and the Laws regarding the Nature of Heat* 



\n 



which will enable us more definitely to recognize the manner in 

 which the deportment of the vapour diverges from the law of M. 

 and Gr. Assuming the correctness of the law, if psQ denote the 

 value oips for 0^, we must set in agreement with (20.), 



ps __a + t 

 ps'o'^ a ' 



and would therefore obtain for the differential quotients -j- • ( "^j 

 a constant quantity, that is to say, the known coefficient of ex- 

 pansion — = 0*003665. Instead of this we derive from (26.), 

 when in the place oi s—a we set s itself simply, the equation 

 ps ^m — n.e^^ a-\-t 



m-'n 



(38.) 



and from this follows 



d rps \ 1 in—nll-\-k(a + t)]^^ 



dt\ pSn J 



m—n 



(39.) 



The differential quotient is therefore not a constant, but a func- 

 tion which decreases with the increase of temperature, and 

 which, when the numbers given by (26«.) for m, n and ky are 

 introduced, assumes among others the following values : — 



Table IV. 



We see from this that the deviations fi-om the law of M. and 

 G. are small at low temperatures j at high temperatures, how- 

 ever, for example at 100° and upwards, they are no longer to be 

 neglected. 



It may perhaps at first sight appear strange that the values 



found for -rrX — ) are less than 0*003665, as it is known that 

 dt \psq/ ^ 



for those gases which deviate most from the law of M. and G., 



as carbonic acid and sulphurous acid, the coefficient of expansion 



is not smaller but greater. The differential quotients before 



