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k

k

k Sentence Examples

  • While vitamin K supplementation is necessary for most people who suffer with the conditions listed above, there are some people who should avoid taking supplements in amounts above the RDA of 65 mcg unless directed by a doctor to do so.

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  • The best modern authorities are K.

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  • At Kiel, K.

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  • Diamond color is also critical to Daniel K engagement rings: all stones must be of D or G color grades to be placed in Daniel K designs, a level of quality that less than 1 percent of the world's diamond supply can achieve.

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  • K.

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  • At Sodankyla, in 1882-1883, K.

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  • In Styria, according to K.

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  • 16, 1899, p. 128; (84) K.

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  • Munchen, p. 187) and K.

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  • Wittmann, Monumenta Wittelsbacensia (Urkundenbuch, Munich, 1857-1861); K.

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  • k.

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  • Delbrtick and K.

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  • Waitz, Deutsche Verfassungsgeschichte, 3rd ed., revised by K.

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  • (Leipzig, 1889); K.

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  • Novodvorsky, The Struggle for Livonia, 1570-1582 (Rus.) (St Petersburg, 1904); K.

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  • Grossen (1892); K.

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  • Wallis Budge (1896, 2 vols., with English translation); the Syriac text of pseudo-Callisthenes by Budge (Cambridge, 1889); cp. K.

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  • 21 3-33 2; K.

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  • Nowack (2nd ed., 1905), K.

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  • In 1904 K.

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  • Schonhals, Biographie des K.

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  • Roth, Ethnological Studies among the North-west-central Queensland Aborigines (London, 1897); Mrs K.

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  • 8vo (London, 1883); K.

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  • The cases of two, four and six squares had been given by K.

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  • Willer and K.

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  • Many lives of Tetzel have been published on the Protestant and on the Catholic side, the most recent being Korner's (1880), K.

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  • - Wireless Telegraphy The early attempts to achieve electric telegraphy involved the use of a complete metallic circuit, but K.

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  • Tommasina, 8 K.

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  • K.

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  • Tomaschek, "Die alten Thraker" in Sitzungsberichte der k.

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  • to allow him to dissolve parliament, entrusted Signor Giolitti, a Piedmontese deputy, sometime treasury minister in the Crispi cabinet, with the formation of a ministry of the Left, which contrived to obtain six months supply on account, and dissolved the Chamber, The ensuing general election (November 1892), marked by unprecedented violence and abuse of official pressure upon B k the electorate, fitly ushered in what proved to be scandals, the most unfortunate period of Italian history since the completion of national unity.

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  • Stromberger, Bertold von Regensburg, der grässte Volksredner des deutschen Mittelalters (1877), K.

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  • g', k, k', 1, m, The Anthomedusa in form is generally deep, bell-shaped.

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  • k, Stomach.

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  • 68, k), absent in Chondrophorida and Cystophorida; they are contractile and resemble, both in appearance, structure and function, the umbrella of a medusa, with radial canals, ring-canal and velum; but they are without manubrium, tentacles or sense-organs, and are always bilaterally symmetrical, a peculiarity of form related with the fact that they are attached on one side to the stem.

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  • k, Nectocalyces (swimming bells).

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  • Wilmans, Jahrbiicher des deutschen Reichs unter K.

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  • (k) In England the Constitutions of Clarendon added a provision for appeal to the king, " and if the archbishop shall have failed in doing justice recourse is to be had in the last resort (postremo) to our lord the king, that by his writ the controversy may be ended in the court of the archbishop; because there must be no further process without the assent of our lord the king."

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  • (k) Excommunication was either greater or less.

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  • C. Warren, Buddhism in Translations (Cambridge, Mass., 1896); Mrs Rhys Davids, Buddhist Psychology (London, 1900); K.

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  • - K.)

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  • 1, K).

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  • Apical cell, p. Wall marking limit between the plerome k, initial segment of root-cap. P and the pleriblem Pb.

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  • k,o.

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  • E, epidermis; q, phellogen; 1, cells, and ~1, the pheliogen of the lenticel; k, cortical parenchyma, containing chlorophyll.

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  • 2, K).

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  • I, J, K).

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  • Sunden, "De tribunicia potestate a Lucio Sulla imminuta" in Skrifter utgifna of k.

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  • Carlsson, Beitrdge zur Kenntniss der Anatomie der Schwimmvogel; K.

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  • Museum, 1891; K.

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  • A favourite contrast for which there is more to be said is that drawn between the m k agico-religious spell-ritual, that says in effect, "My will be done," and the spirit of "Thy will be done" that breathes through the highest forms of worship. Such resignation in the face of the divine will and providence is, however, not altogether beyond the horizon of primitive faith, as witness the following prayer of the Khonds of Orissa: "We are ignorant of what it is good to ask for.

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  • 546 (1904); K.

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  • In many cases it acts as a reducing agent (when used in the presence of acids); thus, permanganates are reduced to manganous salts, iodates are reduced with liberation of iodine, &c., 2KMnO 4 + 550 2 + 2H 2 0 = K 2 SO 4 + 2MnSO 4 + 2H 2 SO 4; 2K103+ 550 2 + 4H 2 O =1 3 + 2KHSO 4 + 3H2S04.

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  • Solutions of persulphates in the cold give no precipitate with barium chloride, but when warmed barium sulphate is precipitated with simultaneous liberation of chlorine: K 2 S 2 0 8 + BaC1 2 = BaSO 4 + K 2 SO 4 + C1 2.

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  • Trithionic acid, H2S306, is obtained in the form of its potassium salt by the action of sulphur dioxide on a solution of potassium thiosulphate: 2K 2 S 2 0 3 -f3S0 2 = 2K 2 S 3 0 6 -{- S; or by warming a solution of silver potassium thiosulphate KAgS 2 0 3 = Ag 2 S K 2 S 3 0 6; whilst the sodium salt may be prepared by adding iodine to a mixture of sodium thiosulphate and sulphite: Na 2 S0 3 -fNa 2 S 2 0 3 -f12 = Na 2 S 3062NaI.

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  • The solution obtained may be evaporated in vacuo until it attains a density of 1.46 when, if partially saturated with potassium hydroxide and filtered, it yields crystals of potassium pentathionate, K 2 S 5 0 6.3H 2 0.

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  • Ten segments can be recognized - according to the studies of K.

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  • The chief points in the life-history of Stylops and Xenos, which are parasitic on certain bees (Andrena) and wasps (Polistes), have been investigated by K.

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  • The morphology of the abdomen, ovipositor and genital armature is dealt with by K.

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  • France, lx., 1891); in the Bruchidae by Riley (Insect Life, iv., v., 1892-1893; and in the Strepsiptera (Stylopidae) by K.

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  • Townsend, The Great Schoolmen (1881); K.

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  • ': opal e ° °o T A R ple ' ag a ',ap iJ,wl Karkinit A C K r B L Scale, English Miles D S E A 32 Stavropol P O L A PI A N L A s E Derbent ° I?

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  • Soc. i.; K.

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  • 1896); C. K.

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  • As illustrating the general impoverishment of the Russian peasantry, it may be stated that the arrears of taxation owed by them have increased enormously since 1882, when they a, ounted to £2,854,000, until in 1900 the total amount was put k £15,222,000.

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  • A History of Russian Diplomacy under the Empress Elizabeth Petrovna, 1741-1762 (1899); The First Romanovs, 1613-1725 (1905); K.

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  • P. Thomsen, The Relation between Ancient Russia and Scandinavia and the Origin of the Russian State (London, 1877); the series of works by K.

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  • K.)

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  • 8), and a rather larger distance in America k FIG.

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  • For a non-partisan account of Xavier's work in the East, see K.

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  • (K.

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  • There is a Russian translation by Neviedomski (7 parts, Moscow, 1883-1886), and an Hungarian version of cc. 1-38 by K.

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  • Wiegand and Schrader in 1895-1898 have laid bare the site of the Greek Priene, and the same has been done for the remains of Magnesia ad Maeandrum by French excavators in 1842-1843 and the German expedition under K.

