How to use Y in a sentence

y
  • The enlarged glandular structure of the walls of the rectum is frequent in the Pectinibranchia, as is also though not universal the gland marked y, next to the rectum.

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  • Whether through jealous y of the ascendancy which Turgot had acquired over the king, or through the natural incompatibility of their characters, he was already inclined to take sides against Turgot, and the reconciliation between him and the queen, which took place about this time, meant that he was henceforth the tool of the Polignac clique and the Choiseul party.

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  • But in his character as phenomena must be examined or what may be neglected p y g in economic inquiry.

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  • B, The diblastula has become a trochosphere by the development of the ciliated ring y r (optical section).

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  • Y oshamin desired to raise himself above the Primal Light, but failed in the attempt, and was punished by removal out of the pure aetherial world into that of inferior light.

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  • The only direct reply made to the Explicatio was the Tractatus de vera excommunicatione (1590) by Theodore Beza, who found himself rather savagely attacked in the Confi y matio thesium; e.g."

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  • Of Herrera's writings, the most valuable is his Historia general de los hechos de los Castellanos en las islas y tierra firme del Mar Oceano (Madrid, 1601-1615, 4 vols.), a work which relates the history of the Spanish-American colonies from 1492 to 1554.

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  • For example, the con Head muscles y traction of the tergo A 's sternal muscles, connect r.

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  • An air-tube consists of an epithelium of large polygonal cells with a thin basement-membrane externally and y a chitinous layer internally, the lastnamed being continuous with the outer cuticle.

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  • His attempt at classification was certainly better than that of Linnaeus; and it is rather curious that the researches of the latest ornithologists point to results in some degree comparable with Brisson's systematic arrangement, for they refuse to keep the birds-of-prey at the head of the Class A y es, and they require the establishment of a much larger number of " Orders " than for a long while was thought advisable.

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  • The last seven of its fourteen volumes include the Class A y es, and the first part of them appeared in 1809, but, the original author dying in 1815, when only two volumes of birds were published, the remainder was brought to an end in 1826 by his successor, who afterwards became well known as an entomologist.

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  • The most novel feature, and one the importance of which most ornithologists of the present day are fully prepared to admit, is the separation of the class A y es into two great divisions, which from one of the most obvious distinctions they present were called by its author Carinatae' and Ratitae, 2 according as the sternum possesses a keel (crista in the phraseology of many anatomists) or not.

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  • He also admitted among his characteristics a physiological consideration (apparently derived from Oken 1) dividing the class A y es into two sections Altrices and Praecoces, according as the young were fed by their parents or, from the first, fed themselves.

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  • Herein he divided the class A y es into two subclasses, to which he applied the names of Insessores and Grallatores (hitherto used by their inventors Vigors and Illiger in a different sense), in the latter work relying chiefly for this division on characters which had not before been used by any systematist, namely that in the former group monogamy generally prevailed and the helpless nestlings were fed by their parents, while the latter group were mostly polygamous, and the chicks at birth were active and capable of feeding themselves.

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  • No doubt they all agreed in saying that they were prosecuting Y g Y g Y P g a search for what they called the true system of nature; but that was nearly the end of their agreement, for in what that true system consisted the opinions of scarcely any two would coincide, unless to own that it was some shadowy idea beyond the present power of mortals to reach or even comprehend.

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  • Starting from the basis " that the phrase `birds are greatly modified reptiles' would hardly be an exaggerated expression of the closeness " of the resemblance between the two classes, which he had previously brigaded under the name of Sauropsida (as he had brigaded the Pisces and Amphibia as Ichthyopsida), he drew in bold outline both their likenesses and their differences, and then proceeded to inquire how the A y es could be most appropriately subdivided into orders, suborders and families.

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  • At Z is the treasury of St Mark, which was originally one of the towers belonging to the old ducal palace; E, site of old houses; G, clocktower; H, old palace of procurators; J, old library; M, two columns; N, Ponte della Paglia; 0, Bridge of Sighs; W, Giants' Staircase; X, sacristy of St Mark; Y, Piazzetta.

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  • Its cartesian equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is r 2 = 2a 2 cos 20.

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  • Such curves are given by the equation x 2 - y 2 = ax 4 -1bx 2 y 2 +cy 4 .

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  • Amongst its buildings are the Gothic five-naved church of St Barbara, begun in 1368, the Gothic church of St Jacob (14th centur y) and the Late Gothic Trinity church (end of 15th century).

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  • This light railway runs at a considerable elevation (some 700 ft.), commanding a view across the valley and lake of Tan y Bwlch.

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  • This question can readily be answered as regards the past forty years or so, for which material g p y y ?

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  • Bitumen is, in its various forms, one of the most widel y -distributed of substances, occurring in strata of every geological age, from the lowest Archean rocks to those now in process of deposition, and in greater or less quantity throughout both hemispheres, from Spitzbergen to New Zealand, and from California to Japan.

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  • But Strabo, Pliny and Ptolemy, as well as the y better Moslem geographers, drew the eastern only under the Graeco-Roman administration that we find a definite district known as Syria, and that was at first restricted to the Orontes basin.

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  • The conversion of Basuto A land into a crown colony contributed alike to the Y pros perityof the Basuto,the security of the property of neighbouring colonists and a peaceful condition among the natives of South Africa generally.

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  • The Malays to-day are Sunni Mahommedans of the school of Shafi`i, and the y habitually use the terms Orang Malayu, i.e.

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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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  • Of the total population 71.36% were Sla y s, who were scarcely distinguishable from their Bohemian neighbours.

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  • The name of Czech, however, is usually reserved for the Bohemians, while the Sla y s of Moravia and West Hungary are called Moravians and Slovacs.

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  • At this period there seemed a strong probability of the junction of the north-western and southeastern Sla y s, and the formation of a great Slavonic power to east of the German empire.

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  • Meanwhile the Spanish governor-general, Manuel Macias y Casado, had ordered the forces under his command in the southern part of the island to fall back towards the ridge of mountains intersecting it from east to west, just north of the town of Coamo.

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  • The best modern critical account in Spanish is Salvador Brau, Puerto Rico y su historia (Valencia, 1894).

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  • There are now n-, y varieties of the cultivated oat included under two principr races - common FIG.

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  • The first question has not yet been solved, although it has been speculated upon y ?

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  • We derived this substance from ethane by introducing a meth y l group; hence it may be termed " methylethane."

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  • Similarly, greater atomic complexity is reflected in a further decrease in the ratio C y /Cy.

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  • Then the number of single bonds is 2n - m-2p, and the heat of combustion becomes H,=nE+m77+p(2X - Y).

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  • If triple bonds, q in number, occur also, and the energy of such a bond be Z, the equation for H becomes H = nE-+-mn -1-p(2X - Y) +q(3X - Z).

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  • Thomsen deduces the actual values of X, Y, Z to be 14.71, 13.27 and zero; the last value he considers to be in agreement with the labile equilibrium of acetylenic compounds.

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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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  • In Egypt we find them classified as avyyeve;s, 46rtpot rag cvyyevEat y, apXcvwµarocuAalEs, 7rpwTot 0LAot, q5LAot (in the narrower sense),Sca60xoc. For the Seleucid kingdom vwyyEvEis,7rpWToc 0LAoc and 4'LAot are mentioned.

