The Steam Engine Familiarly Explained and Illustrated / With an historical sketch of its invention and progressive improvement; its applications to navigation and railways; with plain axioms for railway speculators

by Dionysius Lardner

(131.) The method by which steam is used in the single-acting steam engine of Watt is, in all respects, similar, except that the piston, instead of being urged downwards by the force of the atmosphere, is pressed by steam of a force equal to the atmospheric pressure. It is evident, however, that this does not alter the mechanical result.

We have stated that a considerable increase of power, from a given quantity of steam, was produced by cutting off the steam after the piston had made a part of its descent, and allowing the remainder of the descent to be produced by the expansive force of the steam already admitted. We shall now more fully explain the principle on which this increase of power depends.

Let A B ([fig. 69].,) as before, represent a tube, the bottom of which is equal to a square foot, and let P be a piston in it, resting upon a cubic inch of water spread over the bottom; and let w be an empty vessel, the weight of which exactly counterpoises the piston. By the application of the lamp, the water will be converted into steam of the atmospheric pressure, and the piston will be raised from P to P´, through the height of one foot, the space in the tube beneath it being filled with steam, and the vessel w will have descended through one foot. Let half a ton of water be now poured into the vessel W; its weight will draw the piston P´ upwards, so that the steam below it will expand into a larger space. When the piston P´ was only balanced by the empty vessel W, it was pressed downwards by the whole weight of the atmosphere above, which amounts to about one ton: now, however, half of this pressure is balanced by the half ton of water poured into the vessel W; consequently the effective downward pressure on the piston P´ will be only half a ton, or half its former amount. The piston will therefore rise, until the pressure of the steam below it is diminished to the same extent. By what has been already explained, this will take place when the steam is allowed to expand into double its former bulk; consequently, when the piston has risen to P´´, one foot higher, or two feet from the bottom of the tube, the steam will then exactly balance the downward pressure on the piston, and the latter will remain stationary; the vessel W, with the half ton of water it contains, will have descended one foot lower, or two feet below its first position. Let the steam now be cooled and reconverted into water, and at the same time let another half ton of water be supplied to the vessel W; the pressure below the piston being entirely removed, the atmospheric pressure will act above it with undiminished force; and this force, amounting to one ton, will draw up the vessel W, with its contents. When the piston descends, as it will do, to the bottom of the tube, the ton of water contained in the vessel W will be raised through two perpendicular feet.[49]

Now, in this process it will be observed that the quantity of steam consumed is not more than in the former case, viz. the vapour produced by boiling one cubic inch of water. Let us consider, however, the mechanical effect which has resulted from it; half a ton of water has been allowed to descend through one foot, while a ton has been raised through two feet: deducting the force lost by the descent of half a ton through one foot from the force obtained by the ascent of one ton through the two feet, we obtain for the whole mechanical effect one ton and a half raised through one foot; for it is evident that half a ton has been raised from the lowest point to which the vessel W descended one foot above that point, and one ton has been raised through the other foot, which is equivalent to one ton and a half through one foot.

Comparing this with the effect produced in the first case, where the steam was condensed without causing its expansion, it will be evident that there is an increase of 50 per cent. upon the whole mechanical effect produced.

But this is not the limit of the increase of power by expansion. Instead of condensing the steam when the piston had arrived at P´´, let a further quantity of water amounting to one sixth of a ton be poured into the vessel W, in addition to the half ton which it previously contained; the effective pressure on the piston P´´, being only half a ton, will be overbalanced by the preponderating weight in the vessel w, and the piston will consequently ascend. It will become stationary when the steam by expansion loses a quantity of force equal to the additional weight which the vessel W has received: now, that vessel, having successively received a half and a sixth of a ton will contain two thirds of a ton; consequently the effective downward pressure on the piston will be only a third of a ton, and the steam to balance this must expand into three times the space it occupied when equal, to the atmospheric pressure. It must therefore ascend to P´´´, three feet above the bottom of the tube. If the steam in the tube be now condensed, and at the same time one third of a ton of water be supplied to the vessel W, so as to make its total contents amount to one ton, the piston will descend, being urged downwards by the unresisted atmospheric pressure, and the ton of water contained in the vessel W will be raised through three perpendicular feet.

In this case, as in the former, the total quantity of steam consumed is that of one cubic inch of water; but the mechanical effect it produces is still further increased. To calculate its amount, we must consider that half a ton of water has fallen through two feet, which is equivalent to a ton falling through one foot, besides which the sixth part of a ton has fallen through one foot. The total loss, therefore, by the fall of water has been one ton and one sixth through one foot, while the force gained by the ascent of water has been one ton raised through three feet, which is equivalent to three tons through one foot. If, then, from three tons we deduct one and one sixth, the remainder will be one ton and five sixths raised through one foot; this effect being above 80 per cent. more than that which is produced in the first case, where the steam was not allowed to expand.

To carry the inquiry one step further: Let us suppose that, upon the arrival of the piston at P´´´, a further addition of water to the amount of one twelfth of a ton be added to it: this, with the water it already contained, would make the total contents three fourths of a ton; consequently, the effective pressure upon the piston would now be reduced to one fourth of the atmospheric pressure. The atmospheric steam would balance this when expanded into four times its original volume: consequently, the piston would come to a state of rest at P´´´´, four feet above the bottom of the tube, and the vessel W would consequently have descended through four perpendicular feet. If the steam in the tube be now condensed as in the former cases, and at the same time a quarter of a ton of water be added to the vessel W, the piston will descend to the bottom of the tube, and the ton of water in the vessel W will be raised through four perpendicular feet. To estimate the mechanical effect thus produced, we have, as before, to deduct the total force lost by the fall of water from the force gained by its elevation: the water has fallen in three distinct portions: first, half a ton has fallen through three perpendicular feet, which is equivalent to one ton and a half through one foot; secondly, one sixth of a ton has fallen through two perpendicular feet, which is equivalent to one third of a ton through one foot; and thirdly, one twelfth of a ton has fallen through one foot: these added together will be equivalent to one ton and eleven twelfths through one foot. One ton has been raised through four feet, which is equivalent to four tons through one foot: deducting from this the force lost by the descent, the surplus gained will be two tons and one twelfth through one foot, being about 108 per cent. more than the force resulting from the condensation of steam without expansion.

To the increase of mechanical effect to be produced in this way, there is no theoretical limit. According to the manner in which we have here explained it, to produce the greatest possible effect by a given extent of expansion, it would be necessary to supply the water or other counterpoise to the vessel W, not in separate masses, as we have here supposed, but continuously, so as to produce a regular motion of the piston upwards.

Such is the principle on which the advantages of the expansive engine of Watt and Hornblower depend, explained so far as it can be without the aid of the language and reasoning of analysis.[50]