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  • The chief modern authorities are K.

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  • The best editions are those by K.

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  • Ettmiiller first applied Lachmann's ballad-theory to the poem (1841), and K.

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  • There are many translations of the epic into modern German, the best known being that of K.

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  • 2 So K.

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  • The most valuable branch is the oyster N,; : E, A i=De;I{1a iladelphia ', o K E .'

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  • And as in Hebrew, the six letters b g d k p t are aspirated when immediately preceded by any vowel sound.

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  • Among other distinguished Russian explorers in Asia, the names of Lessar, Annentkov (who bridged the Trans-Caspian deserts by a railway), P. K.

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  • Berghaus, Landbuch des Herzogtums Pommern (Berlin, 1865-1876); the Codex Pomeraniae diplomaticus, edited by K.

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  • Barthold, Geschichte von Rugen and Pommern (Hamburg, 1839-1845); K.

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  • Glycerin was discovered in 1779 by K.

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  • Ramsay, Angevin Empire (London, 1903); K.

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  • He has only one symbol (written somewhat like a final sigma) for an unknown quantity, which he calls apc0µ6s (defined as "an undefined number of units"); the symbol may be a contraction of the initial letters ap, as A Y, K Y, D Y O, &c., are for the powers of the unknown (Suvaµcs, square; icu(30s, cube; Svva,uo& va i ccs, fourth power, &c.).

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  • 5, c. ecr k FIG.

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  • e, em, k, lx, n, int, ecr, to the edge of the free mantle-skirt, is the conical shell.

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  • Close to this the small renal organ (i, mediad) and the larger renal organ (k, to the right and posteriorly) are seen, also the pericardium (1) and a coil of the intestine (int) embedded in the compact liver.

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  • k, 1, p, J affords a means of test ing the conclusion that we have in Lankester's 4 capito-pedal bodies the rudimentary ctenidia.

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  • k antero-postero median section 6, 7, with following additions.

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  • Narrow process of the same running below the intestine and leading by k into the pericardium.

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  • K, Complete eversion of H.

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  • Beneath the ciliated groove is placed an elongated ganglion (olfactory ganglion) connected by a nerve to the supraintestinal (therefore the primitively dextral) ganglion of the long h, k, m, Stomach.

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  • k, Opening of the albuphrodite duct, which very soon becomes miniparous gland into P Y the hermaphrodite entwined in the spire of a gland - the duct.

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  • The latter opens e, Hermaphrodite duct into the common duct at the point k, (uterine portion).

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  • 39, k).

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  • k, Retractor muscles.

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  • The Oncidiidae are, according to K.

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  • Kirchentag, and two years later founded and edited (1850-1861), with Neander and K.

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  • This assemblage is now generally regarded as a great division (phylum or sub-phylum) of the animal kingdom and known by K.

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  • The recent suggestion of K.

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  • k, Episternum.

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  • 12, k), which have a renal function.

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  • k, Kidney tubes.

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  • These results were confirmed by the observations of K.

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  • lxxvi., 1904); K.

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  • - K.

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  • lxxiv., 1899); K.

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  • Wissens., Wien, lvi., 1889); K.

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  • Korschelt and K.

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  • lxix., 1897); K.

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  • et des todiers, which, though belonging to the same category as all the former, differs from them in its more scientific treatment of the subjects to which it refers; and, in 1808, K.

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  • That the different ranks or degrees of circular groups exhibited in the animal kingdom are Nine k in number, each being involved within the other."

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  • Among contem p orary writers in a more popular style are John Burroughs; Herbert K.

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  • Lastly, the square was extended southwards in the 16th century, when the new palace of the procurators, K, was built by Scamozzi.

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  • Bushnell..1896-1900George K.

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  • Graber, K.

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  • Again he heated fluorspar with oil of vitriol, as K.

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  • Schulze, August Neander (1890); and K.

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  • His collected works were translated into German and published by K.

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  • k n (S, -chunb a° Kwang`Chen ?,?z - `; r' 4; .

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  • .o K il -ju tong-chin A B Longitude East 14 of Greenwich C 8° 3: E 44 legend, were bathing one day in a lake under the Chang-pai-Shan mountains when a passing magpie dropped a ripe red fruit into the lap of one of them.

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  • It is found most convenient to make use of the sag of the wire produced when it is stretched between two fixed points (K 1 K 2, fig.

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  • 4; K.

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  • k' b Ft.Myers un i!

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  • Its consonants are k, g, ng, ch, j, n, t, d, n, p, b, m, y, r, l, w, s, h.

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  • Final k and h are all but suppressed in the utterance.

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  • Stadt Basel (3 vols., 1906 sqq.); K.

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  • The name cerargyrite is a Greek form (from itpas, horn, and a pyvpos, silver) of the older name hornsilver, which was used by K.

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  • Ru2C16.4KC1; Ru 2 C1 6.4NH 4 C1, &c. The pure tetrachloride, RuC1 4, has not been isolated, but is chiefly known in the form of its double salts, such as potassium ruthenium chloride, K 2 RuC1 6, which is obtained when finely divided ruthenium is fused with caustic potash and potassium chloride is gradually added to the fused mass (U.

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  • In 1887 he was created C.M.G., and in 1888 K.

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  • He studied theology at Bonn (from 1822) under K.

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  • PANENTHEISM, the name given by K.

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  • Black, K.

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  • Priestley and K.

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  • Thus copper sulphate was CuO+S0 3, potassium sulphate 2S0 3 +P00 2 (the symbol Po for potassium was subsequently discarded in favour of K from kalium).

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  • The metals may be arranged in a series according to their power of displacing one another in salt solutions, thus Cs, Rb, K, Na, Mg, Al, Mn, Zn, Cd, Tl, Fe, Co, Ni, Sn, Pb, (H), Sb, Bi, As, Cu, Hg, Ag, Pd, Pt, Au.

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  • Group I.: the alkali metals Li, Na, K, Rb, Cs, and also Ag, monovalent; Cu, monovalent and divalent; Au, monovalent and trivalent.

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  • These discoveries were followed by Daniel Rutherford's isolation of nitrogen in 1772, and by K.

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  • However, in 1833, Berzelius reverted to his earlier opinion that oxygenated radicals were incompatible with his electrochemical theory; he regarded benzoyl as an oxide of the radical C 14 H 1Q, which he named " picramyl " (from 7rucp6s, bitter, and &uvyalk, almond), the peroxide being anhydrous benzoic acid; and he dismissed the views of Gay Lussac and Dumas that ethylene was the radical of ether, alcohol and ethyl chloride, setting up in their place the idea that ether was a suboxide of ethyl, (C2H5)20, which was analogous to K 2 0, while alcohol was an oxide of a radical C 2 H 6; thus annihilating any relation between these two compounds.

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  • The rapidity of the method, and the accurate results which it gave in the hands of a practised experimenter, led to its systematization by Jens Jakob Berzelius and Johann Friedrich Ludwig Hausmann, and in more recent times by K.

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  • To K.

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  • Progress in forensic chemistry was only possible after the reactions of poisons had been systematized; a subject which has been worked out by many investigators, of whom we notice K.

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  • Eliminating a and b between these relations, we derive P k V k /Tk= 8R, a relation which should hold between the critical constants of any substance.

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  • From the relation between the critical constants Pk Vk/Tk = 37 R or T k /P k = 3 .

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  • 7V k / R, and since Vk is proportional to the volume at absolute zero, the ratio T k /P k should exhibit additive relations.

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  • K= (I +2a)/(I -a), or a=(K-I)/(K+2), where K is the dielectric constant and a the fraction of the total volume actually occupied by matter.

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  • According to the electromagnetic theory of light K = N2, where N is the refractive index for rays of infinite wave-length.

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  • The relation they suspected to be of the form -yS = KT, where K is a constant analogous to R, and S the surface containing one gramme-molecule, y and T being the surface tension and temperature respectively.

