Motion of the Air. 385 



498. It is by a train of reasoning precisely similar, that we 

 ascertain the quantity of condensed air which will make its 

 escape from a vessel into the atmosphere in a given time. Let 

 A be the density of the condensed air, and h' the height of a 

 homogeneous atmosphere corresponding to it; also let D be the 

 density of the atmosphere. The air having for its density A, 

 will obviously, when mixing with the atmosphere, have the same 

 velocity as though it were rushing into a vacuum with the den- 

 sity A D. Now the height of a homogeneous fluid corres- 

 ponding to this density is found by the proportion 



A: A D:: ft' : fc' ^LZ^.. 



From the equation v =. \/2 g s, it will be seen that the velo- 

 cities acquired by falling from different heights are proportional 

 to the square roots of these heights. If therefore, v be taken to 

 represent the velocity of common air rushing into a vacuum, and 

 h the height of the corresponding homogeneous atmosphere, we 



shall have, u being the velocity belonging to the height h' - -< 



whence 



Moreover the proportion 



D : A : : h : h', 

 gives 



therefore 



JA A D |A ~o 



- . = v - . 

 DA \ D 



Let A' be the density of the condensed air after the time t, b 

 being, as before, the bulk of the vessel, and a a section of the 

 Mech. 49 



