KEPLER'S PROBLEM KERMES puted from the observations of Tycho Brahe When a is given, z is easily found from the the distances of Mars from the sun at different trigonometrical tables; but there is no direct points of his orbit, found that the orbit was way, unless by infinite series, of finding x not circular, as had always been supposed when z is given, which is the case that occurs by astronomers till then, but elliptical; and in astronomy. The determination of r in terms that the sun occupies one of the foci of the of z constitutes what is called Kepler's Problem. ellipse. He afterwards discovered the same Solutions of this important problem are to be thing to be true of the earth's orbit; and found in most works on astronomy. They are thence extended it by analogy to all the other generally tentative, depending on a combination planets. Newton demonstrated in the Principia of geometrical and trigonometrical principles; that if a body projected in space is acted upon but two very elegant ones, purely analytical, by a central force varying inversely as the are given by Professor Wallace, in the Memoirs square of the distance, the body will necessarily of the Royal Astronomical Society, vol. ix. p. 185. describe one of the three conic sections; but The first of these solutions is as follows:whether the orbit, will be an ellipse, an hyperbola, or a parabola, depends on the intensity of the force with which it is projected. Kepler was led to the discovery of his second law by a comparison of the sectors formed by two contiguous radii vectores and the anglos included between them. The data which he assumed were not rigorously exact; but Newton afterwards demonstrated from the theory of dynamics that the fact is necessarily true of all motions regulated by a central force, whatever the law of that force may be. The history of the discovery of the third law is remarkable. Kepler had long been persuaded that some numerical relation must exist between the periodic times of the planets In order and their distances from the sun. to discover this relation he tried successively many hypotheses, each of which involved a mass of tedious calculation. He began by comparing the intervals between the planetary orbits with the five regular solids; and having failed in this speculation, as well as in various others, he at length thought of comparing the different roots and powers of the periods and distances. After many attempts and failures, he at last perceived the analogy of which he had been so long in search. sera quidem respexit inertem, Respexit tamen et longo post tempore venit, he exclaims; and in the fulness of his delight he has recorded the year and day on which the discovery was made. It was the 8th of May, 1618; and, as Professor Playfair has remarked, perhaps philosophers will agree that there are few days in the scientific history of the world which deserve so well to be remembered.' (Dissertation iv. Encyclopædia Britannica.) 1. Find ', a first approximation to the eccentric anomaly r, by this formula, tan (x' — }~) = ——e 2. Find y such that 1+e tanz. sin (y-c)=sin (Here x- -z must be expressed in seconds of a 4. Then the eccentric anomaly, x=x'+c. The computation of the eccentric anomaly by this method is extremely simple. Keramohalite. A hydrated subsulphate of alumina having the same composition as Aluminite. It occurs in crystalline crusts and in six-sided tables near Königsberg in Hungary, associated with Iron Vitriol. Keraphyllite. A species of Hornblende. [CARINTHINE.] Kerargyrite (Gr. κépas, a horn; &pyvpos, silver). Native chloride of silver. [HORN SILVER.] Kerasite (Gr. Képas). A synonym of chlorocarbonate of lead. [CROMFORDITE.] Kerate. [HORN SILVER.] Keratonyxis (Gr. képas, a horn, vúķis, a puncturing). A term applied by the German surgeons to the operation of couching, performed by introducing a needle through the cornea or horny coat of the eye, and depressing or breaking the opaque lens. such Keratophyllite (Gr. κέρας, and φύλλον, α leaf). A mineralogical synonym of Actinolite. Keri-chetib (Heb.). In Philology, the Kepler's Problem. The discovery made by Kepler, that the planetary orbits are ellipses name given to various readings in the Hebrew When any having the sun in the focus which is common Bible. Keri signifies that which is read, and to each ellipse, and that the line which joins chetib that which is written. the centres of the sun and a planet passes over various readings occur, the false reading or equal areas in equal times, made it necessary chetib is written in the text, and the true to solve a problem which transcended the reading or keri is written in the margin, with geometry of his age: Supposing the semi-p under it. These corrections, which are about transverse axis of a