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mutual

mutual

mutual Sentence Examples

  • We agreed on our mutual commitment.

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  • We both have a mutual problem.

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  • It was a terrific speech and they both nodded in mutual agreement.

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  • It was a terrific speech and they both nodded in mutual agreement.

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  • Certainly. It's not as if they don't have a mutual interest in this business.

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  • I want mutual trust and love.

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  • By mutual agreement, Alex had final say in decisions, but they were supposed to discuss it first.

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  • Was it wishful thinking, or was there a mutual attraction between them?

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  • They have thus upheld the true contractual nature of concordats and the mutual juridical obligation which results from them.

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  • We both managed a smile at our mutual concern.

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  • The feeling is mutual.  You're the reason I spent so much time in Hell.

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  • The feeling is mutual.  You're the reason I spent so much time in Hell.

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  • They had rated each other highly in the entanglement, and by mutual consent began repeat­ing the performance regularly.

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  • They had rated each other highly in the entanglement, and by mutual consent began repeat­ing the performance regularly.

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  • Marriage was based on mutual respect.

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  • That Chateaubriand, Madame de Stael, and others spoke certain words to one another only affected their mutual relations but does not account for the submission of millions.

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  • The gemeente - consisting only of those bound by the communal oath for mutual help and defence - elected their own magistrates.

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  • BINARY SYSTEM, in astronomy, a system composed of two stars revolving around each other under the influence of their mutual attraction.

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  • BINARY SYSTEM, in astronomy, a system composed of two stars revolving around each other under the influence of their mutual attraction.

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  • Although Ethel and Fred had never met, that didn't stop them from developing a strong mutual dislike, fueled via telephone mes­sages and third-party comments.

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  • It was of the nature of a contract, entered into by mutual promise, the clasping of hands, and exchange of an agreement in writing (tabula hospitalis) or of a token (tessera or symbolum), and was rendered hereditary by the division of the tessera.

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  • Since concordats are contracts they give rise to that special mutual obligation which results from every agreement freely entered into; for a contract is binding on both parties to it.

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  • But with these reservations it must unhesitatingly be said that concordats are bilateral or synallagmatic contracts, from which results an equal mutual obligation for the two parties, who enter into a juridical engagement towards each other.

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  • It is for this reason that concordats always present a clearly marked character of mutual concession, each of the two powers renouncing certain of its claims in the interests of peace.

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  • These include the mutual distances of some of the stars in the Pleiades, a few observations of the apparent diameter of the sun, others of the distance of the moon from neighbouring stars, and a great number of measurements of the diameter of the moon.

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  • They are formed by the action of nitrous fumes on ammoniacal solutions of cobaltous salts, or purpureo-salts, or by the mutual reaction of chlorpurpureosalts and alkaline nitrites.

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  • The Tugendbund is an alliance of virtue: it is love, mutual help... it is what Christ preached on the Cross.

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  • While Dean distrusted the Dawkins, given their mutual animosity toward one another, any collective effort on their part—on any project—seemed questionable, if not impossible.

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  • After a few moments of mutual silence, both men rose and returned to their rooms.

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  • Cynthia was the first to comment but Dean at first dismissed her concerns as mutual nervousness.

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  • By mutual agreement, announced to Howie by our silence, no discussion about Julie took place unless initiated by Howie himself.

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  • Obviously there was a mutual physical attraction between them, but that was all.

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  • We are building the Internet to connect with each other better, to share information, to collaborate, to offer mutual support, and so on.

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  • To the sending currents, however, the bridge offers only apparent ohmic resistance due to the fact that the current entering the mid-point of the winding flows through the two halves or arms in opposite direction, and, owing to the winding being on the same iron core, the mutual inductive effect of the two arms on one another neutralizes the self-induction to the sending currents.

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  • As it grew darker, I was startled by the honking of geese flying low over the woods, like weary travellers getting in late from Southern lakes, and indulging at last in unrestrained complaint and mutual consolation.

