Theory of Heat to the Steam-engine. 



431 



will show that this simplified formula agrees sufficiently well with 

 the more accurate method of calculation above alluded to : — 



50. In order to be able to distinguish between the eiFects of 

 the two different kinds of expansions to which the two last of the 

 equations (XVII) refer, it will perhaps be best to consider in the 

 first place a steam-engine in which only one of them takes place. 

 We will commence, therefore, with one of the machines which 

 are said to work without expansion. 



In this case e, which expresses the relation of the volumes 

 before and after expansion, equals 1, and at the same time 

 Tg=T2; so that the equations (XVII) assume a simpler form. 



The last of these equations becomes identical, and therefore 

 vanishes. Further, many terms of the first will admit of elimi- 

 nation, because they now become like the corresponding terms 

 of the second, from which they before differed only by containing 

 Tg instead of T^. Introducing the above-mentioned quantity k 

 at the same time, we now obtain 



W 



k' 



(V. 



V(I - €) [Pc.-Pq) - lcT{p^ -Po) 



AkUn 



+p< 



-Po) 



(XVIII) 



The first of these two equations is exactly the same as the one 

 which we also obtain by Pambour^s theory, if in (XII) we make 

 6=1, and introduce V instead of B. The difference therefore 

 consists merely in the second equation, which takes the place of 

 the simple relation between volume and weight assumed by 

 Pambour. 



51. To the quantity e, which occurs in these equations and 

 represents the vicious space as a fractional part of the whole 

 space set free to the vapour, we will give the value 0'05. The 

 quantity of liquid which the vapour carries with it on entering 

 the cylinder varies in different machines. Pambour states that 

 it amounts on the average to 0*25 in locomotives, but in stationary 

 engines to much less, probably only to 0'05 of the whole mass 

 entering the cylinder. In our example we will make use of the 

 latter number, according to which the ratio of the whole mass 

 entering the cylinder is to the vaporous part of the same as 