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  • Ch is always to be sounded as in church, g is always hard; y always represents a consonant; whilst kh and gh stand for gutturals.

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  • This map was repeatedly revised, Antgria- g P P Y ?

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  • Vergara y Velasco's Atlas de geografia colombiana (1906-1908); Ecuador is fairly well represented by Th.

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  • Since that time, however, valuable maps have been published by an Oficina de mensura de tierras, by a seccion de geografia y minas connected with the department of public works, by the Oficina hidrografica, and more especially in connexion with surveys necessitated by the boundary disputes with Argentina, which were settled by arbitration in 1899 and 1902.

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  • Although many " General " and other meetings were held in different Period of parts of the country for the purpose of setting P Y P P g forth Quakerism, the notion that the whole Christian church would be absorbed in it, and that the Quakers were, in fact, the church, gave place to the conception that they were " a peculiar people " to whom, more than to others, had been given an understanding of the will of God.

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  • The name Visby is derived from the old Norse y e (sanctuary) and by (town).

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  • The United State s h a d in 1 forbidden any a 794 Y m par ticipation by American subjects in the slave trade to foreign countries; they now prohibited the importation of slaves from Africa into their own dominions.

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  • This was known as the Moret Law, having been carried through the house of representatives by Senor Moret y Prendergast, then minister for the colonies.

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  • Fully realizing, the difficult P Y g?

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  • Y of finding and applying a criterion of the presence or absence of consciousness, it is none the less desirable, in the interests of psychology, to state that truly instinctive acts (as defined) are accompanied by consciousness.

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  • Also a unit class is any class with the property that it possesses a member x such that, if y is any member of the class, then x and y are identical.

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  • A relation (R) is serial when (I) it implies diversity, so that, if x has the relation R to y, x is diverse from y; (2) it is transitive, so that if x has the relation R to y, and y to z, then x has the relation R to z; (3) it has the property of connexity, so that if x and y are things to which any things bear the relation R, or which bear the relation R to any things, then either x is identical with y, or x has the relation R to y, or y has the relation R to x.

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  • Two relations R and R' are said to be ordinally similar, if a one-one relation holds between the members of the two fields of R and R', such that if x and y are any two members of the field of R, such that x has the relation R to y, and if x' and y are the correlates in the field of R' of x and y, then in all such cases x has the relation R' to y', and conversely, interchanging the dashes on the letters, i.e.

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  • If m and n are finite cardinal numbers, the rational number m/n is the relation which any finite cardinal number x bears to any finite cardinal number y when n X x = m X y.

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  • The product of two complex numbers of the second order - namely, l e l +x 2 e 2 and y i e l +y 2 e 2, is in this case defined to mean the complex (x i y i - x 2 y 2)e i +(x i y 2 +x 2 y 1)e 2.

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  • Its central bureau, with departments of the interior, religion and education, finance and justice, was established at Serajevo; and its members were largely recruited among the Austrian Sla y s, who were better able than the Germans to comprehend the local customs and language.

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  • In the latter year was created the Real Audiencia de la Plata y Charcas, a royal court of justice having jurisdiction over Upper Peru and the La Plata provinces of that time.

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  • This vicious system, grafted as it was upon an inefficient administration, and added to the weight of a continually depreciated currenc y, debased both by ill-advised fiscal measures and by public cupidity, formed one of the principal causes of the financial embarrassments which assailed the treasury with ever increasing force in the latter part of the 16th and during the 17th and 18th centuries.

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  • When he had ruthlessly quelled the resistance offered to his accession by his brothers, who both fell in the struggle for the throne, Selim undertook his campaign in Persia, having first extirpated the Shia heresy, prevalent 5 e 12 m, g P Y, P 1512152.0.

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  • The Porte, unable to resist, was obliged to consent to the convention of Ainali Ka y ak (March 10, 1779) whereby the Russian partisan, Shahin Girai, was recognized as khan of the Crimea, the admission of Russian vessels to navigate Turkish waters was reaffirmed and Russia's right of intervention in the affairs of the Danubian principalities was formally recognized.

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  • Five years later Potemkin induced the chiefs of the Crimea and Kuban to hold a meeting at which the annexation of their country to Russia was declared, Turkey giving her consent by a convention, signed at Constantinople, on the 8th of January 1784, by which the stipulations as to the liberty of the Tatars contained in the treaty of Kuchuk Kainarji and the convention of Ainali Ka y ak were abrogated.

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  • Russia, desirous of deriving some return for the support which she had given the sultan during his rupture with the French, induced the Porte to address to her a note in which the right of intervention in the affairs of the principalities, conferred on her by the treaty of Kainarji and reaffirmed in the convention of Ainali Ka y ak, was converted into a specific stipulation that the hospodars should be appointed in future for seven years and should not be dismissed without the concurrence of the Russian ambassador at Constantinople.

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  • The Kurds, the constant oppressors of that people, had received official recognition and almost complete immunity from the control o f the civil law by being formed into a Y g eo Y manry frontier-guard known as the Hamidian cavalry.

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  • In J u d y 1909, however, the Greek flag was hoisted in Canea and Candia, and it was only lowered again after the war-ships of the protecting powefs had been reinforced and had landed an international force.

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  • The inhabitants are a brave and warlike race of mountaineers, and aided by the natural strength of their countr y they have hitherto preserved their independence.

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  • The connexion that seemed to be first established was between variations in the quantity of water transported from the tropical to the sub-polar Atlantic and variations in the intensit y of solar radiation.

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  • Water and carbonic acid are synthesized, under the action of sunlight, to form sugar, starch or some other carboh y drate and this is then combined with simple nitrogenous salts to form proteid.

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  • Without attempting to answer this question categorically, it may be pointed out that within the limits of the family (Ptychoderidae) which is especially characterized by their presence there are some species in Y art dY YY cts, posterior limit of collar.

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  • Hamburg probably had its origin in a fortress erected in 808 by Charlemagne, on an elevation between the Elbe and Alster, as a defence against the Sla y s, and called Hammaburg because of the surrounding forest (Hamme).

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  • The town, rebuilt after this disaster, was again more than once devastated by invading Danes and Sla y s.

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  • When the solutions may be taken as effectively dilute, so that the gas laws apply to the osmotic pressure, this relation reduces to E _ nrRT to c1 ey gE c2 where n is the number of ions given by one molecule of the salt, r the transport ratio of the anion, R the gas constant, T the absolute temperature, y the total valency of the anions obtained from one molecule, and c i and c 2 the concentrations of the two solutions.

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  • In the preface it is stated that Howel, "seeing the laws and customs of the country violated with impunity, summoned the archbishop of Menevia, other bishops and the chief of the clergy, the nobles of Wales, and six persons (four laymen and two clerks) from each comot, to meet at a place called Y Ty Gwyn ar Da y, or the white house on the river Tav, repaired thither in person, selected from the whole assembly twelve of the most experienced persons, added to their number a clerk or doctor of laws, named Bllgywryd, and to these thirteen confided the task of examining, retaining, expounding and abrogating.

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  • The act also declares the validit y of leases made by a simoniac or simoniacallypresented person, if bona fide and for valuable consideration to a lessee ignorant of the simony.

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  • Among other rivers having a westerly direction may be mentioned the Tambre, the Ulla and the Lerez or Ler, which falls into the Atlantic by estuaries or rigs called respectively Ria de Muros y Noya, Ria de Arosa and Ria de Pontevedra.