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  • Now the value of K, -y being measured in dynes and M being the molecular weight of the substance as a gas, is in general 2.121; this value is never exceeded, but in many cases it is less.

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  • n is the mean number of molecules which associate to form one molecule, then by the normal equation we have y (Mnv) 3 =2.121(r -6°); if the calculated constant be K 1, then we have also y(Mv)3=K,(r-6°).

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  • Normal values of K were given by nitrogen peroxide, N204, sulphur chloride, S 2 C1 21 silicon tetrachloride, SiC1 4, phosphorus chloride, PC1 3, phosphoryl chloride, POC1 31 nickel carbonyl, Ni(CO) 4, carbon disulphide, benzene, pyridine, ether, methyl propyl ketone; association characterized many hydroxylic compounds: for ethyl alcohol the factor of association was 2.74-2.43, for n-propyl alcohol 2.86-2.72, acetic acid 3.62 -2.77, acetone 1 .

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  • The ordinary structural formula of potassium sulphate is K - O - S - O - K.

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  • Such parallel overgrowths, termed episomorphs, are very common among the potassium and sodium felspars; and K.

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  • K, Na, Cs, Rb, Li; Tl, Ag.

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  • Jacobson, Lehrbuch der organischen Chemie; Richter-Anschutz, Organische Chemie (I I th ed., K 2 S04 K2 S04 (NH 4) 2 SO 4 =o% SO 4 = coo FIG.

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  • K A1um=z00% K Alum= o/, Tl Alum= o% Tl Alum_ zoo FIG.

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  • K PO 4 = z00% NI-4112P04= x00% FIG.

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  • e, Retinaculum enclosing a k, Line of division between the nerve.

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  • Gundlach, Hesse and die Mainzer Stiftsfehde (Marburg, 1899); Walther, Literarisches Handbuch fir Geschichte and Landeskunde von Hesse (Darmstadt, 1841; Supplement, 1850-1869); K.

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  • In Phoenician itself and in the other Semitic alphabets the position of the middle legs of the W is altered so that the symbol takes such forms as or V or w, ultimately ending sometimes in a form like K laid sideways, he.

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  • Tiemann and K.

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  • Another Greek, Eumenes of Cardia, was chief secretary (apxtypa k uaTEUS).

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  • There seems to be even less chance for the combination of coloured strata and hachures proposed by K.

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  • The diphthong ai is 1 K.

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  • In 1 Facsimiles of it have been published by Desjardins(1869-1871), by K.

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  • minor K  ? ?

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  • (y!K R.Fubsuy Man?

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  • Kunstmann's Entdeckung Amerikas (Munich, 1859), K.

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  • 'Eav aµap T'n0" [f 6 aSEXIpOS UOv K aT v, TiUE6 ELp'nv7J iS7rayE g AE'Y0v a6TOv vOv..

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  • For the early stages of Kabbalistic theories, see K.

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  • by K.

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  • Gieseler, and Karl Immanuel Nitzsch for colleagues, he was called in 1827 to Göttingen to succeed K.

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  • Knorre and K.

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  • Better results have attended the process of K.

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  • The next period was inaugurated in analysis by K.

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  • Mechanik in ihrer Entwickelung (Prague, 1883), English translation under the title, The Science of Mechanics (London, 1893) K.

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  • Ga Rakh Sofia Srule zi C.; Emine B ie C A lC K Sazopolis ?1.

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  • ry °Alessi Mata j `M Kadt K cui 0.

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  • I 90`ls K cr?wSao 3?t` rin l se vai?

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  • von Hahn (in " Denkschriften " of the K.

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  • Hercher (1873); see also K.

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  • Similar native iron has later been found by K.

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  • Nathorst, Otversigt of K.

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  • Storm, Studies on the " Vineland " Voyages (Copenhagen, 1889); Extraits des Memoires de la Societe Royale des Antiquaires du Nord (1888); K.

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  • Sillem (1903); Gallois, Geschichte der Stadt Hamburg (1853-1856); K.

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  • Grimm, Deutsche Rechtsalterthiimer (Göttingen, 1828); K.

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  • xix.; K.

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  • Here the ions are potassium and the group Ag(CN)2.1 Each potassium ion as it reaches the cathode precipitates silver by reacting with the solution in accordance with the chemical equation K--+KAg(CN) 2 =2KCN+Ag, while the anion Ag(CN) 2 dissolves an atom of silver from the anode, and re-forms the complex cyanide KAg(CN) 2 by combining with the 2KCN produced in the reaction described in the equation.

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  • The tests for a salt, potassium nitrate, for example, are the tests not for KNO 3, but for its ions K and NO 3, and in cases of double decomposition it is always these ions that are exchanged for those of other substances.

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  • If µ be the molecular conductivity, and its value at infinite dilution, the fractional number of molecules dissociated is k /µop, which we may write as a.

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  • The number of undissociated molecules is then I - a, so that if V be the volume of the solution containing I gramme-molecule of the dissolved substance, we get q= and p= (I - a)/V, hence x(I - a) V =yd/V2, and constant = k.

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  • a V(I - a) This constant k gives a numerical value for the chemical affinity, and the equation should represent the effect of dilution on the molecular conductivity of binary electrolytes.

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  • The equation then becomes a 2 /V = k, or a = A / Vk, so that the molecular conductivity is proportional to the square root of the dilution.

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  • Thus in the case of cyanacetic acid, while the volume V changed by doubling from 16 to 1024 litres, the values of k were 0.00 (37 6, 373, 374, 361, 362, 361, 368).

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  • The mean values of k for other common acids were - formic, 0.0000214; acetic, o 0000180; monochloracetic, 0.0.0155; dichloracetic, 0.051; trichloracetic, 1.21; propionic, 0.0000134.

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  • The value of k, however, does not keep constant so satisfactorily in the case of highly dissociated substances, and empirical formulae have been constructed to represent the effect of dilution on them.

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  • In dilute solution such substances as hydrochloric acid and potash are almost completely dissociated, so that, instead of representing the reaction as HC1+KOH = KC1 d-H20, we must write The ions K and Cl suffer no change, but the hydrogen of the acid and the hydroxyl (OH) of the potash unite to form water, which is only very slightly dissociated.

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  • Like other plateaus, the great plateau of the centre of Asia, stretching from the Himalayas to Bering Strait, 2 has on its surface a number of gentle eminences (angehaufte Gebirge of K.

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  • (K,Li)3[Al(OH,F)2]FeAl2S15016 Biotite.

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  • (H,K)2(Mg,Fe)2(A1,Fe)2(S104) 3 Phlogopite..

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  • [H,K, (MgF)13Mg3A1(S104)3 The water which is present in muscovite.

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  • j, k, 1, Lateral muscles (j, an 26, Interior of dorsal valve.

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  • teriors; k, middles; 1, g, Umbonal muscular impresoutsiders), enabling the sions (open valves).

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  • It was long a matter in discussion whether the animal could displace its valves sideways when about to open its shell, but this has been actually observed by Professors K.

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    0
  • Let k such transpositions be necessary; then the expression X(kal aa2 N a 3.

    0
    0
  • are called the elements of the determinant; the term (-) k alaa20a37...anv is called a member of the determinant, and there are evidently n!

    0
    0
  • expression for the determinant becomes Z(-) k aitia2aa3y...anv, viz.

    0
    0
  • From the value of A we may separate those members which contain a particular element a ik as a factor, and write the portion aik A ik; A k, the cofactor of ar k, is called a minor of order n - i of the determinant.

    0
    0
  • a ll a33 ��� a32 a33 ��� a3n an2 an3 ��� ann Similarly A ik, the cofactor of aik, is shown to be the product of (-) i+k and the determinant obtained by erasing from A the ith row and k th column.

    0
    0
  • Since the determinant having two identical rows, and an3 an3 ��� ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+��� +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+�� � +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+��� +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+���+aniAnk = 0 (k .>

    0
    0
  • Similarly ali a21 a31 A =E a ik a2k a3k A li i > k > r, z�k'r alr a2r air 23',!

