Mr. J. Ivory on the Comtitidion of the Atmosphere. 83 



ascertaining die rate of the deciease of temperatiu'e. In three 

 of these instances the temperature decreases with extreme 

 slowness, and in one with unusual rapidity. Setting aside 

 these four cases, the irregularity of which may be ascribed to 

 local peculiarities, the remaining 38, extending through a lai'ge 

 scale of temperature, and embracing every variety ot" altitude, 

 give a mean ascent of 164>'7 metres, or 90 English fathoms, 

 for one degree of depression of the centigrade thermometer. 

 The greatest altitude included in the 38 measurements is 

 Gay-Lussac's ascent, — nearly 7600 yards ; and in this parti- 

 cular case, the height for one degree of depression comes out 

 equal to Q5 fathoms. The only general inference that can be 

 drawn from a comparison of all the experiments is this: That 

 the decrease of heat is nearly proportional to the increase of 

 altitude, the rate being about one degree of the centigrade 

 thermometer for every 90 fathoms of ascent. But this law 

 must be understood as belonging to a mean state of the atmo- 

 sphere, and as occasionally liable to great irregularities, more 

 especially in the vicinity of the earth's surface. 



Now if we adopt the law of an equable decrease of heat 

 in proportion to the altitude, the conditions required for the 

 equilibrium of elastic fluids will enable us to determine the 

 gradation of heat and pressure in the atmosphei'e. For the 

 investigation of this point, I shall refer to a paper on the 

 astronomical refi'actions printed in the Philosophical Trans- 

 actions for 1823. Supposing that, at the earth's surface, the 

 pressure of the air, its density, and the function for tempera- 

 ture, are each represented by unit, it is shown in the paper 

 cited, that when the density is reduced to 1 — co by ascending 

 in the atmosphere, the pressure or the elasticity of the air will 



5 



be equal to (1 — w)^, and the function for temperature to 



1 

 (! — «>)■*. Applying these formulae to the measurements of 

 Ramond, they ai'e found to give very accurate results. And 

 if we seek the expression of the height at which the diminished 

 density 1 — w will take place, we fall upon the usual formula 

 for measuring heights with the barometer. The actual state 

 of the atmosphere is therefore as well represented as the na- 

 ture of the iiKjuiry seems to permit. 



Professor Leslie has investigated a formula for the increased 

 capacity of rarefied air, or for computing the heat disengaged 

 or absorbed when a mass of air undergoes a given condensa- 

 tion or rarefaction. In the whole ot experimental science, 

 perhaps, no other instance will be found in which it is so dif- 

 ficult to form exact and adequate ideas of the train of investi- 

 gation, and the degree of precision that must be attached to 

 L2 the 