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  • Vivero Bay and the Ria del Barquero y Vares are of a similar character; while the harbour of Ferrol ranks among the best in Europe, and is the chief naval station on the northern coast of Spain.

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  • Y ...a n v, the summation being for all permutations of the n numbers, is called the determinant of the n 2 quantities.

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  • In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.

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  • From the differential coefficients of the y's with regard to the x's we form the functional.

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  • We may equally express the result as 4,(al)Y'(a2)...0 (am) =0, (a 8 -fa t) =0.

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  • It is thus possible to study simultaneously all the theories which depend upon operations of the group. Symbolic Representation of Symmetric Functions.-Denote the s 8 s elementar symmetric function a s by al a 2 a3 ...at pleasure; then, Y y si,, si,...

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  • P y q +...

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  • To exhibit any covariant as a function of uo, ul, a n = (aiy1+a2y2) n and transform it by the substitution fi y 1+f2 y where f l = aay 1, f2 = a2ay -1, x y - x y = X x thence f .

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  • As new axes of co-ordinates we may take any other pair of lines through the origin, and for the X, Y corresponding to x, y any new constant multiples of the sines of the angles which the line makes with the new axes.

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  • The substitution for x, y in terms of X, Y is the most general linear substitution in virtue of the four degrees of arbitrariness introduced, viz.

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  • Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.

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  • The Vivarais mountains and the northern Cevennes approach the right banks of the Rhone and Saone closely, and on that side send their waters by way of short torrents to those rivers; on the west side the streams a y e tributaries of the Loire, which rises at the foot of Mont Mezenc. A short distance to the south on the same side are the sources of the Allier and Lot.

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  • Thus they make Mer y a sort of watch tower over the entrance into Afghanistan on the north-west and at the same time create a stepping-stone or etape between north-east Persia and the states of Bokhara and Samarkand.

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  • In Hindu (the Puranas), Parsi and Arab tradition, Mer y is looked upon as the ancient Paradise, the cradle of the Aryan families of mankind, and so of the human race.

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  • In the latter part of the 8th century Mer y became obnoxious to Islam as the centre of heretical propaganda preached by Mokanna.

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  • A younger brother of Toghrul, Daud, took possession of Mer y and Herat.

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  • It was about this time that Mer y reached the zenith of her glory.

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  • During the reign of Sultan Sanjar or Sinjar of the same house, in the middle of the 11th century, Mer y was overrun by the Turkish tribes of the Ghuzz from beyond the Oxus.

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  • In 1221 Mer y opened its gates to Tule, son of Jenghiz Khan, chief of the Mongols, on which occasion most of the inhabitants are said to have been butchered.

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  • On the death of the grandson of Jenghiz Khan Mer y was included (1380) in the possessions of Timur-iLeng (Tamerlane), Mongol prince of Samarkand.

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  • Mer y remained in the hands of Persia until 1787, when it was captured by the emir of Bokhara.

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  • East of the old Seljuk capital is Giaur Kalah, the Mer y of the Nestorian era and the capital of the Arab princes.

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  • If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.

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  • If F T is the force along r and F t that along t at right angles to r, F r =X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = - r 3 sin 0.

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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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  • The play of the beam is limited by a stop S and a screw R, the latter being so adjusted that when the end Y of the beam is held down the two air-gaps are of equal width.

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  • The equites remained' at home, or only went out as members of the general's staff, their places being taken by the equites equo p y ivato, the cavalry of the allies and the most skilled horsemen of the subject populations.

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  • The y are really excretory glands, and communicate with the exterior by a very minute aperture on the posterior face of the coxa of the fifth limb on each side.

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  • The mark of Meissen was originally a district centring round the castle of Meissen or Misnia on the Middle Elbe, which was built about 920 by the German king Henry I., the Fowler, as a defence against the Sla y s.

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  • As Meissen was relieved from the attacks of the Sla y s by the movement of the German boundary to the east, its prosperity increased.

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  • Latreille 6 published a new classification of the Vertebrata, which are primarily divided into Haematherma, containing the three classes of Maminifera, Monotremata and A y es; and Haemacryma, also containing three classes - Reptilia, Amphibia and Pisces.

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  • Huxley adopted Latreille's view of the distinctness of the Amphibia, as a class of the Vertebrata, co-ordinate with the Mammalia, A y es, Reptilia and Pisces; and the same arrangement was accepted by Gegenbaur and Haeckel.

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  • The pp g y Dutch were unable, however, to extend their power beyond the limits of the town, until the arrival of Count John Maurice of Nassau-Siegen in 1636.

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  • The of two brothers Andrada were called to the ministry razil' y 1822.

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  • Throughout the middle ages it was the scene of vigorous struggles between Sla y s, Byzantines, Franks, Turks and Venetians, the chief memorials of which are the ruined strongholds of Mistra near Sparta, Gerald (anc. Geronthrae) and Monemvasia, "the Gibraltar of Greece," on the east coast, and Passava near Gythium.

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  • The first of his original pieces performed was Der y politiske Kandestober (The Pewterer turned Politician); he wrote other comedies with miraculous rapidity, and before 1722 was closed, there had been performed in succession, and with immense success, Den Vaegelsindede (The Waverer), Jean de France, Jeppe paa Bjerget, and Gert the Westphalian.

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  • The y ear is divided into two seasons, summer, which begins in October and ends in March, and winter, which fills up the rest of the year.

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  • Da Gama made no landing here and, like Discovery the rest of South Africa, Natal was neglected by the and early g Y his tory.

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  • In July the Natal ministry J Y Y learnt that it was not the intention of the Imperial government to endeavour to hold the frontier in case hostilities arose, but that a line of defence considerably south of the frontier would be taken up. This led to a request on their part that if the Imperial government had any reason to anticipate the breakdown of negotiations, " such steps may be at once taken as may be necessary for the effectual defence of the whole colony."

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  • The government met the crisis by renewed energy in harbour works, railway construc y gy y tions and the development of the natural resources of the country.

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  • The gg Y divergent interests of the various colonies threatened indeed a tariff and railway war when the Customs Convention (provisionally renewed in March 1906) should expire in 1908.

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  • To Anselm speciall y belongs the motto Credo ut intelligam, or, as it is obscurity of the schools..

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  • William of Champeaux (1070-1121), who is reputed the founder of a definitely formulated Realism, much Y as Roscellinus is regarded as the founder of Nominalism, was instructed by Roscellinus himself in dialectic. Unfortunately none of William's philosophical works have survived, and we depend upon the statements of his opponent Abelard, in the Historia calamitatum mearum, and in certain manuscripts discovered by Cousin.

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  • The monotheistic influence of Aristotle and his Arabian commentators shows itself in Albert and Aquinas, at the outset, in the definitive fashion in which the " mysteries " y sof the Trinity and the Incarnation are henceforth detached from the sphere of rational or philosophical theology.

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  • He subsequently organized the army of Italy and the two departments into which Corsica had been divided, was deputy to the Council of the Five Hundred, and accepted various offices under the Consulate and the Empire, being minister of police and of wa y ..

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  • This forcible intrusion of a nonAryan race altered the whole history of Europe; but its peculiar significance lay in the fact that it permanently divided the northern from the southern and the eastern from the western Sla y s.

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  • It was a confused four-cornered struggle between the emperor and the Turks, the Turks and Transylvania, Michael of Moldavia and Y ?

