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unaltered

unaltered Sentence Examples

  • So what is it that keeps unaltered in the moving triangle ?

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  • This is the only case of an ancient Greek fountain of such an early date, unaltered and intact.

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  • This is the only case of an ancient Greek fountain of such an early date, unaltered and intact.

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  • (I) The bulk of the solution is unaltered, except that its temperature may be raised owing to the usual heating effect which is proportional to the square of the strength of the current.

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  • (I) The bulk of the solution is unaltered, except that its temperature may be raised owing to the usual heating effect which is proportional to the square of the strength of the current.

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  • The parcels into which the Lombards had divided the peninsula remained thus virtually unaltered, except for the new authority acquired by the see of Rome.

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  • Brewers' wort remains unchanged for years, milk keeps permanently sweet, and these and other complex liquids remain unaltered when freely exposed to air from which all these minute organisms are removed.

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  • If the bead is coloured we may have present: cobalt, blue to violet; copper, green, blue on cooling; in the reducing flame, red when cold; chromium, green, unaltered in the reducing flame; iron, brownish-red, light-yellow or colourless on cooling; in the reducing flame, red while hot, yellow on cooling, greenish when cold; nickel, reddish to brownish-red, yellow to reddish-yellow or colourless on cooling, unaltered in the reducing flame; bismuth, yellowish-brown, light-yellow or colourless on cooling; in the reducing flame, almost colourless, blackish-grey when cold; silver, light yellowish to opal, somewhat opaque when cold; whitish-grey in the reducing flame; manganese, amethyst red, colourless in the reducing flame.

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  • The mere retention of the same crystal form by homologous substances is not a sufficient reason for denying a morphotropic effect to the substituent group; for, in the case of certain substances crystallizing in the cubic system, although the crystal form remains unaltered, yet the structures vary.

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  • That country, left by the Treaty of Berlin with its status unaltered, was in a continued condition of disturbance.

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  • Here the middle part of the solution is unaltered and the number of ions liberated is the same at either end, but the amount of salt left at one end is less than that at the other.

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  • If either ion carried with it some of the unaltered salt or some of the solvent, concentration or dilution of the liquid would be produced where the ion was liberated.

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  • Hence experiments without separating diaphragms are to be preferred, and the apparatus may be considered effective when a consideraable bulk of intervening solution is left unaltered in composition.

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  • If some of the anions, instead of being simple iodine ions represented chemically by the symbol I, are complex structures formed by the union of iodine with unaltered cadmium iodide - structures represented by some such chemical formula as I(CdI 2), the concentration of the solution round the anode would be increased by the passage of an electric current, and the phenomena observed would be explained.

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  • It extends, with unaltered character, from Mukden and Kirin.

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  • Brewers' wort remains unchanged for years, milk keeps permanently sweet, and these and other complex liquids remain unaltered when freely exposed to air from which all these minute organisms are removed.

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  • If some of the anions, instead of being simple iodine ions represented chemically by the symbol I, are complex structures formed by the union of iodine with unaltered cadmium iodide - structures represented by some such chemical formula as I(CdI 2), the concentration of the solution round the anode would be increased by the passage of an electric current, and the phenomena observed would be explained.

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  • St Michael's church at Hamburg, built as late as 1762 and unaltered in 1880, had a 17th-century pitch, a' 407.9.

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  • The picturesque fortifications also by which the city is surrounded remain almost unaltered as they were in the 15th century.

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  • For such functions remain unaltered when each root receives the same infinitesimal increment h; but writing x-h for x causes ao, a1, a 2 a3,...

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  • If an article made of cut sheet be immersed for a few minutes in a bath of melted sulphur, maintained at a temperature of 120 0 C., the rubber absorbs about one-tenth of its weight of that element, and, although somewhat yellowish in colour from the presence of free sulphur, it is still unvulcanized, and unaltered as regards general properties.

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  • In the case of such altered deposits surface exploration alone is likely to be misleading, and it is important to push the underground exploration far enough to reach the unaltered part of the deposit, or at least deep enough to make it certain that there is a sufficient quantity of altered or enriched ore to form the basis of profitable mining operations.

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  • On descending into the substratum the finer material decreases and more stones are met with; farther down are seen larger fragments of unaltered rock closely packed, and this brash or rubble grades insensibly into the unbroken rock below.

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  • It contains a certain amount of unaltered caustic lime and slacked lime, along with sulphates and sulphides of lime, some of which have an evil odour.

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  • When distant vision remains unaltered, but, owing to gradual failure of the accommodative apparatus of the eye clear vision within 8 in.

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  • In the " dry " methods the silver is converted into sulphide or chloride, the gold remaining unaltered; in the " wet " methods the silver is dissolved by nitric acid or boiling sulphuric acid; and in the electrolytic processes advantage is taken of the fact that under certain current densities and other circumstances silver passes from an anode composed of a gold-silver alloy to the cathode more readily than gold.

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  • It can be kept unaltered in dry air, but the smallest trace of moisture in the atmosphere leads to the evolution of minute quantities of acetylene and gives it a distinctive odour.

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  • It may be regarded as generated either by a trapezette moving in a direction at right angles to itself and changing its top but keeping its breadth unaltered, or by an ordinate moving so that its foot has every possible position within a rectangular base.

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  • The three series also differ when heated: the trimetallic salts, containing fixed bases are unaltered, whilst the monoand dimetallic salts yield metaand pyrophosphates respectively.

