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In existographies, Thomas Newcomen (1664-1729) (IQ:#|#) [RGM:714|1,500+] (EP:17) (CR:29) was an English metal monger and engineer, who built on the Papin engine (1690) and Savery engine (1698), guided by help from Robert Hooke, to make his 1712 Newcomen engine, the first marketable steam engine; by 1732, there were, supposedly, more than 100 Newcomen engines in Britain and Europe, and 2,000 Newcomen engines by 1800.

Overview
The following is a summary of the connection of Thomas Savery, his Savery engine (1698), and Newcomen, and his Newcomen engine (1705), and supposedly some correspondence notes written by Robert Hooke to Newcomen about some of the piston and cylinder ideas of Denis Papin:

“It is supposed that Savery’s engine was perfectly well known to Newcomen, and that the latter may have visited Savery at his home in Modbury, which was but fifteen miles from the residence of Newcomen. It is thought, by some biographers of these inventors, that Newcomen was employed by Savery in making the more intricate forgings of his engine. Harris, in his Lexicon Technicum (1704) states that drawings of the engine of Savery came into the hands of Newcomen, who made a model of the machine, set it up in his garden, and then attempted its improvement; but Switzer (Hydrostatics, 1729) says that Newcomen was as early in his invention as Mr. Savery was in his.

A depiction of a c.1705 Newcomen engine. [1]
Newcomen was assisted in his experiments by John Calley, who, with him, took out the patent. It has been stated that a visit to Cornwall, where they witnessed the working of a Savery engine, first turned their attention to the subject; but a friend of Savery has stated that Newcomen was as early with his general plans as Savery.

After some discussion with Calley, Newcomen entered into correspondence with Dr. Hooke, proposing a steam-engine to consist of a steam-cylinder containing a piston similar to that of Papin’s, and to drive a separate pump, similar to those generally in use where water was raised by horse or wind power. Dr. Hooke advised and argued strongly against their plan, but, fortunately, the obstinate belief of the unlearned mechanics was not overpowered by the disquisitions of their distinguished correspondent, and Newcomen and Calley attempted an engine on their peculiar plan. This succeeded so well as to induce them to continue their labors, and, in 1705, to patent, in combination with Savery—who held the exclusive right to practice surface-condensation, and who induced them to allow him an interest with them—an engine combining a steam-cylinder and piston, surface-condensation, a separate boiler, and separate pumps.”
— Robert Thurston (1878), A History of the Steam Engine (pgs. 57-58) [1]

The pipe h is used to keep the top of the piston covered in water, to prevent air leaks, which was a device of Newcomen, but likely learned from his correspondence with Hooke and the work of Papin, via Hooke.

Another take on the Newcomen, Hooke, Savery, Papin connection is:

“Savery spent some time in Cornwall, attempting to persuade mine owners to adopt his engine. It was probably during this time that he became known to Thomas Newcomen. Newcomen was an ironmonger from Dartmouth, a small port town near Cornwall. Through his trade, he would have been able to work with brass, copper and tin, as well as iron, and he would also have been familiar with the drainage problems that beset mining in the area. Unfortunately, little is known about Newcomen personally (there is not, for example, a known likeness of him), or about the development of his engine; inevitably, conjecture must fill some of the gaps. Newcomen was a man of some reading, and he was acquainted with Dr Robert Hooke. According to John Farey, writing in the 1820s, there survived notes written by Hooke on the subject of Denis Papin, a Huguenot émigré who had also been involved in early steam engine prototypes. The notes - written in Hooke's own hand - were apparently written for Newcomen's benefit. Hooke died in 1703 so, assuming this story is credible, it suggests that Newcomen was interested in steam engineering from at least that date. This is corroborated by Newcomen's contemporary, the Swede Marten Triewald, who wrote that the ‘work on the prototype of the fire-engine was carried on for ten years.’ In their invaluable history of the Newcomen engine, John Allen and Lionel Rolt suggest that much of Newcomen's time may have been spent working with small-scale models.”
— Sean Bottomley (2014), The British Patent System and the Industrial Revolution 1700-1852: from Privilege to Property (pg. 235)

In 1869 to 1875, Thomas Lidstone, an architect (Ѻ) of Dartmouth, the town where Newcomen carried out his steam engine experiments, published a series of pamphlets, with engravings, and quoted early letters, on the details of Thomas Newcomen and his invention. [2]

Newcomen engine

An artistic rendition of the Newcomen's engine. (Ѻ)

Quotes | On
The following are about or related quotes:

“Newcomen had been as early in his invention as Savery was in his, only the latter being nearer the Court, had obtained his patent before the other knew it, on which account Newcomen was glad to come in as a partner to it.”
— Stephen Switzer (1729), An Introduction to a General System of Hydrostatics and Hydraulics (pg. 342) (Ѻ)

“I had gone on a walk on a fine Sabbath afternoon. I had entered the Green [of Glasgow] by the gate at the foot of Charlotte Street—had passed the old washing-house. I was thinking upon the engine at the time, and had gone as far as the herd's house, when the idea came into my mind that as steam was an elastic body it would rush into a vacuum, and if a communication were made between the cylinder and an exhausted vessel it would rush into it, and might be there condensed without cooling the cylinder. I then saw that I must get rid of the condensed steam and injection water if I used a jet, as in Newcomen's engine. Two ways of doing this occurred to me. First, the water might be run off by a descending pipe, if an outlet could be got at the depth of 35 or 36 feet, and any air might be extracted by a small pump. The second was to make the pump large enough to extract both water and air. ... I had not walked further than the Golf-house when the whole thing was arranged in my mind.”
— James Watt (1765), reflection on inspiration moment on improving Newcomen’s steam engine, May (Ѻ)

“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 [3]

References
1. Thurston, Robert. (1878). A History of the Growth of the Steam-Engine (txt) (pgs. 57-59). Appleton and Company.
2. (a) Lidstone, Thomas. (1869). Some Account of the Residence of the Inventor of the Steam-Engine. Longmans.
(b) Lidstone, Thomas. (1871). A Few Notes and Queries about Newcomin (who made ye first Steam-Engine), and a Drawing of his Engine, his House (and Fire-Place), and Something about his Kettle, his Monument. London: Pardon and Son.
(b) Lidstone, Thomas. (1875). Notes on the Model of Newcomen’s Steam Engine (1705). Publisher.
3. Gould, Sabine. (1908). Devonshire Characters and Strange Events (§: Savery and Newcomen, Inventors, pgs. 487-501) (WS). John Lane.

External links
● Thomas Newcomen – Wikipedia.
● Thomas Newcomen – BBC History.
● Thomas Newcomen – NNDB.