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  • Jellachich, who as a soldier was devoted to the interests of the imperial house, realized that the best way to break the revolutionary power of the Magyars and Germans would be to encourage the Slav national ideas, which were equally hostile to both; to set up against the Dualism in favour at Pest and Vienna the federal system advocated by the Sla y s, and so to restore the traditional Habsburg principle of Divide et impera.

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  • All hope of crushing revolutionary Vienna with Magyar aid was thus at an end, and Jellachich, who on the 10th issued a proclamation to the Croat regiments in Italy to remain with their colours and fight for the common fatherland, was free to carry out his policy of identifying the cause of the southern Sla y s with that of the imperial army.

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  • In the Hungarian diet, which met on the 2nd of July, the influence of the conservative cabinet was wholly overshadowed by that of Kossuth, whose inflammatory orations - directed against the disruptive designs of the Sla y s and the treachery of the Austrian government - precipitated the crisis.

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  • On the 17th of February 1867 a responsible inde pendent ministry was formed under Count Gyula 'p y y ' of 1867.

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  • Y, 9 P ?, PP ment of a Coalition cabinet 2 under Dr Sandor Wekerle was announced, the world was taken completely by surprise.

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  • A close observer of the multifarious low life of Hungary, Mikszath has, in his short stories, given a delightful yet instructive picture of all the minor varied phases of the peasant life of the Sla y s, the Palocok, the Saxons, the town artisan.

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  • We may therefore conveniently take as our unit, in place of x, a number y such that x=6y.

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  • Let X and Y be the related quantities, their expressions in terms of selected units A and B being x and y, so that X=x.A, Y = y.

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  • We take a fixed line OX, usually drawn horizontally; for each value of X we measure a length or abscissa ON equal to x.L, and draw an ordinate NP at right angles to OX and equal to the corresponding value of y .

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  • Y is represented by the length of the ordinate NP, so that the representation is cardinal; but this ordinate really corresponds to the point N, so that the representation of X is ordinal.

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  • In the first class come equations in a single unknown; here the function which is equated to zero is the Y whose values for different values of X are traced, and the solution of the equation is the determination of the points where the ordinates of the graph are zero.

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  • Now suppose that the formula (2) has been established for every power of A+a up to the (n-i)th inclusive, so that (ii_ I) = (n- I) (r), (y I) = (n -1) (r _ l).

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  • Therefore, if (n-i) 1P+11 is divisible by (p+I)!, 'n 1P+11 is divisible b y (p +i) !.

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  • The binomial theorem for positive integral index may then be written (x + y) n = -iyi +.

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  • Simultaneous equations in two unknowns x and y may be treated in the same way, except that each equation gives a functional relation between x and y.

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  • We cannot, for instance, say that the fraction C _2 I is arithmetically equal to x+I when x= I, as well as for other values of x; but we can say that the limit of the ratio of x 2 - I to x - I when x becomes indefinitely nearly equal to I is the same as the limit of x+ On the other hand, if f(y) has a definite and finite value for y = x, it must not be supposed that this is necessarily the same as the limit which f (y) approaches when y approaches the value x, though this is the case with the functions with which we are usually concerned.

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  • Suppose, for instance, that y=x 2; then to every rational value of x there corresponds a rational value of y, but the converse does not hold.

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  • Thus there appear to be discontinuities in the values of y.

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  • It can be proved by geometry that (aA-H3B) +yC = aA+(aB+- y C) = (a + 1 3+ 7) P, where P is in fact the centroid of masses a, 13, y placed at A, B, C respectively.

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  • It is the value of y which is generally denoted by q= q'; a special symbol for x is desirable, but has not been established.

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  • The values of x and y are different, unless V (qq o) = o.

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  • A particular case of the last equation, namely, y 2 = ax e + 1, sorely taxed the resources of modern algebraists.

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  • The words "y coed" are added to distinguish this Bettws from several others in Wales, especially that near Llandeilo Fawr, Carmarthenshire, not far from the Bettws hills.

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  • Bettws y coed is a favourite village for artists and tourists.

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  • The best-known streams and waterfalls are Llugwy, Lledr, with Rhaiadr y wenol (Swallow falls), Conwy and Machno falls.

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  • During the 'seventies Austro-Hungarian policy was increasingly successful in checking intercourse between the Yugosla y s of the monarchy and those outside its bounds.

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  • The period between 1883 and 1903 is the most humiliating in the modern history of the southern Sla y s.

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  • Disunion had reduced the Yugosla y s to an almost negligible quantity in Balkan politics.

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  • The Serbian court, instead of being a centre of perpetual scandal and misrule, resumed its true position as a focus of national aspirations, and this change was not lost upon the Yugosla y s of " the other side."

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  • The Serbian and Bulgarian anthems were sung on the streets, collections were made in every village for the Balkan Red Cross funds, and when Austria-Hungary mobilized, protests were heard on every side against the bare possibility of war with Serbia, which to the Yugosla y s would be a veritable civil war.

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  • Among the Yugosla y s the students had always dabbled unduly in politics, and this tend-.

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  • The entry of Italy into the war was a serious set-back to the Yugoslav cause, for under the Treaty of London (April 27 1915) she was to obtain, in the event of an Entente victory, wide districts in Gorizia, Carniola, Istria and Dalmatia, peopled by not less than 700,000 Yugosla y s.

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  • By this time it was sufficiently obvious that the Yugosla y s were tacitly if not explicitly agreed upon a triple parallel policy, framed for all contingencies.

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  • The growing self-confidence of the Austrian Sla y s was shown by the bluntness of their refusal to cooperate with the new Premier, Doctor von Seidler, whose offer of portfolios to their leaders drew from Count Tisza a strong protest in the Hungarian Parliament.

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  • The Czechs and Yugosla y s, finding the door thus shut in the face of their national aspirations, even in the modified Habsburg form, naturally stiffened in their opposition.

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  • The Yugosla y s were represented by Trumbic and his Committee and by 12 deputies of the Serbian Skupstina, the Czechoslovaks by Benes and Stefanik, the Poles by Zamorski, Skirmunt and Seyda, the Rumanians by Draghicescu, Lupu and Mironescu.

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  • The effect of the congress and of this propaganda was to hasten the disintegration in the Austro-Hungarian army, and the High Command (in a communiqué of July 27) admitted that wholesale defections of the Czechoslovaks and the Yugosla y s had.

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  • That this recognition had not already been accorded before the collapse of the Central Powers began was due to disunion among the Yugosla y s themselves.

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  • Trumbic on his part could not enter a purely Serbian Cabinet without prejudicing that freedom of choice of his compatriots in the Dual Monarchy, upon which the moral case of the Yugosla y s depended.

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  • Meanwhile the whole Nationalist press of Italy, actively, encouraged by Sonnino and his entourage, opened a fierce campaign against the Yugosla y s and their western supporters, which rapidly developed into agitation against the Allies.

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  • On March 3, however, Italy, who had steadily refused to recognize the accomplished fact of Yugoslav unity and insisted on the Conference only admitting the Yugosla y s as a " Serbian " delegation, declined American arbitration and threatened to withdraw altogether from Paris unless their territorial demands were conceded.

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  • This in turn strengthened the hands of the extreme section among the Yugosla y s, who now advanced the full ethnographic claim, involving Trieste and Gorizia as well as Dalmatia and Istria, and at the same time increased their demands against Bulgaria, Austria and Albania.

