Mr. J. Ivory 07i the Constitution of the Atmosphere. 243 



there is no restriction to the arbitrary number ?«, which may 

 vary from zero to infinity. But it has here been attempted to 

 deduce the laws of elastic fluids, established independently by 

 experiments, from the relations that subsist between the varia- 

 tions of the bulk of a mass of air, the heat that enters into 

 combination in a latent form, and the heat of temperature sen- 

 sible to the thermometer. From this view of the subject it 

 follows that m cannot be less than 3 ; for this is its value in 

 the atmosphere imagined by Dalton, in which air of a given 

 density possesses the greatest possible degree of cold that can 

 be produced by rarefaction. If we suppose that m is less than 

 3, we contemplate an atmosphere in which the density, the 

 pressure and the temperature cannot subsist together accord- 

 ing to the laws observed in nature. But m may have any 

 value greater than 3. Although the cold in the atmosphere 

 cannot be supposed to pass the limit imposed by nature, it 

 may fall short of that liirat by means of heat transferred from 

 the contiguous fluid or received from other sources. Expe- 

 rience shows that this is the fact ; for the cold at any height 

 is less than what would be produced by dilating the air to the 

 degree that prevails at that height. The value of m varies 

 above 3, according as we suppose that a less or greater por- 

 tion of the heat of combination is restored to the rarefied air 

 from extraneous sources ; and it becomes infinitely great when, 

 the whole heat of combination being supplied, the same tem- 

 perature prevails uniformly in every part of tlie atmosphere. 

 So long as m has a finite value, the total height of the atmo- 

 sphere is limited, and equal to Z x (ra + 1 ), or to 5 {m + 1 ) in 

 miles. But in the atmosphere of equable temperature, when 

 m is infinitely great, the height is unlimited. 



In order to find the particular atmosphere which, in the 

 class we are considering, approaches nearest to that of na- 

 ture, we must determine m so as to make the gradation of 

 heat agree with what is actually observed at the earth's sur- 

 face. Allowing that the centigrade thermometer is depressed 

 one degree for every 90 fathoms of ascent, we shall therefore 

 have 90 = i|ixO« + l), 



13 

 m= -. 



In round numbers m is thus equal to 4 ; and the pressure and 



temperature will be expressed in terms of the density by these 



equations, viz. 4 



' /; = g T 



H h '> In 