planet's orbit to be represented by 1, and the eccentricity by e; also the mean anomaly at any given instant of time by z, and the eccentric anomaly by x, both being reckoned from the perihelion, Kepler found the relation between the angles x and z to be expressed by the equation z=x-e sin x. 280 1,000 in number, have been generally attributed to Ezra. (Kennicott, Dissertatio Generalis.) Kermes (Arab. little worm). An insect found in many parts of Asia and the south of Europe; the Coccus ilicis of Linnæus. They were long taken for the seeds of the tree on which they live, and hence called grains of kermes. They KERMES MINERAL are used as a red and scarlet dye. Before the introduction of cochineal, kermes was the most esteemed drug for dyeing scarlet. The tapestries of Brussels and other parts of Flanders, which have lost little of their original brilliancy, even after a lapse of 200 years, were dyed with kermes. (Beckmann's History of Inventions; Bancroft's Permanent Colours.) Hermes Mineral. A name given by the old chemists to the precipitated sulphide of antimony, in consequence of its reddish colour. Kermesite. Native oxy-sulphide of antimony. Kerned Letters. In Printing, those types which have their faces hanging over one or both sides of their shanks or bodies. In Greek, for example, where the vowels are almost always cast in this manner, the kerned will admit all kinds of accents or breathings (each cast upon a separate piece of metal), and may become f,,, d‚ Ñ‚ ñ, îì‚ Ã‚ Ñ, ñ, ñ, ñ, ñ, ħ, as required by the printer. Kerodon (Gr. Kĥp, a heart; odoús, a tooth). A genus of herbivorous Rodents, characterised 4-4 by molar teeth, each composed of two 4-4 equal parts, of which the transverse section presents a cordiform or heart-shaped figure; the two parts are united on the external side in the upper, and on the internal side in the lower jaw. The incisors are two in number in both jaws, and present the form common to the Cavies, to which family the present genus belongs. The species are small, scarcely equalling the Guinea-pig in size. They are peculiar, with the other Cavies, to the South American continent. Kerolite (Gr. «ŋpós, wax, and Aloos, stone). A native hydrated silicate of manganese, which occurs in kidney-shaped masses of a white, yellow, or green colour, at Zöblitz in Saxony, Frankenstein in Silesia, and in Harford county, Maryland. Kersey (probably a corruption of Jersey, whence it originally came). A kind of coarse cloth, usually ribbed, and woven from long wool. It is chiefly manufactured in the north of England. Kerseymere, on the other hand, is a thin stuff, generally woven plain from the finest wools; and hence it has been inferred that these two terms, the meaning of which is so distinct, cannot be referred to the same origin. Kerseymere is said to have derived its appellation from Cashmir, a country which produces the finest wool and is celebrated for the works of its looms. In England it is principally manufactured in the western districts. Kestrel. The Falco Tinnunculus of Linnæus, one of the common English birds of prey. Ketch (Dan. kettsch; Dutch, kits). An almost obsolete form of two-masted vessel, carrying a tall mainmast and shorter mizzen. It was a favourite form for yachts, and more especially for mortar-vessels. Ketchup. A name of Eastern origin, said to come from kitjap, the Japanese name for some similar condiment. With us it is usually KEY prepared from mushrooms, champignons, and similar fungi, by sprinkling them, when broken up, with salt, and boiling the expressed juice with spice. Mr. Berkeley, one of our most learned fungologists, states, however, that the better plan is to let the juice strain without squeezing, and after standing for twelve hours to rack it off clear and bottle it, filling the top of the bottle up with alcohol, in which the proper spices have been previously steeped. Prepared in this way, it retains its peculiar flavour more perfectly than when boiled. Ketchup is often prepared for sale from agarics collected almost indiscriminately, no care being taken to discard poisonous species. The best ketchup is prepared from Agaricus campestris, but a very good quality may be obtained from an admixture of other species, especially A. procerus, if care is used. Walnut ketchup, a similar preparation from green walnuts, is also of frequent use in domestic economy. Ketone or Acetone. A term used by chemists to designate one of the products of the dry distillation of the barium, calcium, or lead salt of the volatile acids. Amongst these products is a compound which has been termed the ketone of the acid, and which bears the same relation to the acid from which it has been obtained, as acetone does to acetic acid. [ACETONE.] Keuper. The uppermost division of