If it be asked how it is advantageous to use half the quantity of steam at twice the pressure, when it takes perhaps twice the quantity of fuel to raise the steam to the double pressure, the answer is, that it can be shown analytically that the total force exerted by steam acting expansively is greater than that which would be exerted by steam of a constant pressure, equal to the mean of those exerted, first, at the moment the steam-valve is closed, and, secondly, wheu the piston arrives at the end of its stroke ; consequently, as less steam may be used to produce the required effect, a saving of fuel is the result, or in other words, the quantity of steam may be much less than half, at double the pressure, or the pressure much less than doubled, to pro duce the same effect.
As long as a continued force of any kind produces a continued motion with a constant velocity in any body, the forte must be in equilibrium with the resistance it has to overcome ; for if the force were greater than the resistance, it would produce an accelerating motion, which is contrary to the supposition : and if the resistance became greater than the force, the velocity would retard till the equi• librium were produced : as long,therefore, as a steam-engine is moving with a constant velocity, the presssre on the piston must be equal to the resistance to be overcome, consisting of the net work to be done, together with the friction of the various !was, the resistance of the uncondensed steam, of the air on the oppoeite side of the piston, and of other sources of resistance, which all concur to produce the gross resistance to be overcome. Putting r' for the pressure of the steam on each unit of surface of the piston, and R for the resistance for the satne unit, or for the quotient obtained by dividing the total resistance by the number of units of surface, we have — n (A) as the first equation of condition; but since the velocity of the motion must be taken into consideration, when the peers or force of the engine is to be determined, we must consider the velocity with which this pressure is applied, or, in other words, the rate at which the Mom is applied to the cylinder ; and it is obvious that when the engine is mewing with a constant velocity, the supply to the piston must be exactly that produced in the same time by the evaporation going on in the boiler. If, therefore, s expresses the volume of wafer evaporated in n unit of time and transmitted to the cylinder, and en the ratio of the volume of steam, formed under the pressure r in the boiler, to the volume of water Which produced it, ms would express the volume of steam generated in each unit of time under the pressure P : by passing into the cylinder this steam assumes the pressure r', and, neglecting the further change produced by the variation in the tem.
perature of steam in changing from pressure r to pressure the volume of that quantity of steam would be inversely as the pressures by Marlette's law; consequently the volume ens, when transferred to the cylinder, would become nt s — • and putting v for the velocity of r'' the piston and a for its area, a r will be tho volume of steam expended in each unit of time; hence we get ar = ms (B) eliminating r' between equations (A) and (B), wo obtain ens r = — . a rase n = - at, ern s for the relocity, resistance, and evaporation, when the other quantities are known ; it must be observed, however, that the element neglected in these general deductions, namely, the change produced by the variation in temperature, has an important influence on the result, and must therefore now be taken into account.
= + q p (C) is the general expression for the steam during its action in the engine, being the volume, and p the pressure, and n and q constants, determined by experiments, for different kinds of engines.
• It can be shown that the density end relative volume of a vapour, whether or not in contact with tho liquid, may be deduced, if its pressure and tempera. tura are known ; and that when in contact with tho liquid, the temperature varies directly with the pressure. In dedncing formula for the steam-engine, it Is necessary to be able to determine an expression for the relative volume of the steam In contact with the water, or the volume of the steam at the maximum of density and pressore at any'proposed temperature. Now this cannot be done from the existing formula for analytical reasons, and it becomes necessary to adopt some empirical formula, for determining this relative volume of steam at its maximum of density, in terms of its pressure only; this formula mast be tested by its conformity with experiment. The late N. Navicr proposal for this purpose, 1000 0'09 + 0.0000484p in which Is is the ratio of tho volume of steam to an equal weight of water, and p the pressure ; but this formula, though true within certain limits of pressure, is not consistent with experiments at pressures lower than the atmospheric, and the following is propounded by II. do Tombola, as more correct and 10000 = 0.4127 0.00233 for condensing engines; 10000 /4 1'421 + 0.0023p for nen-condensing engines ; p tieing the pressure in pounds on the square foot. These formula In general terms therefore are expressed by 1 m p in the text.