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  • If the heating be with charcoal, the trimetallic salts of the alkalis and alkaline earths are unaltered, whilst the monoand di-salts give free phosphorus and a trimetallic salt.

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  • Some of these bishoprics were under the authority of the archiepiscopal see of Cologne, others under that of Mainz, and this arrangement was unaltered when in 834 Hamburg was raised to an archbishopric. In 847 the bishopric of Bremen was united with Hamburg, but the authority of this archbishopric extended mainly over the districts north and east of the Elbe.

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  • The General Council, a secession from the General Synod, was organized in 1867, and accepts the "unaltered" (invariata) Augsburg Confession in its original sense, and the other Lutheran symbols as explanatory of the Augsburg Confession.

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  • In Brewster's Edinburgh Journal of Science for 1828 he described his machine for polishing the speculum, which in all essential points remained unaltered afterwards.

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  • with the Ratio Studiorum of Aquaviva (1599), which long remained unaltered and was only partially revised by J.

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  • All four Gospels also were to be placed in the 2nd century, though that according to Matthew retained many features unaltered from the Judaistic original upon which it was based.

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  • (It may be remarked that the eastern limb in all unaltered Cistercian churches is remarkably short, and usually square.) To the east of each limb of the transept are two square chapels, divided according to Cistercian rule by solid walls.

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  • Most of the plains are underlain by Cretaceous and early Tertiary shales and sandstones lying nearly unaltered and undisturbed where they were deposited, although now raised far above sea-level, particularly along the border of the Rocky Mountains where they were thrust up into foot-hills when the range itself was raised.

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  • Their configuration was determined by their relationship to their oxalo-derivatives; the cis-dichloro chloride, [CrC 2 H 4 (NH 2) 2 C1 2 ]Cl-H 2 0, compound with potassium oxalate gave a carmine red crystalline complex salt, [Cr{C2H4(NH2)2}C204][CrC2H4(NH2)2-(C204)2]12H20, while from the trans-chloride a red complex salt is obtained containing the unaltered trans-dichloro group [CrC2H4(NH2)2 C12]

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  • This tendency to vote the entire party ticket is the more pronounced because under the system of voting in use in many of the states all the candidates of the party are arranged on one ticket, and it is much easier to vote a straight or unaltered ticket than to change or " scratch " it.

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  • Magnesium sulphide, MgS, may be obtained, mixed with some unaltered metal and some magnesia, as a hard brown mass by heating magnesia, in sulphur vapour.

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  • Hartmann has an affinity with all these predecessors, and with Spinoza, with whom he agrees that there is but one substance unaltered by the plurality of individuals which are only its modifications.

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  • The college remained unaltered until 1496, when Margaret, countess of Richmond, obtained letters patent from her son, Henry VII., to found a chantry, in connexion with which she established a school.

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  • The number of states of which the empire consists has remained unaltered;i occasional disputes have been settled harmoniously in a legal The em- manner.

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  • The mature pollengrain is, like other spores, a single cell; except in the case of some submerged aquatic plants, it has a double wall, a thin delicate wall of unaltered cellulose, the endospore or intine, and a tough outer cuticularized exospore or extine.

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  • Yet, even after the French had passed the frontier, Alexander still protested that his personal sentiments towards the emperor were unaltered; " but," he added, " God Himself cannot undo the past."

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  • It is present quite unaltered in certain passages, specifically traceable to Judaism, e.g.

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  • Goethe's hero changed with the author's riper experience and with his new conceptions of man's place and duties in the world, but the Gretchen tragedy was taken over into the finished poem, practically unaltered, from the earliest Faust of the Sturm and Drang.

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  • The church, substantially unaltered, forms an almost unique Christian relic. It has been called Roman, but is later.

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  • The form of the iota, and even the style of ornamentation, has been handed down unaltered from the earliest times.

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  • It was in the pressing to its extreme consequences of the conception of uncompromising identity which is to be found in Leibnitz, that the contradictions took their rise which Herbart aimed at solving, by the method of relations and his doctrine of the ultimate plurality of " reals," The logic of relations between conceptual units, themselves unaltered by the relation, seems a kind of reflection of his metaphysical method.

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  • It contains a certain amount of unaltered caustic lime and slacked lime, along with sulphates and sulphides of lime, some of which have an evil odour.

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  • When distant vision remains unaltered, but, owing to gradual failure of the accommodative apparatus of the eye clear vision within 8 in.

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  • This tendency to vote the entire party ticket is the more pronounced because under the system of voting in use in many of the states all the candidates of the party are arranged on one ticket, and it is much easier to vote a straight or unaltered ticket than to change or " scratch " it.

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  • Consideration of the definition of the determinant shows that the value is unaltered when the suffixes in each element are transposed.

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  • 3 is absolutely unaltered by transformation, and is termed the absolute invariant.

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  • - zn +9 1 -z2.1 -z3....1-z8; and since this expression is unaltered by the interchange of n and B we prove Hermite's Law of Reciprocity, which states that the asyzygetic forms of degree 0 for the /t ie are equinumerous with those of degree n for the The degree of the covariant in the variables is e=nO-2w; consequently we are only concerned with positive terms in the developments and (w, 0, n) - (w - r; 0, n) will be negative unless nO It is convenient to enumerate the seminvariants of degree 0 and order e=n0-2w by a generating function; so, in the first written generating function for seminvariants, write z2 for z and az n for a;.

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  • The linear transformation replaces points on lines through the origin by corresponding points on projectively corresponding lines through the origin; it therefore replaces a pencil of lines by another pencil, which corresponds projectively, and harmonic and other properties of pencils which are unaltered by linear transformation we may expect to find indicated in the invariant system.

