On the Relation between the Changes , Sfc. 121 



this formula must relate to its condition be/ore it has so 

 parted with the heat which was rendered sensible by the 

 compression. 



2. But it is known also, by experiment, that after the air 

 has parted with the heat that was developed by compres- 

 sion, the expansive force of the air is only in the simple 

 ratio of N. The heat it has parted with was, therefore, so 

 much as would cause, ceteris paribus^ an increased expansive 

 force of N^. 



Before proceeding, let 



T be the number of degrees temp, above 32", that the 

 air has when its volume is unity, and expansive force 

 unity. 



t the number of degrees increase of temp, to be im- 

 parted to- it above T. 



F the multiple of expansive force, per square inch, 

 which the air acquires at temp. T + ^ (the bulk remain- 

 ing the same). 



3. Now, it is already known by experiment that one de- 

 gree of rise in sensible temperature while the air is allowed 

 to expand under same pressure, expands air ^^^^ of what its 

 volume was at 32°. Or, if the volume be kept constant, one 

 degree rise in the temperature of the unexpanded mass in- 

 creases its expansive force by ^^o when the temperature is 

 32°. In other words, 



^=1 + 180^1 •■• '=(F-l)x(480 + T) 

 That is to say, the quantity of additional heat required by a 

 mass of air to make its expansive force to be F, is, in all 

 cases, so much heat as will raise the sensible temperature of 

 that mass (F — 1) x (480 + T) degrees. 



Wherefore, reverting to the first conclusion, that the heat 

 parted with (after air has been compressed, and when it has 

 cooled down to the previous temperature) is as much as 

 must, when existing in it, — have multiplied the expansive 

 force by N*, this N^ becomes the F of the last formula, and 

 the last formula with this substitution becomes 

 ^=(N*-l)x(480 + T) 



