Newcomen's engine raises the water entirely by the pressure of the atmosphere ; for the steam is employed merely as the most expeditious method of displacing the air, and then producing a void, into which the atmospherical pressure may impel the first mover of the machine [1].

A Newcomen steam engine has no need of steam of great or dangerous pressure for it operates with very moderate heat. It was safer than a Savery pump. The power of Newcomen's engine is not bounded by the strength of the boilers, and vessels, to resist internal pressure, but only by the dimensions which it is practicable, and expedient to make boilers, and cylinders, to contain the requisite quantity of steam, of the ordinary pressure, and the strength which can be given to the working lever, chains, and other parts, which communicate the force of the piston, to the rod of the pump. Newcomen's engine can also be applied to other mechanical purposes, besides that of raising water. For instance, to blow air by bellows or pumps, into a furnace; or, by connecting a crank and fly-wheel with the rod, which is suspended from the extremity of the great lever, the reciprocating motion of the great lever may be changed into a circular motion. It took however another 50 years after the first erection of a Newcomen engine before a crank and flywheel were applied to a Newcomen engine. Savery's engine is necessarily restricted to the purpose of raising water, and could not be applied to work mills, except by the intervention of a water-wheel [2].

We see from historical documents that at Newcomen's time the technology was not advanced enough to cope with steam pressures much above atmospheric pressure. Savery must have used at least 2 atmospheric pressures above the pressure of the atmosphere to push up water to 20 meters. Increasing the pressure to achieve higher heights caused from time to time problems with the boilers bursting. This set a limit to which height water could be pushed up by steam. Savery had proposed to employ his devices in stages, but it was impractical to have a more than one Savery fire engine deployed in the same shaft of a mine.

The advantage of the Newcomen engine was that it could operate a chain of mechanical pumps, which could pump water in stages. However, this also came at a price. The design with a sturdy and heavy beam introduced mechanical losses and also each pump added losses. John Farey describes a Newcomen machine that produced 8.03 HP at the piston (indicated power) but the effective power to raise water from a depth of 54 feet was only 2.67 HP [3]. Machine and pumps together introduced losses of 67%. Therefore, sometimes it is said that the Newcomen steam engine was less effective than a Savery engine. This is obviously only true, (see losses by cooling a cylinder from the outside) if the Savery pump used internal condensation that was first introduced to the Newcomen engine. As Newcomen and Savery worked together, this invention of Newcomen probably at some stage will have been introduced also to Savery's pump.

Newcomen was assisted by John Calley, also spelt John Cawley, a plumber and glass-blower. We do not know what were the contributions of Calley but it was hazard a guess that Newcomen supplied the brains and Calley most of the technical skill [4]. Newcomen and Calley were later described as amateurs which after a great deal of laborious attempts, eventually succeeded in getting the engine to run, but because they lacked the necessary mathematicians or philosophers (=scientific) knowledge to calculate the powers and proportion the parts, they were incredibly lucky to find what they were looking for by accident [5]. This in no way lessens their merits. European patent laws does not require that an inventor intellectually understands his inventions or can explain the underlying physical laws correctly. The only requirement is that an inventor describes his invention so that anyone can rebuild it in a reasonable time.

The regulator RSYZ is composed of a circular lid R that is installed over the boiler's top opening and below the working cylinder. A throat pipe S, attached to the upper side of the lid R, provides a fluid connection between the boiler and the cylinder. A  valve plate Y is pivotally mounted with a square shank z to a pivot arrangement v w x below the throat pipe S. The pivot arrangement vwx comprises a square cone v, with a hollow inside that is also a square cone through which the square shank z form-fits and passes through from a side below the lid R to a side above the lid R. Thus the square cone v and the square shank z share a same pivot axis, which is directed vertically upright and perpendicular to the valve plate Y. Compared to a 4 inch diameter cock-valve, which is of a similar size, this regulator valve's construction only caused 1⁄10 of the friction. [Desanguliers].

A regulator spanner PQ has an end with a square opening and an arm that is split in its middle in two branches for receiving a flat end O of a forked rod MON between the two branches. The branches are fitted with several through holes, allowing to pass a fastening pin q through these through holes and a corresponding hole of the flat end O of the forked rod MON. The square shaped closed end P of a regulator spanner PQ engages the squared cone v of the regulators pivot arrangement vwx with its closed end P. When the forked rod MON pushes in the direction of the regulator, the spanner PQ pivots the plate Y anti-clockwise into the opened position opening the fluid connection, allowing steam from the boiler to enter the cylinder. Conversely, when the forked rod MON pulls with the flat end O of the forked rod MON towards the plug rod, the spanner PQ pivots the plate Y clockwise and the fluid connection is interrupted, preventing steam entering the working cylinder. As there is a slight overpressure in the boiler the regulator plate  is pressed against the lower side of the throat pipe S and therefore seals the fluid connection sufficiently. 

The regulator spanner PQ is connected to a rocking mechanism by a forked rod M O N. The rocking mechanism, as will be described below in more detail, toggles between two positions and by pulling and pushing on the forked rod M O N  unlocks and shuts the regulator instantaneously. The forked rod M O N has a single end O, that is movably connected to the end of the arm Q of the regulator spanner PQ, and two fork arms M, N on its other end. The two fork arms M, N, are suspended by a stirrup I K from an arbor tree AB.

