in geometrical Progression for equal Increments of Heat. 247 



the temperature of a mass of air, under a constant pressure, 

 undergoes any change indicated by HI on the common scale 

 of an air-thex'mometer, the corresponding change in its quan- 

 tity of heat may be denoted by the area AHIB between the 

 ordinates BI and AH; and let DEF be a similar curve cut- 

 ting all the ordinates and areas of ABC in the ratio of 

 AH : DH : : VI : n, and consequently making area DHIE 



= — (AHIB), which therefore represents (art. 4) the 



change which the quantity of heat would have undergone had 

 the air been confined in an inextensible vessel during the 

 change of temperature HI. Let the common scale, of which 

 HI is a part, be continued downward to the point G answer- 

 ing to —448° Fahrenheit; then (art. 3) the volume had 

 changed, under a constant pressure, in the ratio of GH to 

 GI whilst the temperature shifted from H to I. But now 

 suppose the air, which has acquired the temperature I and 

 undergone a change of heat equal to AHIB, to be instantly re- 

 stored to its original volume, whereby the temperature reaches 

 the point K on the scale. It is evident that the air is now 

 brought to the same temperature as if the quantity of heat in 

 it had undergone the change DHKF = AHIB, with its ori- 

 ginal volume all the while invariable. 



During the restoration of the air to its original volume, its 

 quantity of heat is supposed constant; but the density has 



been changed in the ratio of GH to GI, and the pressure 

 (art. 1) in the same ratio compounded (art. 3) with the ratio 

 of GI to GK for change of temperature ; that is, as GH to 

 GK. Hence (art. 5) 



GK 

 GH 



GH 



p Lil ? 1 



= ~ ; -7TVT = -V ; n ioff 



GK 



1 ClI 



// ' UH §' " (ill 



and therefore log GK— log GH : log GI — log GH ::vi:n. 



But 



