FOR HIGH LEVELS IN THE EARTH's ATMOSPHERE. 43 



gdz = — vdp. (10) 



By solving (9) for v and substituting in (10) we obtain 



,..= -^»xrxJ. (11) 



But from (1) we see that 



dV = gdz, 



and if we substitute this in (11) we have 



dv^_m.T.'^J^. (12) 



-'o P 



By integrating formula (12) from p = po to p =^ pi we obtain 



T;,-i^.=W'V.'ii (1.3, 



or by substituting from equation (7) 



e!' 



pprT.'-p. (14) 



dp 



'Jpx 



In the calculation of 11 f'- we may start with equation (12). First solving for 

 and then integrating from V = Fy to V = Vi we obtain 



V 



or 





whence by (8) we find 



n^'=^j,.,(i -^""-'"'''0 ^). ^^^^ 



Now by substituting the values 



;j„ = 2.4934 X 32.1726 x 846.728, 

 v^ = 1 /0.080 259, 

 r„= 459.4 + 32.0 = 491.4, 

 in equation (14) we obtain the following expression 



2.4934 X 32.1726 x 846.728 



^"0 0.080259 X 49 



846.728 P» f7» 