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  • Tardieu suggested a compromise by which the port and district of Fiume with most of eastern Istria and a total population of over 200,000 (mainly Yugosla y s) would form a small buffer state between Italy and Yugoslavia, under the guarantee of the League of Nations.

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  • The sole justification for such a claim lay in the terms of the Treaty of London, which the Yugosla y s could not adopt as a basis without stultifying their whole position against Italy.

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  • Vivipara, ovipara, a y es, pisces, serpentes et Scorpio - and contains descriptions and illustrations of a large number of animal forms with reference to the lands inhabited by them.

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  • Taking co-ordinates in the plane of the screen with the centre of the wave as origin, let us represent M by, n, and P (where dS is situated) by x, y, z.

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  • We will now apply the integrals (2) to the case of a rectangular aperture of width a parallel to x and of width b parallel to y.

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  • The limits of integration for x may thus be taken to be -2a and -Fla, and for y to be -2b, +2b.

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  • To calculate the roots of (5) we may assume u=(m+1)7r-y= U-y, (3), where y is a positive quantity which is small when u is large.

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  • When, as in the application to rectangular or circular apertures, the form is symmetrical with respect to the axes both of x and y, S = o, and C reduces to C = ff cos px cos gy dx dy,.

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  • The principle gives an instantaneous solution of the question of the ultimate optical efficienc y in the method of " mirror-reading," as commonly practised in various physical observations.

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  • In spite of any inequality between p and p', the definition will be good to this order of approximation, provided a and y vanish.

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  • When the plane zx is not a plane of symmetry, we have to consider the terms in xy, 2 y, and y 3 .

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  • Curvature of the primary focal line having a very injurious effect upon definition, it may be inferred from the excellent performance of these gratings that y is in fact small.

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  • The aperture of the unretarded beam may thus be taken to be limited by x = - h, x = o, y= - 1, y= +1; and that of the beam retarded by R to be given by x =o, x =h, y = - 1, y = +l.

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  • Descending series of the semi-convergent class, available for numerical calculation when u is moderately large, can be obtained from (12) by writing x=uy, and expanding the denominator in powers of y.

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  • The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...

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  • For the osculating circle at any point includes the whole of the y curve which lies beyond; and the successive convolutions envelop one another without intersection.

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  • Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.

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  • According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)dz It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).

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  • Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).

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  • Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?

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  • Moreover, it is very doubtful whether the word r y ?c can be translated " Director."

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  • He is also found confirming his old rival Arnulf in the see of Reims; summoning Adalbero or Azelmus of Laon to Rome to answer for his crimes; judging between the archbishop of Mainz and the bishop of Hildesheim; besieging the revolted town of Cesena; flinging the count of Angouleme into prison for an offence against a bishop; confirming the privileges of Fulda abbey; granting charters to bishoprics far away on the Spanish mark; and, on the eastern borders of the empire, erecting Prague as the seat of an archbishopric for the Sla y s.

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  • In December m this assembly met at Potchefstroom, and for three y, weeks was engaged in modelling the constitution 1856.

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  • He was highly esteemed in devout circles as the author of De la aficiOn y amor de Jesus (1630), and De la aficion y amor de Maria (1630), both of which were translated into Arabic, Flemish, French, German, Italian and Latin.

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  • It may be safely said of all those living things which are large enough to enable us to trust the evidence of microscopes, that they are heterogeneous optically, and that their different parts, and especially the surface layer, as Life and contrasted with the interior, differh sicall and organiza- P Y ?

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  • But many of the simpler P Y ler P forms of life may undergo desiccation to such an extent as to arrest their vital manifestations and convert them into the semblance of not-living matter, and yet remain potentially alive.

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  • His real name was Juan de Yepez y Alvarez; in religion he was known as Juan de San Matias till 1568, when he adopted the name of Juan de la Cruz.

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  • The judicial power is vested in a supreme federal court, called the Corte Federal y de Casacion, and such subordinate tribunals as may be created by law.

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  • There are several mechanics' schools (Antes y Oficios) in the larger cities, and a large number of private schools.

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  • The public revenues are derived from customs taxes and charges on imports and exports, transit taxes, cattle taxes, profits on coinage, receipts from state monopolies, receipts from various public services such as the post office, telegraph, Caracas waterworks, &c., and sundr y taxes, fines and other sources.

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  • The attacks of the Sla y s and Avars upon Thessalonica were heroically repulsed by the inhabitants.

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  • In December 1721 his father died, leaving him property (rather more than four thousand 'l y res a year), which was soon increased by a pension of half the amount from the regent.

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  • The grateful perfumed powder abir or rand y is composed either of rice, flour, mango bark or deodar wood, camphor and aniseed, or of sandalwood or wood aloes, and zerumbet, zedoary, rose flowers, camphor and civet.

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  • The growth and population of London previous to the Igth century is considered under Histor y, ad fin.

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  • Other museums are Sir John Soane's collection in Lincoln's Inn Fields and the Museum of Practical Geology in Jermyn Street, while the scientific societies have libraries and in some cases collections of a specialized character, such as the museums of the Royal College of Surgeons, the Royal Architectural Society, and the Society of Art and the Parkes Museum of the Sanitar y Institute.

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  • Holinshed (who was followed by Shakespeare in 2 Henry VI., act 4 sc. 6) tells us that when Cade, in 1450, forced his way into London, he first 45 Y of all proceeded to London Stone, and having struck his sword upon it, said in reference to himself and in explanation of his own action, " Now is Mortimer lord of this city."

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  • This allegiance therefore frequently changed, but Lo ndon retained its identity and individuality all Y Y through.

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  • A chap-book called Vida politica y militar de Don Tomas Zumalacarregui, which gives the, facts of his life with fair accuracy, is still very popular in Spain.

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  • Y g g The air passes through a reducing valve from the main to an auxiliary tank, in which the pressure is, say, 125 lb, and thence to the driving cylinders.

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  • Norman Holbrook, successfull y passed the mine-fields of the Straits and torpedoed the old Turkish battleship " Messudieh " at anchor.

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  • The beaches which had been selected were, enumerating from right to left, " S " in Morto Bay, " V " and " W " on either side of Cape Helles at the south-western end, and " X " and " Y " on the outer shore; " V " and " W " were regarded as of primary importance, as those two beaches offered suitable landing places from the point of view of subsequent operations.

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  • The attacks at " S " and " Y " were intended to be subsidiary; but great importance was attached to that at " X " owing to the vicinity of this point to " W."

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  • As it turned out, the actual disembarkations at " S," " X " and " Y " were carried out without any very great difficulty; but the troops detailed for " W " beach only gained a footing after incurring very heavy losses and by a display of indomitable resolution, while at " V " the operation went very near to failing altogether.

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  • The troops detailed for " Y " beach had also got into serious difficulties, and as it turned out they had to be withdrawn next morning.

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  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

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  • The existence of internal strains in glass can be readil y recognized by examination in polarized light, any signs of double refraction indicating the existence of strain.

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  • This baptism may not be conferred until the candidate has reached an age of discrimination and capacity to remember obligations, p y cere seven years being fixed as the earliest age, but it is generally deferred until manhood.

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  • Plauen was probably founded by the Sla y s.

