On the Height of Mountains, Headlands, fyc. 17 



place, P' the pressure at any other place, and D' its corresponding 

 density, we shall have P : D: ;P' : D'; that is, the pressure is to 

 the density in a constant ratio, and may be represented by n : 1 ; 



.\P : D::P' : ~D'::n : l. 



Consequently, D=^P, 

 D'=£P', 

 D"=£P", &c. 



That is, the density at any place is equal to, or may be measured 



by the £th of the pressure of the column of the atmosphere above 



that place, or by the ^th of the compressing force. 



Hence, if we make P stand for the pressure at the surface A, 



and let each of the parts AB, BC, CD, &c. be equal 1, then will 



~P represent the weight or pressure of the part AB, and 



n — 1 

 . P — ^P= P=the pressure at B, 



and 



n 

 n — \ 



P=the density or weight of BC. 



{n-iy 



In the same way, — — — P=the pressure at C, 



n 



{n-\y 



n 3 



P=the pressure at D, &c. &c. 



So that the pressure, and consequently the density, will decrease 

 in a geometrical progression, as the altitudes increase in an arith- 

 metical progression. 



Calling the density at the surface d n , and the several altitudes 

 1, 2, 3, 4, &c, we shall have the following corresponding series. 

 Altitudes, 0, 1, 2, 3, 4, 5, &c. 



Corresponding densities, d n , d n ~\ d n ~ 2 , d n ~ 3 , d n '\ d n ~ 5 } &c» 



Vol. xliv, No. 1.— Oct.-Dec. 1842. 3 



