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[1] “It is now about six years since Mr. Savery set up one of them for that curious gentleman, Mr. Balle, at Cambden-house, Kensington, near London, … “

John Farey, A Treatise on the Steam Engine, London 1827, page 107, citing Bradley, “New Improvements of Planting and Gardening, 1718. The location mentioned is Kensington, near London. Based on the publication date of 1718, it's reasonable to estimate that the engine in question was erected around 1712.

„When this engine begins to work, you may raise four of the receivers full of water in one minute ; which is fifty-two gallons raised 58 feet (A gallon of water, ale-measure, weighs 10.2 lbs. which x 52 gallons = 530 • 4 lbs. x 58 ft. = 30763 lbs. raised 1 foot, which is nearly a horse-power, or about 8 1/4 men's power.) and at that  rate, in an hour's time, may be flung up three thousand one hundred and twenty gallons; which is above eighty-six barrels or, if there were two receivers, one to suck while the other discharged itself, as has been practised, then we might raise six thousand two hundred and forty gallons in the same time. The prime cost of such an engine is about 50 l. and the quantity of coal required for each working is about half a peck; so that the expense will be very inconsiderable in comparison to what the carriage of water upon horses would amount to and in such countries where wood is plenty the expense would be much less.”

Ibid.

The Savery engine was installed in a private home, which suggests it was likely used intermittently rather than continuously. Desaguliers suggests that the engine was run for an hour, but if needed could be run four or five hours. This intermittent usage pattern would have significant implications for its efficiency. Each time the engine was started, a considerable amount of energy would be expended just to heat the machine to its operating temperature. This frequent cooling and reheating cycle would result in substantial heat loss, contributing to the engine's poor overall efficiency.

[2] "I had an experimental Proof of this at Westminster in the Year 1728 or 9. When Mr. Jones (commonly call'd Gun-Jones) built a working Model of the Leaver-Engine in my Garden, (which Model he had a mind to present to the King of Spain.) I had at the same time near the Place where he erected his Engine, one in Savery’s way, which rais'd ten Tons an Hour about 38 Feet high."

J.T. Desaguliers, “A Course of Experimental Philosophy, Vol. II, London 1744, pages 489. Desaguliers compares in his book a Savery engine with a model of a Newcomen engine. Desaguliers refers to the Newcomen engine as a "Leaver-Engine". However, it's unfortunate that Desaguliers does not provide any data on the engine's fuel consumption. Without this critical information, it's impossible to calculate the thermal efficiency of the machine.

[3] "He [Mr. Jones] made his Boiler of the exact Size of mine, and his Cylinder was six Inches Bore, and about two Feet in Length. When his Model or Leaver-Engine was finished, it rais'd but four Tons per Hour into the fame Cistern as mine. It cost him 300 l. and mine, having all Copper Pipes, had cost me but 80 Pounds."

J.T. Desaguliers, “A Course of Experimental Philosophy, Vol. II, London 1744, pages 489/490.

Desaguliers demonstrated a keen understanding of the scale-dependent factors affecting engine performance. He recognized that the model's small size (cylinder volume about 11 liters) was a primary cause of its poor efficiency. Specifically, the smaller piston in the model experienced disproportionately high friction relative to its size, significantly impacting the engine's overall performance. It was not until decades later that James Watt made the crucial observation again with an even smaller and non-functioning model of a Newcomen engine. It took Watt quite a long time to finally recognize that the unfavorable surface-to-volume ratio in the miniature steam engine cylinder could lead to a dramatic increase in heat losses. In this scaled-down model, the issue was so severe that the reduced-scale boiler was unable to supply a sufficient flow of steam to counter the rapid cooling and condensation effects.

Given the known cylinder size (11 liters) and the reported volume of water pumped per unit of time, we can infer that this Newcomen engine model was operating at a minimum speed of approximately 6 strokes per minute. However, it was likely running at a slightly higher rate, perhaps closer to 7 or 8 strokes per minute, in order to overcome the frictional losses inherent in the system.

30 This engine… was set up at a dye-house in the borough of Southwark, near London Bridge, in 1792 ; The cylinder is 24 inches diameter, = 452*4 square inches area, or 576 circular inches. The length of the stroke of the piston is 5 feet ; and it makes 21 double strokes per minute, so that the piston passes through 210 feet per minute.

The expenditure of steam is 660 cubic feet per minute, or at the rate of 33 cubic feet per minute, to each horse power. The effective pressure upon the piston is 6*944 lbs. per square inch, or (X 452*4 squ. inc. =) 3142 lbs. for the effective force of the piston, taking a mean of all its variations throughout the stroke ; and this force acting through a space of 210 feet per minute, is equivalent to 660 000 lbs. raised one foot per minute, or -f- 33 000 lbs. = 20 horse power. The utmost force that the piston can ever exert may be computed at 1 1 lbs. per circular inch, or (X <576 circ. inc. = ) 6336 lbs. zr 2* 83 tons ; and the strength of all the parts must be adapted to resist this force, without any danger of breaking."

Desaguliers, “A Course of Experimental Philosphy, Vol. II, London 1744, pages 495/496