Graphical depiction of Boyle's law: that pressure P and volume V of a body of gas bodies vary inversely:$P \propto \frac{1}{V} \,$
In gas laws, Boyle's law (TR:69), aka "Towneley's hypothesis" (Boyle, 1662) or "Mariotte's law" (in Europe), states that for a system of gas particles (atoms and or molecules) at constant particle number and temperature the pressure and volume of the gas are inversely related. This is stated in equation form as:

$PV = K\mid_{n,T} \,$

Said another way, Boyle's law states that for a body of gas at constant number of particles n and temperature T the product of the measure of the pressure P and volume V of gas will be a constant K. The law was stated in 1662 by Irish chemist Robert Boyle.

Towneley-Power
In 1653, Englishman scientist Richard Towneley and physician Henry Power began performing various experiments, supposedly with vacuums and barometers, among other devices, out of which they elucidated the gas law that pressure varies inversely with volume.

The story as to how this result came to be known as Boyle’s law, however, is a bit convoluted. Initially, Towneley and Power, being amateur scientists, did not publish their results immediately, but that in 1660, following the publication of Irish chemist Robert Boyle’s New Experiments on the Spring of the Air, Power sent a paper entitled “Additional Experiments Made at Towneley Hall, in the Years 1660 and 1661, by the Advice and Assistance of that Heroic and Worthy Gentleman Richard Towneley”, to his friend English physician William Croone (1633-1684), in London. [3] Power, however, neglected to put his name on the paper and Croone, likewise, failed to mention who the author of the paper was, when he sent the paper to Boyle.

Boyle, in turn, read the paper and in the 1662, second edition of his Spring of the Air, credited Towneley for the discovery of the gas law, and stated in a reply to Jesuit scientist Francis Linus (1595-1675), a prominent objector to the first edition, that he had not realized that the relation that pressure times volume equals a constant applied to his own data until Richard Towneley pointed it out. [4] This was Boyle's first mention of the law that the volume of a gas varies inversely to the pressure of the gas.

According to another version as to how Boyle may have become acquainted with the Towneley-Power experimental work, there is some mention that Power may have incorporated some version of the pressure times volume equals constant gas law in his 1661 manuscript Experimental Philosophy, and that and early draft of this was seen by Boyle. [6] Another proposal is that Towneley may have discussed his gas law with Boyle when he visited London in the winter of 1661-62. These latter two suppositions, however, are in need of further corroboration.

Boyle-Hooke
Prior to receiving the Power-Towneley gas law theory, in 1658, Boyle and his assistant Robert Hooke had built a combination air pump-vacuum, or what they called a "pneumatical engine", based on the design of German engineer Otto Guericke’s vacuum pump in the 1657 book Mechanical Hydraulic Pneumatics by German scientist Gaspar Schott. [1] After conducting a number of experiments with their air pump, Boyle, as mentioned, published the results in the 1660 book New Experiments on the Spring of the Air.

It is generally viewed that the actual first enunciation of the Boyle’s law is found in appendix to the 1662 second edition. Specifically, an appended second edition section A Defence of the Doctrine Touching the Spring and Weight of the Air, chapter V, entitled "Two new experiments touching the measure of the force of the spring of the air compressed and dilated", contains a statement of the Law in column six of the first table (on the condensation of air): [2]

“What that pressure should be according to the hypothesis, that supposes the pressures and expansions to be in reciprocal proportion.”

In mathematical formulation, this would translate as:

$\text{pressure} \propto \frac{1}{\text{volume}} \,$

Boyle, supposedly, confirmed the Power-Towneley discovery through experiments and published the results. Boyle's law is based on experiments with air, which he considered to be a fluid of particles at rest, within or between small invisible springs. The actual person to call this "Boyle's law" is a bit elusive, although, by 1774, the name "Boyle's law" was in common usage.

Deviations
In 1787, Dutch scientist Martinus Marum (1750-1837) set out to test whether Boyle’s famous law about the inverse relation between the volume of a gas and the pressure held under all circumstances. [7] Marum found deviations from ammonia, such that at about 70 pounds of pressure (5 atmospheres), the expected drop in volume did not occur, but rather the gas began to become liquid. Marum concluded: [8]

“The aeriform state of whatever fluids ceases to exist, and they are changed into liquids, when they are exposed to the necessary degree of pressure.”