    0
    0
  • We may say that, in the resulting determinant, the element in the ith row and k th column is obtained by multiplying the elements in the kth row of the first determinant severally by the elements in the ith row of the second, and has the expression aklb11+ak2b12+ak3b13��� +aknbin, and we obtain other expressions by transforming either or both determinants so as to read by columns as they formerly did by rows.

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  • If we form the product A.D by the theorem for the multiplication of determinants we find that the element in the i th row and k th column of the product is akiAtil+ak2A12 +��� +aknAin, the value of which is zero when k is different from i, whilst it has the value A when k=i.

    0
    0
  • such that Aik=Aki, for the determinant got by suppressing the ith row and k th column differs only by an interchange of rows and columns from that got by suppressing the k th row and i th column.

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    0
  • � Oxl d 2x 77n If we have new variables z such that zs=4s(yl, Y2,...yn), we have also z s =1 Y 8(x1, x2,���xn), and we may consider the three determinants which i s 7xk, the partial differential coefficient of z i, with regard to k .

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  • Resultants.-When we are given k homogeneous equations in k variables or k non-homogeneous equations in k - i variables, the equations being independent, it is always possible to derive from them a single equation R = o, where in R the variables do not appear.

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  • R is a function of the coefficients which is called the " resultant " or " eliminant " of the k equations, and the process by which it is obtained is termed " elimination."

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  • CY The proof being of general application we may state that a system of values which causes the vanishing of k polynomials in k variables causes also the vanishing of the Jacobian, and in particular, when the forms are of the same degree, the vanishing also of the differential coefficients of the Jacobian in regard to each of the variables.

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  • The general theory of the resultant of k homogeneous equations in k variables presents no further difficulties when viewed in this manner.

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    0
  • Discriminants.-The discriminant of a homogeneous polynomial in k variables is the resultant of the k polynomials formed by differentiations in regard to each of the variables.

    0
    0
  • It is the resultant of k polynomials each of degree m-I, and thus contains the coefficients of each form to the degree (m-I)'-1; hence the total degrees in the coefficients of the k forms is, by addition, k (m - 1) k - 1; it may further be shown that the weight of each term of the resultant is constant and equal to m(m-I) - (Salmon, l.c. p. loo).

    0
    0
  • Similarly, if a form in k variables be expressible as a quadratic function of k -1, linear functions X1, X2, ...

    0
    0
  • Xic-1, the coefficients being any polynomials, it is clear that the k differentials have, in common, the system of roots derived from X1= X 2 = ...

    0
    0
  • function of separations of (li'12 2 13 3 ...) of specification (si 1 s 22 s 33) Suppose the separations of (11 1 13 2 1 3 3 ...) to involve k different specifications and form the k identities �1s � s Al A 2 A3 ..

    0
    0
  • (S - 1, 2, ...k), where (m�lsm"`2sm"`38...) is one of the k specifications.

    0
    0
  • The law of reciprocity shows that p(s) = zti (m 1te2tmtL3t) t=1 st It 2t 3t viz.: a linear function of symmetric functions symbolized by the k specifications; and that () St =ti ts.

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  • A table may be formed expressing the k expressions Pa l), P(2),...P(1) as linear functions of the k expressions (m"`'sm�2sm�3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry.

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    0
  • By solving k linear equations we similarly express the latter functions as linear functions of the former, and this table will also be symmetrical.

    0
    0
  • +(m -3) D 5(213) (214) (15) - (13) (14) (14), as= and and we see further that (alai +a2a2+...+amam) k vanishes identically unless (mod m).

    0
    0
  • an_1 i a n, and in general a n-k a 2 is the symbol for Q k.

    0
    0
  • = a k; and if we wish to denote, by umbrae, a product of coefficients of degree s we employ s sets of umbrae.

    0
    0
  • For the substitution rr xl =A 11 +1 2 12, 52=A21+�2E2, of modulus A1 �i = (Al�.2-A2�1) = (AM), A 2 �2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A l�l +ai(A1/.22+A2�1) +7,2X2/22, A2 = ao�l +2a1�1/�2 +a 2�2 � We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?

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  • By similarly transforming the binary n ic form ay we find Ao = (aI A 1 +a2 A2) n = aAn A l = (alAi - I -a 2 A 2) n1 (a1�1 +a2m2) = aa a � - A i n-1 A2, n-k k n-k k n-k k A = (al l+a2A2) (al�1+a2�2) = a A � =A 1 A2, so that the umbrae A1, A 2 are a A, a � respectively.

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  • we may write (AB)i(AC)j(BC)k...

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    0
  • (ab)i(ac)j(bc)k..., that the symbolic product (ab)i(ac)j(bc)k..., possesses the invariant property.

    0
    0
  • Notice, therefore, that the symbolic product (ab)i(ac)j(bc)k...

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    0
  • In order that (ab)i(ac)j(bc)k...

    0
    0
  • possess the invariant property, and we may write (AB) i (AC)'(BC) k ...A P E B C...

    0
    0
  • = t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(bc)k...aibxc2...

    0
    0
  • 2 (ac)(bc)anx xibn-i -1 x = (bc)2anbn-2Cn-2 + (ac)2an x x x The weight of a term ao°a l l ...an n is defined as being k,+2k2+...

    0
    0
  • of a4) of a 4) k m!

    0
    0
  • l ax 2 2 ax i l This is called the kth transvectant of f over 4); it may be conveniently denoted by (f, (15)k.

    0
    0
  • (a m b n) k (ab) kamkbn-k x, x - x it is clear that the k th transvectant is a simultaneous covariant of the two forms.

    0
    0
  • n of k; if k = o we have the product of the two forms, and for all values of k>n the transvectants vanish.

    0
    0
  • It is obvious that, when k is uneven, the kth transvectant of a form over itself does vanish.

    0
    0
  • We have seen that transvection is equivalent to the performance of partial differential operations upon the two forms, but, practically, we may regard the process as merely substituting (ab) k, (OW for azbx, 4x t ' respectively in the symbolic product subjected to transvection.

    0
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  • (f, 4)) k +(f, 4)) k +�(f, 4/) k +a�(1, 4)')k; and, moreover, if we require to find the kth transvectant of one linear system of forms over another we have merely to multiply the two systems, and take the k th transvectant of the separate products.

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  • The process of transvection is connected with the operations 12; for?k (a m b n) = (ab)kam-kbn-k, (x y x y or S 2 k (a x by) x = 4))k; so also is the polar process, for since f k m-k k k n - k k y = a x by, 4)y = bx by, if we take the k th transvectant of f i x; over 4 k, regarding y,, y 2 as the variables, (f k, 4)y) k (ab) ka x -kb k (f, 15)k; or the k th transvectant of the k th polars, in regard to y, is equal to the kth transvectant of the forms. Moreover, the kth transvectant (ab) k a m-k b: -k is derivable from the kth polar of ax, viz.

    0
    0
  • k (DwAk) Ak 0; (D (� A k) Ak =wJ.

    0
    0
  • k k According to the well-known law for the changes of independent variables.

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  • Now D A xA k = (n - k) A k; A� A k = k A?1; D �A A k = (n - k) A k+1;D m� A k = kA k; (n - k)A ka - w Ak - 1 aA k = O; a _ J (n - k) A k +l A k = O; kA k Ak = wJ; equations which are valid when X 1, X 2, � 1, �2 have arbitrary values, and therefore when the values are such that J =j, A k =ak� Hence °a-do +(n -1)71 (a2aa-+...

    0
    0
  • % -k Y k = (af) k a n x.

    0
    0
  • uo; 4, 1=0=f.; where u 0 =1, u1=o, assume that tfik = (af) k ay -k = f.

    0
    0
  • u k =�y.

    0
    0
  • ukx(n-2) � Taking the first polar with regard to y (n - k) (a f) xa x -k-l ay+ k (af) k-l ay -k (ab) (n -1) b12by n kn-2k-1 n-1 k(n-2) =k(n- 2)a u x u5+nax ayux and, writing f 2 and -f l for y1 and 3,21 (n-k)(a f) k+ta i k-1 + k (n - 1)(ab)(a f) k-1 (b f)4 1 k by-2 = (uf)u xn-2k-1?

