for determining the Heights of Mountains. 311 



In M. Poisson's Traite de Mecanique (Art. 624—6.) the 

 following equations are given : 



p=kp{l+uQ) {!.); dp=-g'pdz{2.); ^ = ^. -^^ 



whereof (2.) = weight of the stratum dz at the height z. Now 

 as (1.) refers to an atmosphere of variable density and tem- 

 perature, and (2.) to variable density alone, I consider that 

 (2.) (3.) ought to be changed to 



dp== - g'p{\ -^ ct^)dz (4.) 



p k {r -\- zy k ^ 



by neglecting the variation of the centrifugal force. 

 Integrating (5.) 



At the lower station k^k (l+«^/), ^/=mean heat of lower 

 station ; hence as shown by M. P. 



metres , <? / \ T rr\t » 



18337-46(1+^') J 1 „ 5550 + T\ h 



1 --002588 COS.24/ I 



+ 2log.(l+?)} (I+?) (7.) 



5550 + T' h 

 Therefore, if A = first factor, /=A'log. ^^^o + T ' A'* 



. Mz' 



{o.™..„g.(^±^)|,-} 



r 



;g = s' + 8 » : if the upper station be on a mountain 



z=z' +— oz. 



o 



As an example, the following one, given by M. Poisson, may 

 be taken. 



Required the height of Guanaxuato (the true height 

 = 2084.'°-46), h = 0'"-76315, A'=0'»-60095, T=^=25°3, 

 T' = /i = 21°-3, ^^ = 21°. 



M. Poisson finds 2''=2077™*98; therefore by my formula 



/=2077-98 (l+^^) 



1 + -002(21 -3 + 25-3) 



