Mechanical Theory of Heat to the Steam Engine. 193 



compressed, we could not make the assumption that in the be- 

 ginning no fluid water is present, because then the vapor would 

 not remain at a maximum density, but would be overheated by 

 the heat produced during the compression. In the expansion 

 on the other hand, the steam remains not only at a maximum 

 density, but a part of it is in fact condensed, and it is precisely 

 the diminution of m produced thereby, to which the table re- 

 fers. The initial temperature is assumed as 150° C, and corres- 

 ponding values of ^ are given for the times when the tempera- 

 ture has sunk by the expansion to 125°, 100°, etc. The tem- 

 perature estimated from the freezing point is denoted by as 

 heretofore, to distinguish it from the absolute temperature repre- 

 sented by T. *, 



t 



150° 



125° 



100° 



15° 



50° 



25° 



m 

 M 



1 



0-956 



0911 



0-866 



0-821 



0-116 



16. In order to express the relation between the volume v and 

 the temperature, we have in the first place equation (6), namely 

 v = mu + Mv. The quantity cr occurring here, which signifies 

 the volume of a unit of weight of the liquid, changes very little 

 with the temperature, and as besides the whole value of a is 

 very small with respect to we may with the more propriety 

 neglect the small changes which it undergoes, and we will there- 

 fore consider cr and consequently also the product Ma as con- 

 stant. We have therefore only to determine the product mu. 

 For this purpose we only need to substitute in the equation (VII,) 

 for r, the expression given in (vi,) whereby we obtain 

 * . dp [dp\ Me. T 



d f) 



The differential coefficient — = which occurs here is to be looked 



d T 



on as known ; p itself is known as a function of the temperature, 

 and consequently by this equation, the product mu is determined, 

 and from it we obtain by addition of i/o- the sought quantity v. 

 In the following table, there is again collected a series of 

 v 



values of the fraction — , which are deduced from this equation, 



for the same case to which the foregoing table relates. For the 



sake of comparison, those values of — are also added, which we 



should obtain if the two assumptions usually made heretofore in 

 the theory of the steam engine were correct. (1.) that the steam 



SECOND SERIES, VOL. XXII, NO. 65. — SEPT., 1856. 



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