the Air-Thermometer. 



337 



On the common scale of an air-thermometer, let the straight 

 line AB = — . From B draw BCD at right angles to 



AB, making BC to BD as the specific heat of air under a constant 

 volume is to its specific heat under a constant pressure, or as 1 

 to Tc. Through C and D describe two rectangular hyperbolas 

 having A for their centre, and AB for an asymptote. 



Let T — r, the temperature of a mass of air, be increased r 



degrees, or from B to E : Then AE =: . Draw EG pa- 



rallel to BD, and meeting the curves in F and G ; hence 

 EF : EG : : 1 : A,', and so of every such parallel. If this in- 

 crease of temperature take place under a constant volume, the 

 additional heat may be represented by the area BCFE, but if 

 under a constant pressure, by area BDGE. For in the hyper- 

 bola, as is well known^ the variations of the area are as those of 

 the logarithms of the abscissae. Suppose the temperature to 

 have increased under a constant pressure, and then let the vo- 

 lume of air be instantly reduced to its former magnitude, the 

 temperature by this operation will be farther augmented i de- 

 grees, or from E to H, making area HIFE = CDGF. For 

 the heat at first added now brings the temperature to the same 

 pitch, as if it had been added to the original volume all the 

 while invariable. 



By the property of the hyperbola, the area BCFE represents 



log 



AE 

 AB* 

 AH 



Hence also area HIFE = CDGF = (Ar — 1) log ~ 



, .... , , „ AE*-^ AH 

 = loo^ itf:') and thereiore -r~^ — -rz^, 

 ° AE AB AE 



JULY OCTOBER 1826. 



