In 1556, Georg Agricola, German mineralogist, in his his De Re Metallica, described a number of pumps, suction, ball and chain, and bucket; one elaborate installation, at Chemnitz, e.g., lifted water 660-feet in three stages with pumps of the ball-and-chain design, that was operated by 96 horses, working four hours and resting twelve, in teams of eight to a pump.
In 1589, in a translation of one of Hero's Spiritalia
, the following diagram of a four-cylinder
"one-horse" pump was presented, which shows one horse being "worked", per unit time, to turn a set of inter-meshed gears, which turns a crank arm, which work a set of four siphon-like piston and cylinder pumps, which thus work to lift water out of flooded mines, to heights of about 30-feet, as shown, therein illustrating the transformation of rotary motion
to reciprocating motion
via gears: 
In 1615, Salomon de Caus, in his The Reasons for Moving Forces, gave the following illustration of a "four-horse pump" for draining a mines: 
In 1702, Thomas Savery, in regards to his Savery engine, commented the following:
“Water, in its fall from any determinate height, has simply a force answerable and equal to the force that raises it. So that an engine which will raise as much water as two horses working together at one time in such a work can do, and for which there must be constantly kept ten or twelve horses for doing the same, then, I say, such an engine will do the work or labor of ten or twelve horses; and whereas this engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work, it will be improper to stint or confine its uses and operation in respect of water-mills.”
— Thomas Savery (1702), Miner’s Friend (pg. 26)
In 1734, Marten Triewald, in his Short Description of the Atmospheric Engine
, stated that the Newcomen engine
, installed at the mines at Dannemore, for pumping out water, was doing as much work as “66 horse-whims, each drawn by 4 pairs of horses, or altogether 528 horses in 24 hours.”  In c.1735, John Desaguliers calculated that the "power of one horse" equals 27,500 foot-pounds. 
In 1739, one Newcomen engine
installed at a colliery at Fresnes, France, with a 30-inch diameter cylinder
and a 9-foot piston
stroke, which lifted water at a rate of 15 strokes per minute, from 90-feet below the surface, working 48-hours per week, with little human attendance, replaced a previous system of 50-men and 20-horses, working in shifts throughout the week.  This version of the Newcomen engine, accordingly, was a 20 hp engine, roughly speaking.
In c.1765, John Smeaton
equated "power of one horse" to be equivalent to 5 men or to 22,916 pounds of water raised one foot high in one minute against the force
In 1772, Smeaton conducted a number of experiments on various Newcomen engines
of various sizes and improvements, aka Smeaton engines
, to compile the following horsepower table: 
(add) Bolton & Watt
In 1762, Matthew Bolton, after inheriting a large sum of money upon his father’s death, opened the “Soho works” manufacturing plant, which made clocks and timepieces. The mill, at this time, was operated by horses, being that water-power (running rivers) were lacking at Soho. Being that the power of horse was irregular and sometimes failed, he soon began to contemplate the possible application of the steam engine to his mill.
“The enormous expense of the horsepower put me upon thinking of turning the mill by fire.” He continued that he had been recently making fruitless experiments on the subject. On Feb 22, 1766, Boulton wrote Benjamin Franklin about this and sent him a model he had made.  Soon thereafter, English inventor John Roebuck, a correspondent of Boulton’s, told him of a young Scottish inventor named James Watt who had been making recent progress with model steam engines. Boulton then invited Watt to visit him at Soho, which he did on a return from a visit to London. In 1775, Boulton and Watt formally entered into partnership, and it was mainly through the energy and self-sacrifice of Boulton, who devoted all the capital he had or could borrow to the enterprise, that the steam engine was at length made a commercial success; and for the next eleven years the Soho Foundry they made Watt's steam-engines for colliery owners to pump water out of mines, the Boulton & Watt engine being four times more powerful than Thomas Newcomen's original design.
— Matthew Bolton (1766), “Letter to Friend”
In 1782, James Watt
found, via experiment, that a “brewery horse” was able to produce 32,400 foot-pounds per minute.
In 1783, Watt and Matthew Boulton
, working together, standardized the figure of one “horsepower” at 33,000 foot-pounds per minute, in order to classify their engines for sale, and by 1809, this was generally accepted as equivalent of 1 horsepower, as it is today. This meaning that this was the amount of mechanical effect that the average “brewery horse” could produce in one minute (see: mechanical equivalent of heat). In other words, through experiment, it was determined that one horse, on average, could work a rotational device, such to turn gears, resulting in the lifting of 33,000 pounds of water out of a mine in one minute.