THERMODYNAMICS. 273 



AD, BE . . . ad, be . . . &c. Instead of sending the substance round the 

 curve, let it go through the series of steps ADBEC . . . cebda . . . 



In the limit the heat received along each piece AD is the same as 

 that along each piece AB, for, sending the substance round the cycle 

 ABDA, the area ABD is the mechanical equivalent of the difference 

 between the heat received along AB and that given out along DA, since 

 BD is an adiabatic ; and this area is an indefinitely small fraction of the 

 area ADda, which is itself only a fraction of the heat received along AD. 



We may, therefore, as far as concerns heat taken in or given out, 

 replace the curve ABO ... by the steps ADBEC . . . 



Let Q AB Q BC Q CD ... be the heats received along AB, BO, CD . . . 

 respectively, or, as we have just shown, along AD, BE, OF . . . 



Let Q c6 Q 6a ... be the heats yielded along cb, ba . . . which are 

 sensibly equal to those along eb, da . . . If now we imagine the sub- 

 stance to be sent round the cycle ADda, we see that this is the kind of 

 cycle already considered. 



where A and O a are the temperatures at A and a. 

 Sending it round the cycle BEei 



QBC Qrf> 



B and 6 being the temperatures at B and b and so on. 



If we regard the negative sign as denoting that the substance receives 

 negative heat we may add up all the equations and denote the result by 



where each element of heat received is to be divided by the temperature 

 of the substance when receiving it. Using the notation of the Integral 

 Calculus the result may be written, 



fdQ 



)~e 



round a reversible cycle. 



This deduction is often quoted as the Second Law of Thermodynamics 

 but it appears preferable to consider the fundamental experience, given 

 at the beginning of the chapter, as constituting the law. In reversible 

 cycles then we have 



by the first law I dQ = Work done, 



by the second law I ^ = 0. 



J v 



the former telling us the relation between the heat disappearing and 

 the work done, and the latter giving a relation between the heat and the 

 temperature. 



8 



