342 PRACTICAL MATHEMATICS 



Hence log e p - \og e p = - ch 



l 8e- = ~ch 

 Po 



P = P(f~ fih 



Let PO Ib. per sq. ft. be the pressure and W Q Ib. the weight of a 

 cubic foot of air at datum level. 



77 



Then W Q = cp , or c = 



Po 



tp n h 



and p = p Q e v 



(2) When the temperature does not remain constant, 



i_ 

 Then pv n = Const, and w = cp" 



dp 1 



fn n 



dh p 



\p " dp = - c \dh + Const 



1^ 

 = ch + Const 



u 



i-i 



but when h = 0, p = p Q , ^ = Const 



1 



n 



n / j_i i_l \ 



_ \ Po n P n I = CH 

 71 1 ^ ' 



jW^ji-teY-"}-^ 



n - 1 \p Q / } 



but when h = 0, p = p Q and w = W Q 



- w/> 



Then w = cp Q n and c = 2. 



XT j w Pof-, f P\ l ~\ 

 Hence h = - 1 ( ^- ) 



n 1 w > ^i? / J 

 Also pu = RT, where T is the absolute temperature 



p v T 

 and - = _ 



Po v o T o 



but ^Y-J, or^ 1 



