Barometer applied to the Measurement of Heights. 357 

 p aA(l + 0,00208 n.) (i.) 



The coefficient a is constant for the same elastic fluid, but is dif- 

 ferent in different fluids, and requires to be determined in each, 

 particular case. 



471. In applying the results above stated to the mass of air 

 which composes the atmosphere, we take into consideration only 

 a single vertical column of air, supposed to rest upon the surface 

 of the earth and to extend indefinitely upward. We may con- 

 ceive of the surrounding mass or atmosphere as congealed or ren- 

 dered solid. If it were previously in a state of equilibrium, this 

 state will not be disturbed by such a supposition ; so that the 

 column in question will still be in equilibrium as before* Now 

 the force which acts upon the particles of air is gravity, which 

 may, without sensible error, be regarded as exerting itself in 

 the direction of the aerial column throughout its whole extent, 

 or at least as far as it is necessary to take any account of it. Ac- 

 cordingly, it is necessary, in order to an equilibrium, that the den- 

 sity, the pressure, and the temperature should be considered as 

 uniform throughout a horizontal stratum of infinitely small thick- 

 ness. The column being composed of an infinite number of 

 these strata or lamina, let h be the height or distance from the 

 surface of the earth of one of these strata, A the density of this 

 stratum, T its temperature, g / its gravity, p its elastic force, 6 its 

 base, and d h its thickness. We shall have dp for the pressure 

 exerted upon the inferior base, and 6 (p dp) for the pressure 

 upon the superior base ; the difference rf dp must be equal to 

 the weight 6 A g / d h of this stratum. Hence, by suppressing the 

 common factor <*, we have the equation 



dp A g f d h, 



or, substituting for A its value _f deduced from equation (i), 

 the fraction 0,00208 being for the sake of brevity represented 



bye, 



~ d P=Xtt* dh - 

 Whence 



