Question:  the Royal Society was unable to meet its promise to finance the publication of Newton's "Philosophiae Naturalis Principia Mathematica" and let this to the clerk of the society who was best known for computing what?

Context paragraphs:
Edmond Halley: Edmond (or Edmund) Halley, FRS (pronounced ; 8 November [O.S. 29 October] 1656 – 25 January 1742 [O.S. 14 January 1741] ) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of Halley's Comet.  He was the second Astronomer Royal in Britain, succeeding John Flamsteed.

General Scholium: The General Scholium is an essay written by Isaac Newton, appended to his work of "Philosophiæ Naturalis Principia Mathematica", known as the "Principia".  It was first published with the second (1713) edition of the "Principia" and reappeared with some additions and modifications on the third (1726) edition.  It is best known for the "Hypotheses non fingo" ("I do not frame hypotheses") expression, which Newton used as a response to some of the criticism received after the release of the first edition (1687).

The System of the World (novel): The System of the World is a novel by Neal Stephenson and is the third and final volume in "The Baroque Cycle".  The title alludes to the third volume of Isaac Newton's "Philosophiae Naturalis Principia Mathematica", which bears the same name.

Isaac Newton: Sir Isaac Newton {'1': ", '2': ", '3': ", '4': "} ( ; 25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution.  His book "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics.  Newton also made pathbreaking contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

Newton's minimal resistance problem: Newton's minimal resistance problem is a problem of finding a solid of revolution which experiences a minimum resistance when it moves through the homogeneous fluid with constant velocity in the direction of the axis of revolution, named after Isaac Newton, who studied the problem in 1685 and published in 1687 in his Principia Mathematica.  This problem is considered as one of the first problems solved in the calculus of variations, which appeared even before the brachistochrone problem.  Newton published the solution in Principia Mathematica without his derivation and David Gregory was the first person who approached Newton and persuaded him to write an analysis for him.  Then the derivation were shared to his students and peers by Gregory.

De Historia piscium: De Historia Piscium, Latin for "The History of Fish," was a scientific book written by Francis Willughby and published by the Royal Society in 1686.  It was unpopular and sold poorly, causing severe strain on the finances of the society.  This resulted in the society being unable to meet its promise to finance the publication of Newton's "Philosophiae Naturalis Principia Mathematica" (""Mathematical Principles of Natural Philosophy"", better known simply as "Principia"), leaving this to Edmond Halley, who was then the clerk of the society.  After Halley had personally financed the publication of "Principia", he was informed that the society could no longer afford to provide him the promised annual salary of £50.  Instead, Halley was paid with left-over copies of "De Historia Piscium".

Philosophiæ Naturalis Principia Mathematica: Philosophiæ Naturalis Principia Mathematica (English pronunciation , Latin for "Mathematical Principles of Natural Philosophy"), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687.  After annotating and correcting his personal copy of the first edition, Newton published two further editions, in 1713 and 1726.  The "Principia" states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically).  The "Principia" is considered one of the most important works in the history of science.

Newton's law of universal gravitation: Newton's law of universal gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.  This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.  It is a part of classical mechanics and was formulated in Newton's work "Philosophiæ Naturalis Principia Mathematica" ("the "Principia""), first published on 5 July 1687.  (When Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him; see the History section below.)

Isaac Newton in popular culture: Isaac Newton was an English mathematician, natural philosopher, theologian, alchemist and one of the most influential scientists in human history.  His "Philosophiae Naturalis Principia Mathematica" is considered to be one of the most influential book in the history of science, laying the groundwork for most of classical mechanics by describing universal gravitation and the three laws of motion.  In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus.

Method of Fluxions: Method of Fluxions is a book by Isaac Newton.  The book was completed in 1671, and published in 1736.  Fluxion is Newton's term for a derivative.  He originally developed the method at Woolsthorpe Manor during the closing of Cambridge during the Great Plague of London from 1665 to 1667, but did not choose to make his findings known (similarly, his findings which eventually became the "Philosophiae Naturalis Principia Mathematica" were developed at this time and hidden from the world in Newton's notes for many years).  Gottfried Leibniz developed his form of calculus independently around 1673, 7 years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and fluents..." from 1666.  Leibniz however published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion notation form of calculus in part during 1693.  The calculus notation in use today is mostly that of Leibniz, although Newton's dot notation for differentiation formula_1 for denoting derivatives with respect to time is still in current use throughout mechanics and circuit analysis.

Supporting paragraphs: De Historia piscium Edmond Halley
Answer: the orbit of Halley's Comet