164 



If from this be subtracted the power developed, P (i V, there re- 

 mains the expression of the energy received by the body on the whole ; 

 that is, the difference between the energy received and the energy 

 given out, viz. — 



dY=d . Q-P^V= 



This quantity is a complete differential, its integral being 



a.t = a.(q+/.q + (q^-i)/c^v) 



When the expansive power P c^ V is wholly expended in moving 

 the particles of the expanding body itself, that motion being ulti- 

 mately extinguished and converted into heat by friction, the above 

 quantity, d Y, represents the entire quantity of heat which the body 

 has consumed at the end of the process. 



In a machine producing power by the alternate expansion and con- 

 traction of a body under the influence of heat, let Q^ and Q,^ repre- 

 sent the greatest and least quantities of heat possessed by the body. 

 Then, to work to the best advantage, the body must receive heat and 

 convert it into expansive power at the constant heat Q^, and give 

 out heat by compression at the heat Q2, when the ratio of the heat 

 converted into power to the total heat expended will be 



Q1-Q2 



In the Second Sub-Section, the author, still abstaining from the 

 use of any hypothesis, investigates such properties of temperature 

 as are deducible from the following 



Definition of Equal Temperatures : — 

 Two portions of matter are said to have Equal Temperatures, 

 when neither tends to communicate heat to the other. 

 Hence immediately follows a 



COROLLARY. 



All bodies absolutely destitute of heat have equal temperatures. 



The ratio of the real specific heats of two substances being de- 

 fined to be the ratio of the quantities of heat which equal weights of 

 them possess at equal temperatures, the following Theorem is 

 proved : — 



