text:
Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy) often referred to as simply the Principia, is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The Principia is written in Latin and comprises three volumes, and was authorized, imprimatur, by Samuel Pepys, then-President of the Royal Society on 5 July 1686 and first published in 1687.

The Principia is considered one of the most important works in the history of science. The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of Mathematical Principles of Natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." Joseph-Louis Lagrange described it as "the greatest production of a human mind". It has been called the "greatest scientific work in history", and the "supreme expression in human thought of the mind's ability to hold the universe fixed as an object of contemplation".

A more recent assessment has been that while acceptance of Newton's laws was not immediate, by the end of the century after publication in 1687, "no one could deny that [out of the Principia] a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally".

The Principia forms a mathematical foundation for the theory of classical mechanics. Among other achievements, it explains Johannes Kepler's laws of planetary motion, which Kepler had first obtained empirically. In formulating his physical laws, Newton developed and used mathematical methods now included in the field of calculus, expressing them in the form of geometric propositions about "vanishingly small" shapes. In a revised conclusion to the Principia, Newton emphasized the empirical nature of the work with the expression Hypotheses non fingo ("I frame/feign no hypotheses").

After annotating and correcting his personal copy of the first edition, Newton published two further editions, during 1713 with errors of the 1687 corrected, and an improved version of 1726.

Expressed aim and topics covered
The Preface of the work states:

"... Rational Mechanics will be the sciences of motion resulting from any forces whatsoever, and of the forces required to produce any motion, accurately proposed and demonstrated ... And therefore we offer this work as mathematical principles of his philosophy. For all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena ..."

The Principia deals primarily with massive bodies in motion, initially under a variety of conditions and hypothetical laws of force in both non-resisting and resisting media, thus offering criteria to decide, by observations, which laws of force are operating in phenomena that may be observed. It attempts to cover hypothetical or possible motions both of celestial bodies and of terrestrial projectiles. It explores difficult problems of motions perturbed by multiple attractive forces. Its third and final book deals with the interpretation of observations about the movements of planets and their satellites.

The book:
 * shows how astronomical observations verify the inverse square law of gravitation (to an accuracy that was high by the standards of Newton's time);
 * offers estimates of relative masses for the known giant planets and for the Earth and the Sun;
 * defines the motion of the Sun relative to the Solar System barycenter;
 * shows how the theory of gravity can account for irregularities in the motion of the Moon;
 * identifies the oblateness of the shape of the Earth;
 * accounts approximately for marine tides including phenomena of spring and neap tides by the perturbing (and varying) gravitational attractions of the Sun and Moon on the Earth's waters;
 * explains the precession of the equinoxes as an effect of the gravitational attraction of the Moon on the Earth's equatorial bulge; and
 * gives theoretical basis for numerous phenomena about comets and their elongated, near-parabolic orbits.

The opening sections of the Principia contain, in revised and extended form, nearly all of the content of Newton's 1684 tract De motu corporum in gyrum.

The Principia begin with "Definitions" and "Axioms or Laws of Motion", and continues in three books:

Book 1, De motu corporum
Book 1, subtitled De motu corporum (On the motion of bodies) concerns motion in the absence of any resisting medium. It opens with a collection of mathematical lemmas on "the method of first and last ratios", a geometrical form of infinitesimal calculus.

The second section establishes relationships between centripetal forces and the law of areas now known as Kepler's second law (Propositions 1–3), and relates circular velocity and radius of path-curvature to radial force (Proposition 4), and relationships between centripetal forces varying as the inverse-square of the distance to the center and orbits of conic-section form (Propositions 5–10).

Propositions 11–31 establish properties of motion in paths of eccentric conic-section form including ellipses, and their relationship with inverse-square central forces directed to a focus and include Newton's theorem about ovals (lemma 28).

Propositions 43–45 are demonstration that in an eccentric orbit under centripetal force where the apse may move, a steady non-moving orientation of the line of apses is an indicator of an inverse-square law of force.

Book 1 contains some proofs with little connection to real-world dynamics. But there are also sections with far-reaching application to the solar system and universe:

Propositions 57–69 deal with the "motion of bodies drawn to one another by centripetal forces". This section is of primary interest for its application to the Solar System, and includes Proposition 66 along with its 22 corollaries: here Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions, a problem which later gained name and fame (among other reasons, for its great difficulty) as the three-body problem.

Propositions 70–84 deal with the attractive forces of spherical bodies. The section contains Newton's proof that a massive spherically symmetrical body attracts other bodies outside itself as if all its mass were concentrated at its centre. This fundamental result, called the Shell theorem, enables the inverse square law of gravitation to be applied to the real solar system to a very close degree of approximation.

Book 2, part 2 of De motu corporum
Part of the contents originally planned for the first book was divided out into a second book, which largely concerns motion through resisting mediums. Just as Newton examined consequences of different conceivable laws of attraction in Book 1, here he examines different conceivable laws of resistance; thus Section 1 discusses resistance in direct proportion to velocity, and Section 2 goes on to examine the implications of resistance in proportion to the square of velocity. Book 2 also discusses (in Section 5 ) hydrostatics and the properties of compressible fluids; Newton also derives Boyle's law. The effects of air resistance on pendulums are studied in Section 6, along with Newton's account of experiments that he carried out, to try to find out some characteristics of air resistance in reality by observing the motions of pendulums under different conditions. Newton compares the resistance offered by a medium against motions of globes with different properties (material, weight, size). In Section 8, he derives rules to determine the speed of waves in fluids and relates them to the density and condensation (Proposition 48; this would become very important in acoustics). He assumes that these rules apply equally to light and sound and estimates that the speed of sound is around 1088 feet per second and can increase depending on the amount of water in air.

Less of Book 2 has stood the test of time than of Books 1 and 3, and it has been said that Book 2 was largely written to refute a theory of Descartes which had some wide acceptance before Newton's work (and for some time after). According to Descartes's theory of vortices, planetary motions were produced by the whirling of fluid vortices that filled interplanetary space and carried the planets along with them. Newton concluded Book 2 by commenting that the hypothesis of vortices was completely at odds with the astronomical phenomena, and served not so much to explain as to confuse them.

Book 3, De mundi systemate
Book 3, subtitled De mundi systemate (On the system of the world), is an exposition of many consequences of universal gravitation, especially its consequences for astronomy. It builds upon the propositions of the previous books and applies them with further specificity than in Book 1 to the motions observed in the Solar System. Here (introduced by Proposition 22, and continuing in Propositions 25–35 ) are developed several of the features and irregularities of the orbital motion of the Moon, especially the variation. Newton lists the astronomical observations on which he relies, and establishes in a stepwise manner that the inverse square law of mutual gravitation applies to Solar System bodies, starting with the satellites of Jupiter and going on by stages to show that the law is of universal application. He also gives starting at Lemma 4 and Proposition 40 the theory of the motions of comets, for which much data came from John Flamsteed and Edmond Halley, and accounts for the tides, attempting quantitative estimates of the contributions of the Sun and Moon to the tidal motions; and offers the first theory of the precession of the equinoxes. Book 3 also considers the harmonic oscillator in three dimensions, and motion in arbitrary force laws.

In Book 3 Newton also made clear his heliocentric view of the Solar System, modified in a somewhat modern way, since already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the Solar System. For Newton, "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and that this centre "either is at rest, or moves uniformly forward in a right line". Newton rejected the second alternative after adopting the position that "the centre of the system of the world is immoveable", which "is acknowledg'd by all, while some contend that the Earth, others, that the Sun is fix'd in that centre". Newton estimated the mass ratios Sun:Jupiter and Sun:Saturn, and pointed out that these put the centre of the Sun usually a little way off the common center of gravity, but only a little, the distance at most "would scarcely amount to one diameter of the Sun".

Commentary on the Principia
The sequence of definitions used in setting up dynamics in the Principia is recognisable in many textbooks today. Newton first set out the definition of mass

"The quantity of matter is that which arises conjointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass."

This was then used to define the "quantity of motion" (today called momentum), and the principle of inertia in which mass replaces the previous Cartesian notion of intrinsic force. This then set the stage for the introduction of forces through the change in momentum of a body. Curiously, for today's readers, the exposition looks dimensionally incorrect, since Newton does not introduce the dimension of time in rates of changes of quantities.

He defined space and time "not as they are well known to all". Instead, he defined "true" time and space as "absolute" and explained:

"Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to perceptible objects. And it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. ... instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical discussions, we ought to step back from our senses, and consider things themselves, distinct from what are only perceptible measures of them."

To some modern readers it can appear that some dynamical quantities recognised today were used in the Principia but not named. The mathematical aspects of the first two books were so clearly consistent that they were easily accepted; for example, Locke asked Huygens whether he could trust the mathematical proofs and was assured about their correctness.

However, the concept of an attractive force acting at a distance received a cooler response. In his notes, Newton wrote that the inverse square law arose naturally due to the structure of matter. However, he retracted this sentence in the published version, where he stated that the motion of planets is consistent with an inverse square law, but refused to speculate on the origin of the law. Huygens and Leibniz noted that the law was incompatible with the notion of the aether. From a Cartesian point of view, therefore, this was a faulty theory. Newton's defence has been adopted since by many famous physicists—he pointed out that the mathematical form of the theory had to be correct since it explained the data, and he refused to speculate further on the basic nature of gravity. The sheer number of phenomena that could be organised by the theory was so impressive that younger "philosophers" soon adopted the methods and language of the Principia.