the Trias of continental geologists. It consists generally of a series of variegated marls (marnes irisées), of red, grey, or blue colour, passing into green marls, black clay, and fine-grained sandstones. Rock-salt and gypsum abound in these deposits, and the upper members of the new red sandstone of Cheshire and other parts of England are also characterised by the presence of the same minerals. The keuper contains not unfrequently remains of plants distinct from those of the coal measures, and even from those of the Bunter sandstein, the lowest division of the Trias. Kevels (called also Ranges). On Shipboard, timbers projecting at a small angle from the sides, to which are belayed the sheets and tacks by which the mainsail and the foresail are extended. Kevel heads are the ends of certain top timbers which, projecting above the ordinary line of gunwale, form bitts round which ropes can be made fast. Key (A.-Sax. cæg). In Architecture, a piece of wood let into the back of another in the contrary direction of the grain, to preserve the last from warping. The term is also applied to the portion of lime and hair rendering that forces its way between the joints of the laths, in plasterer's work, and serves to uphold the body of the work. Key or Key Note. In Music, the principal or fundamental note in a composition, on which frequent closes or cadences are made. It is that in which the piece usually begins and ends, and is, as it were, the musical standard to which regard must be had in all the other combinations of sounds in the composition, and KEY STONE under whose influence they are. [TONIC.] The key of a composition may be either major or minor, according as the scale has a major or a minor third. KILLINITE Axotomous Iron-ore. A slightly magnetic titaniferous iron-ore from Gastein. Kidnapping (a word of doubtful origin: Mr. Wedgwood refers it to nab-steal, and kid Key Stone. The middle voussoir of the [slang]=child). In Law, the forcible abducarch of a bridge, or the arch stone at the tion of anyone from his own country into ancrown or immediately over the centre of the other. It is an offence at common law. By 11 arch. The length of the key stone, or thick- & 12 Wm. III. c. 7, penalties were denounced ness of the archivolt at the top, is usually made against masters of vessels having on board perabout or of the span by the best archi-sons who had been kidnapped against their will. tects. The practice of engineers is rather different; it is based upon the empirical formula derived from Perronet's experience, in which, calling e the thickness, then e=0·0347 d + 0.325; d representing the span if the vault be semicircular, and double the radius if the vault be over the centre. The dimensions above quoted are in mètres. Key-board. In Music, the series of levers in a keyed instrument, as a pianoforte, organ, or harpsichord, upon which the fingers press to produce percussion of the strings, or in the organ the opening of valves. It consists of short black and long white keys. Keyser's Pills. A once celebrated mercurial preparation, the active ingredient in which is the acetate of mercury. Khalif. [CALIPH.] Khan. In Persia, properly speaking, the title of an officer or governor, added after his name. The sovereigns of many independent states of Northern Asia are styled khans. Khan is frequently used by our own countrymen to signify an Eastern CARAVANSERA [which see]; in which travellers find a gratuitous lodging, provided their stay be limited to a single night. Khât. [KAT.] Khay. A Senegal Cedrelaceous tree, called K. senegalensis, the bark of which is used as a febrifuge on the banks of the Gambia, and the wood of which resembles mahogany. It is, in fact, closely allied to the mahogany-tree, Swietenia Mahagoni. Khotbah (Arab.). A peculiar form of prayer used in Mohammedan countries at the commencement of public worship in the great mosques on Friday at noon. It was originally performed by the Prophet himself, and by his successors till the time of Mohammed VIII. (A. D. 936), who appointed special ministers for the purpose, on which footing it has continued to the present time. The khotbah is chiefly a 'confession of faith,' and a general petition for success to the Mohammedan religion. It is divided into two distinct parts, between which the officiating khatib or priest makes a considerable pause, and is regarded by the Mussulmans as the most solemn and important part of their worship. The insertion of his name in this prayer has always been considered one of the chief prerogatives of the sultan of Turkey. Khus-khus or Cuscus. The fragrant Indian grass, Andropogon muricatus. Kibdelophane (Gr. «íßdnλos, spurious) or This enactment was probably occasioned by the practice, not uncommon in those days, of