90 Mr. J. Ivory on the Constitution of the Jlimosphere. 



nature alone, without any hypothetical assumption that may 

 possibly involve a physical absurdity. This is one of the at- 

 mospheres considered in the paper already cited: it corre- 

 sponds to the supposition of m = 3 * ; the total height is about 

 20 miles ; and the horizontal refraction will be found equal to 

 33' 7" at the mean temperature of 50° of Fahrenheit, and the 

 barometric pressure of 30 inches. 



A fain, if we allow the temperature lost by the rarefaction 

 in the close vessel to be completely restored, the relative elas- 

 ticity within the vessel will be equal to the relative density, 

 and the function for temperature will be equal to unit. In 

 this condition of the rarefied air, the temperature is always 

 the same whatever be the degree of dilatation. If in the equa- 

 tions (H) we put/3 = g = 1 — CO, that is, if we suppose that 

 the relative pressure is equal to the relative density, we shall 

 obtain 



r = c~', 

 q = c~*; 

 and these formulae determine the height of air having a given 

 degree of rarefaction in an atmosphere in every part of which 

 the same temperature prevails. This atmosphere, as it is the 

 simplest that can he imagined, so it is the first that presented 

 itself to the consideration of geometers : its height is milimited ; 

 and the horizontal refraction is equal to 37' 34". 



It is however certain that neither of the two atmospheres 

 we have been considering coincides with that of nature. This 

 point seems to be sufficiently established by having proved 

 that in both cases the equilibrium is unstable, and would be 

 overturned by the least motion communicated by any exter- 

 nal cause. But other considerations confirm the same conclu- 

 sion. For, in one, the temperature is the same at all heights, 

 whereas in the real atmosphere the temperature diminishes as 

 the height increases. And, in the other, the temperature in 

 ascending is precisely equal to the heat absorbed by the rare- 

 faction ; but, in nature, the first of these quantities is much 

 less than the second. But although neither of the two atmo- 

 spheres agrees exactly with that of nature, they are not un- 

 deserving of notice, both on account of the properties they 

 possess in common, and because, as will soon appear, they are 

 the limits on either hand between which the real atmosphere 

 is contained. 



Returning to the rarefied air in the close vessel, the elasti- 



city is equal to (1 — w)' at the instant of rarefaction, and to 

 1 — w when the air has acquired the same temperature that 



* Phil. Trans. 1823, p. 4.39. 



prevails 



