Motion of Gases. 379 



Hence the rate of influx, which may be measured by the infi- 

 nitely small quantity of air passing the aperture during the 

 instant d t with this velocity, will be denoted by 



D A 



X D0d t = 6dt+/2gi>h(D A). 



Putting these two values of the rate of influx equal to each other, 

 we have 



tf dt A/2g-i>/i(D A) 6dA, 

 and 



d t = , -- X 



> A 

 Hence, by integrating, we obtain 



t = , ,- = X ^~^TA + C. 



i 6 V 2 g D h 

 To find the constant C, it will be observed, that when t = 0, 



A = 0, and \/ D A = A/ D . We have, therefore, for the cor- 

 rected integral 



t = - - /f X ( 4/D - \/D A 



\^ 



491. When D =: A, the motion ceases, and the value of f, or 

 the time of completely filling the vessel, becomes 



b b 



i or 7~7r =r T' or Art /I' nearl 7' 

 



Suppose, for example, the capacity of the vessel to be 8 cubic 

 feet, or nearly a wine hogshead, and that the aperture by which 

 air of the ordinary density, or 1, enters, is an inch square, or T i 

 of a foot. In this case 4 A/ ~h 4 A/27807 = 668, nearly ; and 

 hence 



( = = = J "' 72 nearl y- 



