|A 1744 printing of a Newcomen engine, from John Desaguliers Course in Experimental Philosophy. |
In 1705, Newcomen had some form of steam engine either operational or in the inception stage (Lidstone, 1875).
In 1710, Newcomen had teamed up with John Calley, glazier and plumber, of Dartmouth in the county of Southampton (Anabaptists) made then several experiments in private, and having brought it to work with a piston, etc., in the latter end of the year 1711, made proposals to draw the water at Griff in Warwickshire (Desaguliers, c.1740).
“In 1712 Newcomen and his partner, Cawley, contracted to erect an engine at Wolverhampton. Next, they erected two engines near Newcastle. The fourth was put up at Leeds in 1714. The fifth was erected in Cornwall at Wheal Fortune in 1720, and was on a larger scale than any previously constructed, having a cylinder of nearly four feet in diameter, and its performance was regarded as extraordinary, since it made fifteen strokes a minute, and drew up at each stroke a hogshead of water from a depth of 180 feet.”— Sabine Gould (1908), Devonshire Characters and Strange Events 
In 1712, the first Newcomen engine was installed at Tipton, Staffordshire and used to pump water from the workings of the Coneygre Colliery, for the next thirty years. 
The following is a retrospect synopsis of the operation of Newcomen's engine:
“Thomas Newcomen, ironmonger and preacher on occasion, completed his engine in 1712 after years of experimenting. His first engine was installed at Dudley Castle in Staffordshire to pump water from a mine. Newcomen's partner, John Calley or Cawley, a plumber and glazier of Dartmouth, provided the manual skill. Newcomen's contribution was an ingenious mixture of familiar devices with ideas of his own. He took the copper kettles and furnaces of brewers to supply the steam for the same kind of cylinder and piston which had been used for lifting water as far back as Roman times and condensed the steam below the piston within the cylinder to create there a partial vacuum which would allow the weight of the atmosphere above to force the piston down. Instead of using Savery's method of creating the vacuum by dashing cold water on the outside and thus condensing the steam, Newcomen sprayed water directly into his vertical cylinder. This condensed the steam, created the vacuum, and allowed the atmospheric pressure to force the piston down. To put this downward pull of the piston to work, he connected its rod by a chain to a horizontal and centrally pivoted working beam, or walking beam as it was later called, and fastened the other end of the beam by a chain and rod to the piston or plunger in the pump cylinder. As new steam was admitted below the first piston and the vacuum broken, this piston was raised again by the weight at the other end of the working beam, and the piston of the pump was lowered to its original position. Thus, the reciprocating motion, up and down, was complete.”— Richard Kirby (1956), Engineering in History (pgs. 162-64) 
|An animation of the operation of the Newcomen engine (1712), showing how first steam, from the boiler, at right, is put into the piston and cylinder, above the boiler, which is then cooled, by a spray of cold water, at the point when the piston is at its highest position in the cylinder, which makes a vacuum in the cylinder, which thus forces, via atmospheric pressure, the the piston down; and the cycle repeats. The head of the piston is connected via a rod to a rocker arm, which thus imparts work in the form of reciprocating motion to a water pump on the other end of the rocker arm.|
The following is another sketch of a Newcomen engine: 
In 1732, there were, supposedly, more than 100 Newcomen engines in Britain and Europe, and 2,000 Newcomen engines by 1800, as some have claimed. 
The Newcomen engine was superseded and or upgraded by the Smeaton engine (1769-1777), the Pickard engine (1780), and then by the Watt engine (1781).
The following are related quotes:
“In about the year 1710, Thomas Newcomen, ironmonger, and John Calley, glazier, of Dartmouth in the county of Southampton (Anabaptists) made then several experiments in private, and having brought it to work with a piston, etc., in the latter end of the year 1711, made proposals to draw the water at Griff in Warwickshire; but their invention meeting not with reception, in March following, through the acquaintance of Mr. Potter of Bromsgrove in Worcestershire, they bargained to draw water for Mr. Back of Woolverhampton, where, after a great many laborious attempts, they did make the engine work; but not being either philosophers to understand the reasons, or mathematicians enough, to calculate the powers, and to proportion the parts, very luckily by accident found what they sought for. They were at a loss about the pumps, but being so near Birmingham, and having the assistance of so many admirable and ingenious workmen, they soon came to the method of making the pump valves, clacks, and buckets; whereas they had but an imperfect notion of them before. One thing is very remarkable; as they at first were working, they were surprised to see the engine go several strokes, and very quick together, when after a search they found a hole in the piston, which let the cold water into condense the steam in the inside of the cylinder, whereas before they had always done it on the outside. They used before to work with a buoy in the cylinder enclosed in a pipe, which buoy rose when the steam was strong, and opened the injection, and made a stroke; thereby they were capable of only giving six, eight, or ten strokes in a minute, until a boy, Humphry Potter, who attended the engine, added (what he called scoggan) a catch that the beam Q always opened: and then it would go 15 or 16 strokes in a minute. But this being perplexed with catches and strings, Mr. Henry Beighton, in an engine he had built at Newcastle on Tyne in 1718, took them all away, the beam itself simply supplying all much better. N.B. about the Tear 1717, I communicated to Mr. Beighton, the use of the steel-yard over the puppet-clack, or safety valve, which be applied to some engines. The way of leathering the piston was found by accident in about 1713: having then screwed a large broad piece of leather to the piston, which turned up the sides of the cylinder two or three inches; in working it wore through, and cut that piece from the other, which falling flat on the piston, wrought with its edge to the cylinder, and having been in a long time, was worn very narrow; which being taken out, they had the happy discovery, whereby they found that a bridle rein, or even a soft thick piece of rope or match going round would make the piston air and water-tight.”— John Desaguliers (c.1740), A Course in Experimental Philosophy, Volume Two (pgs. 532-33)
“As the story goes, Humphrey Potter, Newcomen’s boy who was supposed to open and close the steam valve, attached what he called a ‘scoggan’, so that the beam would trip the valve each time and do his work while he went fishing.”— Richard Kirby (1956), Engineering in History (pg. 164) 
1. Coneygre Colliery (1712) – SolarNavigator.net.
2. (a) Desaguliers, John. (1744). A Course in Experimental Philosophy, Volume Two (§13: Fire-Engine, pgs. 464-; Newcomen, 3+ pgs). W. Innys, 1744.
(b) Kirby, Richard; Withington, Sidney; Darling, Arthur; and Kilgour, Frederick. (1956). Engineering in History (pg. 163). Courier, 1990.
3. Kirby, Richard; Withington, Sidney; Darling, Arthur; and Kilgour, Frederick. (1956). Engineering in History (pg. 42). Courier, 1990.
4. John Smeaton – Engineering-Times.com.
5. MacLeod, Christine. (1988). Inventing the Industrial Revolution: the English Patent System, 1660-1800. Cambridge University Press.
6. Gould, Sabine. (1908). Devonshire Characters and Strange Events (§: Savery and Newcomen, Inventors, pgs. 487-501) (WS). John Lane.
● Moore, David. (2015). “Newcomen Atmospheric Engine” (Ѻ), David Moore, Jul 12.
● Newcomen steam engine – Wikipedia.