Rules of Reason
Perhaps to reduce the risk of public misunderstanding, Newton included at the beginning of Book 3 (in the second (1713) and third (1726) editions) a section titled "Rules of Reasoning in Philosophy". In the four rules, as they came finally to stand in the 1726 edition, Newton effectively offers a methodology for handling unknown phenomena in nature and reaching towards explanations for them. The four Rules of the 1726 edition run as follows (omitting some explanatory comments that follow each):

 * 1) We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
 * 2) Therefore to the same natural effects we must, as far as possible, assign the same causes.
 * 3) The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
 * 4) In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

This section of Rules for philosophy is followed by a listing of "Phenomena", in which are listed a number of mainly astronomical observations, that Newton used as the basis for inferences later on, as if adopting a consensus set of facts from the astronomers of his time.

Both the "Rules" and the "Phenomena" evolved from one edition of the Principia to the next. Rule 4 made its appearance in the third (1726) edition; Rules 1–3 were present as "Rules" in the second (1713) edition, and predecessors of them were also present in the first edition of 1687, but there they had a different heading: they were not given as "Rules", but rather in the first (1687) edition the predecessors of the three later "Rules", and of most of the later "Phenomena", were all lumped together under a single heading "Hypotheses" (in which the third item was the predecessor of a heavy revision that gave the later Rule 3).

From this textual evolution, it appears that Newton wanted by the later headings "Rules" and "Phenomena" to clarify for his readers his view of the roles to be played by these various statements.

In the third (1726) edition of the Principia, Newton explains each rule in an alternative way and/or gives an example to back up what the rule is claiming. The first rule is explained as a philosophers' principle of economy. The second rule states that if one cause is assigned to a natural effect, then the same cause so far as possible must be assigned to natural effects of the same kind: for example, respiration in humans and in animals, fires in the home and in the Sun, or the reflection of light whether it occurs terrestrially or from the planets. An extensive explanation is given of the third rule, concerning the qualities of bodies, and Newton discusses here the generalisation of observational results, with a caution against making up fancies contrary to experiments, and use of the rules to illustrate the observation of gravity and space.

General Scholium
The General Scholium is a concluding essay added to the second edition, 1713 (and amended in the third edition, 1726). It is not to be confused with the General Scholium at the end of Book 2, Section 6, which discusses his pendulum experiments and resistance due to air, water, and other fluids.

Here Newton used the expression hypotheses non fingo, "I formulate no hypotheses", in response to criticisms of the first edition of the Principia. ("Fingo" is sometimes nowadays translated "feign" rather than the traditional "frame," although "feign" does not properly translate "fingo"). Newton's gravitational attraction, an invisible force able to act over vast distances, had led to criticism that he had introduced "occult agencies" into science. Newton firmly rejected such criticisms and wrote that it was enough that the phenomena implied gravitational attraction, as they did; but the phenomena did not so far indicate the cause of this gravity, and it was both unnecessary and improper to frame hypotheses of things not implied by the phenomena: such hypotheses "have no place in experimental philosophy", in contrast to the proper way in which "particular propositions are inferr'd from the phenomena and afterwards rendered general by induction".

Newton also underlined his criticism of the vortex theory of planetary motions, of Descartes, pointing to its incompatibility with the highly eccentric orbits of comets, which carry them "through all parts of the heavens indifferently".

Newton also gave theological argument. From the system of the world, he inferred the existence of a god, along lines similar to what is sometimes called the argument from intelligent or purposive design. It has been suggested that Newton gave "an oblique argument for a unitarian conception of God and an implicit attack on the doctrine of the Trinity". The General Scholium does not address or attempt to refute the church doctrine; it simply does not mention Jesus, the Holy Ghost, or the hypothesis of the Trinity.

Halley and Newton's initial stimulus
In January 1684, Edmond Halley, Christopher Wren and Robert Hooke had a conversation in which Hooke claimed to not only have derived the inverse-square law but also all the laws of planetary motion. Wren was unconvinced, Hooke did not produce the claimed derivation although the others gave him time to do it, and Halley, who could derive the inverse-square law for the restricted circular case (by substituting Kepler's relation into Huygens' formula for the centrifugal force) but failed to derive the relation generally, resolved to ask Newton.

Halley's visits to Newton in 1684 thus resulted from Halley's debates about planetary motion with Wren and Hooke, and they seem to have provided Newton with the incentive and spur to develop and write what became Philosophiae Naturalis Principia Mathematica. Halley was at that time a Fellow and Council member of the Royal Society in London (positions that in 1686 he resigned to become the Society's paid Clerk). Halley's visit to Newton in Cambridge in 1684 probably occurred in August. When Halley asked Newton's opinion on the problem of planetary motions discussed earlier that year between Halley, Hooke and Wren, Newton surprised Halley by saying that he had already made the derivations some time ago; but that he could not find the papers. (Matching accounts of this meeting come from Halley and Abraham De Moivre to whom Newton confided.) Halley then had to wait for Newton to "find" the results, and in November 1684 Newton sent Halley an amplified version of whatever previous work Newton had done on the subject. This took the form of a 9-page manuscript, De motu corporum in gyrum (Of the motion of bodies in an orbit): the title is shown on some surviving copies, although the (lost) original may have been without a title.

Newton's tract De motu corporum in gyrum, which he sent to Halley in late 1684, derived what is now known as the three laws of Kepler, assuming an inverse square law of force, and generalised the result to conic sections. It also extended the methodology by adding the solution of a problem on the motion of a body through a resisting medium. The contents of De motu so excited Halley by their mathematical and physical originality and far-reaching implications for astronomical theory, that he immediately went to visit Newton again, in November 1684, to ask Newton to let the Royal Society have more of such work. The results of their meetings clearly helped to stimulate Newton with the enthusiasm needed to take his investigations of mathematical problems much further in this area of physical science, and he did so in a period of highly concentrated work that lasted at least until mid-1686.

Newton's single-minded attention to his work generally, and to his project during this time, is shown by later reminiscences from his secretary and copyist of the period, Humphrey Newton. His account tells of Isaac Newton's absorption in his studies, how he sometimes forgot his food, or his sleep, or the state of his clothes, and how when he took a walk in his garden he would sometimes rush back to his room with some new thought, not even waiting to sit before beginning to write it down. Other evidence also shows Newton's absorption in the Principia: Newton for years kept up a regular programme of chemical or alchemical experiments, and he normally kept dated notes of them, but for a period from May 1684 to April 1686, Newton's chemical notebooks have no entries at all. So, it seems that Newton abandoned pursuits to which he was formally dedicated and did very little else for well over a year and a half, but concentrated on developing and writing what became his great work.

The first of the three constituent books was sent to Halley for the printer in spring 1686, and the other two books somewhat later. The complete work, published by Halley at his own financial risk, appeared in July 1687. Newton had also communicated De motu to Flamsteed, and during the period of composition, he exchanged a few letters with Flamsteed about observational data on the planets, eventually acknowledging Flamsteed's contributions in the published version of the Principia of 1687.

Preliminary version
The process of writing that first edition of the Principia went through several stages and drafts: some parts of the preliminary materials still survive, while others are lost except for fragments and cross-references in other documents.

Surviving materials show that Newton (up to some time in 1685) conceived his book as a two-volume work. The first volume was to be titled De motu corporum, Liber primus, with contents that later appeared in extended form as Book 1 of the Principia.

A fair-copy draft of Newton's planned second volume De motu corporum, Liber Secundus survives, its completion dated to about the summer of 1685. It covers the application of the results of Liber primus to the Earth, the Moon, the tides, the Solar System, and the universe; in this respect, it has much the same purpose as the final Book 3 of the Principia, but it is written much less formally and is more easily read.

It is not known just why Newton changed his mind so radically about the final form of what had been a readable narrative in De motu corporum, Liber Secundus of 1685, but he largely started afresh in a new, tighter, and less accessible mathematical style, eventually to produce Book 3 of the Principia as we know it. Newton frankly admitted that this change of style was deliberate when he wrote that he had (first) composed this book "in a popular method, that it might be read by many", but to "prevent the disputes" by readers who could not "lay aside the[ir] prejudices", he had "reduced" it "into the form of propositions (in the mathematical way) which should be read by those only, who had first made themselves masters of the principles established in the preceding books". The final Book 3 also contained in addition some further important quantitative results arrived at by Newton in the meantime, especially about the theory of the motions of comets, and some of the perturbations of the motions of the Moon.

The result was numbered Book 3 of the Principia rather than Book 2 because in the meantime, drafts of Liber primus had expanded and Newton had divided it into two books. The new and final Book 2 was concerned largely with the motions of bodies through resisting mediums.