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  • Moreover the second term on the left contains (a f)' c -2b z 2 = 2 (a f) k-2b x 2 - (b) /0-2a 2 � if k be uneven, and (af)?'bx (i f) of) '-la if k be even; in either case the factor (af) bx - (bf) ax = (ab) f, and therefore (n-k),bk+1 +M�f = k(n-2)f.(uf)uxn-2k-1; and 4 ' +1 is seen to be of the form f .14+1.

    0
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  • take and Uk = (af) k ai k the linear factor which occurs to the second power in f.

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  • The discriminant, whose vanishing is the condition that f may possess two equal roots, has the expression j 2 - 6 i 3; it is nine times the discriminant of the cubic resolvent k 3 - 2 ik- 3j, and has also the expression 4(1, t') 6 .

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  • For, since -2t 2 =0 3 -21f 2, 6,-3j(-f) 3, he compares the right-hand side with cubic resolvent k 3 -21X 2 k - j 2.

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  • of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)�x4; and it can be shown that 0, x, 1P are the three conjugate quadratic factors of t above mentioned.

    0
    0
  • We have A +k 1 f =0 2, O+k 2 f = x2, O+k3f =4) 2, and Cayley shows that a root of the quartic can be xpressed in the determinant form 1, k, 0.1y the remaining roots being obtained by varying 1, k, x the signs which occur in the radicals 2 u The transformation to the normal form reduces 1, k 3, ?

    0
    0
  • If 4) = rx.sx, the Y2 =1 normal form of a:, can be shown to be given by (rs) 4 .a x 4 = (ar) 4s: 6 (ar) 2 (as) 2rxsy -I- (as) 4rx; 4) is any one of the conjugate quadratic factors of t, so that, in determining rx, sx from J z+k 1 f =o, k 1 is any root of the resolvent.

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    0
  • To determine them notice that R = (a6) and then (f, a 5) 5 = - R 5 (k1 +k2+k3) (f, a 4 5) 5 = - 5R5 (m 1 k 1+ m 2 k 2+ m 3 k 3), (f, a352) 5 = -10R5 (m21ke +m2k2+m3k3) three equations for determining k 1, k2, k3.

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    0
  • These may be written, for the binary nie, Zka k _.

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    0
  • l aa k -x 2 d d- = 0; Z(nk)ak+l adk - x ldd2=0; or in the form d d 52-x 2(7 =0, O - x1ax2 = 0; where 0 = ao d a l + 2a 1 -?...+na,,_id an, 0 = nal dao -?

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    0
  • The general form of perpetuant is (4 K 3 A 2"`) and the generating function 1-z2.1-z3.1-z4 In general when 0 is even and =20, the condition is a l a 2 ...U 24 II(v 1 +a 2)II(a l +a 2 +cr 3)...II(Q 1 +a 2 -}-...

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    0
  • (1-20) The actual form of a perpetuant of degree 0 has been shown by MacMahon to be +1 K0_1+1 K 3+20-4 K2, 01, 0-2, 0-3, ...3, 2), K 0, Ke -1, ...K 2 being given any zero or positive integer values.

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    0
  • Or, lastly, we may leave the exponents h, k, j,1, untouched and consider the product i i i 2 .

    0
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  • The alchemists designated it by the sign of Saturn k.

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  • A German translation of the last is contributed by K.

    0
    0
  • A substance of which the real susceptibility is will, when surrounded by a medium having the susceptibility k', behave towards a magnet as if its susceptibility were - -}-4,rK').

    0
    0
  • K is a commutator for reversing the direction of the magnetizing current, and G a galvanometer for measuring it.

    0
    0
  • 9) from F to D, while at the same time the commutator K is rapidly worked, a series of alternating currents of gradually diminishing strength being thus caused to pass through the magnetizing coil.

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  • The current passes through the rocking key K, which, when thrown over to the right, places a in contact with c and b with d, and when thrown over to the left, places a in contact with e and b with f.

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  • When the switch S is closed, K acts simply as a commutator or current-reverser, but if K is thrown over from right to left while S is opened, not only is the current reversed, but its strength is at the same time diminished by the interposition of the adjustable resistance R2.

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  • The reversing key K having been put over to the left side, the short-circuit key S is suddenly opened; this inserts the resistance R, which has been suitably adjusted before hand, and thus reduces the current and therefore the magnetizing force to a known value.

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  • To continue the process, the key K is turned over to the right-hand side, and then, while S is open, is turned back, thereby not only reversing the direction of the current, but diminishing its strength by an amount depending upon the previous adjustment of R2.

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    0
  • The experiments of K.

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  • Y Y' is a so.- iron yoke, which rocks upon knife-edges K and constitutes the beam of the balance.

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  • and K.

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  • Trans., 1888, 179A, 325), who found that the initial value of K was I.

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    0
  • Nagaoka and K.

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  • Mag., 18 99, 1 7, 539; K.

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    0
  • Verh., 1904, 6, 4, 21 I; K.

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    0
  • Nagaoka, who also, in conjunction with K.

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    0
  • The influence of temperature varying between wide limits has formed the subject of a research by K.

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    0
  • Mag., 1898, 46, 261; 1902, 4, 45; K.

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    0
  • 13; K.

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  • Further contributions to the subject have been made by K.

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    0
  • The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the rotatory power, or rotational coefficient.

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    0
  • The following values of K for different metals are given by E.

    0
    0
  • The subject, which is of importance in connexion with theories of magnetostriction, has been investigated by K.

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    0
  • Owing to the difficulty of determining the magnetization I and the susceptibility K with accuracy, it has not yet been possible to submit this formula to a quantitative test, but it is said to afford an indication of the results given by actual experiment.

    0
    0
  • K Xis'.

    0
    0
  • The best modern determinations of the value of K for gaseous oxygen agree very fairly well with that given by Faraday in 18J3 (Exp. Res.

    0
    0
  • 0, so that Io 6 K =33700/0.

    0
    0
  • If V is the volume of a ball, H the strength of the field at its centre, and re its apparent susceptibility, the force in the direction x is f= K'VH X dH/dx; and if K',, and are the apparent susceptibilities of the same ball in air and in liquid oxygen, K' Q -K'o is equal to the difference between the susceptibilities of the two media.

    0
    0
  • The magnetic properties of the metal at different temperatures and in fields up to 1350 units have been studied by P. Curie (loc. cit.), who found that its " specific susceptibility " (K) was independent of the strength of the field, but decreased with rise of temperature up to the melting-point, 273° C. His results appear to show the relation - K X10 6 = I'381 - O'o0155t°.

    0
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  • Putting t°= - 182 in the equation given above for Curie's results, we get K X Io 6 = - 1.66, a value sufficiently near that obtained by Fleming and Dewar to suggest the probability that the diamagnetic susceptibility varies inversely as the temperature between-182° and the melting-point.

    0
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  • de Phys., 18 95, 4, 204) of the specific susceptibility K of other diamagnetic substances at different temperatures.

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    0
  • For all diamagnetic substances, except antimony and the value of K was found to be independent of the temperature.

    0
    0
  • If W is the weight of iron present per c.c. at about io° C., then for ferric salts Io 6 K =266W-0'77 and for ferrous salts 10 6 K =206W - 077, the quantity - 0.77 arising from the diamagnetism of the water of solution.

    0
    0
  • Annexed are values of Io 6 K for the different salts examined, w being the weight of the salt per c.c. of the solution.

    0
    0
  • Sitz., 1897, 106, II.a, p. 623, and 1898, 107, II.a, p. 5) the atomic susceptibilities k of the metals nickel, chromium, iron, cobalt and manganese in solutions of their salts are as follows: - Fe(i) is iron contained in FeC1 2 and Fe(2) iron contained in Fe2(NOs)s.

    0
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  • Curie has shown, for many paramagnetic bodies, that the specific susceptibility K is inversely proportional to the absolute temperature 0.

