Nature and their Mutual Dependence. 13 



From (Ersted's later experiments upon development of heat 

 through compression of water, we may infer approximately that 

 the development of heat is proportional to the pressure, so that 

 2, 3, 4, &c. times as much heat is developed by 2, 3, 4, &c. at- 

 mospheres of pressure as by 1 atmosphere of pressure. 



If we then imagine a unit of mass of a certain liquid, and we 

 suppose its density = D' and its volume = Y' at the tempera- 

 ture T', and if we put the pressure on unit of surface =gmh, and 

 if we further suppose that the pressure is changed and becomes 

 =//, then the temperature rises to (T'-f#'), the density becomes 

 p', and the volume becomes Y f . We thus have 



p'=D'(l+ S % (23) 



$' denoting the degree of condensation. But s' always being very 

 small, we have with sufficient approximation 



Y'^Y'^-s') (24) 



If, further, the coefficient of compression for one atmosphere 

 at the temperature T' is denoted by /3, then, conformably to 

 (Ersted's experiments, we have 



\gmh J' ' 



since the pressure of air gmh is supposed to be equal to one 

 atmosphere, and the development of temperature for one atmo- 

 sphere of pressure is denoted by e'. 



If both equations (25) are resolved with regard to p 1 , and if 

 formula (24) is taken into account, then we have 





whence follows 



(26) 



S '=f3j 



which, substituted in the equation (23), gives 



P '=D'(l+/3|-} 

 When the second equation (26) is differentiated, then we get 



dp' —gmh . — r • 