But the Liber Secundus of 1685 can still be read today. Even after it was superseded by Book 3 of the Principia, it survived complete, in more than one manuscript. After Newton's death in 1727, the relatively accessible character of its writing encouraged the publication of an English translation in 1728 (by persons still unknown, not authorised by Newton's heirs). It appeared under the English title A Treatise of the System of the World. This had some amendments relative to Newton's manuscript of 1685, mostly to remove cross-references that used obsolete numbering to cite the propositions of an early draft of Book 1 of the Principia. Newton's heirs shortly afterwards published the Latin version in their possession, also in 1728, under the (new) title De Mundi Systemate, amended to update cross-references, citations and diagrams to those of the later editions of the Principia, making it look superficially as if it had been written by Newton after the Principia, rather than before. The System of the World was sufficiently popular to stimulate two revisions (with similar changes as in the Latin printing), a second edition (1731), and a "corrected" reprint of the second edition (1740).

Halley's role as publisher
The text of the first of the three books of the Principia was presented to the Royal Society at the close of April 1686. Hooke made some priority claims (but failed to substantiate them), causing some delay. When Hooke's claim was made known to Newton, who hated disputes, Newton threatened to withdraw and suppress Book 3 altogether, but Halley, showing considerable diplomatic skills, tactfully persuaded Newton to withdraw his threat and let it go forward to publication. Samuel Pepys, as president, gave his imprimatur on 30 June 1686, licensing the book for publication. The Society had just spent its book budget on De Historia piscium, and the cost of publication was borne by Edmund Halley (who was also then acting as publisher of the Philosophical Transactions of the Royal Society): the book appeared in summer 1687. 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 leftover copies of De Historia piscium.

Beginnings of the Scientific Revolution

Nicolaus Copernicus had moved the Earth away from the center of the universe with the heliocentric theory for which he presented evidence in his book De revolutionibus orbium coelestium (On the revolutions of the heavenly spheres) published in 1543. Johannes Kepler wrote the book Astronomia nova (A new astronomy) in 1609, setting out the evidence that planets move in elliptical orbits with the Sun at one focus, and that planets do not move with constant speed along this orbit. Rather, their speed varies so that the line joining the centres of the sun and a planet sweeps out equal areas in equal times. To these two laws he added a third a decade later, in his 1619 book Harmonices Mundi (Harmonies of the world). This law sets out a proportionality between the third power of the characteristic distance of a planet from the Sun and the square of the length of its year.

The foundation of modern dynamics was set out in Galileo's book Dialogo sopra i due massimi sistemi del mondo (Dialogue on the two main world systems) where the notion of inertia was implicit and used. In addition, Galileo's experiments with inclined planes had yielded precise mathematical relations between elapsed time and acceleration, velocity or distance for uniform and uniformly accelerated motion of bodies.

Descartes' book of 1644 Principia philosophiae (Principles of philosophy) stated that bodies can act on each other only through contact: a principle that induced people, among them himself, to hypothesize a universal medium as the carrier of interactions such as light and gravity—the aether. Newton was criticized for apparently introducing forces that acted at distance without any medium. Not until the development of particle theory was Descartes' notion vindicated when it was possible to describe all interactions, like the strong, weak, and electromagnetic fundamental interactions, using mediating gauge bosons and gravity through hypothesized gravitons.

Newton's role
Newton had studied these books, or, in some cases, secondary sources based on them, and taken notes entitled Quaestiones quaedam philosophicae (Questions about philosophy) during his days as an undergraduate. During this period (1664–1666) he created the basis of calculus and performed the first experiments in the optics of colour. At this time, his proof that white light was a combination of primary colours (found via prismatics) replaced the prevailing theory of colours and received an overwhelmingly favourable response and occasioned bitter disputes with Robert Hooke and others, which forced him to sharpen his ideas to the point where he already composed sections of his later book Opticks by the 1670s in response. Work on calculus is shown in various papers and letters, including two to Leibniz. He became a fellow of the Royal Society and the second Lucasian Professor of Mathematics (succeeding Isaac Barrow) at Trinity College, Cambridge.

Newton's early work on motion
In the 1660s Newton studied the motion of colliding bodies and deduced that the centre of mass of two colliding bodies remains in uniform motion. Surviving manuscripts of the 1660s also show Newton's interest in planetary motion and that by 1669 he had shown, for a circular case of planetary motion, that the force he called "endeavour to recede" (now called centrifugal force) had an inverse-square relation with distance from the center. After his 1679–1680 correspondence with Hooke, described below, Newton adopted the language of inward or centripetal force. According to Newton scholar J. Bruce Brackenridge, although much has been made of the change in language and difference of point of view, as between centrifugal or centripetal forces, the actual computations and proofs remained the same either way. They also involved the combination of tangential and radial displacements, which Newton was making in the 1660s. The difference between the centrifugal and centripetal points of view, though a significant change of perspective, did not change the analysis. Newton also clearly expressed the concept of linear inertia in the 1660s: for this Newton was indebted to Descartes' work published 1644.

Controversy with Hooke
Hooke published his ideas about gravitation in the 1660s and again in 1674. He argued for an attracting principle of gravitation in Micrographia of 1665, in a 1666 Royal Society lecture On gravity, and again in 1674, when he published his ideas about the System of the World in somewhat developed form, as an addition to An Attempt to Prove the Motion of the Earth from Observations. Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, along with a principle of linear inertia. Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. Hooke also did not provide accompanying evidence or mathematical demonstration. On these two aspects, Hooke stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified" (indicating that he did not yet know what law the gravitation might follow); and as to his whole proposal: "This I only hint at present", "having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e., "prosecuting this Inquiry").

In November 1679, Hooke began an exchange of letters with Newton, of which the full text is now published. Hooke told Newton that Hooke had been appointed to manage the Royal Society's correspondence, and wished to hear from members about their researches, or their views about the researches of others; and as if to whet Newton's interest, he asked what Newton thought about various matters, giving a whole list, mentioning "compounding the celestial motions of the planets of a direct motion by the tangent and an attractive motion towards the central body", and "my hypothesis of the lawes or causes of springinesse", and then a new hypothesis from Paris about planetary motions (which Hooke described at length), and then efforts to carry out or improve national surveys, the difference of latitude between London and Cambridge, and other items. Newton's reply offered "a fansy of my own" about a terrestrial experiment (not a proposal about celestial motions) which might detect the Earth's motion, by the use of a body first suspended in air and then dropped to let it fall. The main point was to indicate how Newton thought the falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical, but he went on hypothetically to consider how its motion could continue if the solid Earth had not been in the way (on a spiral path to the centre). Hooke disagreed with Newton's idea of how the body would continue to move. Several commentators have followed Hooke in calling Newton's spiral path mistaken, or even a "blunder", but there are also the following facts: (a) that Hooke left out of account Newton's specific statement that the motion resulted from dropping "a heavy body suspended in the Air" (i.e. a resisting medium), see Newton to Hooke, 28 November 1679, document #236 at page 301, "Correspondence", vol. 2 cited above, and compare Hooke's report to the Royal Society on 11 December 1679, where Hooke reported the matter "supposing no resistance", see D Gjertsen, "Newton Handbook" (1986), at page 259); and (b) that Hooke's reply of 9 December 1679 to Newton considered the cases of motion both with and without air resistance: The resistance-free path was what Hooke called an 'elliptueid'; but a line in Hooke's diagram showing the path for his case of air resistance was, though elongated, also another inward-spiralling path ending at the Earth's centre: Hooke wrote "where the Medium ... has a power of impeding and destroying its motion the curve in wch it would move would be some what like the Line AIKLMNOP &c and ... would terminate in the center C". Hooke's path including air resistance was therefore to this extent like Newton's (see "Correspondence", vol. 2, cited above, at pages 304–306, document #237, with accompanying figure). The diagrams are also available online: see Curtis Wilson, chapter 13 in "Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A, Tycho Brahe to Newton", (Cambridge UP 1989), at page 241 showing Newton's 1679 diagram with spiral, and extract of his letter; also at page 242 showing Hooke's 1679 diagram including two paths, closed curve and spiral. Newton pointed out in his later correspondence over the priority claim that the descent in a spiral "is true in a resisting medium such as our air is", see "Correspondence", vol. 2 cited above, at page 433, document #286. A short further correspondence developed, and towards the end of it Hooke, writing on 6 January 1680 to Newton, communicated his "supposition ... that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance." (Hooke's inference about the velocity was actually incorrect. )

In 1686, when the first book of Newton's Principia was presented to the Royal Society, Hooke claimed that Newton had obtained from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time (according to Edmond Halley's contemporary report) Hooke agreed that "the Demonstration of the Curves generated therby" was wholly Newton's.

A recent assessment about the early history of the inverse square law is that "by the late 1660s", the assumption of an "inverse proportion between gravity and the square of distance was rather common and had been advanced by a number of different people for different reasons". Newton himself had shown in the 1660s that for planetary motion under a circular assumption, force in the radial direction had an inverse-square relation with distance from the center. Newton, faced in May 1686 with Hooke's claim on the inverse square law, denied that Hooke was to be credited as author of the idea, giving reasons including the citation of prior work by others before Hooke. Newton also firmly claimed that even if it had happened that he had first heard of the inverse square proportion from Hooke, which it had not, he would still have some rights to it in view of his mathematical developments and demonstrations, which enabled observations to be relied on as evidence of its accuracy, while Hooke, without mathematical demonstrations and evidence in favour of the supposition, could only guess (according to Newton) that it was approximately valid "at great distances from the center".

