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of harmonic proportionals, there be taken any series of equidistant terms, that series will be harmonically proportional And this kind of proportion has several other properties common with arithmetic and geometric proportions.

When three terms are so disposed, that the difference of the 1st and 2d difference of the 2d and 3d :: 3d: 1st, they are said to be in a contra-harmonic proportion. Thus 6, 5, 3, and 12, 10, 4, are contra-harmonics. For 6 -5:5 3:: 3:6; and 12 - 10: 10 4 4 12. Or, supposing h greater than n, if the 2d term be greater than the 1st: Then h n + n2, h2 + n2, h2 + hn, are contra-harmonics, for h n · h2:n::h+hn hn + n2.

hn

But if the 1st term exceeds the second, h2 + hn, h2 + n2, h n + n2, are contraharmonics. For hn2. - n2: h2 - hn:: h n + n2 : h2 + h n.

PROPOSITION, in logic, part of an argument wherein some quality, either negative or positive, is attributed to a subject, as God is just." While the comparing of our ideas is considered merely as the act of the mind, assembling them together, and joining or disjoining them according to the result of its perceptions, this operation is called judgment. But when these judgments are expressed in words, they then bear the name of propositions. Hence a proposition is a sentence expressing some judgment of the mind, whereby two or more ideas are affirmed to agree or disagree: and as our judgments include at least two ideas, one of which is affirmed or denied of the other; so a proposition must have terms corresponding to these ideas. The idea of which we affirm or deny, and of course the term expressing that idea, is called the subject of the proposition; and the idea affirmed or denied, as also the term answering to it, is called its predicate; thus in the proposition, God is omnipotent, God is the subject, it being of him VOL. X.

that we affirm omnipotence: and omnipotent is the predicate, because we affirm the idea expressed by that word to belong to God.

PROPOSITION, in mathematics, is either some truth advanced, and shown to be such by demonstration, or some operation proposed and its solution shown If the proposition be deduced from several theoretical definitions compared together, it is called a theorem; if from a praxis, or series of operations, it is called a problem.

PROPOSITION, in poetry, the first part of a poem wherein the author proposes briefly, and in general, what he is to say in the body of his work. It should comprehend only the matter of the poem, that is, the action and the persons that act. Horace prescribes modesty and simplicity in the proposition, and would not have the poet promise too much, nor raise in the reader too great ideas of what he is going to relate.

PROSERPINACA, in botany, a genus of the Triandria Trigynia class and order. Natural order of Inundatæ. Hydrocharides, Jussieu. Essential character: calyx three parted, superior: corolla none; drupe with a three-celled nut. There is but one species, viz P. palustris, a native of Virginia in marshes.

PROSODY, that part of grammar which treats of the quantities and accents of syllables, and the manner of making ver

ses.

The English prosody turns chiefly on two things, numbers and rhyme.

PROSONOMASIA, a figure in rheto ric, whereby allusion is made to the likeness of a sound in several names or words.

PROSOPIS, in botany, a genus of the Decandria Monogynia class and order. Natural order of Lomentaceæ. Leguminosa, Jussieu. Essential character: calyx bell-shaped, five-toothed; stigma simple; legume linear, many-seeded. There is but one species, viz. P. spicigera; it is a native of most parts of the Coromandel coast, flowering during the cold season; the pod of this tree is the only part used; it is nearly an inch in circumference, and from six to twelve inches long; when ripe, it is brown and smooth, containing besides the seeds, a large quantity of a brown mealy substance, which the natives eat; it has a sweetish agreeable taste.

PROSOPOPEIA, a figure in rhetoric, whereby we raise qualities, or things inanimate, into persons. This figure is divided into two parts: 1. when good and bad qualities, accidents, and things in.

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PROTEA. in botany, a genus of the Tetrandria Monogynia class and order. Natural order of Aggregatæ. Protea, Jussieu. Essential character: corolla fourcleft, or four-petalled; anthers linear, inserted into the petals below the tip; calyx proper, none; nut one-seeded, supe. rior. There are sixty-four species; these are all shrubs, and natives of the Cape of Good Hope.

PROTECTION of parliament. See ARREST and PRIVILEGE.

PROTEST, in law, is where one openly affirms, that he does either not at all, or but conditionally, yield his consent to any act, or to the proceeding of a judge in court, wherein his jurisdiction is doubtful, or to answer upon his oath further than by law he is bound. It is also that act, by which the holder of a foreign bill of exchange declares that such bill is dishonoured. Further, it is that act of a master, on his arrival with his ship from parts beyond the seas, to save him and his owners harmless and indemnified from any damage sustained in the goods of her lading, on account of storms. See BILLS OF EXCHANGE and INSURANCE.