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  • Any additional pressure applied to the fluid will be y transmitted equally to every point in the case of a liquid; this principle of the transmissibility of 1 1 pressure was enunciated by Pascal, 1653, and FIG.

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  • As the molten metal is run in, the upward thrust on the outside mould, when the level has reached PP', is the weight of metal in the volume generated by the revolution of APQ; and this, by a theorem of Archimedes, has the same volume as the cone ORR', or rya, where y is the depth of metal, the horizontal sections being equal so long as y is less than the radius of the outside FIG.

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  • Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.

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  • Thus if the plane is normal to Or, the resultant thrust R =f fpdxdy, (r) and the co-ordinates x, y of the C.P. are given by xR = f f xpdxdy, yR = f f ypdxdy.

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  • Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.

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  • As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

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  • If the liquid is stirred up by the rotation R of a cylindrical body, d4lds = normal velocity reversed dy = - Rx- Ry ds (5) ds 4' + 2 R (x2 + y2) = Y, (6) a constant over the boundary; and 4,' is the current-function of the relative motion past the cylinder, but now V 2 4,'+2R =o, (7) throughout the liquid.

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  • Inside an equilateral triangle, for instance, of height h, - 2Ra/3y/h, (8) where a, 13, y are the perpendiculars on the sides of the triangle.

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  • Consider the motion given by w=U(z+a2/z), (I) 4,=U(r+- r) cos 0= U + a1x, so that (2) = U (r-)sin 0= U(i -¢) y.

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  • Then 4, =o over the cylinder r = a, which may be considered a fixed post; and a stream line past it along which 4, = Uc, a constant, is the curve (r - ¢2) sin 0=c, (x2 + y2) (y - c) - a 2 y = o, (3) a cubic curve (C3).

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  • Over a concentric cylinder, external or internal, of radius r=b, 4,'=4,+ Uly =[U I - + Ui]y, (4) and 4" is zero if U 1 /U = (a 2 - b2)/b 2; (5) so that the cylinder may swim for an instant in the liquid without distortion, with this velocity Ui; and w in (I) will give the liquid motion in the interspace between the fixed cylinder r =a and the concentric cylinder r=b, moving with velocity U1.

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  • If the direction of motion makes an angle 0' with Ox, tan B' = d0 !dam _ ?xy 2 = tan 20, 0 =-10', (9) dy/ y and the velocity is Ua2/r2.

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  • In a similar way the more general state of motion may be analysed, given by w =r ch2('-y), y =a+, i, (26) as giving a homogeneous strain velocity to the confocal system; to which may be added a circulation, represented by an additional term in w.

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  • Example 3.-Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream function 1//1 is to be made to satisfy the conditions v 2 /1 =0, 111+IRx 2 = IRa 2, or /11 =o when x= = a, +b1+IRx 2 = I Ra2, y ' 1 = IR(a 2 -x 2), when y = b Expanded in a Fourier series, 2 232 2 cos(2n+ I)Z?rx/a a -x 7r3 a Lim (2n+I) 3 ' (1) so that '?"

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  • A relative stream line, along which 1/,' = Uc, is the quartic curve y-c=?![2a(r-x)], x = 4a2y2-(y g)4, r- 4a2y2 +(y c) 4, 7) 4 a (y-c) 4a(y and in the absolute space curve given by 1', dy= (y- c)2, x= 2ac_ 2a log (y -c) (8) 2ay y - c 34.

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  • Similarly, with the function (19) (2n+ I) 3 ch (2n+ I) ITrb/a' (2) Changing to polar coordinates, x =r cos 0, y = r sin 0, the equation (2) becomes, with cos 0 =µ, r'd + (I -µ 2)-d µ = 2 ?-r3 sin 0, (8) of which a solution, when = o, is = (Ar'+) _(Ari_1+) y2,, ?

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  • For instance, with n = I in equation (9), the relative stream function is obtained for a sphere of radius a, by making it, y' =1y+2Uy 2 = 2U(r 2 -a 3 /r) sin?

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  • In the absolute path in space cos Ili = (2 - 3 sin 2 6)/1/ (4-sin 2 6), and sin 3 B = (y 3 -c 2 y)/a 3, (19) which leads to no simple relation.

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  • The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.

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  • As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.

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  • The corresponding expression for two orthogonal cylinders will be With a 2 = co, these reduce to / y /, = Uy (I ra 2 p22 +-C24)..

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  • The extension to the case where the liquid is bounded externally by a fixed ellipsoid X= X is made in a similar manner, by putting 4 = x y (x+ 11), (io) and the ratio of the effective angular inertia in (9) is changed to 2 (B0-A0) (B 1A1) +.a12 - a 2 +b 2 a b1c1 a -b -b12 abc (Bo-Ao)+(B1-A1) a 2 + b 2 a1 2 + b1 2 alblcl Make c= CO for confocal elliptic cylinders; and then _, 2 A? ?

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  • Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..

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  • The components of force, X, Y, and N, acting on the liquid at 0, and reacting on the body, are then X=It.

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  • Y was there crowned legitimate king.

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  • P Y administrative abilities of his father, and the success of his reign was not commensurate with the vanity of the ruler.

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  • His successor was Nabo oPP Y P lassar, between whom and the last king of Assyria war broke out.

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  • Later on he chose Mer y for his residence, and was the owner of a house and garden there.

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  • The first of these bands with whom Florence came into contact was the Great Company, commanded by the count of Lando, which twice entered Tuscany Y but was expelled both times by the Florentine troops (1358-1359).

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  • This g Y P Y PP Y infamous law, however, aroused so much opposition that some of the very men who had proposed it assembled in secret to discuss its abolition, and a quarrel between the Albizzi and the Ricci having weakened the parte, a balia of 56 was agreed upon.

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  • The signory appointed Piero Capponi, a man of great ability and patriotism, and experienced in diplomacy, the gonfaloniere Francesco Valori, the Dominican Giorgio Vespucci, and the jurisconsult and diplomatist Domenico Bonsi, rule, 's every five years, appointed all the magistrates and Y Y PP g syndics to conduct the negotiations with the French king.

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  • For outdoor culture the long-rod s y stem is generally preferred.

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  • For centuries, they exercised the power of life and death; a stone stands where the gallows were formerly erected, and indicates that here they exercised jur y regalia.

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  • Extraction of cane juice by diffusion (a process more fully described under the head of beetroot sugar manufacture) is adopted in a few plantations in Java and Cuba, in Louisiana Etr cti o n and the Hawaiian Islands, and in one or two factories y f i in Egypt; b u t hitherto, except under exceptional conditions (as at Aska, in the Madras Presidency, where the local price for sugar is three or four times the London price), it would not seem to offer any substantial advantage over double or triple crushing.

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  • The intercept on the axis of y is 2a/7r; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected.

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  • Its water-holding capacity is great, but it is often acid, and when dr y it is light and incapable of supporting the roots of plants properly.

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  • On the stiff soils overl y ing the chalk it was formerly the custom to dig pits through the soil to the rock below.

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  • The instrument, described by Oviedo (Historia de las Indias Occidentales, Salamanca, 1535), consisted of a small hollow wooden tube, shaped like a Y, the two points of which being inserted in the nose of the smoker, the other end was held into the smoke of burning tobacco, and thus the fumes were inhaled.