carrying away by force or fraud labouring persons to serve in the plantations in America. This clause is repealed by 9 Geo. IV. c. 31, by which masters of vessels are made punishable for leaving abroad any of their men against their will, an offence now punishable under stat. 17 & 18 Vict. c. 104 s. 206. The stealing of children away from persons having the lawful custody of them (popularly termed kidnapping) is felony under stat. 24 & 25 Vict. c. 100. Kidneys. The organs in which the urine is secreted: there is one on each side in the loins, near the first lumbar vertebra, and behind the peritonæum. The pelvis of the kidney terminates in the ureter, and is divided into several portions called calyces, into each of which a papilla projects, through the minute orifices of which the secreted urine passes into the cavity called the pelvis, and thence by the ureter into the bladder. [RENAL ORGANS.] Kiesel Schiefer (Ger.). A peculiar silicious schist of the lower division of the upper carboniferous series of the Rhine is thus named. This schist is often black and loaded with carbon. It is found in other countries not unfrequently in the same state and association. Kieserite. A sulphate of magnesia found at the Stassfurth salt mine, near Magdeburg. Kigelia (Mozamb. Kigelikeia). The name of a genus of African Crescentiacea, the only species of which, K. pinnata, is a large spreading tree, with pinnate leaves, and long pendent fruit. The latter, when roasted, are used as an outward application in rheumatic complaints; and the tree itself is held sacred in Nubia, the negroes celebrating beneath it those religious festivals which take place by moonlight. Kikekunemalo. A resin, resembling copal, brought from America, where it is used medicinally. It forms excellent varnishes. Kilbrickenite. A bluish-grey variety of sulphide of antimony and lead, found in Ireland at Kilbricken, Clare county. Kilkenny Coal. [ANTHRACITE.] · · Killas. A Cornish name for the clay slate which forms what is called in mining language the country, in those parts where mineral veins are worked. The name is applied very indefinitely by miners, and has no strict geological use or meaning. Killinite. A mineral, sometimes described as a variety of Spodumene, from Killiney, near Dublin. It is a hydrated silicate of alumina, containing potash and oxide of iron. KILOGRAMME Kilogramme. A French measure of weight equal to 1,000 grammes, and to 2-2046 lbs. avoirdupois. Kilomètre. A thousand mètres; equal to 1,093 yards nearly. KING rotations [ROTATIONS, COMPOSITION AND RESOLUTION OF] any position whatever can be given to such a plane, by imparting to it a helical motion around a given axis, the central axis. Further, the motion of such a plane at any Kilt. A loose dress, extending from the instant may not only be regarded as consisting waist to the knee in the form of a petticoat; of a simultaneous sliding along, and rotation worn in the Highlands by men, and by children around the central or, as it is often called, the in the Lowlands. The term is, according to instantaneous sliding axis; it is also equiJamieson, unquestionably Gothic. The High-valent to two simultaneous rotations, without landers designate the kilt as the filibeg. This sliding, around two axes which do not intersect singular national dress is fast hastening into one another, and to which the name of reciprocal disuse; and but for a few Highland regiments or conjugate lines has been given. The number in which it is still maintained, it would probably of pairs of reciprocal lines having the above long ago have been universally superseded by property is infinite; one line, however, being the dress of the Lowlanders. chosen arbitrarily, the other is perfectly defined. The mutual inclination of two such reciprocal lines varies from zero to a right angle, and amongst the pairs at right angles to each other, one always lies in the plane under consideration, of which it is called the characteristic, and the other cuts the plane perpendicularly in a point to which the name of focus has been given. These terms were introduced by Chasles, whose memoirs on the subject in the Comptes Rendus de l'Acad. des Sciences, 1843, are well worthy of study. The first is obviously in accordance with Monge's definition of a characteristic, since it is the line common to two consecutive positions of the moving plane. Kimeridge Clay. A blue slaty clay, containing carbonate and sulphate of lime. It is a thick and important deposit in the south of England, where it forms the base of the upper division of the oolites, and contains a bituminous shale called the Kimeridge coal. In France, there is a corresponding bed of clay at Honfleur, at the mouth of the Seine. In the north of Bavaria the celebrated lithographic