

(XIV) 



\^*i>wi!V»\ Theory of Heat to the Bteam^engim) •N't*"! 349 



+ ?/i3W3(;?3-/o) +/^oA(Fo-y o)-M(r(/o-i?o) ' 



^;^:)£-*y.c(T2 -n) + A/.o^"o(y 1 -A) + AM(7( ;?, --p\) 

 ^ = ^ + (M +/i)c log ^2.^.1. ;^^: ii *.£{ Ar 



^39. Before endeavouring to render these equations more con- 

 venient for application, it may not be without interest to show 

 how, for an imperfect steam-engine, the same expressions may- 

 be arrived at by a method before alluded to, and opposite to the 

 one just applied. In order to avoid prolixity in this digression, 

 however, we will only consider two of the imperfections provided 

 for in the above equations, viz. the presence of vicious space, and 

 the existence of a smaller pressure in the cylinder than in the 

 boiler during the time that the vapour is passing into the former. 

 On the other hand, we shall assume the expansion to be com- 

 plete, therefore Tg=To, and the magnitudes T^, T'^, and T"q to 

 be equal. 



In this determination we shall have to employ the equation (2), 

 to which we will give the following form : — 



The first term on the right-hand side of this equation denotes 

 the work which could be obtained from the employed quantity 

 of heat Qi, which in our case is represented by m^r-^ + Mc(Ti — TJ, 

 did not two imperfections exist. This term has been already 

 calculated in § 23, and found to be 



i[m.r, + M<T,-T„)-To(^ + Mclog|i)]. ===""" 



The second term denotes the loss of work caused by those two 

 imperfections. The magnitude N contained therein has been 

 calculated in. § ?6,, ^nd,is^epresettt^d Jbyth^.^xpregsjpA in equa- 

 tion (38). ^, V ...biiJin^Kio siiJ ^ro^i.yxp 1:^18 '..aO<> '' 



Substitut^§^%^j|)^o^^^^fg^OKiflH,,^g^fgregoin^ equation. 



we have ^._ ,, -iirno'-b ^^^ MriiK^oq. ^r ?j rfer/aii ■ 



W'= i[m,.,~^%r,-hMc(T,-To)-(M + /.)cTolog|^ +^,r,]. 



That this equation actually coincides with the equations (XIV), 

 may be easily seen by using the third in order to eliminate % 

 from the first, and then setting T3=To=T^o=T'o. 



In the same manner we might make allowance for the loss of 