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  • If when the aperture is given, the wave-length (proportional to k1) varies, the composition of the integrals is unaltered, provided E and n are taken universely proportional to X.

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  • In either case (as also with a prism) the position of minimum deviation leaves the width of the beam unaltered, i.e.

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  • The practice may be modified according to the size of estate by selecting more than one plant each year, but the principle remains unaltered.

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  • The obvious phenomena to be explained by any theory of electrolysis are the liberation of the products of chemical decomposition at the two electrodes while the intervening liquid is unaltered.

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  • The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.

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  • Io) is unaltered.

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  • The importance of the bounding line of the graph lies in the fact that we can keep it unaltered while we alter the graph as a whole by moving OX up or down.

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  • (ii.) Instead of examining what happens as r increases, let us examine what happens as h/x decreases, r remaining unaltered.

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  • Such a conclusion would be in the face of the principle of energy, which teaches plainly that the retardation in question leaves the aggregate brightness unaltered.

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  • Their selection and election were governed by the same laws as in Natal proper, and on the establishment of the Union the franchise qualifications - which practically exclude natives - remained unaltered.

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  • For the body alone the resultant of the components of momentum W V -cos andW V sin 0 is W V -sec. lb, acting along 00', and so is unaltered.

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  • yet by any means can keep the identical surface occupied by it a plane of zero potential, the boundary conditions will remain the same, and therefore the field of force to the left of PO will remain unaltered.

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  • By continuing the treatment of these in the ordinary way of refining, poling and granulating, all the foreign matters other than gold, copper and silver are removed, and, by exposing the granulated metal to a high oxidizing heat for a considerable time the copper may be completely oxidized while the precious metals are unaltered.

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  • Various agencies are at work tending to modify the composition of the atmosphere, but these so neutralize each other as to leave it practically unaltered.

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  • The house in which the poet Cowley spent the last years of his life remains, and the chamber in which he died is preserved unaltered.

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  • The acceleration therefore remains the same, and the velocity is unaltered.

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  • 70, at a distance x from the vertex, the horizontal component of the resultant (tangent to the curve) will be unaltered; the vertical component V will be simply the sum of the loads between 0 and F, or wx.

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  • The entire form of divine worship remained therefore unaltered.

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  • Thorold Rogers published in the Academy, 28th February 1885, a letter of Smith to William Pulteney, written in 1772, from which he thought it probable that the work lay "unrevised and unaltered" in the author's desk for four years.

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  • On the constitution of Dublin as a county borough in 1898, the positions and duties of its corporation were left practically unaltered.

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  • But in the end the American invasion failed and the treaty made at Ghent in 1814 left the previous status unaltered.

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  • It is a sandy tract, in parts well wooded, diversified with several small sheets of water, and to a great extent preserves its natural characteristics unaltered.

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  • The system was, on the advice of an Anglo-Indian official (Sir John Scott), modified and simplified in 1891, but its essential character remained unaltered.

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  • increased the power of his ministry, the personnel of which remained unaltered.

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  • The total absence of fossils is a remarkable fact, and one for which it is difficult to account, as the beds are for the most part quite unaltered.

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  • Both titles were borrowed by the Merovingian kings for the administrative machinery of the Frank empire, and under them the functions of the duke remained substantially unaltered.

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  • The fused mass is then extracted with water to remove potassium chloride, and warmed with hydrochloric acid to remove unaltered chlorate, and finally extracted with water again, when a residue of practically pure perchlorate is obtained.

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  • If now the assemblage be brought into any other position relative to the earth, without alteration of the mutual distances, this is equivalent to a rotation of the directions of the forces relatively to the assemblage, the ratios of the forces remaining unaltered.

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  • It is to be noticed that the parameter c of the cylindroid is unaltered if the two pitches h, k be increased by equal amounts; the only change is that all the pitches are increased by the same amount.

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  • The components of the resultant force R are unaltered, but the new components of couple are found to be L=LyZ+zY,~

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  • Again, if two bodies are connectedbya string or rod, and if the hypothetical displacements be adjusted so that the distance between the points of attachment is unaltered, the corresponding stress may be ignored.

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  • the relative velocity of the two bodies is reversed in direction, but unaltered in magnitude.

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  • In the time ~5t a certain impulse is given to the first particle in the direction (say) from P to Q, whilst an equal and opposite impulse is given to the second in the, direction from Q to P. Since these impulses produce equal and opposite momenta in the two particles, the resultant lineal momentumof the system is unaltered.

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  • In the case of a rigid body we must suppose that those forces adjust themselves so as to preserve the mutual distances of the various particles unaltered.

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  • For we have seen that r is constant when there are no extraneous forces; and r is evidently not affected by an instantaneous impulse which leaves the angular momentum Cr, about the axis of symmetry, unaltered.

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  • Yet there are abundant signs that the native human instincts, the natural human appetites, remained unaltered and alive beneath the crust of orthodoxy.

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  • But the Greek cities retained monarchical government throughout, and both the domestic art and the principal religious cults remained almost unaltered.

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  • The place - names throughout the Principality may be said to group themselves roughly into four divisions: (i.) Pure and unaltered Celtic names; (ii.) Corrupted or abbreviated Celtic names; (iii.) English names; (iv.) Scandinavian and foreign names.

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  • Tudno, Afan, Padarn, &c. To the second division - those place-names which have been corrupted by English usage - belong most of the older historic towns, in striking contrast with the rural villages and parishes, which in nearly all cases have retained unaltered their original Celtic names.

