of Air and the Gases, and the Velocity of Sound. 5 



diminished from unit to 1 — w. When the rarefied air has 

 resumed the general temperature on the outside, it is obvious 

 that 1 - CO will likewise represent the elasticity within the ves- 

 sel. But at the instant of the rarefaction, the heat absorbed 

 by' the dilated air will produce a certain degree of cold, and 

 consequently a diminution of elasticity. Taking the letters t 

 and i in the meaning we have explained, i will denote the 

 depression of the thermometer within the vessel at the instant 

 of the rarefaction ; and the elasticity of the dilated air will, at 

 the same instant, be equal to 



I 4- a T — ai 



If the dimensions of the vessel be suddenly lessened, the 

 density of the confined air will be increased to 1 + w, and 

 heat will be evolved. The elasticity within the vessel at the 

 instant of condensation will be equal to 



1 + «T + ai 



but it will change to 1 + w in a short moment of time when 

 all the heat of condensation is dissipated. 



In these experiments the sole cause of the heat / is the en- 

 larcrement or diminution of the volume, or the variation of the 

 density, of the mass of air. It has no dependence on the ex- 

 ternal temperature r. If the temperature be varied, the elastic 

 force of the air within the vessel will be proportionally aug- 

 mented or diminished; but the combined heat / will not be 

 affected by the heating or cooling, so long as the containing 

 vessel remains unchanged in its dimensions. If the dilated or 

 condensed air be reduced to its original volume, the heat ot 

 combination will be disengaged and become sensible to the 

 thermometer, or it will be absorbed and disappear from that 

 instrument ; and this will be the case whether the restoration 

 of volume be made at the original temperature r, or at any 

 other temperature greater or less than t. The volume oi a 

 mass of air or its densitv, and its heat of combination, are two 

 thin<rs inseparably united ; and no change can be made m 

 one without a conseciucnt alteration of the other. In the lan- 

 guage of the Mathematics, the one is a function of the other; 

 and it will readily appear IVorn what has been saul, that the 

 density of a mass of air may be expressed in terms ot its heat 

 of combination by an equation of this form, viz. 



the function <p being liable to no limitation, except that it must 

 be equal to unit when i = 0, in order that the density may 



resume 



