316 REPORT — 1841. 



(in feet) is described by it, and the number N registered by it. Whilst the 

 number N is registered by the indicator, L is shown by the ordinary counter, 

 and the number U thus determined being multiplied by the number of square 

 inches in the piston of the engine, will give the whole work yielded by the steam. 

 The sign + is to be taken according as the steam pressure P is in the act 

 of increasing or diminishing, or as the piston of the indicator is in the act of 

 yielding to the pressure of the steam upon it, or to the pressure of the springs ; or 

 according as the friction F, which is always opposed to the direction in which 

 it is moving, is acting in a direction opposite to the pressure of the steam 

 upon it or in the same direction. An ambiguity results, therefore, from the 

 introduction of this sign, which is got rid of in the case of ordinary or double 

 acting engines, by the consideration that in such engines the steam pressure 

 increases only during an exceedingly small period of time, whilst the steam- 

 valve is in the act of opening, during which small period of time the piston 

 of the engine remains at rest ; at the expiration of this time the distance of 

 the wheel from the apex of the cone is less, by reason of the friction ; the 

 positive sign is therefore to be taken Avhilst it remains at this distance, that 

 is, until the expansion begins. Throughout the rest of the stroke the steam 

 pressure diminishes, and the negative sign is to be taken. Thus, if the steam 

 be expanded p times, the correction for friction becomes 



+ JL,,L_j:/i_iU,or-FLA-n 



TVr- P TT r- \ p J TT 7-2 \ p ) 



In respect to double acting engines, tiherefore, and generally of all engines 

 except the Cornish engines, we have 



u = ^^p ^-^-^(\-V\ (2.) 



6 ?'° A sm J m r- \ p ) 



In the Cornish engines, when the down-stroke has been completed and the 

 equilibrium valve opened, the piston of the indicator is relieved of all pres- 

 sure, and the integrating wheel ascends to the apex of the cone, and remains 

 there as long as the valve remains open ; it ceases therefore to partake in the 

 revolution of the cone during that time, and no number is registered. The 

 closing of the equilibrium valve produces again an excess of pressure on the 

 superior surface of the piston of the engine and of the indicator, and the in- 

 tegrating wheel begins to descend from the apex of the cone, and to be car- 

 ried round by it in the opposite direction to its former revolution, this pres- 

 sure continually increasing until the stroke is completed ; the formula must 

 be taken, in respect to this period of the action of the indicator, with the po- 

 sitive instead of the negative sign ; so that if No represent the number re- 

 gistered in a reverse order by the indicator when applied to a Cornish engine, 

 or the number which the indicator subtracts in the up-strokes from the 

 number N, registered by it in the down-strokes, and if the equilibrium valve 



be supposed to be closed when — ^th of the stroke remains to be completed ; 



n 



so that if L represent the space described in the down-strokes of the engine 

 whilst N, is registered, — L will represent the space described in the up- 

 strokes of the piston whilst the number No is in the act of being registered ; 

 then representing the units of work done upon a square inch of the piston 

 during the down-strokes by U,, and during the up-strokes {against the load) 

 by Uo, we have 



IT r-* A sm » It r'^ \ p / 



