°\t>.%V^vv Theory of Heat to the Steam-engine. 437 



in the condenser, this case will be the one to which equation (XI) 

 refers, and which for a given quantity of heat — the temperatures 

 at which the heat is received and imparted being also considered 

 as given — furnishes the greatest possible quantity of work. 



(2) The case of a machine, again, having no vicious space, and 

 when the pressure in the cylinder is again equal to that in the 

 boiler, but where the expansion is not, as before, complete, but 

 only continued until the ratio e : 1 is obtained. This is the case 

 to which equation (X) refers; only in order to determine the 

 amount of expansion, the change caused by the same in the 

 temperature of the vapour was before supposed to be known, 

 whilst here the expansion is determined according to the volume, 

 and the change of temperature must be afterwards calculated 

 therefrom. 



(3) The case of a machine with vicious space and incomplete 

 expansion, and where, of the former favourable conditions, the 

 only one which remains is that during the entrance of the vapour 

 the pressure in the cylinder is the same as in the boiler, so that 

 the volume has its smallest possible value. 



To these cases may be added the one already mentioned, where 

 the last favourable condition is relinquished, and the volume has 

 a greater than its minimum value. 



For the sake of comparison, all these cases, with the exception 

 of the first, are also calculated according to Pambour's theory. 

 The reason of the exception is, that the equations (29«) and 

 {29b) do not here suffice ; for even the one which is intended for 

 small pressures cannot be applied below one-half, or at most one- 

 third of an atmosphere, whereas here the pressure ought to de- 

 crease to one-fifth of an atmosphere. 



The following are the numbers given by our equations in the 

 first of the above cases : — 



For all the rest of the above cases the results are given in the 

 following Table, where the numbers referring to a machine with- 

 out vicious space, are again separated from the rest by a hori- 

 zontal line. The volumes after expansion are alone given, 

 because the corresponding ones before expansion, being in all 

 cases smaUer in tie, prppprtioix 9;f ^ ; i^ijiay be easily found ; — 

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