SECT, viii.] MANAGEMENT OF THE STEAM ENGINE. 269 



The area P Q R S is proportional to the force of steam on the piston during the 

 stroke ; but the steam is not exerting the greatest power in proportion to the quan- 

 tity of fuel when this area is the greatest ; for when the steam acts by expansion, 

 the area described will resemble the figure P Q R S, the steam being cut off at C, 

 and more power will be exerted by a given quantity of steam. In the same engine 

 doing different quantities of work the figures show two cases ; the black lines 

 represent the power when the throttle valve is used for regulation, and the dotted 

 lines when the engine is regulated by cutting off the steam. 



561. Let p be the number of Ibs. on a circular inch of the indicator piston, 

 which causes it to descend a inches, and let m be the length of the line a b, 



measured in inches on the diagram drawn by the indicator, then a : m : : p : , 



the pressure exerted by the steam in Ibs. on a circular inch, at the point a of the 

 descent of the piston. Thus, if by trial 2 Ibs. per circular inch causes the piston to 



descend 1 inch, then T* = - - = 2 m ; or each inch of the indicator would 



correspond to 2 Ibs. per circular inch. 



If the distance the tracer moves horizontally be divided into equal parts, and 

 the vertical distance between the lines P Q and R S be taken at each point of 

 division, and the sum of these distances, less half the distance P S, be taken and 

 divided by the number of divisions, the result will be the mean distance the piston 

 of the indicator moves over ; and calling this mean distance m, it will be, 



ffl D 



= the mean pressure on the steam piston in Ibs. per circular inch. 1 



a 



562. To MEASURE THE USEFUL EFFECT OF AN ENGINE. The preceding 

 methods only give the state of parts, but the useful effect depends on the whole 

 being in order ; and the most simple and convenient mode of measuring the effect 

 is by means of friction. 2 If the rim of a brake wheel on the engine shaft of a 

 known diameter be pressed with a force producing a known degree of friction, 

 which is exactly equal to the effect of the engine at its working speed, then it is 

 clear that if the friction this pressure produces be ascertained, the power of the 

 engine will be equal to the friction multiplied by the velocity of the rubbing 

 surface. 



1 The indicator was invented by Watt, (Robison's Mech. Phil. vol. ii. p. 156.) and the sliding 

 board and tracer were afterwards applied by Mr. Southern. Figures made by the board and 

 tracer, as far back as 1802, are still to be found amongst the archives of Soho. 



2 It is for use in those cases where the work itself is not susceptible of accurate measure ; and 

 almost all engines for impelling machinery are in this class. The power of engines for raising 

 water is easily computed. 



