12 M. L. A. Colding on the Universal Powers of 



gas at constant pressure (i. e. of variable volume) and at constant 

 volume is denoted by <y, then, as the coefficient of expansion ct is 

 the same for all gases, we find 



■ = - ,_gmh / 



and by taking the ratio between the quantities of specific heat 

 for these gases, we get 



"V V .7 (21) 



co 1 d 7 -i y 



which exactly is Dulong's formula according to which the specific 

 heat of the gases is calculated*. 



I shall briefly make use of these formulae to determine the de- 

 velopment of heat which takes place during the propagation of 

 sound in an aeriform body. 



If the velocity of the sound be denoted by a } then, according 

 to Poisson, we have 



when we keep the same designations which are used above ; and 

 if the aeriform body is imagined to be unlimited in all direc- 

 tions round a fixed point (the original point of the coordinates 

 at which the undulation commences), and if, after the lapse Of 

 time /, r is used to denote the radius vector of the point whose 

 coordinates are x, y, z, then the degree of condensation s in this 

 point and at this instant is determined by the equation 



,= l[F(r-tf) -f(r + at)], 



F and/ representing two arbitrary functions; if this expression 

 for 5 is substituted in the equation (17), we get the quantity 

 of heat developed, 



q="[F(r-at)-f(r + at)]. .... (22) 



Next let us examine the quantity of heat developed through 

 compression of liquid bodies. 



Here it will be convenient to start from (ErstecPs experiments 

 upon the compression of fluids. Agreeably to the said experi- 

 ments, it may be taken for granted that when a fluid for one 

 atmosphere of pressure is compressed by a fraction of volume 

 equal to /3, then this fluid is compressed 2/3, 3/3, 4/3, &c. by the 

 pressure of 2, 3, 4, &c. atmospheres. 



* SeeMemoires de V Academic Royale des Sciences de VInstitut de France, 

 vol. x. p. 188. 



