Proceedings of the Polytechnic Association. 1085 



curastances which are employed in the engine. But it clearly shows 

 why an engine which admits the steam at or near boiler pressure, and 

 automatically cuts it off at a point in the stroke proportionate to the 

 load, is more economical than one which has a fixed or no cut-off, and 

 a variable load, the power and speed being regulated by a throttle- 

 valve. It also shows graphically the benefit of large passages and 

 pipes, a tight, quick moving valve, and a proper amount of com- 

 pression. 



This mode of expressing the value of mechanical arrangements in 

 steam engineering, was first published, it is believed, in a pamphlet 

 issued by the firm of which the writer is a member, about a year ago. 

 As it was not practicable in the limits of an advertising pamphlet to 

 fully elucidate the grounds upon which the comparison was based, 

 and because many even among the profession do not seem to under- 

 stand the mode of delineating the theoretical diagram, I have taken 

 the present occasion to enter into a more explicit description and 

 explanation of what I believe to be a new and interesting investiga- 

 tion. 



■In the foregoing, I have assumed that steam expands according to 

 Mariotte's law, for the reason that were it a perfect gas instead of 

 vapor, it would follow that law in its expansion, and it is not impro- 

 per, for the purpose of comparison, to so consider it ; while that law 

 admits of a ready construction of the theoretical diagram without the 

 necessity of tables or pressures, or the use of logarithms. But should 

 any one prefer to use the modified law of expansion of steam deduced 

 from the experiments of Regnault, the Franklin Institute and others, 

 it can be done by employing the tables of pressures and volumes 

 given in most collections of engineering formulae. To facilitate this, 

 I have constructed the scale shown in Fig. 6, which is a series of 

 expansion-curves, as per such tables, laid down to different scales of 

 pressures. The terminal pressure having been ascertained, the same 

 is found on the curve having the same scale of pressure as the indica- 

 tor diagram. The distance between that point in the curve and the 

 line of no volume is then divided into as many divisions as there are 

 in the diagram, and at each division will be found its corresponding 

 pressure. 



This curve may be also described by first finding the ordinates of a 

 hyperbolic curve, based on a terminal pressure equal to the 0.941 

 power of the true terminal pressure, and then extracting the 0.941 

 root of each of these ordinates. 



