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



The increment of heat which the body receives while the pres- 

 sure passes from p' tojo'-f dp' will be, according to formula (14), 



( v=f^.iog(i + ,4) 



the integral of which, with sufficient approximation, may be 

 written 



when we suppose q' = q' Q for #'=0. 



, Hence is derived the specific heat of the fluid, 



■i-jjrj (*> 



By comparing the specific heat of a gas, formula (20), with 

 the specific heat of a fluid, formula (28), we find 



o) _B f y . 



or if the density of the fluid at 0° is denoted by D' , then is 



D' =U.D', 



U being the known function of the temperature T ; which repre- 

 sents the law of the expansion of the fluid by heat under con- 

 stant pressure. On account of this the above equation may be 

 written 



^-^O.^^.^.' (00) 



Suppose now, as a particular case, that the gas in question 

 is atmospheric air and that the fluid is distilled water, both at 

 the temperature 0°, then is 



U = l, —=0-2669, ?^=0'001299, and a = 0-00366; 



COj 1) 



further, in consequence of the best observations upon the velocity 

 of sound at 15 0, 9 C, 7=1-407. When these values are sub- 

 stituted and the equation is resolved with regard to e', then we 

 find 



e'= b 6 .K 7 degree Celsius, 



which development of heat exactly agrees with that derived from 

 some experiments which Oersted made a few years ago upon the 

 compressibility of water at different temperatures. 



If the specific quantities of heat for two fluids at the tempera- 