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  • A large majority of the English members, 265 out of 400, were to be elected by the counties, where voters must possess land or personal property of the value of £ 200, while in the boroughs the franchise remained unaltered.

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  • The bill passed through parliament unaltered, the only jarring note in the debates in either house concerning the exclusion of natives from the franchise (save in the Cape province).

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  • It has a specific gravity of 5.78 and always contains some unaltered antimony trichloride (from 6 to 20%, G.

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  • Prepared in this way it contains a small quantity of the unaltered chloride, which can be removed by ether or carbon bisulphide.

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  • In the earlier experiments on smaller animals the potency of the toxin was modified for the first injections, but in preparing antitoxin for therapeutical purposes the toxin is used in its unaltered condition, the horse being the animal usually employed.

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  • Under the new system modelled upon that of the Bombay municipality, this body, styled the corporation, remains comparatively unaltered; but a large portion of their powers is transferred to a general committee, composed of twelve members, of whom one-third are elected by the corporation, one-third by certain public bodies and one-third are nominated by the government.

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  • In the resolution which was adopted on the 2nd of March the chamber," imbued with the ideas which presided over the foundation of the Congo State and inspired the Act of Berlin,"expressed its confidence in the proposals which the commission of reforms was elaborating, and decided" to proceed without delay to the examination of the projected law of the 7th of August 1901, on the government of Belgium's colonial possessions."The report of the reforms commission was not made public, but as the fruit of its deliberations King Leopold signed on the 3rd of June 1906 a number of decrees embodying various While the commission was sitting, further evidence was forthcoming that the system complained of on the Congo remained unaltered, and that the" reforms "of June 1906 were illusory.

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  • Thesiger, consul at Boma, who in a memorandum on the application of the labour tax, after detailing various abuses, added," The system which gave rise to these abuses still continues unchanged, and so long as it is unaltered the condition of the natives must remain one of veiled slavery."Eight days later (on the 5th of March) an additional act was signed in Brussels annulling the clauses in the treaty of cession concerning the Fondation, which was to cease to exist on the day Belgium assumed the sovereignty of the Congo and its property to be absorbed in the state domains.

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  • The intensity of the light diminishes merely because the total energy, though unaltered, is distributed over a wider and wider surface as the rays diverge from the source.

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  • In a similar way the absorption of light in the coloured gas chlorine is found to be unaltered if the thickness is reduced by compression, because the density is increased in the same ratio that the thickness is reduced.

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  • In 1291 Bedfordshire was an archdeaconry including six rural deaneries, which remained practically unaltered until i 880, when they were increased to eleven with a new schedule of parishes.

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  • Some words indeed 2 - such as laudare, to praise, ducere, to lead - retain unaltered the forms under which they were used by Virgil and Cicero.

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  • Wooden pulleys are preferably made of maple, the rim being formed of small sections morticed, pinned and glued together, with the grain set in such directions that any warping of the material will leave the cylindrical form practically unaltered.

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  • can be applied to n, n', the denominator n remaining unaltered.

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  • Hence, so long as the denominator remains unaltered, we can deal with, exactly as if they were numbers, any operations being performed on the numerators.

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  • In former times the juniper seems to have been a very well-known plant, the name occurring almost unaltered in many languages.

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  • It is unaltered by ignition in hydrogen.

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  • Other views of the nature of the Psilotaceous synangium are, however, possible, and indeed the existence of both simple and complicated sporangiophores in the Sphenophyllaceae leaves the question open as to whether the synangium in existing Psilotaceae is a relatively simple type of sporangiophore which has persisted unaltered or is the result of reduction from a more elaborate structure.

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  • It may be added, that if the lines are converted into columns, and the columns into lines, in such a way as to leave the dexter diagonal unaltered, the value of the determinant is unaltered; the determinant is in this case said to be transposed.

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  • The Navy Discipline Act was revised in 1749, and remained unaltered till 1865.

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  • Langstroth's space-measurements have remained practically unaltered notwithstanding the many improvements in hive-making, and in the various sizes of movable frames, since introduced and used in different parts of the world.

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  • Although various modifications have since been made in minor details - all tending to improvement - its main features are unaltered.

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  • Nothing is altered as to objective magnification, however, as the first surface is plane, and the employment of the immersion means that the value of f l ' 'is unaltered.

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  • In the Wealden of Belgium, for example, specimens of Ferns and Coniferae occur, in the form of lignite, which can be sectioned, like recent plants, with a razor, and exhibit an almost unaltered structure.

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  • It is only in the rare cases where a very young twig is preserved that the primary structure of the stem is found unaltered.

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  • The primary structure f ` is only found unaltered in the 1 1, 1 ` by means of a cambium set in very Il 111/1/1, 1 1 early, xylem being formed internally and phloem externally in a perfectly normal manner.

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  • tiXynvcs, sense of pain), sensibility is unaltered.

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  • A second edition of the Kritik, with some modifications, appeared in 1787, after which it remained unaltered.

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  • chondrite meteorites, which are primitive and largely unaltered.

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  • dreadnought tiles has been unaltered throughout the century.

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  • The rest of the sensitive emulsion is still unaltered.

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  • It is more likely that dolomitisation fronts formed on the sides of the fault-controlled pathway, with the unaltered marbles remaining essentially impermeable.

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  • Instead, Ida could well have a composition like that of ordinary chondrite meteorites, which are primitive and largely unaltered.