    0
    0
  • k>00 6.

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    0
  • Lindstrom, G., " Researches on the Visual Organs of the Trilobites," K.

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    0
  • During the winter of 1916-7 these volunteers experienced heav y losses; after the Russian revolution in March 1917, Bolshevik sympathies spread among these troops and large sections of the people, while on the other hand national aspirations united the Farmers' Political League (40,000 members), headed by K.

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  • 23, independence was declared, and K.

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    0
  • Stern, on terrestrial magnetism by Goldschmidt, and on the method of least squares by K.

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    0
  • k, Present corm.

    0
    0
  • k', Younger corm produced from k.

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  • wh, Roots from k', which grows at expense of k.

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  • Young corm produced from k', in autumn, which in succeeding autumn will produce flowers.

    0
    0
  • Kerp and K.

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    0
  • over, following the indications already given by K.

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    0
  • Potash alum, K 2 SO 4 �Al 2 (SO 4)a�24H 2 O, crystallizes in regular octahedra and is very soluble in water.

    0
    0
  • Chrome alum, K 2 SO 4 �Cr 2 (SO 4) 3.24H 2 O, appears chiefly as a by-product in the manufacture of alizarin, and as a product of the reaction in bichromate batteries.

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    0
  • Pyevtsoff, K.

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    0
  • Roborovsky and P. K.

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    0
  • Scholl and K.

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    0
  • Stier (1850), K.

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  • " J is aged 40, and K is aged 26; when will J be twice as old as K?

    0
    0
  • Thus P = kQ+R, where k is an integer.

    0
    0
  • Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.

    0
    0
  • The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the equalities = - I.

    0
    0
  • xii.; K.

    0
    0
  • If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element dS at Q is dS 1 dS - p cos k(at - p+ 4 A) = - -- sin k(at - p).

    0
    0
  • If dS =27rxdx, we have for the whole effect 27r œ sin k(at - p)x dx, f P ' or, since xdx = pdp, k = 27r/A, - k fr' sin k(at - p)dp= [- cos k(at - p)]°° r.

    0
    0
  • cos k(at-r), it is necessary to suppose that the integrated term vanishes at the upper limit.

    0
    0
  • The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

    0
    0
  • 2 2 c os k d x d y] .

    0
    0
  • We readily find (with substitution for k of 27r/X) a2b S n J s in fl „2a2E2 „2b2n2 f2X2 f2X2 as representing the distribution of light in the image of a mathematical point when the aperture is rectangular, as is often the case in spectroscopes.

    0
    0
  • Writing for brevity k =p, k =q, (1), we have for the general expression (§ 11) of the intensity X2 f 212 = S 2 +C 2..

    0
    0
  • f + 1 sin k a - f+ " dxdy = - 2 1h sin n k ?.

    0
    0
  • k p h s i n h .

    0
    0
  • s i n k Eh at - f - f ?

    0
    0
  • We thus get for the disturbance at E, 7 t, due to this stream knl s in f 2f t f t .s i n k at - f - - { - 2 f.

    0
    0
  • The original investigation of Stokes, here briefly sketched, extends also to the case where the streams are of unequal width h, k, and are separated by an interval 2g.

    0
    0
  • Ascending series for C and S were given by K.

    0
    0
  • (11), where r is the distance between the element dx dy dz and the point where a l is estimated, and k = n/b = 27r/X (12), X being the wave-length.

    0
    0
  • See also for ethnological questions, Mongolian hypothesis: K.

    0
    0
  • Iranian hypothesis: K.

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    0
  • K i tchener an idea, and he resolved upon the scheme of fencing in areas by chains of blockhouses such as those already constructed for the protection of the railways.

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    0
  • Hettema, jun., " Geschiedenis van het grondgebied der Zuid-Afrikaansche Republiek," Tijds k.

    0
    0
  • Pernter (Neues fiber den Regenbogen, Vienna, 1888) and by K.

    0
    0
  • K 2 SnO 3 into K2SnF6), which are closely analogous to, and isomorphous with, fluosilicates.

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    0
  • 1 "dass einer der Sektierer von den andern als Christus verehrt werde," K.

    0
    0
  • des k.

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    0
  • Schirrmacher, Die letzten Hohenstaufen (Göttingen, 1871); K.

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    0
  • At present the best texts are those by K.

    0
    0
  • Hozier, The Seven Weeks' War (1867; new edition, London, 1906); Antheil des k.

    0
    0
  • (Leipzig, 1867); Bavarian General Staff, Antheil der k.

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    0
  • Joachim, Die Politik des letzten Hochmeisters in Preussen, Albrecht von Brandenburg (Leipzig, 1892); K.

    0
    0
  • Schultze, "Die altchristlichen Grabstatten Siziliens," Jahrbuch des k.

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    0
  • Amongst special treatises may be mentioned K.

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  • ath ' K;idbrooke Hither Green: Wes i Bromley C Longitude West 0°4' of Greenwich Rai lways....-- underground Canals ' '; County Metropolitan Boroughs ...... :: ...

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    0
  • a g s?o 3 oldeHr? ?k'?o r{d?El rpaoumc „14 ???(?

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  • Benzoflavin, an isomer of chrysaniline,1`is also a dye-stuff, and has been prepared by K.

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  • It is only soluble in a mixture of hydrofluoric and nitric acid, or in solutions of the caustic alkalis, in the latter case yielding hydrogen and a silicate: Si-}-2KHO+H 2 O = K 2 SiO 3 +2H 2.

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  • Potassium percarbonate, K 2 C 2 0 6, is obtained in the electrolysis of potassium carbonate at -10 to -15°.

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  • The five K's are (I) the kes or uncut hair of the whole body, (2) the kachh or short drawers ending above the knee, (3) the kara or iron bangle, (4) the khanda or small steel dagger,(5) the khanga or comb.

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  • For if the liquid of density a rises to the height h and of density p to the height k, and po denotes the atmospheric pressure, the pressure in the liquid at the level of the surface of separation will be ah+Po and pk +po, and these being equal we have Uh = pk.

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  • (I) The principle is illustrated in the article Barometer, where a column of mercury of density a and height h, rising in the tube to the To:ricellian vacuum, is balanced by a column of air of density p, which may be supposed to rise as a homogeneous fluid to a height k, called the height of the homogeneous atmosphere.

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  • this makes k 27,200 ft., about 8300 metres.

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  • With uniform temperature, taking h constant in the gas-equation, dp / dz= =p / k, p=poet/ k, (9) so that in ascending in the atmosphere of thermal equilibrium the pressure and density diminish at compound discount, and for pressures p 1 and 1, 2 at heights z 1 and z2 (z1-z2)11?

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  • In the more general case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po, denoting the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density.

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    0
  • Then dp/dz=kdp/dz = P, = Poe ik, p - po= kpo(ez Ik -1); (16) and if the liquid was incompressible, the depth at pressure p would be (p - po) 1po, so that the lowering of the surface due to compression is ke h I k -k -z= 1z 2 /k, when k is large.

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  • (17) For sea water, A is about 25,000 atmospheres, and k is then 25,000 times the height of the water barometer, about 250,000 metres, so that in an ocean 10 kilometres deep the level is lowered about 200 metres by the compressibility of the water; and the density at the bottom is increased 4%.

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  • (2) (3) Suppose the density p varies as some nth power of the depth below 0, then (7) and the lowering of the surface is 2 ° - z=klog po - z= - k log(1 - k) - zt12 k (20) Po as before in 17).

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  • Proceeding as in § 16 for the determination of the C.P. of an area, the same argument will show that an inclining couple due to K FIG.

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  • The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area.

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    0
  • and as we prove subsequently (§ 37) that the vortex lines are composed of the same fluid particles throughout the motion, the surface m and satisfies the condition of (6) § 23; so that K is uniform throughout the fluid at any instant, and changes with the time only, and so may be replaced by F(t).

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  • d - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.