PROTESTANTS, a term now applied to all Christians who, in any country or of any sect, dissent from the principles and discipline of the church of Rome This name was first given to the following princes of the German Empire; John, Elector of Saxony; George, Elector of Brandenburg, for Franconia; Ernest and Francis, Dukes of Lunenburg, the

the

Landgrave of Hesse, and the Prince of Anhalt. These princes, being seconded by thirteen imperial towns, viz. Stras. bourg, Ulm, Nuremberg, Constance, Rottingen, Windseim, Memmingen, Nortlin gen, Lindau, Kempten, Heilbron, Wissemberg, and St. Gall, solemnly protested against the decree of the Emperor Charles the Fifth, and the diet of Spires, by which it had been decreed to prohibit any fur ther innovations in religion. This Protest was made in the year 1529; from which time all who have renounced, or never agreed to, the doctrines of the Romish church, have been denominated Protestants This class of Christians consequently includes the Huguenots in France, the Refugees in Holland, the Presbyterians in Scotland, as well as the Episcopalians and Nonconformists in England; together with a numerous body of Christians in America. The principal denominations of Protestants in England are, Episcopalians, or church of England, the Presbyterians, the Independents, and the Baptists, general and particular. These, however, have divided themselves into innumerable sects and parties; the prin cipal of which are denominated Arians and Socinians, or, more properly speaking, Unitarians, Sabellians, Calvinists, Sublapsarians, and Supralapsarians, Armini. ans, Baxterians, Antinomians, Brownists, Pædobaptists, Quakers, Methodists, Universalists, Sabbaterians, Moravians, Sandemanians, and Swedenborgians. Concerning these, and other Christian sects, the reader will find very impartial accounts, drawn up in a popular and perspicuous manner, and accompanied with many pious and sensible reflections on the nature and extent of Christian candour in the Rev. J. Evans's "Sketch of the Denominations of the Christian World," eleventh edition. But for more elaborate accounts of the Christian sects, the reader is referred to Dr. Rees's Cyclopedia; the theological, as indeed, every other de partment of which is conducted in a manner every way worthy the literature of a country, where the genuine principles of religious liberty are clearly understood, and extensively encouraged. The sects and parties into which the Protestant religion is divided, have furnished the Roman Catholics, on some occasions, with matter of triumph; asserting that the Protestant faith is deficient in the first mark or characteristic of a true church, viz. that of unity; and unbelievers have not neglected to avail themselves of this circumstance to vilify the Christian religion

altogether, as affording no sufficient data for religious truth, but engendering only strife, animosity, division, and bloodshed: and it must be confessed, that when the enemies of the Protestant faith behold the rarcour, the bigotry, and the malice of many sectaries, and particularly of those sects which are the most numerous and popular, they have but too much ground for their triumphs. When the spirit of Chillingworth shall have influenced the hearts, and directed the lives of all Protestants, their professions will be as consistent as their leading principles are rational and Scriptural. That author, addressing himself to to a Romish writer, speaks of the religion of Protestants in the following terms: "Know then, Sir, that when I say the religion of Protestants is in prudence to be preferred before yours; as, on the one side, I do not understand by your religion the doctrine of Bellarmine or Baronius, or any other private man amongst you, nor the doc trine of the Sorbonne, or of the Jesuits, or of the Dominicans, or of any other particular company among you; but that wherein you all agree, the doctrine of the Council of Trent; so, accordingly, on the other side, by the religion of Protestants I do not understand the doctrine of Luther, or Calvin, or Melancthon; nor the confession of Augsburg or Geneva; nor the catechism of Heidelberg, nor the articles of the church of England-no, nor the harmony of Protestant confessions ; but that wherein they all agree, and which they all subscribe with a greater harmony, as a perfect rule of faith, and action, that is, THE BIBLE! The Bible, I say, the Bible only, is the religion of Protestants. Whatsoever else they be lieve besides it, and the plain irrefragable, indubitable consequences of it, well may they hold it as a matter of opinion; but as a matter of faith and religion, neither can they, with coherence to their own grounds, believe it themselves, nor require belief of it of others, without most high and most schismatical presumption. I, for my part, after a long (and I verily believe and hope) impartial search of the true way to eternal happiness, do profess plainly, that I cannot find any rest for the sole of my foot, but upon this rock only. I see plainly, and with my own eyes, that there are popes against popes, and councils against councils; some fathers against other fathers, and some fathers against themselves; a consent of fathers of one age against consent of fathers of another age; traditive interpretations of Scripture