A first spanner G4 with a first squared opening G at one end of the first spanner G4 and a curved first arm 4 on its other end, a second spanner H5 with a second squared opening H at one end of the second spanner H5 and a second curved arm on its other end 5, and a three-armed spanner CDE with a third squared opening e where the three arms meet, are lined up with their square openings on an arbor tree AB. Round pegs located at the ends of the arbor tree AB allow the arbor tree AB to be mounted rotatably. As all three squared openings form are fit on the arbor tree AB, when one lever is pushed by a pin the other levers are forced to follow this movement as the pins for proper function of the valve gear are always arranged not to block the movements of the levers with one another. 

The three armed lever is known as a Y-lever because it resembles the letter "Y" when inverted. When mounted on the arbor tree AB, two arms of the Y-lever are hanging down and one arm is pointing upwards. The arm hanging down, stretching to the right (towards the plug frame Q), is called in the following the unlocking arm D and the arm hanging down, stretching to the right (towards the regulator) is called in the following the shutting arm E. The arm pointing upwards is named in the following tumbling arm C as it is carrying a weight F, called in the following a tumbling bob. The height of the tumbling bob F can be adapted by a key.

The tumbling bob's motion is constrained by a leather strap. By fastening the middle of the leather strap to the tumbling bob F the leather strap is divided into a right halve with a right end n and a left halve with a left end m. The right end  n of the leather strap is fixed right of the tumbling bob and the left end m of the the leather strap is fixed to the left of the tumbling bob F. Thus the rocking mechanism is a bistable dynamical system having two stable equilibrium states. The first stable state is when the tumbling bob is on the left side, pulling on the right halve of the leather strap, and the second stable state is when the tumbling bob is on the right side, pulling on the left halve of the leather strap. In both stable states the potential energy of the tumbling bob is zero (unless the leather strap breaks).The tumbling bob attains its maximum potential energy when it is sitting above the tumble arm, i.e. the tumble arm is vertically orientated. As soon as the tumbling bob F crosses the vertical line, its torque switches to the opposite side, causing the tumbling bob F to fall to that side. By falling, the tumbling bob's potential energy is transformed into kinematic energy, causing the arbor tree to accelerate. When the opposite leg strikes the stirrup, the linkage of the fork and the spanner opens or closes the regulator valve in a rapid action.. 

An injection cock, embodied as a stopcock, is used to interrupt the flow of water from an injection cistern into the cylinder. The plug of the cock has a narrow, long, upright hole. A squared cone serves as the plug's stem and can accommodate a toothed wheel with a corresponding square opening at its pivot axis. A third lever, commonly known as the F lever has at its pivot axis a segment of a second toothed wheel. The pivot axis of the second toothed wheel is perpendicular to the pivot axis of the first toothed wheel and arranged so that the first and the second toothed wheel engage. The first toothed wheel lays in a horizontal axis, the first pivot axis thus orientated vertically. The second toothed wheel thus is in a vertical plane. When the F lever is lifted or pulled down the first toothed wheel is rotated in the horizontal plane and turns the plug thereby opening or closing the fluid communication between the cold water cistern and the inside of the cylinder.   

The drawing on the right illustrates the situation when the thumbling bob F has crossed the vertical line and is beginning to fall in a circular motion toward the regulator side just before the leg E engages with the stirrup L. 

Once the next pin comes into contact with the cock lever and opens the injection cock, the cylinder side of the beam is still rising.e cylinder and starts to condense the steam. As a result an increasing vacuum is created in the cylinder. As a result, the air pressure experiences no counterpressure and pushes the piston downward, thereby lifting the counterweight and the water in the pump.

A pulley on the first pin pulls the first lever down as the pin rod Q descends, forcing the arbor tree AB to rotate in a clockwise direction and shifting the tumbling bob from its stable position to the unstable vertical position. The lever leg D pushes the stirrup L toward the regulator and instantly closes the regulator valve once the tumbling bob F has left the vertical position and is falling downward in a circular route toward the pin rod Q.  This completes a cycle and a new cycle can begin.

Due to the lack of performance information for atmospheric engines operating at different speeds, or strokes per minute, I developed a small model based on the hypothesis that, after a certain point, the amount of work produced by each stroke decreases exponentially. I further assumed that the maximum power for a Newcomen engine operating at 8 strokes per minute is attained at roughly twice this speed. As a reference point, 8 strokes per minute are used. The generated work corresponds to the maximum amount of work that can be done up to this point or at this speed, respectively. As a result, the relationship between power and strokes per minute up to this point is linear. The power produced by four maximum-power strokes per minute is exactly equal to half the power produced by eight maximum-power strokes per minute. A stroke no longer reaches its full power after this point, although the increased speed still generates more work per minute. The work done each stroke now decreases faster than the increase in speed can make up for it, indicating that the maximum fraction of work per minute has finally been reached.

Due to the lack of a second or third reference point, the curve may be flatter or steeper near the maximum. The graphic does, however, accurately depict that Newcomen engines would operate more effectively at greater speeds. The roadblock in the mind of Newcomen and contemporary engine erectors was presumably to realize that, in order to enhance speed, the weight of the water column to be lifted with each pump stroke needed to be decreased in order to match the lower lifting power of an uncomplete condensation. The idea that a smaller diameter for the pump tubes would allow for improved performance was beyond the comprehension of Newcomen & Co.