Proceedings of the Polytechnic Association. 1079 



styles of engines, under dilfering conditions ; the shape of the dia- 

 grams produced by this instrument giving to a practiced eye, but 

 only to such, an indication of the relative perfection of the valve 

 motion, the size of the passages, and the general efficiency of the 

 machine. But it is desirable to be able to compute these diagrams 

 ih some way which will give a mathematical expression of their 

 several grades of efficiency, and thus enable us to express the com- 

 parative values of diflerent forms of construction, independent of the 

 varying conditions under which the diagrams have been taken, and a 

 method of accomplishing this object forms the subject of the present 

 investigation. » 



It is evident that an engine which has no losses from clearance, 

 condensation or leakage ; which takes the steam at boiler pressure 

 until the point of cut-off, expanding in accordance with the hyper- 

 bolic formula, exhausting at the end of the stroke to atmospheric 

 pressure, or to perfect vacuum, according as it is condensing or non- 

 condensing, performing the back stroke with no back pressure (back 

 pressure being reckoned from atmosphere if non-condensing, or 

 vacuum if condensing), and compressing, if at all, on the hyperbolic 

 curve, would give the utmost power which could be obtained prac- 

 tically from that amount of steam used under that pressure and 

 degree of expansion. And it being self-evident that the engine 

 which approaches nearest in its action to the above has the best pro- 

 portions and arrangement of its mechanism, we will adopt it as a 

 standard, and proceed to institute a comparison of the diagram made 

 by a given engine, with this standard engine, having the scDiie capa- 

 city (including clearance) and xising the same amount of steam with 

 the same hoiler pressure / that is, we propose to compare each dia- 

 gram with a diagram calculated for a theoretically perfect engine 

 under precisely similar circumstances. 



The amount of steam expended in producing the power developed 

 in any particular case, is measurable in two ways : By the amount 

 which enters the cylinder, and by the amount which is discharged 

 therefrom. Had we the exact means of measuring either of these 

 quantities, we should, of course, iind them precisely equal ; but, 

 owing to the unavoidable condensation within the cylinder, part of 

 which is reevaporated during expansion, and of more or less leakage 

 into the cylinder after the valves are closed, the indicator diagram 

 nearly always shows an apparently greater quantity of steam 

 exhausted than received. The exact point of cut-off or suppression 



