If the engine be a condensing one, acting expansively, l' must be made equal the length at which the steam is cut off; if expansion be not employed, 1' must be made equal to 1, or to the whole length of 1 the stroke, in which case the quantity k becomes 1+ c --, and the expres sion for the velocity becomes 1 1v n+qm.' 1+ The part p of the quantity a must be made equal the pressure of the uncondensed steam, &c. If the engine be a non-condensing ono, then p will be equal the atmospheric pressure.
Since from (K) we obtain 8k a in ar = (1+8)2v + p +f) . (L)it might be supposed that when v=0, the resistance would be infinite, a paradox which would appear to vitiate the correctness of the formula. But it must be borne in mind that when v=0, s=0 ; for 8 is the quantity of steam which passes through the cylinder in each unit of time : and since no quantity of steam, however small, can pass with out moving the piston, as long as s has any real value, v will have one too : when therefore v=0, s=0 also ; and then ar=z, and not= oo; that is, the formula becomes indeterminate, but not the less direct, as will appear by considering the other quantities it involves, and the consequences of putting v=0.
By supposing the velocity zero, it is, in the first place, evident that no steam can pass to the cylinder, as has been stated ; consequently there can be no expansion, that is, 1=1'. Again, the velocity being zero, the piston at rest becomes equivalent to the fixed sides of the boiler, and the pressure it sustains is equal to that in the boiler.
The working of an engine may be considered under three condi. tions : first, when it is working with a given pressure of steam, and with any, whatever, load or velocity. Secondly, when it is working with a given pressure, and with that load or velocity compatible with the production of a maximum of useful or net force with that pressure : this may be termed the relative ma.rimum of useful effect And thirdly, when the pressure having been determined to furnish the force most consonant with the action of steam in any specific engine, the load is regulated so as to be that most advantageous for that pressure : this last constitutes the absolute ?maximum of useful effect for that machine.
The three fundamental problems for solution in the calculation of steam-engines consist in determining the velocity, the load, and the rate of evaporation in the boiler, since the useful effect, or net avail able power, is a function of these three quantities; and this net avail able power may be expressed in six different ways : First, by the number of pounds raised to a unit of height in a unit of time.
Secondly, by what is termed the " horse-power " of the engine. Thirdly, by the weight raised by the consumption of lib. of fuel. Fourthly, by the weight raised by the evaporation of a cubic foot of water.
Fifthly, by the number of pounds of fuel, or of cubic feet of water, for each horse-power.
Sixthly, by the number of horses-power which is furnished by each pound of fuel, or by each foot of water.
For the various formula; by which all these problems may be nume rically solved for different kinds of engines, and for the investigations by which those formula: are deduced, we must refer to more compre hensive works ; contenting ourselves here with deducing the general equations for the other unknown quantities of evaporation, useful effect, and horse-power, as we have done for velocity.
From (K) we obtain +P +f] 01) as the expression for the evaporation of which an engine must be cap able to overcome a given resistance r, with a proposed velocity v, s being the quantity of water which is to be converted into steam and transmitted to the cylinder in each unit of time.
The useful or net force of the engine generated in the same unit of time is obviously ary ; since v, the velocity, is in fact the space moved through by the piston in that time; by multiplying therefore both sides of (L) by v we obtain sk [ n Useful force = arv= (1+8)2 1 +8 q + p f] . . (N,) or by multiplying both sides of (K) by ar, we obtain an expression for the same quantity in terms of the load Useful force = arv= srk . (Ns) n + q[(1+ 8)r +p+ f] It will be noticed that for any proposed engine this force does not depend on the pressure of the steam in the boiler, r not entering into these expressions ; but on the evaporation s effected in the boiler in each unit of time.
What is termed a " horse-power " is estimated as 33,000 lbs. raised one foot in a minute [House Pownit] : by dividing therefore the equa tions last 33,000, we get Useful force in horse-power=Useful 33000 and if during the unit of time N lbs. of coals are used in the furnace, Useful force from 1 lb. of fuel = Useful force N We must now return to our general description of the engine and of its modifications.