are pretended, but there are few or none to be found: no tradition but that of Scripture can derive itself from the fountain; but may be plainly proved either to have been brought in in such an age after Christ, or that in such an age it was not in. In a word, there is no sufficient certainty but that of Scripture only, for any considering man to build upon. This, therefore, and this only, I have reason to believe. This I will profess; according to this I will live; and for this, if there be occasion, I will not only willingly, but even gladly, lose my life; though I should be sorry that Christians should take it from me. Propose me any thing out of the book, and require whether I believe it or no, and seem it never so incomprehensible to human reason, I will subscribe it with hand and heart, as knowing no demonstration can be stronger than this: God hath said so, therefore it is true. In other things I will take no man's liberty of judging from him, neither shall any man take mine from me. I will think no man the worse man, nor the worse Christian: I will love no man the less for differing in opinion from me. And what measure I mete to others, I expect from them again. I am fully assured that God does not, and therefore men ought not, to require any more of any man than this: to believe the Scripture to be God's word to endeavour to find the true sense of it; and to live according to it."

Such are the genuine principles of Protestantism; such the spirit by which all Christians ought to be actuated Those men, who, calling themselves Protes. tants, are of a contrary spirit (and it is a lamentable fact that their number is daily increasing) are a disgrace to their profession, and bring dishonour on the common cause of Christianity. Their devotion is enthusiasm, and their zeal madness; while their increasing number portends one of the greatest of all public calamities; threatening to rekindle the latent embers of persecution,-again to light up those fires, which the united efforts of reason, philosophy, and the principles of rational religion have conspired to extinguish for ever. See ARMINIANS, PRESBYTERIANS, PURITANS, REFORMATION, and RoMAN CATHOLICS.

PROTESTATION is a form in pleading, when one does not directly affirm or deny any thing that is alleged by another, or which he himself alleges.

PROTRACTOR is the name of an instrument used for protracting or laying down on paper the angles of a field, or

other figure. The protractor is a small semicircle of brass or other solid matter, the limb or circumference of which is nicely divided into one hundred and eighty degrees: it serves not only to draw angles on paper, or any plane, but also to examine the extent of those already laid down. For this last purpose, let the small point in the centre of the protractor be placed above the angular point, and let the side coincide with one of the sides that contain the angle proposed; then the number of degrees cut off by the other side, computing on the protractor, will show the quantity of the angle that was to be measured. MENSURATION.

See

Protractors are now more usually made in the form of a parallelogram, and properly graduated at the upper edge. See MATHEMATICAL Instruments.

PROVIDENCE, the conduct and direction of the several parts of the universe by a superior intelligent being.

PROVINCE, in law, means the circuit of an Archbishop's jurisdiction, which is subdivided into bishoprics. The ecclesiastical division of this kingdom is into two provinces; viz. Canterbury and York. Provincial constitutions, in this kingdom, were decrees made in the provincial synods, held under divers Archbishops of Canterbury.

PROVISO, in law, is a condition inserted in a deed, upon the observance of which the validity of the deed depends. PROVOST marshal, an officer of the King's navy, who has charge of the King's prisoners taken at sea.

PROVOST, or PREVOT, in the King's stables; his office is to attend at court, and hold the King's stirrup when he mounts his horse, &c. There are four provosts of this kind, each of whom attends in his turn monthly.

PROW, in navigation, denotes the head or fore-part of a ship, particularly in a galley, being that which is opposite to the poop or stern. In the middle of the prow is the beak that cuts the water, on the top of which is commonly some figure or hieroglyphic. The prow is

lower thon the poop, and contains fewer decks.

PRUNELLA, in botany, self-heal, a genus of the Didynamia Gymnospermia class and order. Natural order of Verticillatæ, or Labiatæ Essential character: filaments forked, with an anther on one of the forks; stigma bifid. There are three species.

PRUNELLA, sal, in pharmacy, a prepara

tion of purified saltpetre, called also crystal mineral, made in this manner : having melted any quantity of saltpetre, cast a little flower of sulphur upon it, and when that is burnt throw on more; and continue to do so till the nitre flow as clear as rock-water. Then with a clean iron or brass ladle take it out, and, putting it into moulds till coagulated, preserve it for use.

PRUNING, in gardening and agricul ture, is the lopping off the superfluous branches of trees, in order to make them bear better fruit, grow higher, or appear more regular. Pruning, though an operation of very general use, is nevertheless rightly understood by few; nor can it be learned by rote, or, indeed, wholly by books, but requires a strict observation of the different manners of growth of the several sorts of fruit-trees; the proper method of doing which cannot be known, without carefully observing how each kind is naturally disposed to produce its fruit ; for some do this on the same year's wood, as vines; others, for the most part, upon the former year's wood, as peaches, nectarines, &c. and others upon spurs which are produced upon wood of three, four, &c. to fifteen or twenty years old, as pears, plumbs, cherries, &c. therefore, in order to the right management of fruittrees, provision should always be made to have a sufficient quantity of bearing wood in every part of the trees, and at the same time there should not be a superfluity of useless branches, which would exhaust the strength of the trees, and cause them to decay in a few years. The reasons for pruning of fruit-trees are, 1. To preserve them longer in a vigorous bearing state; 2. To render them more beautiful; and 3. To cause the fruit to be larger and better tasted.

