\^m. Theory of Heat to the Steam-enffine* 351 



this difference. The steam, instead of being allowed to pass off 

 into the atmosphere through a tube as short and wide as possible, 

 is conducted into the chimney and there made to issue through 

 a somewhat contracted blowpipe in order to create an artificial 

 draft. 



In this case an exact determination of the difference is essen- 

 tial to the accuracy of the result. In doing so, regard must be 

 had to the fact, that in one and the same machine the difference 

 is not constant, but dependent upon the velocity with which it 

 works ; and the law which governs this dependency must be 

 ascertained. - Into these considerations, and into the investiga- 

 tions which have already been made upon the subject, I will not 

 here enter, however, because they do not concern the mechanical 

 theory of heat. 



In machines where the vapour from the cylinder is not thus 

 employed, and particularly in machines with a condenser, jo'q dif- 

 fers so little from Pq, and therefore can change so little with the 

 working velocity, that it is sufficient for most investigations to 

 assume a mean value for jo'q. 



Seeing, further, that the magnitude p^ occurs only in one term 

 of the equations (XIV), which term involves the factor <7, it can 

 have but a very small influence on the amount of work j so that 

 without hesitation we may put, in place of jOq, the most probable 

 value oip'^. 



As already mentioned, the pressure /?% in the vicious space 

 may vary very much, according as the cylinder is cut off from 

 the condenser before or after the end of the piston^ s motion. But 

 here, again, in equation (XIV), this pressure, and the magni- 

 tudes dependent thereon, occur only in terms which involve the 

 small factors fi and //-q ; so that we may dispense with an accu- 

 rate determination of this pressure, and rest satisfied with an 

 approximate evaluation. In cases where no particular circum- 

 stances are present to cause p"q to differ essentially fromjo'^, 

 their difference, like the difference between p'^ andjOg, may be 

 neglected, and the most probable value of the mean reaction in 

 the cylinder may be assumed as the common value of all the 

 magnitudes. This value may be represented simply by jOq. 



By introducing these simplifications, the equations (XIV) 

 become 



W= ];Kn-m37-3+Mc(Ti-T3)+/.o^o-/^<T3-To)] 



+ AM.o-{p^-p^ 

 ^=^ + (M + ^)logJ. 



■3 



