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.) On considering more attentively the operation of the machine, the following circumstances gradually unfolded themselves to him.