578 RErouT— 1884. 



incomplete expansion the principal source of loss, as do usually other 

 writers on thermodynamics. 



Thomas Tredgold, writing iu 1827, who, but little later than Carnot, 

 puts the limit to economical expansion at the point subsequently indi- 

 cated and more fully demonstrated by De Pambour, exaggerates the 

 losses due to the practical conditions, but evidently does perceive their 

 nature and general effect. He also shows that under the conditions 

 assumed the losses may be reduced to a minimum, so far as being de- 

 pendent upon the form of the cylinder, by making the stroke twice the 

 diameter. 



The limit of efficiency in heat-engines, as has been seen, is thermo- 

 dynamically determined by the limit of complete expansion. So well 

 is this understood, and so generally is this assumed to represent the 

 practical limit, by writers unfamiliar with the operation of the steam- 

 engine, that every treatise on the subject is largely devoted to the 

 examination of the amount of the loss due to what is always known as 

 'incomplete expansion' — expansion terminating at a pressure higher 

 than the back pressure in the cylinder. The causes of the practical 

 limitation of the ratio of expansion to a very much lower value than those 

 which maximum efficiency of fluid would seem to demand have not been 

 usually considered either with care or with intelligence by writers 

 thoroughly familiar with the dynamical treatment, apart from the modify- 

 ing conditions here under consideration. 



Watt, and probably his contemporaries and successors, for many years 

 supposed that the irregularity of motion due to the variable pressure 

 occurring with high expansion was the limiting condition, and does not 

 at first seem to have realised that the cylinder-condensation discovered 

 by him had any economical bearing upon the ratio of expansion at 

 maximum efficiency. It undoubtedly is the fact that this irregularity 

 was the first limiting condition with the large, cumbrous, long-stroked, 

 and slow-moving engines of his time. Every accepted authority from 

 that day to the present has assumed, tacitly, that this method of waste 

 has no influence upon the value of that ratio, if we except one or two 

 writers who were j>ractitioners rather than scientific authorities. 



Mr. D. K. Clark, publishing his ' Railway Machinery,' in 1855, Avas 

 the first to discuss this subject with knowledge, and with a clear under- 

 standing of the effects of condensation in the cylinder of the steam-engine 

 upon its maximum efficiency. Cornish engines, from the beginning, 

 had been restricted in their ratio of expansion to about one-fourth as a 

 maximum, Watt himself adopting a ' cut-off ' at from one-half to two- 

 thirds. Hornblowei", with his compound engine competing with the 

 single cylinder- engines of Watt, had struck upon this rock, and had been 

 beaten in economy by the latter, although using much greater ratios of 

 expansion ; but Clark, a half century and more later, was, nevertheless, 

 the first to perceive precisely where the obstacle lay, and to state 

 explicitly that the fact that increasing expansion leads to increasing 

 losses by cylinder-condensation, the losses increasing in a much higher 

 ratio than the gain, is the practical obstruction in our progress toward 

 greater economy. 



Clark, after a long and arduous series of trials of locomotive engines, 

 and prolonged experiment looking to the measurement of the magnitude 

 of the waste produced as above described, concludes : ' The magnitude of 

 the loss is so great as to defeat all such attempts at economy of fuel and 