Quotes
The following are related quotes:

“Boyle made a series of measurements with greater compressions until he bad reduced the volume to one quarter of its original value, and obtained a close agreement between the pressure observed and ‘what that pressure should be according to the hypothesis that supposes the pressures and expansions to be in reciprocal proportions’. Mariotte did not state the law until fourteen years after Boyle.”
Joseph Thomson (1902), A Textbook of Physics, Volume One (pg. 124)

“The complicated history of the discovery of Boyle's law has only recently been disentangled by historians. It appears that the law was first proposed by two other British scientists, Henry Power and Richard Towneley, on the basis of their experiments, begun in 1653. They did not publish their results immediately, but after Boyle's first experiments on air pressure had been published in 1660, Power sent a paper describing the results of their joint work to his friend William Croone, in London. The title of the paper was ‘Additional Experiments Made at Towneley Hall, in the years 1660 and 1661, by the advice and assistance of that Heroick and Worthy Gentleman Richard Towneley’. But Power neglected to put his own name on the paper. Croone sent the paper to Boyle, forgetting to mention that Power was the author. Boyle was very careful to give proper credit for the information he had received, and in his monograph of 1662 replying to Linus, he stated that he had not realized that the simple relation PV = constant applied to his own data until Richard Towneley pointed it out. Later scientists, who read Boyle's works carelessly or not at all, assumed that Boyle had made the discovery all by himself.”
— Gerald Holton (1952), Physics: the Human Adventure (co-author: Stephen Brush) (pg. 270)

“Towneley, however, as far as Boyle knew, had not actually verified the ‘PV = c’ rule. And, since Boyle had no way of contacting Towneley, knowing when if ever Towneley would publish his views, or even if Towneley had the means to carry out experiments, Boyle decided to ‘present the reader with that which follow, wherein I had the assistance of the same person [Hooke], that I took notice of in the former chapter, as having written something about rarefaction’. Boyle relates further how Hooke, upon hearing Boyle mention ‘Towneley's hypothesis’, said that he had the year before experimented on that very subject with positive results. Boyle also mentions that Lord Brouncker, too, was doing some work in that area but had not achieved anything conclusive. Since the law was published in a book under Boyle's name, the law became generally known as Boyle's. However, as we have seen, within the very same book, Boyle disclaims being its discoverer and does instead credit the ‘same person, that I took notice of in the former chapter’, who was indeed none other than his assistant Hooke, with both thinking upon and verifying the hypothesis in question. A ‘Boyle side’ to the question of origination is, therefore, nonexistent, as Boyle himself testifies. Also, in his life of Boyle, More expresses the view that Boyle's law was actually more Hooke's than Boyle's.”
— F.F. Centore (1970), Robert Hooke’s Contributions to Mechanics (pg. 59)

“The credit for Boyle's law only began to be questioned within the twentieth-century history of science. Charles Webster [1965] argued that others, particularly Richard Towneley and his friend Henry Power, had experimented and hypothesized about what came to be known as ‘Boyle's law’ before Boyle. Boyle himself referred to ‘Towneley's hypothesis’ in the second edition of his work on the ‘spring of the air’ in 1661. More recently, Power's biographer Trevor Hughes has agreed with Webster. Hughes concluded that ‘Power and Towneley provided both experimental results and their interpretation, which guided Boyle to his experiments and conclusions, which have become accepted as ‘Boyle's Law’.’ Joseph Agassi, by contrast, has defended Boyle's claim to Boyle's law. Towneley merely served as Boyle's student assistant. It was generous of Boyle, first, to mentor Towneley, and secondly, to refer to Towneley at all. Furthermore, the entire affair illustrated how Boyle not only discovered the law, but invented the conventions by means of which discoveries could be quickly recorded in published essays. According to Agassi, ‘It was Boyle who instituted priority rules’ as a ‘means of prompting the advancement of learning (in accord with Bacon's proposals)’. By contrast, Power and Towneley neither rushed into print nor rushed to claim credit. ‘Why did Power refrain from publication?’ asked Agassi. ‘Certainly, if Power had discovered Boyle's law or Townley, the delay in publication looked odd’.”
— Vera Keller (2015), Knowledge and the Public Interest (pg. 247)

References
1. (a) Schott, Gaspar. (1657). Mechanical Hydraulic Pneumatics (Mechanicahydraulica-pneumatica). Würtzburg.
(b) Wilson, George. (1849). “On the Early History of the Air-Pump in England”, The Edinburgh New Philosophical Journal, (pgs. 330-54).
2. Baldwin, W.G. (1998). “Excerpts on Boyle’s Law”, University of Manitoba.
3. William Croone – Wikipedia.
4. Holton, Gerarld J. and Brush, Stephen G. (2001). Physics, the Human Adventure: from Copernicus to Einstein and Beyond (pg. 270). Rutgers University Press.
5. Francis Line – Wikipedia.
6. Power, Henry. (1663). Experimental Philosophy, in Three Books: Containing New Experiments, Microscopical, Mercurial, Magnetical. With some Deductions, and Probable Hypotheses, Raised from Them, in Avouchment and Illustration of the Now Famous Atomical Hypothesis (Boyle, 15+ pgs). London: Martin & Allestry.