Mr. J. Ivory 07i the Constitution of the Atmosphere. 91 



prevails on the outside. In passing from one of these limits 

 to the other, the elasticity will successively acquire every in- 

 termediate degree of magnitude. If therefore ^ (g) or 4i(l— w) 

 denote a function of the density, the value of which is between 



the limits (1 — w)^ and (1 — cu), the elasticity of the air within 

 the vessel will at some instant between the two extreme states 

 be equal to (p (g) or f (1 — w); and by means of the equations 

 (H), we may as before construct an atmosphere in which the 

 elasticity and external pressure will be each equal to ip (1 — co) 

 when the density is equal to 1 — w. Thus innumerable atmo- 

 spheres may be imagined, which are all physically possible. 

 Their existence demands nothing except operations that may 

 be performed with air. In all of them the pressure and tem- 

 perature are not hypothetically determined by assuming alge- 

 braic formulae, which may or may not be consistent with the 

 pi'operties of air ; they are deduced from real considerations, 

 namely, the changes of volume, and the transference which 

 the equilibrium of heat requires. The air in the close vessel 

 at the instant of the rarefaction retains the whole of its abso- 

 lute heat without increase or diminution ; but at any succeed- 

 ing point of time, there is an increase of heat received through 

 the medium of the containing vessel, which affects the tem- 

 perature only. It follows, therefore, that in all tlie interme- 

 diate atmospheres a mass of air receives an increase of its ab- 

 solute heat in ascending above the earth's sui'face, and the loss 

 of temperature at any height is less than the heat absorbed by 

 the rarefaction. As experience shows that this property is 

 one of the characters of the real atmosphere, the cases to 

 which it belongs deserve to be particularly considered. 



Suppose that, in an atmosphere such as we have mentioned, 

 a given mass of air moves upwards. If it is warmer than the 

 particles in contact with it, its temperature will be continually 

 lessened both by transference and absorption, and will finally 

 be reduced to an equaUty with that of the contiguous fluid. 

 If the air has not lost all its motion when arrived at this point, 

 we may compare it in its further progress with the portions of 

 air occupying the same successive places in a state of I'est 

 and equilibrium. It is evident that the external pressure will 

 be the same at the same point of space, whether the air be in 

 motion or at rest. But the extraneous heat communicated at 

 any point to the air in motion will be less than what would 

 be received by a mass occupying the same place permanently 

 in a state of rest. For the particles in their momentary pas- 

 sage will carry of!" less heat than they would have acquired 

 by remaining stationary and exposed to the full effect of the 

 healiijg causes. Hence every mass of air at l•(^st and in cqui- 



M 2 lihrio 