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  • midshipmanand midshipmen's uniform was unaltered apart from the buttons, which were the same as captains ' .

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  • It was verified very exactly by Stas's experiments, in which he removed the oxygen from the ternary compound silver iodate and found that the whole of the silver and the iodine remained in combination with each other as silver iodide; his results prove, to one part in ten millions, that the combining ratio of the silver and the iodine is unaltered by the removal of the oxygen.

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  • It is not difficult to prove that (3) remains unaltered, when this circumstance is taken into account; and it is evident in any case that a correction would depend upon the square of (D' - D).

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  • When unaltered and containing no ferric oxide, the mineral is colourless, but on exposure to the light it very soon becomes of a characteristic indigo-blue colour.

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  • St Michael's church at Hamburg, built as late as 1762 and unaltered in 1880, had a 17th-century pitch, a' 407.9.

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  • The picturesque fortifications also by which the city is surrounded remain almost unaltered as they were in the 15th century.

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  • Yet, so insensible is Schatz to the euphony of his own work, that he proposes, as an alternative for the first and second trombones, two violins an octave higher, the other parts remaining unaltered!

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  • The parcels into which the Lombards had divided the peninsula remained thus virtually unaltered, except for the new authority acquired by the see of Rome.

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  • Prout, who on analysis found they consisted essentially of calcium phosphate and carbonate, and not infrequently contained fragments of unaltered bone.

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  • Even if the conception of the relative sanctity of gods and men remained unaltered, it by no means follows that in primitive times the same precautions were necessary in approaching the former as were demanded by the consciousness of later generations.

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  • The practice may be modified according to the size of estate by selecting more than one plant each year, but the principle remains unaltered.

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  • If the bead is coloured we may have present: cobalt, blue to violet; copper, green, blue on cooling; in the reducing flame, red when cold; chromium, green, unaltered in the reducing flame; iron, brownish-red, light-yellow or colourless on cooling; in the reducing flame, red while hot, yellow on cooling, greenish when cold; nickel, reddish to brownish-red, yellow to reddish-yellow or colourless on cooling, unaltered in the reducing flame; bismuth, yellowish-brown, light-yellow or colourless on cooling; in the reducing flame, almost colourless, blackish-grey when cold; silver, light yellowish to opal, somewhat opaque when cold; whitish-grey in the reducing flame; manganese, amethyst red, colourless in the reducing flame.

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  • The mere retention of the same crystal form by homologous substances is not a sufficient reason for denying a morphotropic effect to the substituent group; for, in the case of certain substances crystallizing in the cubic system, although the crystal form remains unaltered, yet the structures vary.

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  • So what is it that keeps unaltered in the moving triangle ?

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  • That country, left by the Treaty of Berlin with its status unaltered, was in a continued condition of disturbance.

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  • The obvious phenomena to be explained by any theory of electrolysis are the liberation of the products of chemical decomposition at the two electrodes while the intervening liquid is unaltered.

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  • Here the middle part of the solution is unaltered and the number of ions liberated is the same at either end, but the amount of salt left at one end is less than that at the other.

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  • If either ion carried with it some of the unaltered salt or some of the solvent, concentration or dilution of the liquid would be produced where the ion was liberated.

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  • Hence experiments without separating diaphragms are to be preferred, and the apparatus may be considered effective when a consideraable bulk of intervening solution is left unaltered in composition.

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  • If sulphuric acid be added to the vessel containing the zinc, these conditions are unaltered and still no zinc is dissolved.

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  • If an article made of cut sheet be immersed for a few minutes in a bath of melted sulphur, maintained at a temperature of 120 0 C., the rubber absorbs about one-tenth of its weight of that element, and, although somewhat yellowish in colour from the presence of free sulphur, it is still unvulcanized, and unaltered as regards general properties.

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  • It extends, with unaltered character, from Mukden and Kirin.

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  • Consideration of the definition of the determinant shows that the value is unaltered when the suffixes in each element are transposed.

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  • Such a determinant when of uneven degree vanishes, for if we multiply each row by - I we multiply the determinant by (- I) n = -1, and the effect of this is otherwise merely to transpose the determinant so that it reads by rows as it formerly did by columns, an operation which we know leaves the determinant unaltered.

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  • x3 (ll'1T2...) and it is seen intuitively that the number 0 remains unaltered when the first two of these partitions are interchanged (see Combinatorial Analysis).

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  • For such functions remain unaltered when each root receives the same infinitesimal increment h; but writing x-h for x causes ao, a1, a 2 a3,...

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  • The fundamental system connected with n quadratic forms consists of (i.) the n forms themselves f i, f2,�� fn, (ii.) the (2) functional determinants (f i, f k) 1, (iii.) the (n 2 1) in variants (f l, fk) 2, (iv.) the (3) forms (f i, (f k, f ni)) 2, each such form remaining unaltered for any permutations of i, k, m.

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  • 3 is absolutely unaltered by transformation, and is termed the absolute invariant.

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  • The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.

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  • - zn +9 1 -z2.1 -z3....1-z8; and since this expression is unaltered by the interchange of n and B we prove Hermite's Law of Reciprocity, which states that the asyzygetic forms of degree 0 for the /t ie are equinumerous with those of degree n for the The degree of the covariant in the variables is e=nO-2w; consequently we are only concerned with positive terms in the developments and (w, 0, n) - (w - r; 0, n) will be negative unless nO It is convenient to enumerate the seminvariants of degree 0 and order e=n0-2w by a generating function; so, in the first written generating function for seminvariants, write z2 for z and az n for a;.