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  • In regard to methods and apparatus, mention should be made of his improvements in the technique of organic analysis, his plan for determining the natural alkaloids and for ascertaining the molecular weights of organic bases b y means of their chloroplatinates, his process for determining the quantity of urea in a solution - the first step towards the introduction of precise chemical methods into practical medicine - and his invention of the simple form of condenser known in every laboratory.

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  • Hence it still seems best to assume some unknown Aramaic form equivalent to 7rapaicX y as, and then to take the latter in the sense of comfort or encouragement.

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  • The first explorer to enter the sacred Hejaz with a definite scientific object was the Spaniard, Badia y aeblich, who, under the name of Ali Bey and claiming to be the last representative of the Abbasid Caliphs, arrived at Jidda in 1807, and performed the pilgrimage to Mecca.

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  • Deep valleys winding through the barren foothills lead gradually up to the higher mountains, and as the track ascends the scenery and vegetation change their character; the trees which line the banks of the wadi are overgrown with creepers, and the running stream is dammed at frequent intervals, and led off in artificial channels to irrigate the fields on either side; the steeper parts of the road are paved with large stones, substantially built villages, with their masonry towers or da y s, crowning every height, replace the collection of *mud walls and brushwood huts of the low country; while tier above tier, terraced fields cover the hill slopes and attest the industry of the inhabitants and the fertility of their mountains.

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  • They showed a zeal for evangelization which resulted in the establishment of their influence throughout Asia, as is seen from the bishoprics founded not only in Syria, Armenia, Arabia and Persia, but at Halavan in Media, Mer y in Khorasan, Herat, Tashkent, Samarkand, Baluk, Kashgar, and even at Kambaluk (Pekin) and Singan fu Hsi`en fu in China, and Kaljana and Kranganore in India.

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  • The agricultural Sla y s of the Dnieper and the Oka were reduced to tribute, and before the end of the 7th century the Khazars had annexed the Crimea, had won complete command of the Sea of Azov, and, seizing upon the narrow neck which separates the Volga from the Don, had organized the portage which has continued since an important link in the traffic between Asia and Europe.

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  • The arrival of the Varangians amidst the scattered Sla y s (862) had united them into a nation.

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  • The most prolific author of colonial times was Dr Pedro de Peralta y Barnuevo, who wrote more than sixty works, including an epic poem entitled Lima fundada.

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  • The comedies of Segura on the customs of Lima society, entitled Un Paseo a Amancaes and La Saya y Manto, have no equal in the dramatic literature of Spanish America and few in that of modern Spain.

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  • In his youth Ricardo Palma published three books of poems, entitled Armonias, Verbos y Gerundios and Pasionarias, and then, since 1870, devoted his great literary talents to writing the historical traditions of Peru, of which six volumes were published.

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  • About the same time Francesco Maurolico, or Maurolycus, the eminent mathematician of Messina, in his Theore y nata de Lumine et Umbra, written in 1521, fully investigated the optical problems connected with vision and the passage of rays of light through small apertures with and without lenses, and made great advances in this direction over his predecessors.

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  • Although the Finns are not Sla y s, on topographical grounds mention may here be made of Wainamoinen, the great magician and hero of the Finnish epic Kalevala (" land of heroes ").

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  • Bribery was the first weapon employed, and a car- y p dinal's hat was held out as a bait.

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  • The mesodermic portion becomes charged with a yolk-like material (y), and, on the germination of the statoblast, gives rise to the outer layer (mes) of the bud.

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  • Three towns are known to d ave been destroyedHerculaneum at the western base of the y olcano, Pompeii on the south-east side, and Stabiae, still farther sl outh, on the site of the modern Castellamare.

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  • 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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  • English also adopted the value of s for c in the 13th century before e, i and y.

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  • The British evacuated Newport the 25th ^f October 1779, and the French fleet was stationed here from Ju y 1780 to 1781.

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  • During the differences that arose in 1485 between the regent, Anne of Beaujeu, and the dukes of Orleans, Brittany and Alengon, Imbert de Batarn y kept the inhabitants of Orleans faithful to the king.

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  • Otto marched against them, and in a battle fought on the Lechfeld on the 10th of August 955 the king's troops gained a brilliant victory which completely freed Germany from these invaders; while in the same year Otto also defeated the Sla y s who had been ravaging the Saxon frontier.

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  • There was some talk of inducing d J Y Th f i $ g Glad stone to join the Tory government, and on the 29th of November Lord Malmesbury dubiously remarked, " I cannot make out Gladstone, who seems to me a dark horse."

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  • Having been returned again for the university of Oxford, he entered on the active duties of a great office for which he was pre-eminently g P Y House of government in power, but on the 18th of October the commons.

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  • On the 23rd of January 1874 Gladstone announced the dissolution in an address to his constituents, declaring that the authority of the government had o f187atioa g y g of 1874.

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  • In 822 and 823 two great diets were held in the palace, and at the former there were present deputies from the eastern Sla y s, the Avars and the Normans.

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  • His Storia critica di Spagna e della cultura spagnuola in ogni genere (2 vols., 1781-1784) was finally expanded into the Historia critica de Espana y de la cultura espanola (1783-1805), which, though it consists of twenty volumes, was left unfinished; had it been continued on the same scale, the work would have consisted of fifty volumes.

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  • Two-thirds of the inhabitants are Germans; the remainder, chiefly found in the valleys of the Drave and Save, are Sla y s (Slovenes).

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  • Towards the end of the 6th century the last-named began to give way to the Sla y s, who ultimately made themselves masters of the entire district.

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  • Styria was included in the conquests of Charlemagne, and was henceforth comprised in the German marks erected against the Avar and the Sla y.

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  • In the 19th century were Variedades de ciencias, literatura, y artes (1803-1805), among whose contributors have been the distinguished names of Quintana, Moratin and Antillon; Misceldnea de comercio (1819); and Diario general de las ciencias medicas.

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  • The Cronica cientifica y literaria (1817-1820) was afterwards transformed into a daily newspaper.

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  • In the middle of words when t precedes a palatal sound like i (y) which is not syllabic, it coalesces with it into the sound of sh as in position, nation, &c. The change to a sibilant in these cases took place in late Latin, but in Middle English the i following the t was still pronounced as a separate syllable.

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  • It is indeed just possible that the term may originally have signified "true member of a clan," since membership of a phratry was a characteristic of each clan ('y vos).

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  • The small eyes are some- T y p h l o p s bra- times covered by transparent shields.

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  • The Augustan age was one of those great eras in the world like the era succeeding the Persian War in Greece, the Elizabethan age in England, and the beginning of the 19th Lk y.

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  • Hence the density v is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS V f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2) V (x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).

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  • Thus if the ellipsoid is one of revolution, and ds is an element of arc which sweeps out the element of surface dS, we have dS = 27ryds = 27rydx/ (Ts) = 27rydx/ (b y) = 2 p2 dx.

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  • Let us suppose any other surface described in the electric field so as to cut the closel y compacted tubes.

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  • Let us apply the above theorem to the case of a small parallelepipedon or rectangular prism having sides dx, dy, dz respectively, its centre having co-ordinates (x, y, z).

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  • Its angular points have then co-ordinates (x t Zdx, y t Zdy, z * zdz).

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  • The isothermal elasticity - v(dp/dv) is equal to the pressure p. The adiabatic elasticity is equal to y p, where -y is the ratio S/s of the specific heats.

