Motion of Gases. 381 



an instant, are as the densities and velocities conjointly ; hence 



m v : n u : : D v 2 : D' u 2 , 

 and consequently, 



X P/ "~ P - 'DV 2 ' 

 D 



which gives 



ID' D 



u v 



/ ^ D 



Moreover, from the proportion 



p : p -f- q : : D : D X , 

 we obtain 



D (^ -f- q) 



and 



D (p -4- q) 



Whence 



DJ % 



D' D p p 



' " P (P + g) : JP + g' 

 P 



\ 



Substituting this value of - - in the above expression for w, 

 we have the following simple and convenient formula, namely, 



I P 



u = v - t . 



>JjP + g 



494. We have taken no notice of the effect of the air's elasti- 

 city upon the velocity of influx into a void. Let JlBCD be a 

 vessel containing air of any density D. This air is in a state of 

 compression, and if the compressing force be removed it will ex- 

 pand, and its elasticity will diminish with the density. Now its 

 elasticity, in whatever state, is measured by the force which 