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  • Thus if d,/ is the increase of 4, due to a displacement from P to P', and k is the component of velocity normal to PP', the flow across PP' is d4 = k.PP'; and taking PP' parallel to Ox, d,, = vdx; and similarly d/ ' = -udy with PP' parallel to Oy; and generally d4,/ds is the velocity across ds, in a direction turned through a right angle forward, against the clock.

    0
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  • Over any ellipse n, moving with components U and V of velocity, =i+Uy-Vx=[msh(n-a) cos (3+Ucshn] sin k -[msh(n-a) sin (3+Vcchn] cos h; (7) so that ' =o, if U c sh n cos R, V = c ch n sin a, (8) m sh(n - a) m sh(n - a).

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  • The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.

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  • Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a function ' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to Oy and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current function," as it is constant along a stream line (Trans.

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    0
  • Thus, in (5), the cyclic constant k = 27rm.

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    0
  • (to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

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  • Trans., 1890); the solution is given by ch nS2=sn w, shnS2=i cn w (II) so that, round the boundary of the polygon, ik = K', sin n8 =o; and on the surface of the vortex 1P= o, q = Q, and cos n8=sn4p,nB= Zit -am sic, (12) the intrinsic equation of the curve.

    0
    0
  • vertical, where Wh tan 0 = N = (c 2 - cl) c2 g2 tan 0, (6) (7) in which we have put k' 2 = ek 2, where E is a numerical factor depending on the shape.

    0
    0
  • the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

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  • I +W a W a), ' (k) 4 (I I) I+ w- R For a shot in air the ratio W'/W is so small that the square may be neglected, and formula (II) can be replaced for practical purpose in artillery by tan26= n2 = W i (0 - a) (k ð)7()4, (12) if then we can calculate /3, a, or (3-a for the external shape of the shot, this equation will give the value of 6 and n required for stability of flight in the air.

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  • Hamilton (London, 1900-2); K.

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  • Luschan and K.

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  • Labruscae, which, when the attac k is severe, cause the destruction of the leaves, the only part they assail.

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  • See James K.

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    0
  • Eucharistie (1896); Renz, Die Geschichte des Messopferbegriffs (1901); K.

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    0
  • Gorres, Altdeutsche Volksand Meisterlieder (1817); K.

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  • Lyon, Minneand Meistergesang (1882); K.

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  • in length, situated in the north of Pisidia on the frontier of k Phrygia, at an elevation of 3007 ft.

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    0
  • Schlenning in Jahrbuch des K.

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  • He next entered the university of Bonn, but migrated to Erlangen when the professor of chemistry, K.

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    0
  • A MS. discovered at Prague in 1881 contains lines 958-1106, and another, in the Vatican library, discovered by K.

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    0
  • The fragments of the Heliand and the Genesis contained in the Vatican MS. were edited in 1894 by K.

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  • K They seem to have stood in much the same relation to the rulers of Yemen, as the people of Hira to the Persians and the Ghassanids to Rome.

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    0
  • Milne Rae, The Syrian Church in India (1892); K.

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  • Hansisches Urkundenbuch, bearbeitet von K.

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    0
  • Hohlbaum, K.

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    0
  • trans., 1851, Edinburgh), K.

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    0
  • Braune (in Lange's BibelWerk, 2nd ed., 1875), Von Soden (1890), K.

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    0
  • K, sucking Diptera, belonging to various families, but now by common consent restricted to those known to naturalists as Culicidae, or gnats.

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    0
  • The alkaline titanate first produced is converted into crystalline fluotitanate, K 2 TiF 6, which is with difficulty soluble and is extracted with hot water and filtered off.

    0
    0
  • Potassium titanofluoride, K 2 TiF 6.

    0
    0
  • 20; K.

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    0
  • This phase of Iberian theory opens with K.

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    0
  • " Ober die Entstehung der Bezugsformen des baskischen Zeitworts "; Denkschriften der K.

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    0
  • 6-8; K.

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    0
  • According to K.

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  • the common Greek renderings, Kuptos Svv uccov and K.

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  • A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut; f, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.

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    0
  • From Lankester's Treatise on The life history of the order is almost un Zoology, part iv.) k nown, but at the time of hatching the young FIG.

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  • iii.-vii., New York, 1896-1906); James K.

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    0
  • (Oxford, 1897); Miss K.

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    0
  • Schaab, Geschichte der Stadt Mainz (Mainz, 1841-1845); K.

    0
    0
  • The earliest Semitic records give its form as y or more frequently k or The form is found in the earliest inscriptions of Crete, Attica, Naxos and some other of the Ionic islands.

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  • It is hard to decide why Latin adopted the g-symbol with the value of k, a letter which it possessed originally but dropped, except in such stereotyped abbreviations as K.

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  • There are at least two possibilities: (1) that in Latium g and k were pronounced almost identically, as, e.g., in the German of Wurttemberg or in the Celtic dialects, the difference consisting only in the greater energy with which the k-sound is produced; (2) that the confusion is graphic, K being sometimes written I C, which was then regarded as two separate symbols.

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  • The symbol G was a new coinage in the 3rd century B.C. The pronunciation of C throughout the period of classical Latin was that of an unvoiced guttural stop (k).

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  • Zug in die Lombardei vom Jahre 951 (Eisenberg, 1891); and K.

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    0
  • Mr K.

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    0
  • The constant wars of the time left their impress Th D k upon everything.

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  • The history of Kito warewhich, being for the most part faience, belongs to an entirely different category from the Hizen porcelains K -~ spoken of aboveis the history of individual ceramists 10 0.

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  • K!

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  • It is known to Western collectors K

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    0
  • Owen, French Skeptics of the Renaissance (London, 1893); K.

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    0
  • Richter, Verzeichnis der Periodica im Besitze der k.

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    0
  • Grassauer (Vienna, 1898) Konigliche Bibliothek zu Berlin, Alphabetisches Verzeichnis der laufenden Zeitschriften (1908); Systematisches Verzeichnis der laufenden Zeitschriften (1908); Alphabetisches Verzeichnis der laufenden Zeitschriften, welche von der K.

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  • In Berzelius' system + potassium sulphate is to be regarded as K 2 0.S0 3; electrolysis should simply effect the disruption of the positive and negative components, potash passing with the current, and sulphuric acid against the current.

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  • If a solution of potassium acetate be electrolysed the products are ethane, carbon dioxide, potash and hydrogen; in a similar manner, normal potassium succinate gives ethylene, carbon dioxide, potash and hydrogen; these reactions may be represented: CH 3 �CO 2;K CH 3 CO 2 K' CH 2 �CO 2 1K CH 2 CO 2 K' --> I + + I I -i iI + CH 3 �CO 21 K CH 3 CO 2 K' CH 2 �CO 2 iK CH 2 CO 2 K' By electrolysing a solution of potassium ethyl succinate, KO 2 C�(CH 2) 2 CO 2 C 2 H 5, the KO 2 C� groups are split off and the two residues �(CH 2) 2 CO 2 C 2 H 5 combine to form the ester (CH2)4(C02C2H5)2.

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  • The prime minister was Dr. K.

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  • Purizkis (Christian Democrat); of War, Dr. Shimkus (Popular Socialist); of the Interior, K.

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    0
  • Skipitis (Santara); of Education, K.

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    0
  • Skalweit, Landwirtschaft in den Litauischen Gouvernements (1918); Ludwig Sochassever, Memel, der Hafen von Litauen; K.

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  • If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.

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  • If the dielectric or separating insulator has a constant K, then the capacity becomes K times as great.

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    0
  • The simplest method of determining it numerically is, therefore, that adopted by Faraday.4 Table Dielectric Constants (K) of Solids (K for Air = I).

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  • He constructed two equal condensers, each consisting of a metal ball enclosed in a hollow metal sphere, and he provided also certain hemispherical shells of shellac, sulphur, glass, resin, &c., which he could so place in one condenser between the ball and enclosing sphere that it formed a condenser with solid dielectric. He then determined the ratio of the capacities of the two condensers, one with air and the other with the solid dielectric. This gave the dielectric constant K of the material.