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  • +bx 2, every leading coefficient of a simultaneous covariant vanishes by the operation of a+Sib=aoda +alda.2+...+a7,-1d a P+bod b Observe that we may employ the principle of suffix diminution to obtain from any seminvariant one appertaining to a (p-I)i c and a q - I ie, and that suffix augmentation produces a portion of a higher seminvariant, the degree in each case remaining unaltered.

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  • The linear transformation replaces points on lines through the origin by corresponding points on projectively corresponding lines through the origin; it therefore replaces a pencil of lines by another pencil, which corresponds projectively, and harmonic and other properties of pencils which are unaltered by linear transformation we may expect to find indicated in the invariant system.

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  • Io) is unaltered.

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  • The importance of the bounding line of the graph lies in the fact that we can keep it unaltered while we alter the graph as a whole by moving OX up or down.

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  • (ii.) Instead of examining what happens as r increases, let us examine what happens as h/x decreases, r remaining unaltered.

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  • If when the aperture is given, the wave-length (proportional to k1) varies, the composition of the integrals is unaltered, provided E and n are taken universely proportional to X.

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  • In either case (as also with a prism) the position of minimum deviation leaves the width of the beam unaltered, i.e.

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  • Such a conclusion would be in the face of the principle of energy, which teaches plainly that the retardation in question leaves the aggregate brightness unaltered.

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  • Their selection and election were governed by the same laws as in Natal proper, and on the establishment of the Union the franchise qualifications - which practically exclude natives - remained unaltered.

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  • In the case of such altered deposits surface exploration alone is likely to be misleading, and it is important to push the underground exploration far enough to reach the unaltered part of the deposit, or at least deep enough to make it certain that there is a sufficient quantity of altered or enriched ore to form the basis of profitable mining operations.

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  • For the body alone the resultant of the components of momentum W V -cos andW V sin 0 is W V -sec. lb, acting along 00', and so is unaltered.

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  • On descending into the substratum the finer material decreases and more stones are met with; farther down are seen larger fragments of unaltered rock closely packed, and this brash or rubble grades insensibly into the unbroken rock below.

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  • yet by any means can keep the identical surface occupied by it a plane of zero potential, the boundary conditions will remain the same, and therefore the field of force to the left of PO will remain unaltered.

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  • By continuing the treatment of these in the ordinary way of refining, poling and granulating, all the foreign matters other than gold, copper and silver are removed, and, by exposing the granulated metal to a high oxidizing heat for a considerable time the copper may be completely oxidized while the precious metals are unaltered.

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  • In the " dry " methods the silver is converted into sulphide or chloride, the gold remaining unaltered; in the " wet " methods the silver is dissolved by nitric acid or boiling sulphuric acid; and in the electrolytic processes advantage is taken of the fact that under certain current densities and other circumstances silver passes from an anode composed of a gold-silver alloy to the cathode more readily than gold.

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  • It can be kept unaltered in dry air, but the smallest trace of moisture in the atmosphere leads to the evolution of minute quantities of acetylene and gives it a distinctive odour.

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  • Various agencies are at work tending to modify the composition of the atmosphere, but these so neutralize each other as to leave it practically unaltered.

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  • It may be regarded as generated either by a trapezette moving in a direction at right angles to itself and changing its top but keeping its breadth unaltered, or by an ordinate moving so that its foot has every possible position within a rectangular base.

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  • The three series also differ when heated: the trimetallic salts, containing fixed bases are unaltered, whilst the monoand dimetallic salts yield metaand pyrophosphates respectively.

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  • If the heating be with charcoal, the trimetallic salts of the alkalis and alkaline earths are unaltered, whilst the monoand di-salts give free phosphorus and a trimetallic salt.

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  • The house in which the poet Cowley spent the last years of his life remains, and the chamber in which he died is preserved unaltered.

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  • The acceleration therefore remains the same, and the velocity is unaltered.

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  • Some of these bishoprics were under the authority of the archiepiscopal see of Cologne, others under that of Mainz, and this arrangement was unaltered when in 834 Hamburg was raised to an archbishopric. In 847 the bishopric of Bremen was united with Hamburg, but the authority of this archbishopric extended mainly over the districts north and east of the Elbe.

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  • 70, at a distance x from the vertex, the horizontal component of the resultant (tangent to the curve) will be unaltered; the vertical component V will be simply the sum of the loads between 0 and F, or wx.

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  • If the path is to be unaltered by the motion of the aether, as the law of astronomical aberration suggests, this must differ from fds/V by terms not depending on the path - that is, by terms involving only the beginning and end of it.

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  • The entire form of divine worship remained therefore unaltered.

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  • The General Council, a secession from the General Synod, was organized in 1867, and accepts the "unaltered" (invariata) Augsburg Confession in its original sense, and the other Lutheran symbols as explanatory of the Augsburg Confession.

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  • In Brewster's Edinburgh Journal of Science for 1828 he described his machine for polishing the speculum, which in all essential points remained unaltered afterwards.

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  • with the Ratio Studiorum of Aquaviva (1599), which long remained unaltered and was only partially revised by J.

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  • All four Gospels also were to be placed in the 2nd century, though that according to Matthew retained many features unaltered from the Judaistic original upon which it was based.

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  • Thorold Rogers published in the Academy, 28th February 1885, a letter of Smith to William Pulteney, written in 1772, from which he thought it probable that the work lay "unrevised and unaltered" in the author's desk for four years.

