Theory of Heat to the Steam-engine, 485 



than those calculated from our equations ; for at first the former 

 are considerably greater than the latter^ afterwards they approach 

 a little nearer, and finally they are absolutely less. The reason 

 is, that, according to Pambour's theory, the same mass, as at first, 

 always remains vaporous during expansion ; whilst, according to 

 our theory, a part of the liquid accompanying the vaporous mass 

 afterwards evaporates, and the more so the greater the expansion. 



55. In a similar manner we will now consider a machine 

 which works with expansion, and we will further select one with 

 a condenser. 



With reference to the magnitude of the expansion, we will 

 suppose that the cylinder is cut ofi* from the boiler when the 

 piston has completed one-third of its journey. Then foi* the 

 determination of e we have the equation 



e-€=^(l-€); 



whence, retaining the former value, 0*05, of e, 



e= ^ =0-3666 



As before, let the pressure in the boiler be five atmospheres. 

 By good arrangement the pressure in the condenser may be kept 

 below one-tenth of an atmosphere. As it is not always so small, 

 however, and as the reacting pressure in the cylinder always 

 exceeds it a little, we will assume the mean reaction to be one- 

 fifth of an atmosphere (or 152 miUims.), to which the tempera- 

 ture ^o=60°'46 corresponds. Retaining the former assumed 

 value of /, therefore, the quantities requiring application in this 

 example are 



e =0-36667 



6 =0-05 



/ =1-053 \ (56) 



j0i = 3800 



In order to calculate the work, we now only require the value 

 of V to be given. To guide our choice, we must first know the 

 least possible value of V, which we can find, as before, from the 

 second of the equations (XVII) by putting p^ in the place of 

 jOg, and changing the other quantities dependent on jo accord- 

 ingly. In this manner we find for the present case the value 



1-010. 



Starting from this, we will assume, as a first example, that the 

 actual velocity of the machine^s motion has to this minimum a 



