Mr. J. Ivory on the Constitution of the Atmosphere. 87 



Now this passage does not authorise an indefinite accelera- 

 tion in the decrease of heat, as Dr. Young supposes, but only 

 a limited acceleration to a certain height ; beyond which the 

 decrements of heat become less for a given variation of altitude. 

 All that is said will be explained by supposing an anomaly 

 arising from the vicinity of the earth, which ceases at such al- 

 titudes where the temperature of the air is little afflicted by 

 terrestrial objects. 



3. Having now premised such observations as seemed ne- 

 cessary for removing obstructions, and for introducing cleai'- 

 ness into the discussion, I shall next apply to the present re- 

 search the equations which have been investigated in the last 

 Number of this Journal. The elasticity and density of the 

 air at the earth's surface being each represented by unit, and 

 the relative quantities of the same things at any height in the 

 atmosphere being respectively equal to p and q = 1 — w, the 

 equations may be thus written, 



(\ -\- ar — ai-\3 \-\-aT — ai-\-a0 



(\ -\- a r — ai\3 

 1 -t-«T / ■ 



(F) 



1 -f- ar 



Here t is the temi)eratui'e at the earth's surface; / is the 

 number of degrees of the thermometer that measures the heat 

 absorbed when air passes from the density 1 to the density 

 1 — w; and 5 stands for all the accessions or diminutions of 

 heat proceeding from extraneous sources, and affecting the 

 temperature of a mass of air at the given height. These for- 

 mulae determine the equilibrium of the atmosphere, which will 

 take place when the external pressure is equal to the elasti- 

 city. One equation more is still necessary for expressing the , 

 relation between the pressure, the density, and the elevation. 

 Let h denote the length of the mercurial column which ba- 

 lances the pressure of the atmosphere, and D the density of 

 the air at any height x; and let h' and D' stand for the same 

 things at the earth's surface : then we have 



h =/-Bd.v. 



Suppose that / is the length of the homogeneous atmosphere, 



or of a column of air having the uniform density D', and e(|ual 



in weight to the mercurial column h' : then, h' ^=1 x D'; and. 



/i _ ^ D_ d.v 



17 -J -w ^ -r- 



In this equation I is still a variable quantity, for it depends 

 on the temperature at the earth's surface. Now change / to 

 denote the homogeneous atmosphere at some fixed tempera- 

 ture, 