The background described above shows there was basis for Newton to deny deriving the inverse square law from Hooke. On the other hand, Newton did accept and acknowledge, in all editions of the Principia, that Hooke (but not exclusively Hooke) had separately appreciated the inverse square law in the Solar System. Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1. Newton also acknowledged to Halley that his correspondence with Hooke in 1679–80 had reawakened his dormant interest in astronomical matters, but that did not mean, according to Newton, that Hooke had told Newton anything new or original: "yet am I not beholden to him for any light into that business but only for the diversion he gave me from my other studies to think on these things & for his dogmaticalness in writing as if he had found the motion in the Ellipsis, which inclined me to try it ...". ) Newton's reawakening interest in astronomy received further stimulus by the appearance of a comet in the winter of 1680/1681, on which he corresponded with John Flamsteed.

In 1759, decades after the deaths of both Newton and Hooke, Alexis Clairaut, mathematical astronomer eminent in his own right in the field of gravitational studies, made his assessment after reviewing what Hooke had published on gravitation. "One must not think that this idea ... of Hooke diminishes Newton's glory", Clairaut wrote; "The example of Hooke" serves "to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated".

Location of early edition copies
It has been estimated that as many as 750 copies of the first edition were printed by the Royal Society, and "it is quite remarkable that so many copies of this small first edition are still in existence ... but it may be because the original Latin text was more revered than read". A survey published in 1953 located 189 surviving copies with nearly 200 further copies located by the most recent survey published in 2020, suggesting that the initial print run was larger than previously thought. However, more recent book historical and bibliographical research has examined those prior claims, and concludes that Macomber's earlier estimation of 500 copies is likely correct.

 * Cambridge University Library has Newton's own copy of the first edition, with handwritten notes for the second edition.
 * The Earl Gregg Swem Library at the College of William & Mary has a first edition copy of the Principia. Throughout are Latin annotations written by Thomas S. Savage. These handwritten notes are currently being researched at the college.
 * The Frederick E. Brasch Collection of Newton and Newtoniana in Stanford University also has a first edition of the Principia.
 * A first edition forms part of the Crawford Collection, housed at the Royal Observatory, Edinburgh.
 * The Uppsala University Library owns a first edition copy, which was stolen in the 1960s and returned to the library in 2009.
 * The Folger Shakespeare Library in Washington, D.C. owns a first edition, as well as a 1713 second edition.
 * The Huntington Library in San Marino, California owns Isaac Newton's personal copy, with annotations in Newton's own hand.
 * The Bodmer Library in Switzerland keeps a copy of the original edition that was owned by Leibniz. It contains handwritten notes by Leibniz, in particular concerning the controversy of who first formulated calculus (although he published it later, Newton argued that he developed it earlier).
 * The Iron Library in Switzerland holds a first edition copy that was formerly in the library of the physicist Ernst Mach. The copy contains critical marginalia in Mach's hand.
 * The University of St Andrews Library holds both variants of the first edition, as well as copies of the 1713 and 1726 editions.
 * The Fisher Library in the University of Sydney has a first-edition copy, annotated by a mathematician of uncertain identity and corresponding notes from Newton himself.
 * The Linda Hall Library holds the first edition, as well as a copy of the 1713 and 1726 editions.
 * The Teleki-Bolyai Library of Târgu-Mureș holds a 2-line imprint first edition.
 * One book is also located at Vasaskolan, Gävle, in Sweden.
 * Dalhousie University has a copy as part of the William I. Morse collection.
 * McGill University in Montreal has the copy once owned by Sir William Osler.
 * The University of Toronto has a copy in the Thomas Fisher Rare Book Collection.
 * University College London Special Collections has a copy previously owned by the lawyer and mathematician John T. Graves.

In 2016, a first edition sold for $3.7 million.

The second edition (1713) were printed in 750 copies, and the third edition (1726) were printed in 1,250 copies.

A facsimile edition (based on the 3rd edition of 1726 but with variant readings from earlier editions and important annotations) was published in 1972 by Alexandre Koyré and I. Bernard Cohen.
 * The Martin Bodmer Library keeps a copy of the original edition that was owned by Gottfried Wilhelm Leibniz. In it, we can see handwritten notes by Leibniz, in particular concerning the controversy of who first formulated calculus (although he published it later, Newton argued that he developed it earlier).
 * The Wren Library, Trinity College Cambridge has Newton's own copy of the first edition with handwritten annotations.
 * A first edition is also located in the archives of the library at the Georgia Institute of Technology. The Georgia Tech library is also home to a second and third edition.
 * The University of Michigan Special Collections Library owns several early printings, including the first (1687), second (1713), second revised (1714), unnumbered (1723), and third (1726) editions of the Principia.
 * The Royal Astronomical Society holds a first edition, and two copies of the third edition.
 * The Royal Society in London holds John Flamsteed's first edition copy, and also the manuscript of the first edition. The manuscript is complete containing all three books but does not contain the figures and illustrations for the first edition.
 * The John J. Burns Library at Boston College contains a first edition as well as a 1723 copy published between the second and third editions.
 * Yale University owns multiple copies, with a first edition among the collection of Harvey Cushing in the Medical Historical Library of the Harvey Cushing/John Hay Whitney Medical Library, as well as a second edition, housed in the Beinecke Rare Book & Manuscript Library, presented by the author to the Yale College Library in 1714.
 * The George C. Gordon Library at the Worcester Polytechnic Institute holds a third edition copy.
 * The Gunnerus Library at the Norwegian University of Science and Technology in Trondheim holds a first edition copy of the Principia.
 * Haverford College Quaker & Special Collections owns a first edition of the Principia.
 * The Fellows Library at Winchester College owns a first edition of the Principia.
 * The Fellows' Library at Jesus College, Oxford owns a copy of the first edition and second edition.
 * The Old Library of Magdalen College, Oxford owns a first edition copy.
 * The Library of New College, Oxford owns a first edition copy.
 * The Library of Somerville College, Oxford owns a second edition copy.
 * The Southwest Research Institute in Texas owns a third edition copy dated 1726CE.
 * The Teleki-Bolyai Library in Târgu-Mures, first edition, 2-line imprint.
 * The Whipple Museum of the History of Science in Cambridge has a first-edition copy which had belonged to Robert Hooke.
 * The Pepys Library in Magdalene College, Cambridge, has Samuel Pepys' copy of the third edition.
 * University College London library holds a copy in 'Strong Room E' of its Rare Books collection.
 * The University of Wisconsin–Madison Memorial Library at Special Collections
 * The Harry Ransom Center at the University of Texas at Austin holds two first edition copies, one with manuscript additions and corrections.

Second edition, 1713
Two later editions were published by Newton: Newton had been urged to make a new edition of the Principia since the early 1690s, partly because copies of the first edition had already become very rare and expensive within a few years after 1687. Newton referred to his plans for a second edition in correspondence with Flamsteed in November 1694. Newton also maintained annotated copies of the first edition specially bound up with interleaves on which he could note his revisions; two of these copies still survive, but he had not completed the revisions by 1708. Newton had almost severed connections with one would-be editor, Nicolas Fatio de Duillier, and another, David Gregory seems not to have met with his approval and was also terminally ill, dying in 1708. Nevertheless, reasons were accumulating not to put off the new edition any longer. Richard Bentley, master of Trinity College, persuaded Newton to allow him to undertake a second edition, and in June 1708 Bentley wrote to Newton with a specimen print of the first sheet, at the same time expressing the (unfulfilled) hope that Newton had made progress towards finishing the revisions. It seems that Bentley then realised that the editorship was technically too difficult for him, and with Newton's consent he appointed Roger Cotes, Plumian professor of astronomy at Trinity, to undertake the editorship for him as a kind of deputy (but Bentley still made the publishing arrangements and had the financial responsibility and profit). The correspondence of 1709–1713 shows Cotes reporting to two masters, Bentley and Newton, and managing (and often correcting) a large and important set of revisions to which Newton sometimes could not give his full attention. Under the weight of Cotes' efforts, but impeded by priority disputes between Newton and Leibniz, and by troubles at the Mint, Cotes was able to announce publication to Newton on 30 June 1713. Bentley sent Newton only six presentation copies; Cotes was unpaid; Newton omitted any acknowledgement to Cotes.

Among those who gave Newton corrections for the Second Edition were: Firmin Abauzit, Roger Cotes and David Gregory. However, Newton omitted acknowledgements to some because of the priority disputes. John Flamsteed, the Astronomer Royal, suffered this especially.

The Second Edition was the basis of the first edition to be printed abroad, which appeared in Amsterdam in 1714.

Third edition, 1726
After his serious illness in 1722 and after the appearance of a reprint of the second edition in Amsterdam in 1723, the 80-year-old Newton began to revise once again the Principia in the fall of 1723. The third edition was published 25 March 1726, under the stewardship of Henry Pemberton, M.D., a man of the greatest skill in these matters...; Pemberton later said that this recognition was worth more to him than the two hundred guinea award from Newton.

In 1739–1742, two French priests, Pères Thomas LeSeur and François Jacquier (of the Minim order, but sometimes erroneously identified as Jesuits), produced with the assistance of J.-L. Calandrini an extensively annotated version of the Principia in the 3rd edition of 1726. Sometimes this is referred to as the Jesuit edition: it was much used, and reprinted more than once in Scotland during the 19th century.