slates of Solnhofen replace the clays. A small oyster called the Gryphea virgula is very characteristic of this part of the oolitic series. The Portland beds overlie the Kimeridge clay. Kimeridge Coal. A remarkably bituminous shale, found in the Kimeridge clay beds on the south coast of England. It is of dark brown colour and without lustre, it effervesces slightly with acids, contains no iron pyrites, and burns readily with a yellowish, rather smoky and heavy flame. It is associated with slaty pyritous clays. It has been used for burning with little advantage. It would probably better repay distilling, were it not for the disagreeable odour of the oil obtained from it. King. A title of dignity in the languages, extinct and living, of the Teutonic and Gothic races. There is some difference of opinion as to the origin of the word; probably as kon-ung, cyn-ing, it expresses one chosen from the people to rule them, the termination appearing in such words as ætheling, while the first syllable, connected with the Greek yévos, Latin gens, &c., appears also in yun and quean. It would therefore primarily mean one chosen from and Kinematics (Gr. κívnμa, a motion). The by the people to represent and guide them; science of pure motion. It differs from geo- but it has passed through as many shades of metry by the admission of the conceptions of meaning as there are states or nations to be time and velocity, and from dynamics proper by governed. Thus it is applied equally to the conthe exclusion of the conception of force as a stitutional sovereign of England and the absocause of motion. Roberval's method of tan- lute sovereign of Prussia; to the chief magistrate gents and Newton's fluxions are purely kine- of Poland in former times, who was elected, and matical methods. From the kinematics of a to that of England, who succeeds by hereditary point all the properties of curves may be de- right; to the head of a savage tribe or barbaduced, and that frequently with great sim-rous horde, as well as to that of the most plicity. A curve, in fact, may be conceived to be generated by a point moving along a line which at the same time incessantly turns around that point, a definition by which Lamarle has profited in his Théorie Géométrique des Rayons et Centres de Courbure (Bulletins de l'Acad. Roy. de Belgique, tomes 2, 3, 5, 6, also Exposé Géométrique du Calcul Différentiel et Intégral, précédé de la Cinématique du Point, de la Droite et du Plan, Paris 1861). The line is the tangent of the curve, and the relative velocities of translation and rotation determine its curvature. refined and civilised nation. It is expressed in Greek by the word basileus, and in Latin and its cognate languages by rex; but all the nations of Europe have adopted into their respective languages the equivalent terms in use among the people with whom they carry on intercourse. Thus we speak of the Shah of Persia, the Grand Sultan, the Pasha of Egypt, the Dey of Algiers, &c. In countries where the kingly office is hereditary, some form has always been gone through on the accession of a new king, in which there is a recognition on the part of The motion of a rigid body or of an invariable the people of his right; a claim from them system of points is determined, of course, by that he should pledge himself to the perthat of any three points, or of the plane con- formance of certain duties; and generally a taining these three. Now, by the theory of religious ceremony performed, in which the KING CRAB KING'S BENCH anointing him with oil and placing a crown the royal discretion. At a later period they upon his head are conspicuous acts; the were reduced to four; then increased to five, whole solemnity being styled the coronation. and afterwards to six-the chief justice, who In modern Europe the Pope and the Emperor is the highest common law judge, and five assumed as a joint prerogative the right of puisné or younger judges. The Court of King's conferring the dignity of king. Frederick I. of Bench, besides those branches of its jurisdiction Prussia was the first sovereign who assumed which it has in common with the other two the title, and had it acknowledged by the other superior common law courts [COURTS, SUPEstates of Europe without their authorisation. RIOR], has also peculiar authority, or presents In Great Britain, the king exercises the su- more advantages in some particular proceedings. preme executive power, together with a share It is the preferable although not the only in the legislative authority jointly with the tribunal for discharging prisoners under the two houses of parliament. [PARLIAMENT.] The Habeas Corpus Acts. It has control over all right to the throne of England (now extended to inferior courts by means of the process called