242 Mr, J. Ivory on the Constitution of the Atmosphere. 

 Wherefore by equating the equal quantities, 



^ = «Zx \^^-\~^'-^ + A' (K) 



dt I dt \ ■\- a.v— «,% ) 



In the equation just obtained if we suppose i = t, which is 

 the hypothesis of Dalton, then, 



dt ' 



or, since a. = -5 — , and I = 4500 fathoms at the mean tern- 



800 



perature of 50° Fahrenheit, 



— = 67i fathoms. 

 dt ^ 



It thus appears that in the atmosphere of Dalton, the tem- 

 peratui-e decreases exactly at the same rate as the height in- 

 creases, the depression of the mercury in the thermometer 

 being one centesimal degree for every 67| fathoms of ascent. 

 The total altitude is equal to 4- 1, or about 20 miles ; for at 

 that height the density is evanescent. 



But the like properties belong to an indefinite class of at- 

 mospheres. Assume 



^ di I -{- ar — ai 

 m = 3 -— - -r-, ') 



dt l-)-a!T — at 

 then l+ccr-at _/ 1 +<^T-«.i \-^ _ — ; 



1+«T \ 1 + ar / ^ 



and consequently 1 , _L 



p ^ q ~ m 



The essential character of all these atmospheres, including 

 every case in which the height is proportional to the tempera- 

 lure lost in ascending, is marked by a single equation between 

 the pressure and density, viz. 



^ = § ^ + »' ; 

 and the relation between the altitude and the loss of tempera- 

 ture is expressed by this formula, viz. 



X = a.l{m + 1 ) ^ = ^g . t. 



This class of atmospheres has been found in a different way 

 in the paper in the Philosophical Transactions for 1823, al- 

 ready cited. The reasoning in that paper proceeds solely 

 upon the received laws of the equilibrium of elastic fluids; no 

 hypothesis being admitted except the particular condition the 

 consequences of which it is proposed to investigate, namely, 

 that the height ascended shall be proportional to the decrease 

 of temperature. In this manner of considering the subject 



there 