Émilie du Châtelet also made a translation of Newton's Principia into French. Unlike LeSeur and Jacquier's edition, hers was a complete translation of Newton's three books and their prefaces. She also included a Commentary section where she fused the three books into a much clearer and easier to understand summary. She included an analytical section where she applied the new mathematics of calculus to Newton's most controversial theories. Previously, geometry was the standard mathematics used to analyse theories. Du Châtelet's translation is the only complete one to have been done in French and hers remains the standard French translation to this day.

Translations
Four full English translations of Newton's Principia have appeared, all based on Newton's 3rd edition of 1726. The first, from 1729, by Andrew Motte, was described by Newton scholar I. Bernard Cohen (in 1968) as "still of enormous value in conveying to us the sense of Newton's words in their own time, and it is generally faithful to the original: clear, and well written". The 1729 version was the basis for several republications, often incorporating revisions, among them a widely used modernised English version of 1934, which appeared under the editorial name of Florian Cajori (though completed and published only some years after his death). Cohen pointed out ways in which the 18th-century terminology and punctuation of the 1729 translation might be confusing to modern readers, but he also made severe criticisms of the 1934 modernised English version, and showed that the revisions had been made without regard to the original, also demonstrating gross errors "that provided the final impetus to our decision to produce a wholly new translation".

The second full English translation, into modern English, is the work that resulted from this decision by collaborating translators I. Bernard Cohen, Anne Whitman, and Julia Budenz; it was published in 1999 with a guide by way of introduction.

The third such translation is due to Ian Bruce, and appears, with many other translations of mathematical works of the 17th and 18th centuries, on his website.

The fourth complete English translation is due to Charles Leedham-Green, professor emeritus of mathematics at Queen Mary University of London, and was published in 2021 by Cambridge University Press. Prof. Leedham-Green was motivated to produce that translation, on which he worked for twenty years, in part because of his dissatisfaction with the work of Cohen, Whitman, and Budenz, whose translation of the Principia he found unnecessarily obscure. Leedham-Green's aim was to convey Newton's own reasoning and arguments in a way intelligible to a modern mathematical scientist. His translation is heavily annotated and his explanatory notes make use of the modern secondary literature on some of the more difficult technical aspects of Newton's work.

Dana Densmore and William H. Donahue have published a translation of the work's central argument, published in 1996, along with expansion of included proofs and ample commentary. The book was developed as a textbook for classes at St. John's College and the aim of this translation is to be faithful to the Latin text.

Varia

In 1977, the spacecraft Voyager 1 and 2 left earth for the interstellar space carrying a picture of a page from Newton's Principia Mathematica, as part of the Golden Record, a collection of messages from humanity to extraterrestrials.

In 2014, British astronaut Tim Peake named his upcoming mission to the International Space Station Principia after the book, in "honour of Britain's greatest scientist". Tim Peake's Principia launched on 15 December 2015 aboard Soyuz TMA-19M.

Latin versions
First edition (1687)
 * Trinity College Library, Cambridge High resolution digitised version of Newton's own copy of the first edition, with annotations.
 * Cambridge University, Cambridge Digital Library High resolution digitised version of Newton's own copy of the first edition, interleaved with blank pages for his annotations and corrections.
 * 1687: Newton's Principia, first edition (1687, in Latin). High-resolution presentation of the Gunnerus Library copy.
 * 1687: Newton's Principia, first edition (1687, in Latin).
 * Project Gutenberg.
 * ETH-Bibliothek Zürich. From the library of Gabriel Cramer.
 * Philosophiæ Naturalis Principia Mathematica From the Rare Book and Special Collection Division at the Library of Congress

Second edition (1713)
 * ETH-Bibliothek Zürich.
 * ETH-Bibliothek Zürich (pirated Amsterdam reprint of 1723).
 * Philosophiæ naturalis principia mathematica (Adv.b.39.2), a 1713 edition with annotations by Newton in the collections of Cambridge University Library and fully digitised in Cambridge Digital Library

Third edition (1726)
 * ETH-Bibliothek Zürich.

Later Latin editions
 * Principia (in Latin, annotated). 1833 Glasgow reprint (volume 1) with Books 1 and 2 of the Latin edition annotated by Leseur, Jacquier and Calandrini 1739–42 (described above).
 * Archive.org (1871 reprint of the 1726 edition)

English translations

 * Andrew Motte, 1729, first English translation of third edition (1726)
 * WikiSource, Partial
 * Google books, vol. 1 with Book 1.
 * Internet Archive, vol. 2 with Books 2 and 3. (Book 3 starts at p.200.) (Google's metadata wrongly labels this vol. 1).
 * Partial HTML
 * Robert Thorpe 1802 translation
 * N. W. Chittenden, ed., 1846 "American Edition" a partly modernised English version, largely the Motte translation of 1729.
 * Wikisource
 * Archive.org #1
 * Archive.org #2
 * eBooks@Adelaide eBooks@Adelaide
 * Percival Frost 1863 translation with interpolations Archive.org
 * Florian Cajori 1934 modernisation of 1729 Motte and 1802 Thorpe translations
 * Ian Bruce has made a complete translation of the third edition, with notes, on his website.
 * Charles Leedham-Green 2021 has published a complete and heavily annotated translation. Cambridge; Cambridge University Press.

Other links

 * David R. Wilkins of the School of Mathematics at Trinity College, Dublin has transcribed a few sections into TeX and METAPOST and made the source, as well as a formatted PDF available at Extracts from the Works of Isaac Newton.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
User:Hellbent

Musician, local troublemaker

http://www.hogwaller.com

title: User:Hellbent


text:
Polyvinylpyrrolidone

Polyvinylpyrrolidone (PVP), also commonly called polyvidone or povidone, is a water-soluble polymer compound made from the monomer N-vinylpyrrolidone. PVP is available in a range of molecular weights and related viscosities, and can be selected according to the desired application properties.

Medical

There are high-purity injectable grades of PVP available on the market, for specific use in intravenous, intramuscular, and subcutaneous applications.

It is used as a binder in many pharmaceutical tablets; it simply passes through the body when taken orally.

PVP added to iodine forms a complex called povidone-iodine that possesses disinfectant properties. This complex is used in various products such as solutions, ointment, pessaries, liquid soaps, and surgical scrubs. It is sold under the trade names Pyodine and Betadine, among others.

It is used in pleurodesis (fusion of the pleura because of incessant pleural effusions). For this purpose, povidone-iodine is as effective and safe as talc, and may be preferred because of its easy availability and low cost.

PVP is used in some contact lenses and their packaging solutions. It reduces friction, thus acting as a lubricant, or wetting agent, built into the lens. Examples of this use include Bausch & Lomb's Ultra contact lenses with MoistureSeal Technology and Air Optix contact lens packaging solution (as an ingredient called "copolymer 845").

PVP is used as a lubricant in some eye drops, e.g. Bausch & Lomb's Soothe.

PVP was used as a plasma volume expander for trauma victims after the 1950s. It is not preferred as a volume expander due to its ability to provoke histamine release and also interfere with blood grouping.

Autopsies have found that crospovidone (PVPP) contributes to pulmonary vascular injury in substance abusers who have injected pharmaceutical tablets intended for oral consumption. The long-term effects of crospovidone or povidone within the lung are unknown.

Technical
PVP is also used in many technical applications:
 * as a special additive for batteries, ceramics, fiberglass, inks, and inkjet paper, and in the chemical-mechanical planarization process
 * as an emulsifier and disintegrant for solution polymerization
 * to increase resolution in photoresists for cathode ray tubes (CRT)
 * in aqueous metal quenching
 * for production of membranes, such as dialysis and water purification filters
 * as a binder and complexation agent in agricultural applications such as crop protection, seed treatment and coating
 * as a thickening agent in tooth whitening gels
 * as an aid for increasing the solubility of drugs in liquid and semi-liquid dosage forms (syrups, soft gelatine capsules) and as an inhibitor of recrystallisation
 * as an additive to Doro's RNA extraction buffer
 * as a liquid-phase dispersion enhancing agent in DOSY NMR
 * as a surfactant, reducing agent, shape controlling agent and dispersant in nanoparticle synthesis and their self-assembly
 * as a stabilizing agent in all inorganic solar cells

Other uses
PVP binds to polar molecules exceptionally well, owing to its polarity. This has led to its application in coatings for photo-quality ink-jet papers and transparencies, as well as in inks for inkjet printers.

PVP is also used in personal care products, such as shampoos and toothpastes, in paints, and adhesives that must be moistened, such as old-style postage stamps and envelopes. It has also been used in contact lens solutions and in steel-quenching solutions. PVP is the basis of the early formulas for hair sprays and hair gels, and still continues to be a component of some.

As a food additive, PVP is a stabilizer and has E number E1201. PVPP (crospovidone) is E1202. It is also used in the wine industry as a fining agent for white wine and some beers.

In in-vitro fertilisation laboratories, polyvinylpyrrolidone is used to slow down spermatozoa in order to capture them for e.g. ICSI.

