SUDDEN COMPRESSION OF A MASS OF AIR. 119 



From (1) of Art. 68, we have 



P = K?T; (2) 



.-. = KT + Kp-- 

 dp dp 



= KT + K\iT [from (1)]. (3) 



Dividing (3) by (2), we have 



\ d = \ + V = [from (3) of Art. 68], 

 pdp p p p L 



dp , . 



or, -f- = - (4) 



^ P 



Integrating between the limits j' and p, p' andp, we have 





which determines the pressure. 



Also, p' = Kp'T, 



which, divided by (2), gives 



jr = w (6) 



From (5) and (6), we have 



/. T' = T(^L 

 \o / 



which determines the temperature. (See Besant's Hydro- 

 mechanics, p. 118.) 