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  • Their mutual jealousies, combined with the prestige of the empire, and possibly with the selfishness of the pope, who had secured his own position, and was not likely to foster a national spirit that would have threatened the ecclesiastical supremacy, deprived the Italians of the only great opportunity they ever had of forming themselves into a powerful nation.

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  • While the two maintained mutual respect, Jake Weller appeared unsettled in Dean's presence, a combination of insecurity over Dean's more extensive experience and memories of past encounters that had pushed the lawman into compromising situations.

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  • Why hadn't she ever thought about their mutual love of animals?

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  • It was at this time that Marius's jealousy of his legate laid the foundations of their future rivalry and mutual hatred.

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  • When they arrived in Ouray there was a mutual understanding all that lay between them had not been discussed.

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  • Joachim Jung, in his Isagoge phytoscopica (1678), recognized that the plant-body consists of certain definite members, root, stem and leaf, and defined them by their different form and by their mutual relations.

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  • It was not until many centuries had passed that the parts began to be regarded from the point of view of their essential nature and of their mutual relations; that is, morphologically instead of organographically.

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  • Our artificially-established classifications collapse whilst we gain further insight into the mutual affinities of the existing groups.

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  • We five hirelings, as dissimilar as snowflakes, are tripping over one another in an effort to display mutual accommodation.

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  • In addition to the encyclical letter, nineteen resolutions were put forth, and the reports of twelve special committees are appended upon which they are based, the subjects being intemperance, purity, divorce, polygamy, observance of Sunday, socialism, care of emigrants, mutual relations of dioceses of the Anglican Communion, home reunion, Scandinavian Church, Old Catholics, &c., Eastern Churches, standards of doctrine and worship. Perhaps the most important of these is the famous "Lambeth Quadrilateral," which laid down a fourfold basis for home reunion - the Holy Scriptures, the Apostles' and Nicene creeds, the two sacraments ordained by Christ himself and the historic episcopate.

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  • The reigning family, however, became extinct when Duke Julius Francis died in September 1689, and there were at least eight claimants for his duchy, chief among them being John George III., elector of Saxony, and George William, duke of Brunswick-Luneburg-Celle, the ancestors of both these princes having made treaties of mutual succession with former dukes of Saxe-Lauenburg.

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  • He asked about mutual acquaintances, and she became still more animated and chattered away giving him greetings from various people and retelling the town gossip.

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  • By mutual agreement with both Daniel Brennan and Merrill Cooms, our conversations are reduced to an occasional call, for security sake.

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  • If L and N are the inductances of any two circuits which have a coefficient of mutual inductance M, then M/-/ (LN) is called the coefficient of coupling of the circuits and is generally expressed as a percentage.

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  • This alteration of charge caused a corresponding change in the mutual attraction of the plates of the condenser; hence the flexible plate was made to copy the vibrations of the diaphragm of the transmitter.

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  • Mutual benefit and co-operative societies serve the purpose of working-class defence or offence against the employers.

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  • In Italy, people can apply for loans through savings banks, assurance companies and mutual benefit societies.

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  • The present Italian mutual benefit societies resemble the ancient beneficent corporations, of which in some respects they may be considered a continuation.

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  • The problem, then, which plantdistribution presents is twofold: it has first to map out the earths surface into regions or areas of vegetation, and secondly to trace the causes which have brought them about and led to their restriction and to their mutual relations.

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  • Life would be filled with mutual concessions I thought as I tucked my tee shirt into a bottom drawer.

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  • "The FBI is all over the place," he said after our mutual greeting.

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  • After laying down the principle of individual responsibility, he appeals for charity and mutual consideration (xiv.

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  • Yes, they admitted it appeared a large volume of tips bore mutual similarities.

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  • After mutual love-you's, he hung up.

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  • He certainly had Destiny's approval - and the admiration appeared to be mutual.

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  • Mary liked him, and the feelings were obviously mutual.

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  • Could it have been mutual?

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  • The feeling is mutual.

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  • Thus when one carries one's thoughts back to a series of events, one constructs a psychic whole made up of parts which take definite shape and character by their mutual interrelations.

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  • i.) for their warm mutual love, their heroism, and their labours on behalf of the people.

