1082 Transactions of the American Institute. 



3.333, 5., 10. Having found the theoretical pressure at each of the 

 several divisions of the diagram, we then trace a curve through these 

 points ; and where the curve thus found intersects the line of boiler 

 pressure, is the point of theoretical cut-off at which the admission of 

 steam must be suppressed in our theoretical engine to give the same 

 terminal pressure. 



On tlie return stroke, if there is no compression, the theoretical 

 diagram will follow along the atmospheric line or the line of absolute 

 vacuum, according as the engine from which the diagram was taken 

 is non-condensing or condensing, and will extend to the clearance 

 line, and up that to boiler pressure. But if the exhaust valve closes 

 before the end of the return strokes and a quantity of steam is 

 imprisoned in the cylinder to form a cushion, then so much of the 

 cylinder full of steam as is thus imprisoned, is not discharged, but 

 remains in the cylinder, and must be allowed for in our theoretical 

 diagram. We therefore draw a hyperbolic curve tangent to the 

 actual compression line, and extending to the line of boiler pressure, 

 which curve forms the boundary of the theoretical " card." If the 

 engine is condensing, this curve will also extend to the exhaust line, 

 and will form the boundary of the theoretical diagram both on the 

 bottom and at the end. If non-condensing the atmospheric line will 

 bound the diagram until it intersects the compression curve. 



We now have two diagrams tangent at two points, the compres- 

 sion and exhaust ; the one always larger and inclosing the other. 

 The inner one represents what the steam actually performed in the 

 engine, the outer one what the same amount of steam should have 

 done in a perfect engine of the same capacity ; and the proportion 

 which the area of the smaller bears to the larger, gives a very good 

 idea of the relative perfection of the mechanism which was used for 

 developing the power of the steam. This may be expressed in per- 

 centage of the theoretical, and a collection of diagrams so figured, 

 the arrangement of valve-gear in each case being fully noted, is very 

 instructive. 



To facilitate the construction of these tlieoretical diagrams, Mr. A. 

 II. Raynal has devised the scales shown in Figs. 4 and 5. Fig.' 

 4 is for laying off the hyperbolic curve of expansion with rapidity 

 and without the mental effort incidental to mathematical calculations. 

 It is simply a series of secants numbered from the vertical, whose 

 tangents are to each other inversely as their numbers. In using this 

 Bcale, which answers for all scales of pressure, and any number of 



