n \wJ' 



126 WM. THOMSON ON THE CONVECTIVE EQUILIBRIUM 



(2) 



the deduced relation between pressure and density ; and 



dp=—pdx, (3) 



the hydrostatic equation, the variation of gravity at different 

 heights being neglected, and the weight of unit mass (1 lb.) 

 being taken as unit of force. Hence by integration, 



^=1 — Yf' 3 ^^ if; ^^^ brevity, we denote^ by H, 



t X h—i , . 



From (4), (i), and (2), it appears that temperature, pres- 

 sure, and density would all vanish at the very moderate 



height -^ — X H, which is about 90100 feet, or between 



17 and 18 miles, if convective equihbrium existed and if 

 the gaseous laws had application to so low temperatures 

 and densities. It has always appeared to me to be most 

 improbable that there is any limit to our atmosphere ; and 

 no one can suppose that there is a limit at any height 

 nearly so small as 17 or 18 miles. It is difficult to make 

 even a plausible conjecture as to the effects of deviations 

 from the gaseous laws in circumstances of which we know 

 so little as those of air at very low temperatm'es ; but it 

 seems certain that the other hypothesis involved in the 

 preceding equations is violated by actions tending to heat 

 the air in the higher regions. For at moderate elevations 

 above the surface, where we have air following very strictly 

 the gaseous laws, the rate of decrease of temperatm'e 



'4.1 X T 



would, according to equation (4), be — — ^ per foot, that 



1° T 



is to say, per foot, since 11 = 26224 x ^^ 1° Cent. 



329 274 



per 329 feet. Now, the actual decrease, according to Mr, 



