252 Mr. Ivory's Theory of the Velocity of Sound. 



remains, then, to investigate the relation between the elasticity 

 and density of a mass of air that varies its temperature as it 

 dilates and contracts, without losing or receiving any heat 

 from the surrounding medium. 



Put jo', §', fl, for the pressure, density, and temperature of 

 a given mass of air; and suppose that these quantities are 

 simultaneously changed into />, g, 9 + t ; then, we shall have, 



JL — L 1 +a.6 + aT 

 p {' ' 1 + a C 



Again, p' remaining the same, put D for the density at the 

 beginning of the thermometrical scale ; and let i' be the latent 

 lieat requisite to change D into g' : then 



-L- ^ 



D 1 +a^ ' 



D l+/3i'' 



Further let ?"' + i be the latent heat accompanying the change 

 of D into f ; and, 



1_ ^ 1 _Ji 



Hence, _e _ ^ + "■^ . 



From the values that have been found, we now get, 



p \ -\- xi -{- ar -^ 



'IT ~ ~1 +«^ + /Sj I 



> (C) 



^ _ l + ct.6 f ^ 



T ~ l + a^+/3i J 



These formulae express the elasticity and density of the air by 

 means of the initial quantities p', g', 9, and the variations of 

 temperature and latent heat represented by t and i. It must 

 be observed, however, that the mass of air is supposed to vary 

 in an unlimited supply of heat; so that the small increments 

 and decrements of free heat arising from the changes of vo- 

 lume produce no effect on the thermometer, being continually 

 equalized to the temperature of the surrounding bodies. In 

 this case the quantities t and i are independent on one an- 

 other ; the first being the tempei"ature as shown by the ther- 

 mometer, and the second the latent heat connected with the 

 change of bulk. But if the supply of heat were limited, it 

 would be requisite to take into account the free heat evolved 

 or absorbed by the contraction and dilatation of the air. For 

 this purpose we must write t — z" for t in the first of the for- 

 mulae (C); supposing that t is all the heat derived from ex- 

 traneous sources, and + i the variation of the latent heat. In 



a parcel 