Great Britain and Ireland) is hereditary, subject certiorari, which is a writ sued out of this court, to the authority of parliament to limit the suc- by virtue of which proceedings may be removed cession. This was last done by the stat. 12 & into it out of such inferior jurisdiction, whether 13 Wm. III., when it was fixed in the heirs of in criminal or civil cases. It has also an exthe electress Sophia of Hanover, being Protest- clusive authority (except in a few cases) to ants. The duties of the king according to the compel all inferior courts and officers, and in constitution are embodied in the coronation some instances private persons, to perform acts oath, fixed by stat. 1 Wm. & Mary. Incidental of a public nature, and connected with a public prerogatives are legal exceptions in favour duty. By means of a prohibition it can restrain of the crown where its claims clash with all other courts from proceeding where they those of a subject; relating to such matters as descents of lands, debts, &c. The direct prerogatives of the crown are those which attach to the king in respect of his political authority: such as the sanctity of his person; his prerogatives as head of the executive; the power of making war and peace; treaties with foreign powers; military and naval command; the supreme dispensation of justice through his courts; the power of erecting and disposing of offices and honours; the power of issuing proclamations binding on the subject in certain cases, with the advice of his privy council; and, lastly, the supreme government of the national church. The king's revenue is of two sorts, ordinary and extraordinary. The ordinary revenue or patrimony is such as either has subsisted in the crown time out of mind, or has been granted by parliament in exchange for such. [CIVIL LIST.] The extraordinary revenue consists of the supplies annually granted by parliament. [PARLIAMENT; PREROGATIVE.] exceed or misuse their jurisdiction: this is likewise a writ directed to the judge and the plaintiff in the inferior court. A writ of error in law from all inferior courts is, with certain exceptions, returnable in the King's Bench. This court likewise hears and determines cases stated by courts of sessions. The greater proportion of these are questions on the validity of poor's rates, or on parochial settlements. When a court of sessions entertains a doubt on a point of law arising in the argument, it will usually authorise the party against which it decides to have the judgment thus reviewed, the cases being stated in writing. The criminal jurisdiction of the King's Bench is still extensive. It has, at common law, jurisdiction by indictment over every species of criminal offence committed in Middlesex; and in practice misdemeanours, as conspiracies or perjuries, committed in the county, are still indicted in this court, and tried after term at nisi prius among the civil causes. Sometimes also trial at bar, or by the full court, is granted on special application. It has also jurisdiction by criminal information, which lies in cases of misdeKing Post. In Architecture, the middle meanour only; a proceeding which supersedes post of an assemblage of trussed framing, for the necessity of an indictment found by a grand supporting, or rather for suspending, the tie- jury. An information is filed either by the. beam, at the middle, and at the lower ends of the attorney-general ex officio, as it is termed-a struts. In framed partitions the king post is in- proceeding generally adopted in certain mistroduced in the centre of the span, and has the demeanours of a public nature; or at the suit of discharging pieces framed into it in either side. a private party by leave of the court. King's Advocate. The Advocate repre- An information in the nature of a quo warranto senting the crown in the Ecclesiastical and is in form a criminal, but substantially a civil Admiralty Courts. proceeding. It is granted where any subject or King's or Queen s Bench, Court of. In body politic has assumed a franchise or priviLaw, this court originated in the ancient Aula lege not being legally entitled, and to the injury Regia, in which the king was accustomed (as he of some other party or the public. Any indictstill is supposed in the King's Bench by fiction of ment, presentment, &c. found in any part of law) to sit in person, and which followed him in England, may be moved by certiorari into this all his progresses. The judges of the court of court. This court is now to be merged in the King's Bench, as well as of the other superior High Court of Justice, when constituted under courts, formerly varied in number according to the Judicature Act 1873. King Crab. [LIMULUS.] King Fish. A name sometimes applied to the opah (Lampris guttatus, Retz.). |