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  • The loose aggregation of agricultural households gives place t o the organized community with new needs and new g y ideals, and at the same time in religious thought the old vague notion of the numen is almost universally superseded by the more definite conception of the dens - not even now quite anthropomorphic, but with a much more clearly realized personality.

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  • I,151,210 II 1 Czechs, Magyars, Sla y s Bohemia 77,247 01 Hungary 256,347 2.5 Poland 141,908 Rumania 10,377 0.1 Russia 500,797 0 I Total Europe 9,197,014 88.9 3.6 Grand Total 10,339,539 Total Swiss-Switzerland Greeks-Greece Turks-Turkey Europe, not specified 135,736 7,325 3,411 294 North America All other countries 77 6, 071 7.5 366,454 100 0 1'4 4.8 9.5 A very important transformation has taken place in the proportionate number coming from different countries during the last half of the 19th century.

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  • A contemporary account of Clement was written by Augustin de Andres y Sobinas,.

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  • The other, who is commemorated on the 9th of January, was specially venerated at Cluain Ma y scua, Co.

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  • Thus, when it is said that the first y ear of the Incarnation corresponds to the first of the 195th Olympiad, we are to understand that it is only with respect to the last six months of that year that the correspondence takes place.

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  • The name first appears in the list of primitive Zoroastrian settlements contained in the Vendidad Sade, where, however, like most of the names in the same list, - such as Sughudu (Sogdiana), Mouru (Mer y or Margus), Haraquiti (Arachotus or Arghand-ab), Haetumant (Etymander or Helmund), and Ragha (or Argha-stan),--it seems to apply to the river or river-basin, which was the special centre of population.

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  • Under the Tahirids of Khorasan, the Saffarids of Seistan and the Samanids of Bokhara, it flourished for some centuries in peace and progressive prosperity; but during the succeeding rule of the Ghaznevid kings its metropolitan character was for a time obscured by the celebrity of the neighbouring capital of Ghazni, until finally in the reign of Sultan Sanjar of Mer y about 1157 the city was entirely destroyed by an irruption of the Ghuzz, the predecessors, in race as well as in habitat, of the modern Turkomans.

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  • None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, 0, u, Y - the consonants B, c, &c., being reserved for general known quantities - has not been taken up. In this denotation he followed, perhaps, some older contemporaries, as Ramus, who designated the points in geometrical figures by vowels, making use of consonants, R, S, T, &c., only when these were exhausted.

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  • His father was Juan Vicente Bolivar y Ponte, and his mother Maria Concepcion Palacios y Sojo, both descended from noble families in Venezuela.

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  • On the other hand, there are thousands of very small species, and the tiny " fairy-flies " (Myynaridae), whose larvae live as parasites in the eggs of various insects, are excessivel y minute for creatures of such complex organization.

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  • Subsequently the Sla y s were cut off from relations with Taurida by the Mongols, and only made occasional raids, such as that of the Lithuanian prince Olgierd.

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  • On his father's death in 912 he became duke of Saxony, which he ruled with considerable success, defending it from the attacks of the Sla y s and resisting the claims of the German king Conrad I.

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  • Early in 1503 Machiavelli drew up for Soderini a speech, Discorso sull y provisione del danaro, in which the duty and necessity of liberal expenditure for the protection of the state were expounded upon principles of sound political philosophy.

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  • He neglected religion, or regarded it as part of the state machiner y.

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  • Charlemagne's wars in Italy, Spain and Saxony formed part of the common epic material, and there are references to his wars against the Sla y s; but especially he remained in the popular mind as the great champion of Christianity against the creed of Mahomet, and even his Norman and Saxon enemies became Saracens in current legend.

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  • The Spanish versions of Carolingian legends are studied by Mila y Fontanals in De la poesia heroico-popular castellana (Barcelona, 1874).

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  • The sinking of colliery shafts, however, differs considerably from that of other mines, owing to their generally large size, and the difficulties nkingof g g y g ?

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  • A similar position has also been taken up by Schiirer, 3 Holtzmann,4 Gebhardt, 5 W y llie,' and van Manen.

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  • To these things used to y listen at the time, through the mercy of God vouchsafed to me, noting them down, not on paper but in my heart, and constantly by the grace of God brood over my accurate recollections."These are priceless words, for they establish a chain of tradition (John-Polycarp-Irenaeus) which is without a parallel in early church history.

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  • Thus, to within the degree of approximation to which our theory is accurate, the value of y for every gas ought to be one of this series.

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  • There are many thousands of lines in the mercury spectrum, so that from this evidence it would appear that for mercury vapour n ought to be very great, and y almost equal to unity.

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  • The whole work, under the title Primera y segunda parte de la Historia del Piru, was published at Seville in 1571 and was dedicated to King Philip II.

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  • The island is low and fertile, and extensively planted with coco-nut palms. It is continued southwards by an extensive reef, on which stands the chief village, Chobe, the residence of a few Arabs and Ban y an traders.

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  • In the event of the male line of the present ruling family becoming extinct, the female line will succeed in Waldeck, but Pyrmont wil y fall to Prussia.

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  • Y P Here he began to denounce the abuses in the Church, as well as the traffic in mercenaries which had so long been a blot upon his country's honour.

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  • As might have been anticipated, this caused no break in the policy of the English king and his parliament, and a series of famous acts passed in the year 1534 completed and confirmed the independence of the Church of England, which, except during five years under Queen Mary, p g Y Q Y?

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  • Open both to German and French influences, the Netherlands had been the scene of the first executions of Lutherans; they had been a centre of Anabaptist agitation; but Calth y P ?

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  • A philosopher," as Gibbon long ago pointed out, _ who asks from what articles of faith above and against reason the early Reformers enfranchised their followers of P will be surprised at their timidity rather than scandal Y ized by their freedom.

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  • The count y debts in 1908 aggregated $6,076,867.

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  • Close by are the old church of the Jesuits and the mechanics' school (arres y oficios) with its large and well-equipped shops.

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  • Normal and industrial schools for both sexes are maintained, the latter (artes y oficios) performing a very important service for the poorer classes.

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  • The Mexican Geographical Society (Sociedad mexicana de geografia y estadistica), founded in 1833, has rendered invaluable services in the work of exploration and publication; there are also the Geological Society, the Association of Engineers and Architects, and the Society of Natural History.

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  • The only basis of division practicable is Y P language, which must be kept separate in the mind from the others.

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  • In Mexico the former labours of Pimentel and Orozco y Berra are supplemented by those of Bandelier, Penafiel, Herrera and Alfredo Chavero.

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  • They held frequent Art of y q war.

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  • There is no dividing line between first-contact ethnology and -s y g gY gy Th J o pre-contact archaeology.

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  • In its earliest form it ran simply - "Glor y be to the Father, and to the Son, and to the Holy Ghost, world without end, Amen," or "Glory be to the Father, in (or through) the Son, and in (or through) the Holy Ghost."

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  • To the influence of the Arian heres y is also due the Catholic addition - "as it was in the beginning, is now, and ever shall be," the use of which was, according to some authorities, expressly enjoined by the council of Nicaea.

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  • The Diophantine analysis was a favourite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the indeterminate equation ax 2 +1 = y 2, which is known by his name.

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  • After vaguely looking at it a long time, "Il n'y a que moi qui pouvais concevoir la tete de Leonidas," he whispered, and died.

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