In molecular biology, PVP can be used as a blocking agent during Southern blot analysis as a component of Denhardt's buffer. It is also exceptionally good at absorbing polyphenols during DNA purification. Polyphenols are common in many plant tissues and can deactivate proteins if not removed and therefore inhibit many downstream reactions like PCR.

In microscopy, PVP is useful for making an aqueous mounting medium.

PVP can be used to screen for phenolic properties, as referenced in a 2000 study on the effect of plant extracts on insulin production.

Safety
The U.S. Food and Drug Administration (FDA) has approved this chemical for many uses, and it is generally recognized as safe (GRAS). PVP is included in the Inactive Ingredient Database for use in oral, topical, and injectable formulations.

However, there have been documented cases of allergic reactions to PVP/povidone, particularly regarding subcutaneous (applied under the skin) use and situations where the PVP has come in contact with autologous serum (internal blood fluids) and mucous membranes.

Examples of documented allergic reactions:
 * A boy had an anaphylactic response after application of PVP-Iodine for treatment of impetigo. He was found to be allergic to the PVP component of the solution.
 * A woman had experienced urticaria (hives) from various hair products, later found to contain PVP. The woman had an anaphylactic response after povidone-iodine solution was applied internally during a surgery. She was found to be allergic to PVP.
 * A man experiencing anaphylaxis after taking acetaminophen tablets orally was found to be allergic to PVP.

Additionally, Povidone is commonly used in conjunction with other chemicals. Some of these, such as iodine, are blamed for allergic responses. Yet subsequent testing results in some patients show no signs of allergy to the suspect chemical. Allergies attributed to these other chemicals may possibly be caused by the PVP instead.

Properties
PVP is soluble in water and other polar solvents. For example, it is soluble in various alcohols, such as methanol and ethanol, as well as in more exotic solvents like the deep eutectic solvent formed by choline chloride and urea (Relin). When dry it is a light flaky hygroscopic powder, readily absorbing up to 40% of its weight in atmospheric water. In solution, it has excellent wetting properties and readily forms films. This makes it good as a coating or an additive to coatings.

A 2014 study found fluorescent properties of PVP and its oxidized hydrolyzate.

History
PVP was first synthesized by BASF chemist Walter Reppe, and a patent was filed in 1939 for one of the derivatives of acetylene chemistry. PVP was initially used as a blood plasma substitute and later in a wide variety of applications in medicine, pharmacy, cosmetics and industrial production. BASF continues to make PVP, including a pharmaceutical portfolio under the brand name of Kollidon.

title: Polyvinylpyrrolidone


text:
Amanda (software)

The Advanced Maryland Automatic Network Disk Archiver (Amanda) is an open source computer archiving tool that is able to back up data residing on multiple computers on a network. It uses a client–server model, where the server contacts each client to perform a backup at a scheduled time.

Amanda was initially developed at the University of Maryland and is released under a BSD-style license. Amanda is available both as a free community edition and fully supported enterprise edition. Amanda runs on almost any Unix or Unix-like systems. Amanda supports Windows systems using Samba or a native Win32 client with support for open files.

Amanda supports both tape-based and disk-based backup, and provides some useful functionality not available in other backup products. Amanda supports tape-spanning i.e. if a backup set does not fit in one tape, it will be split into multiple tapes.

Enterprise edition
A commercial version of Amanda was developed by the company Zmanda. It includes a management graphical user interface (GUI) and other features such as scheduler, plugin framework, and an optional cloud backup service support. The cloud backup option uses the Amazon S3 service from Amazon Web Services as the cloud storage provider and enables safe offsite storage of the Amanda backup data. The plugin framework allows for application-specific backups and is used by Amanda Enterprise to support applications such as Oracle database, Samba network share, NDMP, etc. Amanda Enterprise also supports image-level backup of live virtual machine running on VMware infrastructure.

title: Amanda (software)


text:
Pathology

Pathology is the study of disease and injury. The word pathology also refers to the study of disease in general, incorporating a wide range of biology research fields and medical practices. However, when used in the context of modern medical treatment, the term is often used in a narrower fashion to refer to processes and tests that fall within the contemporary medical field of "general pathology", an area that includes a number of distinct but inter-related medical specialties that diagnose disease, mostly through analysis of tissue and human cell samples. Idiomatically, "a pathology" may also refer to the predicted or actual progression of particular diseases (as in the statement "the many different forms of cancer have diverse pathologies", in which case a more proper choice of word would be "pathophysiologies"), and the affix pathy is sometimes used to indicate a state of disease in cases of both physical ailment (as in cardiomyopathy) and psychological conditions (such as psychopathy). A physician practicing pathology is called a pathologist.

As a field of general inquiry and research, pathology addresses components of disease: cause, mechanisms of development (pathogenesis), structural alterations of cells (morphologic changes), and the consequences of changes (clinical manifestations). In common medical practice, general pathology is mostly concerned with analyzing known clinical abnormalities that are markers or precursors for both infectious and non-infectious disease, and is conducted by experts in one of two major specialties, anatomical pathology and clinical pathology. Further divisions in specialty exist on the basis of the involved sample types (comparing, for example, cytopathology, hematopathology, and histopathology), organs (as in renal pathology), and physiological systems (oral pathology), as well as on the basis of the focus of the examination (as with forensic pathology).

Pathology is a significant field in modern medical diagnosis and medical research.

History
The study of pathology, including the detailed examination of the body, including dissection and inquiry into specific maladies, dates back to antiquity. Rudimentary understanding of many conditions was present in most early societies and is attested to in the records of the earliest historical societies, including those of the Middle East, India, and China. By the Hellenic period of ancient Greece, a concerted causal study of disease was underway (see Medicine in ancient Greece), with many notable early physicians (such as Hippocrates, for whom the modern Hippocratic Oath is named) having developed methods of diagnosis and prognosis for a number of diseases. The medical practices of the Romans and those of the Byzantines continued from these Greek roots, but, as with many areas of scientific inquiry, growth in understanding of medicine stagnated somewhat after the Classical Era, but continued to slowly develop throughout numerous cultures. Notably, many advances were made in the medieval era of Islam (see Medicine in medieval Islam), during which numerous texts of complex pathologies were developed, also based on the Greek tradition. Even so, growth in complex understanding of disease mostly languished until knowledge and experimentation again began to proliferate in the Renaissance, Enlightenment, and Baroque eras, following the resurgence of the empirical method at new centers of scholarship. By the 17th century, the study of rudimentary microscopy was underway and examination of tissues had led British Royal Society member Robert Hooke to coin the word "cell", setting the stage for later germ theory.

Modern pathology began to develop as a distinct field of inquiry during the 19th Century through natural philosophers and physicians that studied disease and the informal study of what they termed "pathological anatomy" or "morbid anatomy". However, pathology as a formal area of specialty was not fully developed until the late 19th and early 20th centuries, with the advent of detailed study of microbiology. In the 19th century, physicians had begun to understand that disease-causing pathogens, or "germs" (a catch-all for disease-causing, or pathogenic, microbes, such as bacteria, viruses, fungi, amoebae, molds, protists, and prions) existed and were capable of reproduction and multiplication, replacing earlier beliefs in humors or even spiritual agents, that had dominated for much of the previous 1,500 years in European medicine. With the new understanding of causative agents, physicians began to compare the characteristics of one germ's symptoms as they developed within an affected individual to another germ's characteristics and symptoms. This approach led to the foundational understanding that diseases are able to replicate themselves, and that they can have many profound and varied effects on the human host. To determine causes of diseases, medical experts used the most common and widely accepted assumptions or symptoms of their times, a general principle of approach that persists into modern medicine.

Modern medicine was particularly advanced by further developments of the microscope to analyze tissues, to which Rudolf Virchow gave a significant contribution, leading to a slew of research developments. By the late 1920s to early 1930s pathology was deemed a medical specialty. Combined with developments in the understanding of general physiology, by the beginning of the 20th century, the study of pathology had begun to split into a number of distinct fields, resulting in the development of a large number of modern specialties within pathology and related disciplines of diagnostic medicine.

Etymology
The term pathology comes from the Ancient Greek roots of pathos (πάθος), meaning "experience" or "suffering" and -logia (-λογία), "study of". The Latin term is of early sixteenth-century origin and became increasingly popularized after the 1530s.

General pathology

The modern practice of pathology is divided into a number of subdisciplines within the distinct but deeply interconnected aims of biological research and medical practice. Biomedical research into disease incorporates the work of a vast variety of life science specialists, whereas, in most parts of the world, to be licensed to practice pathology as a medical specialty, one has to complete medical school and secure a license to practice medicine. Structurally, the study of disease is divided into many different fields that study or diagnose markers for disease using methods and technologies particular to specific scales, organs, and tissue types.

Anatomical pathology
Anatomical pathology (Commonwealth) or anatomic pathology (United States) is a medical specialty that is concerned with the diagnosis of disease based on the gross, microscopic, chemical, immunologic and molecular examination of organs, tissues, and whole bodies (as in a general examination or an autopsy). Anatomical pathology is itself divided into subfields, the main divisions being surgical pathology, cytopathology, and forensic pathology. Anatomical pathology is one of two main divisions of the medical practice of pathology, the other being clinical pathology, the diagnosis of disease through the laboratory analysis of bodily fluids and tissues. Sometimes, pathologists practice both anatomical and clinical pathology, a combination known as general pathology.

