ON THE THEORY OF THE STEAM-ENGINE. 581 



be approximated to that predicted by the theory of the ideal engine, 

 by special arrangements having for their object the reduction of cylinder 

 waste, such as superheating, ' steam-jacketing,' and ' compounding.' 



Professor Cotterill has given more attention to this subject than any 

 ■writer up to the present time. He devotes a considerable amount of 

 space to the study of the method of absorption and surrender of heat 

 by the metal surfaces enclosing the steam, constructs diagrams which 

 beautifully illustrate this action, and solves the problems studied by him 

 with equal precision and elegance of method. He summarises the ex- 

 perimental work done to the date of writing, and very fully and clearly 

 exhibits the mode of transfer of heat past the piston without transfor- 

 mation into work. Professor Cotterill's treatise on steam, ' considered as 

 a heat-engine,' is invaluable to the engineer. 



Thus the theory of the steam-engine stands to-day incomplete, but 

 on the verge of completion, needing only a little well-directed experi- 

 mental work to supply the doubtful elements. Even these are be- 

 coming determined. Isherwood gives facts showing waste to be 

 proportional, very nearly, if not exactly, to the square root of the ratio 

 of expansion; and Escher, of Zurich, has shown the loss to be also pro- 

 portional to the square root of the time of exposure, or, in other words, 

 to the reciprocal of the square root of the speed of rotation, and it 

 only remains to determine the method of variation of loss with variation 

 of range of temperature to give the whole of the necessary material for 

 the construction of a working theory which will enable the engineer to 

 estimate, in advance of construction, the economic performance of his 

 machine. There will undoubtedly be much more to be done in con- 

 structing an exact theory involving all the physical changes occurring in 

 the working of the heat-engines familiar to us ; but it will yet be done, 

 and probably very soon. It is the hope of the writer that experiments 

 made under his direction recently may furnish the needed data, as the 

 result of the first systematic research directed to that end ; but if this 

 should prove not to be the fact, it cannot be long before direct investiga- 

 tion will secure all essential knowledge. When this is the case, the 

 remarks of those distinguished physioists and engineers, Hallauer and 

 his great teacher Hirn, will be no longer well based upon apparent 

 fact. 



Says Hirn, in his memorable discussion with Zeuner, in regard to 

 this subject : ' Ma conviction reste avjourd'hui ce qu'elle etait ily a vingt arts, 

 une theorie proprement dite de la machine a vapeur est imp>ossible ; la 

 theorie experimentale, etahlie sur le moteur lui-meme el dans toutes les formes 

 oil il a ete essaye, en mecanique appliqu.ee, peat seide conduire a des 

 resultats rigoureux.' 



At present, it seems only possible, in the absence of a complete 

 experimental examination, to do more than to base the determination of 

 the ratio of maximum efficiency upon such experience as is familiar to 

 engineers. Mr. C. E. Emery considers that, for common unjacketed en- 

 gines it is practically safe to take the ratio for maximum duty at a figure 

 expressed by an empirical formula proposed by him : r = (p +37) -^22. 

 The writer has usually taken it, in estimates, as not far from one-half 

 the square root of the boiler pressure expressed, as before, in pounds 

 on the square inch. These points of cut- off are reduced still further by 

 the fact that, commercially, it is better to reduce the size of engine at the 

 expense of efficiency, as the cost of fuel and of similarly variable expenses 