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  • Taking the dielectric constant of air as unity he obtained the following values, for shellac K = 2.0, glass K.

    0
    0
  • 76, and sulphur K = 2.24.

    0
    0
  • [[Table Ii]].-Dielectric Constant (K) of Liquids.

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  • [[Table Iv]].-Dielectric Constants (K) of Gases at '15°' C. and 760 mm.

    0
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  • There are very few substances, however, for which the optical refractive index has the same value as K for steady or slowly varying electric force, on account of the great variation of the value of K with frequency.

    0
    0
  • Suppose that the dielectric has a constant K, then we must multiply both sides by K and the expression for the energy per unit of volume of the field is equivalent to z DE where D is the displacement or polarization in the dielectric.

    0
    0
  • In 1833 Hahn's pamphlet against K.

    0
    0
  • If we write K for the adiabatic elasticity, and k for the isothermal elasticity, we obtain S/s = ECÆF = K/k.

    0
    0
  • K, k, Adiabatic and isothermal elasticities.

    0
    0
  • The solubility of gold in cyanide solutions was known to K.

    0
    0
  • According to Christy, the precipitation with zinc follows equations for 2 according as potassium cyanide is present or not: (1) 4 KAu(CN)2+4Zn+2H20=2Zn(CN)2+ K 2 Zn(CN) 4 +Zn(OK) 2 +4H+4Au; (2) 2KAu (CN) 2 +3Zn+4KCN+2H 2 0 = 2K 2 Zn(CN) 4 +Zn(OK) 2 +4H+2Au; one part of zinc precipitating 3.1 parts of gold in the first case, and 2.06 in the second.

    0
    0
  • When the national Democratic party in 1844 nominated and elected James K.

    0
    0
  • K&rte, s.v.

    0
    0
  • Harnack articles in HerzogHauck's Realencyklopddie (" Athanasianum " and " Konstantinopolitanisches Symbol ") (1896), &c.; K.

    0
    0
  • Holstein (1862-1869); K.

    0
    0
  • East of Bhutan, amongst the semi-independent hill states which sometimes own allegiance to Tibet and sometimes assert complete freedom from all authority, the geographical puzzle of the course of the Tsanpo, the great river of Tibet, has been solved by the researches of Captain Harman, and the explorations of the native surveyor "K.

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  • See his autobiography, Aus meinem Leben: Selbstbiographie von K.

    0
    0
  • Zingerle and K.

    0
    0
  • Let k denote this height, and let PM be denoted by 1.

    0
    0
  • Then, by Boyle's law (u - v+al) (h - k) = (u - v)h, and therefore v=u - al(h - k)/k.

    0
    0
  • The volume u may be determined by repeating the experiment when only air is in the cup. In this case v =o, and the equation becomes (u --al l) (h - k') =uh, whence u = al' (h - k l) /k'.

    0
    0
  • Scudder in K.

    0
    0
  • (4) vi., 1870); C. Stal's Enumeratio Hemipterorum (K.

    0
    0
  • It also gives rise to super-acid salts, such as KHTe03 H2Te03; K 2 TeO 3.3TeO 2.

    0
    0
  • iii.), and Carl K.

    0
    0
  • Stengel and K.

    0
    0
  • k clamps the telescope in declination, n clamps it in right ascension, and the handles m and I provide slow motion in declination and right ascension respectively.

    0
    0
  • Side-shake is prevented by the screws and pieces k, k, k, k.

    0
    0
  • Pertantalic acid, HTaO 4, is obtained in the hydrated form as a white precipitate by adding sulphuric acid to potassium pertantalate, K 3 Ta0 5.

    0
    0
  • The word alkali supplied the symbol for potassium, K (kalium).

    0
    0
  • Tijdsch., 1886, 454-70; Omwerkings en Compilatie-Hypothesen toegepast op de Apoc. van Johannis, 1888) advanced the theory of two Jewish sources (K and 3), which were subsequently worked over by a Christian redactor.

    0
    0
  • If the clause Kai k Tou aiyaros rC:ov µapri)pcov'Incroii in 6 is an addition, then he thinks the source was Jewish and the "blood of the saints" was that shed at the destruction of Jerusalem, and the forecast of the author related to the destruction of Rome.

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  • It was scientifically explored by him, in company with Professors Charles Peabody and Warren K.

    0
    0
  • 4 will convey a general idea of the appearance of sits, - k, m, n showing different stages.

    0
    0
  • Feit and K.

    0
    0
  • Fischer (Leipzig, 1786), and K.

    0
    0
  • Four high roads radiate from Peking, one leading to Urga by way of Shan-hwa Fu, which passes through the Great Wall at Chang-kiu K`ow; another, which enters Mongolia through the.

    0
    0
  • Ku-pei K`ow to the north-east, and after continuing that course as far as Fung-ning turns in a north-westerly direction to Dolonnor; a third striking due east by way of Tung-chow and Yung-Ong Fu to Shan-hai Kwan, the point where the Great Wall terminates on the coast; and a fourth which trends in a south-westerly direction to Pao-ting Fu and on to Tai-yuen Fu in Shan-si.

    0
    0
  • 5), and finds its way into the interior of the wheel, A, driving the air in front of it through the airpassages K, K.

    0
    0
  • The air-ways k, k, in the fixed vanes establish communication between the cores of the vortices and the atmosphere.

    0
    0
  • The wheel D, keyed to the shaft overcoming the resistance to be measured, is driven from wheel N by two bevel wheels L, L, carried in a loose pulley K.

    0
    0
  • A torque applied to the shaft A can be transmitted to D, neglecting friction, without change only if the central pulley K is held from turning; the torque required to do this is twice the torque transmitted.

    0
    0
  • Towards the close of 1793 Fichte received an invitation to succeed K.

    0
    0
  • A Bohemian edition of the works has been edited by K.

    0
    0
  • There are monuments to the naturalist K.

    0
    0
  • Its overthrow was effected by Lavoisier, who showed that combustion was simply an oxidation, the oxygen of the atmosphere (which was isolated at about this time by K.

    0
    0
  • Although the marginal note in the coronation order of Queen Victoria indicates "K.

    0
    0
  • Fullerborn, Beitrage zur physischen Anthropologie der Nord-Nyassaldnder (Berlin, 1902), a fine series of pictures of native types, and Das Deutsche Nyassaand Ruwuma gebiet, Land and Leute (Berlin, 1906); K.

    0
    0
  • Heinzel, "Ober die Nibelungensage," in Sitzungsberichte der K.

    0
    0
  • Schlumberger, Nicephore Phocas (Paris, 1890); K.

    0
    0
  • Valuable also are his papers on Abelian transcendents, and his investigations in the theory of numbers, in which latter department he mainly supplements the labours of K.

    0
    0
  • Doederlein, Gedachtnissrede fiir Herrn K.

    0
    0
  • Returning to Buffalo in 1830 he formed, in 1832, a partnership with Nathan K.

    0
    0
  • 6 By Caphtor the Septuagint has sometimes understood Cappadocia, which indeed may be valid for its age, but the name is to be identified with the Egyptian K(a)ptar, which in later Ptolemaic times seems to mean Phoenicia, although Keftiu had had another connotation.

    0
    0
  • Hitzig, Urgeschichte der Philister (1845), with the theory of the Pelasgic origin of the Philistines; K.

    0
    0
  • Kluckhohn, Geschichte des Gottesfriedens (Leipzig, 1857); K.

    0
    0
  • Potassium osmiate, K 2 0sO 4 2H 2 0, formed when an alkaline solution of the tetroxide is decomposed by alcohol, or by potassium nitrite, crystallizes in red octahedra.

    0
    0
  • Potassium osmichloride, K 2 OsC1 6, is formed when a mixture of osmium and potassium chloride is heated in a current of chlorine, or on adding potassium chloride and alcohol to a solution of the tetroxide in hydrochloric acid.

    0
    0
  • The atomic weight of the metal has been determined by K.

    0
    0
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