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  • On the constitution of Dublin as a county borough in 1898, the positions and duties of its corporation were left practically unaltered.

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  • (It may be remarked that the eastern limb in all unaltered Cistercian churches is remarkably short, and usually square.) To the east of each limb of the transept are two square chapels, divided according to Cistercian rule by solid walls.

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  • Most of the plains are underlain by Cretaceous and early Tertiary shales and sandstones lying nearly unaltered and undisturbed where they were deposited, although now raised far above sea-level, particularly along the border of the Rocky Mountains where they were thrust up into foot-hills when the range itself was raised.

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  • But in the end the American invasion failed and the treaty made at Ghent in 1814 left the previous status unaltered.

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  • Their configuration was determined by their relationship to their oxalo-derivatives; the cis-dichloro chloride, [CrC 2 H 4 (NH 2) 2 C1 2 ]Cl-H 2 0, compound with potassium oxalate gave a carmine red crystalline complex salt, [Cr{C2H4(NH2)2}C204][CrC2H4(NH2)2-(C204)2]12H20, while from the trans-chloride a red complex salt is obtained containing the unaltered trans-dichloro group [CrC2H4(NH2)2 C12]

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  • Magnesium sulphide, MgS, may be obtained, mixed with some unaltered metal and some magnesia, as a hard brown mass by heating magnesia, in sulphur vapour.

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  • Hartmann has an affinity with all these predecessors, and with Spinoza, with whom he agrees that there is but one substance unaltered by the plurality of individuals which are only its modifications.

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  • It is a sandy tract, in parts well wooded, diversified with several small sheets of water, and to a great extent preserves its natural characteristics unaltered.

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  • The college remained unaltered until 1496, when Margaret, countess of Richmond, obtained letters patent from her son, Henry VII., to found a chantry, in connexion with which she established a school.

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  • The number of states of which the empire consists has remained unaltered;i occasional disputes have been settled harmoniously in a legal The em- manner.

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  • The system was, on the advice of an Anglo-Indian official (Sir John Scott), modified and simplified in 1891, but its essential character remained unaltered.

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  • The mature pollengrain is, like other spores, a single cell; except in the case of some submerged aquatic plants, it has a double wall, a thin delicate wall of unaltered cellulose, the endospore or intine, and a tough outer cuticularized exospore or extine.

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  • Yet, even after the French had passed the frontier, Alexander still protested that his personal sentiments towards the emperor were unaltered; " but," he added, " God Himself cannot undo the past."

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  • It is present quite unaltered in certain passages, specifically traceable to Judaism, e.g.

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  • Goethe's hero changed with the author's riper experience and with his new conceptions of man's place and duties in the world, but the Gretchen tragedy was taken over into the finished poem, practically unaltered, from the earliest Faust of the Sturm and Drang.

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  • increased the power of his ministry, the personnel of which remained unaltered.

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  • The church, substantially unaltered, forms an almost unique Christian relic. It has been called Roman, but is later.

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  • The total absence of fossils is a remarkable fact, and one for which it is difficult to account, as the beds are for the most part quite unaltered.

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  • The form of the iota, and even the style of ornamentation, has been handed down unaltered from the earliest times.

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  • Potassium cyanide gives a greenish yellow precipitate of nickel cyanide, Ni(CN) 2, soluble in excess of potassium cyanide, forming a double salt, Ni(CN)2.2KCN, which remains unaltered when boiled with excess of potassium cyanide in presence of air (cf.

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  • Both titles were borrowed by the Merovingian kings for the administrative machinery of the Frank empire, and under them the functions of the duke remained substantially unaltered.

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  • It was in the pressing to its extreme consequences of the conception of uncompromising identity which is to be found in Leibnitz, that the contradictions took their rise which Herbart aimed at solving, by the method of relations and his doctrine of the ultimate plurality of " reals," The logic of relations between conceptual units, themselves unaltered by the relation, seems a kind of reflection of his metaphysical method.

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  • The fused mass is then extracted with water to remove potassium chloride, and warmed with hydrochloric acid to remove unaltered chlorate, and finally extracted with water again, when a residue of practically pure perchlorate is obtained.

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  • If now the assemblage be brought into any other position relative to the earth, without alteration of the mutual distances, this is equivalent to a rotation of the directions of the forces relatively to the assemblage, the ratios of the forces remaining unaltered.

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  • It is to be noticed that the parameter c of the cylindroid is unaltered if the two pitches h, k be increased by equal amounts; the only change is that all the pitches are increased by the same amount.

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  • The components of the resultant force R are unaltered, but the new components of couple are found to be L=LyZ+zY,~

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  • Again, if two bodies are connectedbya string or rod, and if the hypothetical displacements be adjusted so that the distance between the points of attachment is unaltered, the corresponding stress may be ignored.

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  • the relative velocity of the two bodies is reversed in direction, but unaltered in magnitude.

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  • In the time ~5t a certain impulse is given to the first particle in the direction (say) from P to Q, whilst an equal and opposite impulse is given to the second in the, direction from Q to P. Since these impulses produce equal and opposite momenta in the two particles, the resultant lineal momentumof the system is unaltered.

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  • In the case of a rigid body we must suppose that those forces adjust themselves so as to preserve the mutual distances of the various particles unaltered.

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  • For we have seen that r is constant when there are no extraneous forces; and r is evidently not affected by an instantaneous impulse which leaves the angular momentum Cr, about the axis of symmetry, unaltered.

