and from the metal of the cylinder, tends to compensate the first variation by a reverse change of pressure with change of volume.

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 be

come 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 reëvaporation 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 sin

gle-acting engine, and was very soon determined upon after the successful working of the latter had become assured.

Watt had covered in the top of his single-acting engine, to prevent cooling the interior of the cylinder by contact with the comparatively cold atmosphere. When this had been done, there was but a single step required to convert the machine into the double-acting engine. This alteration, by which the steam was permitted to act upon the upper and the lower sides of the piston alternately, had been proposed by Watt as early as 1767, and a drawing of the engine was laid before a committee of the House of Commons in 1774-75. By this simple change Watt doubled the power of his engine. Although invented much earlier, the plan was not patented until he was, as he states, driven to take out the patent by the "plagiarists and pirates" who were always ready to profit by his ingenuity. This form of engine is now almost universally used. The single-acting pumping-engine remains in use in Cornwall, and in a few other localities, and now and then an engine is built for other purposes, in which steam acts only on one side of the piston; but these are rare exceptions to the general rule.

The subject of his next invention was not less interesting. The double-cylinder or "compound" engine has now, after the lapse of nearly a century, become an important and usual type of engine. It is impossible to determine precisely to whom to award the credit of its first concep tion. Dr. Falk, in 1779, had proposed a double-acting engine, in which there were two single-acting cylinders, acting in opposite directions and alternately on opposite sides of a wheel, with which a rack on the piston-rod of each geared.

Watt claimed that Hornblower, the patentee of the "compound engine," was an infringer upon his patents; and, holding the patent on the separate condenser, he was able to prevent the engine of his competitor taking such form as to be successfully introduced. The Hornblower engine was soon given up.

Watt stated that this form of engine had been invented by him as early as 1767, and that he had explained its peculiarities to Smeaton and others several years before Hornblower attempted to use it. He wrote to Boulton: "It is no less than our double-cylinder engine, worked upon our principle of expansion." He never made use of the plan, however; and the principal object sought, apparently, in patenting this, as well as many other devices, was to secure himself against competition.

The rack and sector patented at this time was soon superseded by the parallel-motion; and the last claim, the "steam-wheel" or rotary engine, although one was built of considerable size, was not introduced.

After the patent of 1782 had been secured, Watt turned his attention, when not too hard-pressed by business, to other schemes, and to experimenting with still other modifications and applications of his engine. He had, as early as 1777, proposed to make a steam-hammer for Wilkinson's forge; but he was too closely engaged with more important matters to take hold of the project with much earnestness until late in the year 1782, when, after some preliminary trials, he reported, December 13th: "We have tried our little tilting-forge hammer at Soho with success. The following are some of the particulars: Cylinder, 15 inches in diameter; 4 feet stroke; strokes per minute, 20. The hammer-head, 120 pounds weight, rises 8 inches, and strikes 240 blows per minute. The machine goes quite regularly, and can be managed as easily as a water-mill. It requires a very small quantity of steam—not above half the contents of the cylinder per stroke. The power employed is not more than one-fourth of what would be required to raise the quantity of water which would enable a water-wheel to work the same hammer with the same velocity."

He immediately set about making a much heavier hammer, and on April 26, 1783, he wrote that he had done "a thing never done before "-making his hammer

strike 300 blows a minute. This hammer weighed 74 hundredweight, and had a drop of 2 feet. The steam-cylinder had a diameter of 42 inches and 6 feet stroke of piston, and was calculated to have sufficient power to drive four hammers weighing 7 hundredweight each. The engine made 20 strokes per minute, the hammer giving 90 blows in the same time.

This new application of steam-power proving successful, Watt next began to develop a series of minor inventions, which were finally secured by his patent of April 27, 1784, together with the steam tilt-hammer, and a steam-carriage, or "locomotive engine."

The contrivance previously used for guiding the head of the piston-rod-the sectors and chains, or rack—had never given satisfaction. The rudeness of design of the contriv ance was only equalled by its insecurity. Watt therefore contrived a number of methods of accomplishing the purpose, the most beautiful and widely-known of which is the "parallel-motion," although it has now been generally superseded by one of the other devices patented at the same time-the cross-head and guides. As originally proposed, a rod was attached to the head of the piston-rod, standing vertically when the latter was at quarter-stroke. The upper end of this rod was pivoted to the end of the beam, and the lower end to the extremity of a horizontal rod having a length equal to one-half the length of the beam. The other end of the horizontal rod was coupled to the frame of the engine. As the piston rose and fell, the upper and lower ends of the vertical rod were swayed in opposite directions, and to an equal extent, by the beam and the lower horizontal rod, the middle point at which the piston-rod was attached preserving its position in the vertical line. This form was objectionable, as the whole effort of the engine was transmitted through the parallel-motion rods. Another form is shown in the sketch given of the double-acting engine in Fig. 31, which was free from this defect. The