Theory of Heat to the Steam-engine, 341 



by him, between volume and pressure ; assuming at the same 

 time that the quantity of steam which passes from the boiler 

 into the cylinder in a unit of time, and therefore the quantity 

 which passes during a stroke of the piston, is known from special 

 observations. As before, we will represent by M the whole mass 

 which enters the cylinder during a stroke, and by m the vaporous 

 part of the same. As this mass, of which Pambour only con- 

 siders the vaporous part, fills the space ev^ at the moment of dis- 

 connexion, w^e have, according to (29), the equation 



m.B 



- ^ ^■■- "^^ bTK^ 



where jt?2 represents the pressure at the same moment. From 

 this equation we deduce 



vsiiq adtlo 'X>'6kFr« ^)d^ v >, _- ^ •-" _^, in 'p 7(f ?yv ^ /^q\ 

 f\-- - ' - ' ' ^^ ev' . . J . • . . V 7 



" Multiplying this magnitude by (e— e)i;', the space described 

 by the surface of the piston up to the same moment, we obtain 

 the following expression for the first part of the work : — 



■hi iuiroif' ^ 



The la;w according to which the pressure changes during the 

 expansion which now follows, is also given by equation (29). If 

 at any moment v represents the variable volume, andj»? the cor- 

 responding pressure, then 

 «ij,oa aiiti iioqi; ^1^0 ioii aiiU'^^ m.B ^irjt^jg ttd inT^n^-'^ ai ton 



His expression must be substituted in the integral ['^ ^^^^ ^^ , ■ 

 ^biw nadv/ii)d yifiv VJiXH aoipjftlf^ avodii sdt ,bo2flfiilD ^nxod 



and the integration effected between the limits v = ev^ SLiid.v:=v^; 

 whence, as second part of the work, we obtain 



■W2=mB.logi --v'(l--e>&.^4fi'^?^nYt^(^> 



'lii order 'to' detefmihe the negative work doiie by the reacting 

 pressure during the descent of the piston, this reaction must 

 itself be known. Without at present inquiring into the relation 

 which exists between the reaction and the pressure in the con- 

 denser, we will represent the mean reaction by /?o, so that the 

 work done by it will be expressed by 



There yet remains the work necessary to convey the quantity 

 M of liquid back again into the boiler. Pambour has not sepa- 