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  • Yet there are abundant signs that the native human instincts, the natural human appetites, remained unaltered and alive beneath the crust of orthodoxy.

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  • But the Greek cities retained monarchical government throughout, and both the domestic art and the principal religious cults remained almost unaltered.

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  • The place - names throughout the Principality may be said to group themselves roughly into four divisions: (i.) Pure and unaltered Celtic names; (ii.) Corrupted or abbreviated Celtic names; (iii.) English names; (iv.) Scandinavian and foreign names.

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  • Tudno, Afan, Padarn, &c. To the second division - those place-names which have been corrupted by English usage - belong most of the older historic towns, in striking contrast with the rural villages and parishes, which in nearly all cases have retained unaltered their original Celtic names.

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  • A large majority of the English members, 265 out of 400, were to be elected by the counties, where voters must possess land or personal property of the value of £ 200, while in the boroughs the franchise remained unaltered.

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  • The bill passed through parliament unaltered, the only jarring note in the debates in either house concerning the exclusion of natives from the franchise (save in the Cape province).

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  • It has a specific gravity of 5.78 and always contains some unaltered antimony trichloride (from 6 to 20%, G.

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  • Prepared in this way it contains a small quantity of the unaltered chloride, which can be removed by ether or carbon bisulphide.

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  • In the earlier experiments on smaller animals the potency of the toxin was modified for the first injections, but in preparing antitoxin for therapeutical purposes the toxin is used in its unaltered condition, the horse being the animal usually employed.

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  • Under the new system modelled upon that of the Bombay municipality, this body, styled the corporation, remains comparatively unaltered; but a large portion of their powers is transferred to a general committee, composed of twelve members, of whom one-third are elected by the corporation, one-third by certain public bodies and one-third are nominated by the government.

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  • In the resolution which was adopted on the 2nd of March the chamber," imbued with the ideas which presided over the foundation of the Congo State and inspired the Act of Berlin,"expressed its confidence in the proposals which the commission of reforms was elaborating, and decided" to proceed without delay to the examination of the projected law of the 7th of August 1901, on the government of Belgium's colonial possessions."The report of the reforms commission was not made public, but as the fruit of its deliberations King Leopold signed on the 3rd of June 1906 a number of decrees embodying various While the commission was sitting, further evidence was forthcoming that the system complained of on the Congo remained unaltered, and that the" reforms "of June 1906 were illusory.

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  • Thesiger, consul at Boma, who in a memorandum on the application of the labour tax, after detailing various abuses, added," The system which gave rise to these abuses still continues unchanged, and so long as it is unaltered the condition of the natives must remain one of veiled slavery."Eight days later (on the 5th of March) an additional act was signed in Brussels annulling the clauses in the treaty of cession concerning the Fondation, which was to cease to exist on the day Belgium assumed the sovereignty of the Congo and its property to be absorbed in the state domains.

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  • The intensity of the light diminishes merely because the total energy, though unaltered, is distributed over a wider and wider surface as the rays diverge from the source.

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  • In a similar way the absorption of light in the coloured gas chlorine is found to be unaltered if the thickness is reduced by compression, because the density is increased in the same ratio that the thickness is reduced.

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  • In 1291 Bedfordshire was an archdeaconry including six rural deaneries, which remained practically unaltered until i 880, when they were increased to eleven with a new schedule of parishes.

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  • Some words indeed 2 - such as laudare, to praise, ducere, to lead - retain unaltered the forms under which they were used by Virgil and Cicero.

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  • Wooden pulleys are preferably made of maple, the rim being formed of small sections morticed, pinned and glued together, with the grain set in such directions that any warping of the material will leave the cylindrical form practically unaltered.

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  • can be applied to n, n', the denominator n remaining unaltered.

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  • Hence, so long as the denominator remains unaltered, we can deal with, exactly as if they were numbers, any operations being performed on the numerators.

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  • In former times the juniper seems to have been a very well-known plant, the name occurring almost unaltered in many languages.

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  • It is unaltered by ignition in hydrogen.

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  • Other views of the nature of the Psilotaceous synangium are, however, possible, and indeed the existence of both simple and complicated sporangiophores in the Sphenophyllaceae leaves the question open as to whether the synangium in existing Psilotaceae is a relatively simple type of sporangiophore which has persisted unaltered or is the result of reduction from a more elaborate structure.

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  • It may be added, that if the lines are converted into columns, and the columns into lines, in such a way as to leave the dexter diagonal unaltered, the value of the determinant is unaltered; the determinant is in this case said to be transposed.

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  • The Navy Discipline Act was revised in 1749, and remained unaltered till 1865.

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  • What has just been said as to the treatment of the final vowels in Catalan must be understood as applying only to pure Catalan, unaltered by the predominance of the Castilian, for the actual language is no longer faithful to the principle we have laid down; it allows the.final o atonic in a number of substantives and adjectives, and in the verb it now conjugates canto, temo, sentoa thing unknown in the ancient language.

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  • Langstroth's space-measurements have remained practically unaltered notwithstanding the many improvements in hive-making, and in the various sizes of movable frames, since introduced and used in different parts of the world.

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  • Although various modifications have since been made in minor details - all tending to improvement - its main features are unaltered.

    0
    0
  • Nothing is altered as to objective magnification, however, as the first surface is plane, and the employment of the immersion means that the value of f l ' 'is unaltered.

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  • In the Wealden of Belgium, for example, specimens of Ferns and Coniferae occur, in the form of lignite, which can be sectioned, like recent plants, with a razor, and exhibit an almost unaltered structure.

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