842 Prof. Clausius on the Application of the Mechanical 



rately considered this work, but has included it in the friction 

 of the machine. As I have included it in my formulse, however, 

 in order to have the cycle of operations complete, 1 will also here 

 add it for the sake of easier comparison. As shown by equations 

 (21) and (22), estabhshed in a former example, this work will on 

 the whole be expressed by 



W,= -M<r(p,-po), (34) 



where p^ and Pq respectively represent the pressures in the boiler 

 and condenser. This expression, it is true, is not quite correct 

 for our present case, because by Pq we do not understand the 

 pressure in the condenser itself, but in the parts of the cylinder 

 in communication with the condenser. Nevertheless we will 

 retain the expression in its present form, for owing to the small- 

 ness of 0-, the whole expression has a value scarcely worth con- 

 sideration ; and the inaccuracy, being again small in comparison 

 to the value of the expression itself, may with still greater im- 

 punity be disregarded. 



By adding these four separate amounts of work together, we 

 find the whole work done during the circular process to be 



W=mB(^+los\)-v'(l-e){b+p„)-U<.{p,-p^). (35) 



31. If, lastly, we wish to refer the work to the unit of weight 

 of vapour instead of to a single stroke, during which the quan- 

 tity m of vapour acts, we have only to divide the foregoing value 



. M . 



by m. We will put / in place of the fraction — , which expresses 



the relation which the whole mass entering the cylinder bears to 

 the vaporous part of the same, and whose value is consequently 



a little greater than unity ; V in place of the fraction — •, or the 



whole space offered to the unit of weight of vapour in the cylin- 



W 



der ; and W in place of the fraction — , or the work correspond- 



ing to the unit of weight of vapour. We thus obtain 



W=b(?^ +logl) -Y{i-e)(b+Po)-l.T{p,-po). (XII) 



Only one term of this equation depends upon V, and it con- 

 tains V as factor. As this term is negative, it follows that the 

 work which we can obtain from the unit of weight of vapour is, 

 all other circumstances being the same, greatest when the volume 

 offered to the vapour in the cylinder is smallest. The least value 

 of this volume, which we may approach more and more although 

 we may never quite reach, is that which is found by assuming 



