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A History of the Growth of the Steam-Engine

The inequality of pressure due to expansion

_PV_ _P'_ = ----. _V'_

It is true that the condensation of steam doing work changes this law in a marked manner; but the condensation and reevaporation of steam, due to the transfer of heat to and from the metal of the cylinder, tends to compensate the first variation by a reverse change of pressure with change of volume.

[Illustration: FIG. 28.--Expansion of Steam.]

The sketch shows this progressive variation of pressure as expansion proceeds. It is seen that the work done per unit of volume of steam as taken from the boiler is much greater than when working without expansion. The product of the mean pressure by the volume of the cylinder is less, but the quotient obtained by dividing this quantity by the volume or weight of steam taken from the boiler, is much greater with than without expansion. For the case assumed and illustrated, the work done during expansion is one and two-fifths times that done previous to cutting off the steam, and the work done per pound of steam is 2.4 times that done without expansion.

Were there no losses to be met with and to be exaggerated by the use of steam expansively, the gain would become very great with moderate expansion, amounting to twice the work done when "following" full stroke, when the steam is cut off at one-seventh. The estimated gain is, however, never realized. Losses by

friction, by conduction and radiation of heat, and by condensation and reevaporation in the cylinder--of which losses the latter are most serious--after passing a point which is variable, and which is determined by the special conditions in each case, augment with greater rapidity than the gain by expansion.

In actual practice, it is rarely found, except where special precautions are taken to reduce these losses, that economy follows expansion to a greater number of volumes than about one-half the square root of the steam-pressure; i. e., about twice for 15 or 20 pounds pressure, three times for about 30 pounds, and four and five times for 60 or 65 and for 100 to 125 pounds respectively. Watt very soon learned this general principle; but neither he, nor even many modern engineers, seem to have learned that too great expansion often gives greatly-reduced economy.

The inequality of pressure due to expansion, to which he refers, was a source of much perplexity to Watt, as he was for a long time convinced that he must find some method of "equalizing" the consequent irregular effort of the steam upon the piston. The several methods of "equalizing the expansive power" which are referred to in the patent were attempts to secure this result. By one method, he shifted the centre as the beam vibrated, thus changing the lengths of the arms of that great lever, to compensate the change of moment consequent upon the change of pressure. He finally concluded that a fly-wheel, as first proposed by Fitzgerald, who advised its use on Papin's engine, would be the best device on engines driving a crank, and trusted to the inertia of a balance-weight in his pumping-engines, or to the weight of the pump-rods, and permitted the piston to take its own speed so far as it was not thus controlled.

The double-acting engine was a modification of the single-acting engine, and was very soon determined upon after the successful working of the latter had become assured.

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