88 Mr. J. Ivory on the Constitution of the Atmosphere. 



ture, as zero; then the length, at any given temperature t, 

 will be equal to ^ x (1 + «t) : hence 



h r D dx 



X 



h' J 



D' /(1-f ar) ' 



We therefore obtain these formulae, 



^=/(TTI7)' (H) 



The equations (F) and (H) are the analytical expressions 

 of all the physical relations known to subsist between the 

 pressure, density, temperature, and height of a mass of air in 

 an atmosphere in equilibria. All the four things mentioned 

 depend upon the two variable quantities / and 9 ; or if we put 

 t = i — ^, they depend upon i and /, which represent the heat 

 absorbed, and the temperature lost, by the elevation of a mass 

 of air from the earth's sm-face to the height it occupies. The 

 inquiry into the constitution of the atmosphere is therefore re- 

 duced to investigating the relation that subsists between i and 

 9, or between i and /. 



4. Dalton has supposed that a given mass of air retains the 

 whole of its absolute heat, whatever be its position in the at- 

 mosphere, the temperature lost being just equal to the heat 

 which enters into combination in a latent form. This hypo- 

 thesis is equivalent to making 9 = 0, or i = /, in the preceding 

 formulae. But by an easy appeal to experience we may prove 

 that Dalton's supposition is not agreeable to nature. In the 

 aerial ascent of Gay-Lussac the centigrade thermometer fell 

 from 30°*8 to — 9°-5, the total depression being 40°-3, at the 

 same time that the elasticity of the air was reduced from 1 to 

 0*432, and the density to ^ very exactly. Now from the for- 

 mula „ _ / i+«'f- «'y 



and, when g = y, and t = 31°, it will be found that z = 61°, 

 or about 21° greater than the observed temperature. It ap- 

 pears therefore that, in the atmosphere, the temperature that 

 prevails is much less than the heat absorbed by the rarefaction 

 of the air. 



In a memoir on the Theory of Sound, published in 1807*, 

 M. Poisson has supposed that, when air suffers a small con- 

 densation or rarefaction w, the heat evolved or absorbed is 



* 14* Caliier de PEcolc Poly technique. 



proportional 



