The pressure of steam in the boiler being equal to 120 inches of mercury, the loss from friction, etc. (reckoned as 1/4 of the whole) is 48, which added to 30 inches for the pressure of the atmosphere is 78, and this divided by 120 gives 65/100 as the part of the stroke at which the steam should be cut oft.
The principle of expansion was subsequently adopted by Hornblower, who in 1781 obtained a patent for an expansion engine, arranged as exhibited in the accompanying cut, of which the following is a description extracted from the Encyclopedia Britannica.
Let A and B represent two cylinders, of which A is the largest; a piston moves in each, having their rods C and D moving through collars at E and F. These cylinders may be supplied with steam from the boiler by means of the square pipe G, which has a flange to connect it with the rest of the steam-pipe. This square part is represented as branching off to both cylinders; c and d are two cocks which have handles and tumblers asusual, worked by the plug-beam W. On the fore side of the cylinders is represented another communicating pipe, whose section is also square, or rectangular, having also two cocks, a b. The pipe Y immediately under the cock b establishes a communication between the upper and lower parts of the cylinder B, by opening the cock b. There is a similar pipe on the other side of the cylinder A, immediately under the cock a.
When the cocks c and a are open, and the cocks b and d are shut, the steam from the boiler has free admission into the upper part of the small cylinder B, and the steam from the'lower part of B has free admission into the upper part of the great cylinder A; but the upper part of each cylinder has no communication with its lower part. From the bottom of the great cylinder proceeds the eduction pipe K, having a valve at its opening into the cylinder; it then bends downwards, and is connected with the condenser. Lastly, the pump-rods cause the outer end of the beam to preponderate, so that the quiescent position of the beam is that represented in the figure, the pistons being at the top of the cylinder. Suppose all the cocks open, and steam coming in copiously from the boiler, and no condensation going on in L, the steam must drive out all the air, and at last follow it through the valve Q. Now shut the cocks b and d, and open the escape-valve of the condenser; the condensation will immediately commence, and draw off the steam from the lower part of the great cylinder. There is now no pressure on the under side of the piston of the great cylinder A, and it immediately descends.
The communication Y between the lower part of the cylinder B, and the upper part of the great cylinder A being open, the steam will go from the lower part of B into the space left by the descent of the piston A. It must therefore expand, and its elasticity must diminish, and will no longer balance the pressure of the steam coming from the boiler, and pressing above the piston of B. This piston, therefore, if not withheld by the beam would descend till it came in equilibrio, from having steam of equal density above and below it. But it cannot descend so fast, for the cylinder A is larger than B, and the arch of the beam, at which the great piston is suspended, is no longer than the arm which supports the piston of B; therefore, when the piston of Bhasdescended as far as the beam will permitit, the steam between the two pistons occupies a larger space than it did when both pistons were at the top of their cylinders, and its density diminishes as its bulk increases. The steam beneath the small piston is, therefore, not a balance for the steam on the upper side of the same, and the piston B will act to depress the beam with all the difference of these pressures.
The slightest view of the subject must show, that as the piston descends, the steam that is between them will grow continually rarer and less elastic, and that both pistons will draw the beam downwards. Suppose, now, that each one had reached the bottom of its cylinder: shut the cock a, and the eduction valve at the bottom of A, and open the cocks b and d. The communication being now established between the upper and lower part of each cylinder, their pistons will be pressed equally on the upper and lower surfaces; in this situation, therefore, nothing hinders the counter-weight from raising the pistons to the top. Suppose them arrived at the top: the cylinder B is at this time filled with steam of the ordinary density, and the cylinder A, with an equal absolute quantity of steam, but expanded into a larger space. Shut the cocks b and d, and open the cock a, and the eduction valve at the bottom of A, the condensation will again operate, and cause the pistons to descend; and thus the operation may be repeated as long as steam is supplied; and one measure full of the cylinder B of ordinary steam is expended during each working stroke.
Professor Robison gave a series of elaborate and highly interesting calculations, by which, unluckily for the ingenious inventor, it was demonstrated, that the same effect only is produced in this, as in Mr. Watt's expansion engine; and these calculations were confirmed by the practice of those which Hornblower erected. Although he made an unsuccessful application to Parliament for an extension of the term of his patent, it does not appear that his engine obtained public patronage or approbation.
After the expiration of Watt's patent, the condensing engine, under the hands of different manufacturers, assumed a variety of forms. The accompanying cut represents a portable engine of 12 horse-power, as constructed by Messrs. Rothwell, Hick, & Rothwell, of Bolton.
This engine consists, in the first place, of a large cast-iron plate, firmly bolted to stone or brick-work, on which the whole of the materials are fixed. The beam with all its appendages is by this means supported, without being at all connected with the building, by a double diagonal frame, one half surmounted by an entablature plate, to which the bearers or spring beams are attached, that receive the studs or centres of the radius rod of the parallel motion, the extreme ends of which are supported by a pillar resting on a bracket projecting from the back of the cylinder. The pedestals in which the gudgeon of the beam works, rest on the entablature plate, and are firmly secured by bolts passing through the whole. The side walls on which the foundation plate acts are so far asunder as to allow a sufficiently wide recess to receive the condensing cistern, with its air-pumps and condenser, hot and cold water pumps, as well as to afford room for getting down to secure the end9 of the bolts. The governor is supported by a standard placed directly over the crank shaft, and is turned by a single pair of bevel wheels.