(47.)
Still he found that the force with which the piston descended was considerably less than that which the atmospheric pressure ought to supply, supposing a tolerably perfect vacuum to be produced under the piston. This led him to suspect that the water injected into the cylinder was not perfectly effectual in condensing the steam. The experiments which he had previously made on the increased temperature at which water boils under pressures greater than that of the atmosphere, led him by analogy to the conclusion that it would boil at lower temperatures if it were submitted to a pressure less than the atmosphere, and he was aware that Dr. Cullen and others had then recently discovered that in vacuo, water would boil at so low a temperature as 100°. These notions suggested the probability that the water injected into the cylinder being heated by the condensed steam, might produce vapour of a low temperature [Pg086] and reduced pressure under the piston, which would account for the deficiency he observed in the power of the engine.
No means occurred to him by which he could ascertain, by direct experiment, the temperatures at which water would boil under pressures less than that of the atmosphere. He sought, however, to determine it by the following method. Having ascertained, by repeating and multiplying the experiments which he had tried in 1762, on high-pressure steam, he obtained a table of the temperatures at which water boils at various pressures greater than that of the atmosphere. These results he laid down in a series forming a curve, of which the abscissa represented the temperatures, and the ordinates the pressures. He then continued this curve, backwards as it were, and obtained, by analogy, an approximation to the boiling temperatures, corresponding to pressures less than that of the atmosphere. In other words, having obtained by his experiments a notion, however imperfect, of the law or rule observed by the temperatures at which water boils at different pressures greater than that of the atmosphere, he calculated by the same law or rule what the pressures would be at different pressures less than that of the atmosphere.
Applying these results to the interior of the cylinder of the atmospheric engine, he obtained an approximation to the pressure of the vapour which would be produced from the warm water formed by the cold water injected into the cylinder, and the steam condensed by it; and he accordingly found that vapour, having a pressure seriously injurious to the power of the engine would be produced in the cylinder, unless considerably more water of injection was thrown in than was customary.
It was apparent that the actual quantity of steam usefully employed in the cylinder at each stroke, was only the quantity which filled the cylinder; and therefore, in order to ascertain the quantity of steam lost by the imperfections of the machine, it was necessary to compare the actual quantity of steam transmitted by the boiler to the cylinder at each stroke, with the quantity which would just fill the cylinder. The difference would of course be wasted. But to determine [Pg087] the actual quantity of steam supplied by the boiler to the cylinder, there was no other means than by observing the quantity of water evaporated in the boiler. That being observed, it was necessary to know the quantity of steam which that water formed; and it was therefore necessary to determine the quantity or volume of steam which a given volume of water produced.
(48.)
Let us suppose the piston at the top of the cylinder, and the space in the cylinder below it, filled with steam so as to balance the pressure of the atmosphere above the piston. Under such circumstances the steam, as will presently be explained, must have the temperature of boiling water. But that the steam should have, and should maintain, this temperature, it was evidently necessary that the inner surface of the cylinder in contact with it should have the same temperature: for if it had a lower temperature, it would take heat from the steam, and reduce the temperature of the latter. Now the cylinder being a mass of metal, has a quality in virtue of which heat passes freely through its dimensions, so that its inner surface could not be maintained at a temperature more elevated than that of its dimensions extending from the inner surface to the outer surface. Therefore, to maintain the steam contained in the cylinder at the proper temperature, it was essential that the whole of the solid metal composing the cylinder should be itself at that temperature.
Things being in this state, it was required that a vacuum should be produced under the piston to give effect to the atmospheric pressure above it, by relieving it from the pressure below. This, indeed, would appear to have been attained by introducing as much cold water within the cylinder as would be sufficient to reconvert the steam contained in it into water; but Watt found, in his experiments on the atmospheric model, that the piston would not descend with the proper force, unless a vastly greater quantity of water were introduced into the cylinder than the quantity which he had ascertained to be [Pg088] necessary for the reconversion of the steam into water. The cause of this he perceived and fully explained.
If we suppose as much, and no more, cold water introduced into the cylinder as would reconvert the steam contained in it into water, then we should have in the bottom of the cylinder a quantity of warm water with a vacuum above it: but the entire mass of metal composing the cylinder itself, which was previously at the temperature of boiling water, would still be at the same temperature. The warm water, resting in contact with this metal in the bottom of the cylinder, would be immediately heated by it, and would rise in its temperature, while the metal of the cylinder itself would be somewhat lowered in temperature by the heat which it would thus impart to the warm water contained in it. Under these circumstances, as we shall presently explain, steam would be produced from the water, which would fill the cylinder; and although such steam would not have a mechanical pressure equal in amount to the atmosphere, and therefore would not altogether prevent the piston from descending if it had no load to move, yet it would deprive the engine of so great a portion of its legitimate power as to render it altogether inefficient. But this defect would be removed by throwing into the cylinder a sufficient quantity of cold water, not only to destroy the steam contained in it, but also to cool the entire mass of metal composing the cylinder itself, until it would be reduced to such a temperature that the vapour proceeding from the water contained in it would have so small a pressure that it would not seriously or injuriously obstruct the descent of the piston.
The piston being made to descend with such force as to render the machine practically efficient, it would then be necessary again to make it ascend; and to accomplish this, Watt found that the boiler should supply a quantity of steam many times greater than was necessary to fill the cylinder. Mature reflection on the circumstances which have been just explained, enabled him to discover how this undue quantity of steam was rendered necessary.