Cytopathology

Cytopathology (sometimes referred to as "cytology") is a branch of pathology that studies and diagnoses diseases on the cellular level. It is usually used to aid in the diagnosis of cancer, but also helps in the diagnosis of certain infectious diseases and other inflammatory conditions as well as thyroid lesions, diseases involving sterile body cavities (peritoneal, pleural, and cerebrospinal), and a wide range of other body sites. Cytopathology is generally used on samples of free cells or tissue fragments (in contrast to histopathology, which studies whole tissues) and cytopathologic tests are sometimes called smear tests because the samples may be smeared across a glass microscope slide for subsequent staining and microscopic examination. However, cytology samples may be prepared in other ways, including cytocentrifugation.

Dermatopathology

Dermatopathology is a subspecialty of anatomic pathology that focuses on the skin and the rest of the integumentary system as an organ. It is unique, in that there are two paths a physician can take to obtain the specialization. All general pathologists and general dermatologists train in the pathology of the skin, so the term dermatopathologist denotes either of these who has reached a certainly level of accreditation and experience; in the US, either a general pathologist or a dermatologist can undergo a 1 to 2 year fellowship in the field of dermatopathology. The completion of this fellowship allows one to take a subspecialty board examination, and becomes a board certified dermatopathologist. Dermatologists are able to recognize most skin diseases based on their appearances, anatomic distributions, and behavior. Sometimes, however, those criteria do not lead to a conclusive diagnosis, and a skin biopsy is taken to be examined under the microscope using usual histological tests. In some cases, additional specialized testing needs to be performed on biopsies, including immunofluorescence, immunohistochemistry, electron microscopy, flow cytometry, and molecular-pathologic analysis. One of the greatest challenges of dermatopathology is its scope. More than 1500 different disorders of the skin exist, including cutaneous eruptions ("rashes") and neoplasms. Therefore, dermatopathologists must maintain a broad base of knowledge in clinical dermatology, and be familiar with several other specialty areas in Medicine.

Forensic pathology

Forensic pathology focuses on determining the cause of death by post-mortem examination of a corpse or partial remains. An autopsy is typically performed by a coroner or medical examiner, often during criminal investigations; in this role, coroners and medical examiners are also frequently asked to confirm the identity of a corpse. The requirements for becoming a licensed practitioner of forensic pathology varies from country to country (and even within a given nation ) but typically a minimal requirement is a medical doctorate with a specialty in general or anatomical pathology with subsequent study in forensic medicine. The methods forensic scientists use to determine death include examination of tissue specimens to identify the presence or absence of natural disease and other microscopic findings, interpretations of toxicology on body tissues and fluids to determine the chemical cause of overdoses, poisonings or other cases involving toxic agents, and examinations of physical trauma. Forensic pathology is a major component in the trans-disciplinary field of forensic science.

Histopathology

Histopathology refers to the microscopic examination of various forms of human tissue. Specifically, in clinical medicine, histopathology refers to the examination of a biopsy or surgical specimen by a pathologist, after the specimen has been processed and histological sections have been placed onto glass slides. This contrasts with the methods of cytopathology, which uses free cells or tissue fragments. Histopathological examination of tissues starts with surgery, biopsy, or autopsy. The tissue is removed from the body of an organism and then placed in a fixative that stabilizes the tissues to prevent decay. The most common fixative is formalin, although frozen section fixing is also common. To see the tissue under a microscope, the sections are stained with one or more pigments. The aim of staining is to reveal cellular components; counterstains are used to provide contrast. Histochemistry refers to the science of using chemical reactions between laboratory chemicals and components within tissue. The histological slides are then interpreted diagnostically and the resulting pathology report describes the histological findings and the opinion of the pathologist. In the case of cancer, this represents the tissue diagnosis required for most treatment protocols.

Neuropathology

Neuropathology is the study of disease of nervous system tissue, usually in the form of either surgical biopsies or sometimes whole brains in the case of autopsy. Neuropathology is a subspecialty of anatomic pathology, neurology, and neurosurgery. In many English-speaking countries, neuropathology is considered a subfield of anatomical pathology. A physician who specializes in neuropathology, usually by completing a fellowship after a residency in anatomical or general pathology, is called a neuropathologist. In day-to-day clinical practice, a neuropathologist is a consultant for other physicians. If a disease of the nervous system is suspected, and the diagnosis cannot be made by less invasive methods, a biopsy of nervous tissue is taken from the brain or spinal cord to aid in diagnosis. Biopsy is usually requested after a mass is detected by medical imaging. With autopsies, the principal work of the neuropathologist is to help in the post-mortem diagnosis of various conditions that affect the central nervous system. Biopsies can also consist of the skin. Epidermal nerve fiber density testing (ENFD) is a more recently developed neuropathology test in which a punch skin biopsy is taken to identify small fiber neuropathies by analyzing the nerve fibers of the skin. This test is becoming available in select labs as well as many universities; it replaces the traditional nerve biopsy test as less invasive.

Pulmonary pathology
Pulmonary pathology is a subspecialty of anatomic (and especially surgical) pathology that deals with diagnosis and characterization of neoplastic and non-neoplastic diseases of the lungs and thoracic pleura. Diagnostic specimens are often obtained via bronchoscopic transbronchial biopsy, CT-guided percutaneous biopsy, or video-assisted thoracic surgery. These tests can be necessary to diagnose between infection, inflammation, or fibrotic conditions.

Renal pathology

Renal pathology is a subspecialty of anatomic pathology that deals with the diagnosis and characterization of disease of the kidneys. In a medical setting, renal pathologists work closely with nephrologists and transplant surgeons, who typically obtain diagnostic specimens via percutaneous renal biopsy. The renal pathologist must synthesize findings from traditional microscope histology, electron microscopy, and immunofluorescence to obtain a definitive diagnosis. Medical renal diseases may affect the glomerulus, the tubules and interstitium, the vessels, or a combination of these compartments.

Surgical pathology

Surgical pathology is one of the primary areas of practice for most anatomical pathologists. Surgical pathology involves the gross and microscopic examination of surgical specimens, as well as biopsies submitted by surgeons and non-surgeons such as general internists, medical subspecialists, dermatologists, and interventional radiologists. Often an excised tissue sample is the best and most definitive evidence of disease (or lack thereof) in cases where tissue is surgically removed from a patient. These determinations are usually accomplished by a combination of gross (i.e., macroscopic) and histologic (i.e., microscopic) examination of the tissue, and may involve evaluations of molecular properties of the tissue by immunohistochemistry or other laboratory tests.

There are two major types of specimens submitted for surgical pathology analysis: biopsies and surgical resections. A biopsy is a small piece of tissue removed primarily for surgical pathology analysis, most often in order to render a definitive diagnosis. Types of biopsies include core biopsies, which are obtained through the use of large-bore needles, sometimes under the guidance of radiological techniques such as ultrasound, CT scan, or magnetic resonance imaging. Incisional biopsies are obtained through diagnostic surgical procedures that remove part of a suspicious lesion, whereas excisional biopsies remove the entire lesion, and are similar to therapeutic surgical resections. Excisional biopsies of skin lesions and gastrointestinal polyps are very common. The pathologist's interpretation of a biopsy is critical to establishing the diagnosis of a benign or malignant tumor, and can differentiate between different types and grades of cancer, as well as determining the activity of specific molecular pathways in the tumor. Surgical resection specimens are obtained by the therapeutic surgical removal of an entire diseased area or organ (and occasionally multiple organs). These procedures are often intended as definitive surgical treatment of a disease in which the diagnosis is already known or strongly suspected, but pathological analysis of these specimens remains important in confirming the previous diagnosis.

Clinical pathology
Clinical pathology is a medical specialty that is concerned with the diagnosis of disease based on the laboratory analysis of bodily fluids such as blood and urine, as well as tissues, using the tools of chemistry, clinical microbiology, hematology and molecular pathology. Clinical pathologists work in close collaboration with medical technologists, hospital administrations, and referring physicians. Clinical pathologists learn to administer a number of visual and microscopic tests and an especially large variety of tests of the biophysical properties of tissue samples involving automated analysers and cultures. Sometimes the general term "laboratory medicine specialist" is used to refer to those working in clinical pathology, including medical doctors, Ph.D.s and doctors of pharmacology. Immunopathology, the study of an organism's immune response to infection, is sometimes considered to fall within the domain of clinical pathology.

Hematopathology

Hematopathology is the study of diseases of blood cells (including constituents such as white blood cells, red blood cells, and platelets) and the tissues, and organs comprising the hematopoietic system. The term hematopoietic system refers to tissues and organs that produce and/or primarily host hematopoietic cells and includes bone marrow, the lymph nodes, thymus, spleen, and other lymphoid tissues. In the United States, hematopathology is a board certified subspecialty (licensed under the American Board of Pathology) practiced by those physicians who have completed a general pathology residency (anatomic, clinical, or combined) and an additional year of fellowship training in hematology. The hematopathologist reviews biopsies of lymph nodes, bone marrows and other tissues involved by an infiltrate of cells of the hematopoietic system. In addition, the hematopathologist may be in charge of flow cytometric and/or molecular hematopathology studies.

