9 V 1 9 3 V 1 00 



z A 1Z * X an arc whose tang, is 1, 



0,7854 X 1338 



2 X 123 X 100 = = 4/ 



1338 



499. Even although the density of the confined air were 

 infinitely greater than that of the atmosphere, the time in which 

 it would be reduced would be a finite quantity. For A being 

 infinitely greater than D, the 



IA D 



tan s- J-ir- 



is also infinite, and corresponds to an arc of 90. Hence in this 

 case we have 



t = X 2 X 0,7854. 

 o v 



The capacity of the vessel and the area of the aperture being 

 the same as in the last example, we should have for the time in 

 which this infinitely condensed air would be reduced to the 

 same density with the atmosphere 



x 2 x ' 7854 = 561 " = 8/ 36// 



