£? fi rsB — ^— -*=«-^ • • ( 14 ') 



10 M. L. A. Colcling on the Universal Powers of 



for if the three equations (12) are added after having been mul- 

 tiplied respectively by dx, dy, dz 3 and we observe that 



~ dx + -(-dy-h -~-dz = dp. 

 dx dy * dz l 



then we see that the formula may be written simply 



dq . dm = dxdy dz .dp (13) 



The new increment of energy developed in the unit of mass in 

 the time dt may consequently, for the point in question, be ex- 

 pressed by 



dx dy dz ^ _ 1 



P 



since dm = p . dx dy dz. 



By means of formula (14) we are now without difficulty able 

 to determine the amount of internal energy produced in a unit 

 of mass of a liquid body when it is compressed through external 

 force ; and as the internal energy produced thereby chiefly ap- 

 pears in the shape of energy of heat, we are able to determine 

 the quantity of heat produced by the compression of fluids. 



With regard to this, I shall here call attention to the quan- 

 tity of heat developed in aeriform bodies suffering compression. 



Let us suppose that the gas in question, during the state of 

 equilibrium, has in every place the same density D, and that h 

 and gmh denote the barometric height and the pressure of 

 air answering to this density, g being the force of gravity and m 

 the density of the mercury. Let us further, at any instant during 

 the compression, denote the density and pressure of the gas by 

 p and p, then we have 



p = D(l+s), ......... (15) 



in which s or the degree of condensation may be either positive 

 or negative. 



If the condensation takes place so quickly that heat is neither 

 lost nor received during the motion, and s is only a very small 

 magnitude, then, as is known, 



p=gmh(l + y .s), (16) 



where 7 denotes the ratio between the specific heat at constant 

 pressure and that at constant volume. From this formula, 

 whose correctness increases in the same degree as s is decreased, 

 follows, 



dp =gmh .7 .ds; 



and by substituting this value for dp, together with the expres- 

 sion for p of formula (15), in the equation (14), we get 

 . gmh ds . 



D 'l + s 