Molecular pathology
Molecular pathology is focused upon the study and diagnosis of disease through the examination of molecules within organs, tissues or bodily fluids. Molecular pathology is multidisciplinary by nature and shares some aspects of practice with both anatomic pathology and clinical pathology, molecular biology, biochemistry, proteomics and genetics. It is often applied in a context that is as much scientific as directly medical and encompasses the development of molecular and genetic approaches to the diagnosis and classification of human diseases, the design and validation of predictive biomarkers for treatment response and disease progression, and the susceptibility of individuals of different genetic constitution to particular disorders. The crossover between molecular pathology and epidemiology is represented by a related field "molecular pathological epidemiology". Molecular pathology is commonly used in diagnosis of cancer and infectious diseases. Molecular Pathology is primarily used to detect cancers such as melanoma, brainstem glioma, brain tumors as well as many other types of cancer and infectious diseases. Techniques are numerous but include quantitative polymerase chain reaction (qPCR), multiplex PCR, DNA microarray, in situ hybridization, DNA sequencing, antibody-based immunofluorescence tissue assays, molecular profiling of pathogens, and analysis of bacterial genes for antimicrobial resistance. Techniques used are based on analyzing samples of DNA and RNA. Pathology is widely used for gene therapy and disease diagnosis.

Oral and maxillofacial pathology

Oral and Maxillofacial Pathology is one of nine dental specialties recognized by the American Dental Association, and is sometimes considered a specialty of both dentistry and pathology. Oral Pathologists must complete three years of post doctoral training in an accredited program and subsequently obtain diplomate status from the American Board of Oral and Maxillofacial Pathology. The specialty focuses on the diagnosis, clinical management and investigation of diseases that affect the oral cavity and surrounding maxillofacial structures including but not limited to odontogenic, infectious, epithelial, salivary gland, bone and soft tissue pathologies. It also significantly intersects with the field of dental pathology. Although concerned with a broad variety of diseases of the oral cavity, they have roles distinct from otorhinolaryngologists ("ear, nose, and throat" specialists), and speech pathologists, the latter of which helps diagnose many neurological or neuromuscular conditions relevant to speech phonology or swallowing. Owing to the availability of the oral cavity to non-invasive examination, many conditions in the study of oral disease can be diagnosed, or at least suspected, from gross examination, but biopsies, cell smears, and other tissue analysis remain important diagnostic tools in oral pathology.

Medical training and accreditation

Becoming a pathologist generally requires specialty-training after medical school, but individual nations vary some in the medical licensing required of pathologists. In the United States, pathologists are physicians (D.O. or M.D.) who have completed a four-year undergraduate program, four years of medical school training, and three to four years of postgraduate training in the form of a pathology residency. Training may be within two primary specialties, as recognized by the American Board of Pathology: [anatomical pathology and clinical pathology, each of which requires separate board certification. The American Osteopathic Board of Pathology also recognizes four primary specialties: anatomic pathology, dermatopathology, forensic pathology, and laboratory medicine. Pathologists may pursue specialised fellowship training within one or more subspecialties of either anatomical or clinical pathology. Some of these subspecialties permit additional board certification, while others do not.

In the United Kingdom, pathologists are physicians licensed by the UK General Medical Council. The training to become a pathologist is under the oversight of the Royal College of Pathologists. After four to six years of undergraduate medical study, trainees proceed to a two-year foundation program. Full-time training in histopathology currently lasts between five and five and a half years and includes specialist training in surgical pathology, cytopathology, and autopsy pathology. It is also possible to take a Royal College of Pathologists diploma in forensic pathology, dermatopathology, or cytopathology, recognising additional specialist training and expertise and to get specialist accreditation in forensic pathology, pediatric pathology, and neuropathology. All postgraduate medical training and education in the UK is overseen by the General Medical Council.

In France, pathology is separated into two distinct specialties, anatomical pathology, and clinical pathology. Residencies for both lasts four years. Residency in anatomical pathology is open to physicians only, while clinical pathology is open to both physicians and pharmacists. At the end of the second year of clinical pathology residency, residents can choose between general clinical pathology and a specialization in one of the disciplines, but they can not practice anatomical pathology, nor can anatomical pathology residents practice clinical pathology.

Overlap with other diagnostic medicine
Though separate fields in terms of medical practice, a number of areas of inquiry in medicine and medical science either overlap greatly with general pathology, work in tandem with it, or contribute significantly to the understanding of the pathology of a given disease or its course in an individual. As a significant portion of all general pathology practice is concerned with cancer, the practice of oncology makes extensive use of both anatomical and clinical pathology in diagnosis and treatment. In particular, biopsy, resection, and blood tests are all examples of pathology work that is essential for the diagnoses of many kinds of cancer and for the staging of cancerous masses. In a similar fashion, the tissue and blood analysis techniques of general pathology are of central significance to the investigation of serious infectious disease and as such inform significantly upon the fields of epidemiology, etiology, immunology, and parasitology. General pathology methods are of great importance to biomedical research into disease, wherein they are sometimes referred to as "experimental" or "investigative" pathology.

Medical imaging is the generating of visual representations of the interior of a body for clinical analysis and medical intervention. Medical imaging reveals details of internal physiology that help medical professionals plan appropriate treatments for tissue infection and trauma. Medical imaging is also central in supplying the biometric data necessary to establish baseline features of anatomy and physiology so as to increase the accuracy with which early or fine-detail abnormalities are detected. These diagnostic techniques are often performed in combination with general pathology procedures and are themselves often essential to developing new understanding of the pathogenesis of a given disease and tracking the progress of disease in specific medical cases. Examples of important subdivisions in medical imaging include radiology (which uses the imaging technologies of X-ray radiography) magnetic resonance imaging, medical ultrasonography (or ultrasound), endoscopy, elastography, tactile imaging, thermography, medical photography, nuclear medicine and functional imaging techniques such as positron emission tomography. Though they do not strictly relay images, readings from diagnostics tests involving electroencephalography, magnetoencephalography, and electrocardiography often give hints as to the state and function of certain tissues in the brain and heart respectively.

Pathology informatics
Pathology informatics is a subfield of health informatics. It is the use of information technology in pathology. It encompasses pathology laboratory operations, data analysis, and the interpretation of pathology-related information.

Key aspects of pathology informatics include:
 * Laboratory information management systems (LIMS): Implementing and managing computer systems specifically designed for pathology departments. These systems help in tracking and managing patient specimens, results, and other pathology data.
 * Digital pathology: Involves the use of digital technology to create, manage, and analyze pathology images. This includes side scanning and automated image analysis.
 * Telepathology: Using technology to enable remote pathology consultation and collaboration.
 * Quality assurance and reporting: Implementing informatics solutions to ensure the quality and accuracy of pathology processes.

Psychopathology
Psychopathology is the study of mental illness, particularly of severe disorders. Informed heavily by both psychology and neurology, its purpose is to classify mental illness, elucidate its underlying causes, and guide clinical psychiatric treatment accordingly. Although diagnosis and classification of mental norms and disorders is largely the purview of psychiatry—the results of which are guidelines such as the Diagnostic and Statistical Manual of Mental Disorders, which attempt to classify mental disease mostly on behavioural evidence, though not without controversy —the field is also heavily, and increasingly, informed upon by neuroscience and other of the biological cognitive sciences. Mental or social disorders or behaviours seen as generally unhealthy or excessive in a given individual, to the point where they cause harm or severe disruption to the person's lifestyle, are often called "pathological" (e.g., pathological gambling or pathological liar).

Non-humans
Although the vast majority of lab work and research in pathology concerns the development of disease in humans, pathology is of significance throughout the biological sciences. Two main catch-all fields exist to represent most complex organisms capable of serving as host to a pathogen or other form of disease: veterinary pathology (concerned with all non-human species of kingdom of Animalia) and phytopathology, which studies disease in plants.

Veterinary pathology
Veterinary pathology covers a vast array of species, but with a significantly smaller number of practitioners, so understanding of disease in non-human animals, especially as regards veterinary practice, varies considerably by species. Nevertheless, significant amounts of pathology research are conducted on animals, for two primary reasons: 1) The origins of diseases are typically zoonotic in nature, and many infectious pathogens have animal vectors and, as such, understanding the mechanisms of action for these pathogens in non-human hosts is essential to the understanding and application of epidemiology and 2) those animals that share physiological and genetic traits with humans can be used as surrogates for the study of the disease and potential treatments as well as the effects of various synthetic products. For this reason, as well as their roles as livestock and companion animals, mammals generally have the largest body of research in veterinary pathology. Animal testing remains a controversial practice, even in cases where it is used to research treatment for human disease. As in human medical pathology, the practice of veterinary pathology is customarily divided into the two main fields of anatomical and clinical pathology.

Plant pathology
Although the pathogens and their mechanics differ greatly from those of animals, plants are subject to a wide variety of diseases, including those caused by fungi, oomycetes, bacteria, viruses, viroids, virus-like organisms, phytoplasmas, protozoa, nematodes and parasitic plants. Damage caused by insects, mites, vertebrate, and other small herbivores is not considered a part of the domain of plant pathology. The field is connected to plant disease epidemiology and especially concerned with the horticulture of species that are of high importance to the human diet or other human utility.

title: Pathology