PRUNUS, in botany, bird cherry-tree, a genus of the Icosandria Monogynia class and order. Natural order of Pomacex. Rosacea, Jussieu. Essential character: calyx five-cleft, inferior; petals five; drupe with a nut, having the sutures prominent. There are thirty-three species.

PRUSSIAN blue. A rich pigment has been known for a considerable time under the name of Prussian blue. It is prepared by drying blood, and mixing three parts of the dried residuum with two parts of the potash of commerce, and calcining the mixture in a crucible by a red heat it is then boiled in successive portions of water, which are afterwards mixed together, and concentrated by evaporation. A solution is prepared of one

:

part of sulphate of iron, and two parts of alum, and to this the liquor obtained from the calcined blood and alkali is added, as long as any precipitate is formed. This precipitate is of a green colour, but by washing it with a little dilute muriatic acid, it becomes of a dark rich blue colour. This forms the Prussian blue of commerce. The property of forming the colour depends on a peculiar principle combined with the alkali, that in the formation of the Prussian blue this is transferred to the iron, and that it may be again abstracted from it, by boiling the blue in an alkaline solution; the properties of the alkali are thus changed, and it acquires the power of again forming the precipitate of Prussian blue from a solution of sulphate of iron. The reason the precipitate is thrown down green is, that the alkali is not entirely saturated with the colouring principle; the excess of alkali throws down, therefore, a portion of yellow oxide of iron from the sulphate, which, mingling with the blue precipitate, renders it green, and the muriatic acid gives the deep blue colour, by dissolving, and of course removing this oxide. See PRUSSIC acid.

PRUSSIATES, in chemistry, salts formed with the Prussic acid. These salts have not been attentively examined, on account of their want of permanency, unless they are united with some metallic oxide; but the prussiate of potash and iron, which is a triple salt, has been used by chemists as the best combination of prussic acid for detecting the existence of iron. In chemistry and mineralogy this is a very important substance, as it is capable of indicating whether most metallic substances be present in any solution whatever, and of pointing out the particular metal, and of ascertaining its quantity. This is done by precipitating the metals from their solution, in consequence of the insoluble compound which it forms with them. The colour of the precipitate indicates the particular metal, while its quantity enables us to judge of the proportion of metallic oxide contained in any solution. This salt has obtained, at different times, the names of Prussian alkali, phlogisticated alkali, Prussian test, &c. This salt, though of great importance as a test, is of no use whatever, if it be not quite pure. There are two ways in which this test may be rendered impure, besides the introduction of foreign ingredients, which it is needless to mention, because it is obvious that it must be guarded against.

1. There may be a superabundance of alkali present, or, which is the same thing, there may be mixed with the Prussian test a quantity of pure alkali; or, 2. There may be contained in it a quantity of yellow prussiate of iron, for which prussiate of potash has also a considerable affinity. If the Prussian test contain a superabundance of alkali, two inconveniences follow. This superabundant quantity will precipitate those earthy salts which are liable to contain an excess of acid, and which are only soluble by that excess. Hence alumina and barytes will be precipitated. Another inconvenience arising from the superabundance of alkali in the Prussian test is, that it gradually decomposes the blue prussiate which the test contains, and converts it into a yellow prussiate. In what manner it does this will be understood, after what has been said, without any explanation. On the other hand, when the Prussian alkali contains a quantity of yellow prussiate of iron, as great inconveniences follow. This yellow prussiate has an affinity for prussic acid, which, though inferior to that of the potash, is still considerable; and, on the other hand, the potash has a stronger affinity for every other acid than for the prussic. When, therefore, the test is exposed to the air, the carbonic acid, which the atmosphere always contains, assisted by the affinity between the yellow prussiate and the prussic acid, decomposes the prussiate of potash in the test, and the yellow prussiate is precipitated in the form of Prussian blue, and every other acid produces the same effect. A test of this kind would indicate the presence of iron in every mixture which contains an acid (for a precipitation of Prussian blue would appear), and could not therefore be employed with any confidence.

PRUSSIC acid, in chemistry and the arts, is one of the most important of the acids. It was discovered by accident, about the beginning of the last century, by Diesbach, a chemist of Berlin. This gentleman, wishing to precipitate a decoction of cochineal with an alkali, got some potash, on which he had distilled several times his animal oil, and as there was some sulphate of iron in the decoction, the liquor instantly exhibited a beautiful blue in the place of a red precipitate. Hence he saw the method of producing the same subtance at pleasure, and it soon became an object of commerce, and obtained the name of Prussian blue, from the place

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