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  • In sympathy with this Platonism, the medieval church began by assuming the entire mutual harmony of faith and reason.

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  • Horae Paulinae - mutual confirmations of Acts and Epistles; better, though one-sided.

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  • Organized as they are into a kind of community for mutual protection and mutual help, they soon become masters of the trade wherever they penetrate.

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  • They style themselves " truly spiritual Christians," and in their rejection of the sacraments, their indifference to outward forms, and their insistence on the spiritual interpretation of the Bible (" the letter killeth "), they are closely akin to the Quakers, whom they resemble also in their inoffensive mode of life and the practice of mutual help.

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  • The mutual assurances of unbounded confidence, admiration and sympathy, if there was any genuine sincerity in them, represented merely a transient state of feeling.

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  • On national the 30th of July 1907 she signed a convention with position Japan of mutual respect for treaty and territorial of Russia.

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  • Similarly in Great Britain there is a tendency towards combination by mutual agreement among the companies while they still preserve their independent existence.

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  • As results of Roberval's labours outside the department of pure mathematics may be noted a work on the system of the universe, in which he supports the Copernican system and attributes a mutual attraction to all particles of matter; and also the invention of a special kind of balance which goes by his name.

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  • Mdlle Curchod soon afterwards became the wife of Necker, the famous financier; and Gibbon and the Neckers frequently afterwards met on terms of mutual friendship and esteem.

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  • Richelieu intercepted the letters, and by omissions and falsifications succeeded in destroying their mutual confidence.

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  • In this way we account most simply for the uniformity in the direction in which the planets revolve, and for the mutual proximity of the planes in which their orbits are contained.

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  • Religion was inseparable from ordinary life, and, like that of all peoples who are dependent on the fruits of the earth, was a nature-worship. The tie between deities and worshippers was regarded as physical and entailed mutual obligations.

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  • Under Ventidius Cumanus (48-52) the mutual hatred of Jews and Romans, Samaritans and Jews, found vent in insults and bloodshed.

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  • The protective instinct was responsible for much of this interference with the natural impulse of men of various creeds towards mutual esteem and forbearance.

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  • Some of the inmates of ants' nests are here for the purpose of preying upon the :ants or their larvae, so that we find all kinds of relations between the owners of the nests and their companions, from mutual benefit to active hostility.

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  • Society is conceived as regulated by, mutual obligations, of which the duties of parents and children are the most important.

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  • This was probably the reason why their marriage was annulled by mutual consent in 1151, but contemporary scandal-mongers attributed the separation to the king's jealousy.

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  • An end was put to these disorders only by the mutual agreement of the two contestants, alike horrified and exhausted by the fierce outburst of passion, in September 1905.

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  • Condorcet's statement that Turgot corresponded with Smith is disproved by a letter of Smith to the duc de la Rochefoucauld, published in the Economic Journal (March 1896), p. 165, in which he says, "But tho' I had the happiness of his acquaintance: Turgot owed his appointment to the ministry to Maurepas, the" Mentor "of Louis XVI., to whom he was warmly recommended by the abbe Very, a mutual friend.

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  • In 1818 he was appointed political agent for the states of western Rajputana, where he conciliated the chieftains, settled their mutual feuds and collected materials for his Annals and Antiquities of Rajasthan (2 vols., 1829-1832).

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  • The lord of the manor with his officials and retainers, the peasantry bound to him by ties of personal dependence and mutual rights and obligations, constituted a little world, in which we can watch the play of motives and passions not so dissimilar as we are sometimes led to believe from those of the great modern world.

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  • The results of more than twenty years' labour were set forth in his Hexapla and Tetrapla, in which he placed the Hebrew text side by side with the various Greek versions, examined their mutual relations in detail, and tried to find the basis for a more reliable text of the LXX.

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  • horns, climbing plants, shavings of wood or metal) that too much stress must not be laid on the mutual parentage of spiraliform ornament in different civilizations.

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  • They were pious foundations created for mutual benefit and for purposes of charity.

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  • But the mutual jealousy of the allies saved her.

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  • But, with advancing civilization and the consequent increase in the number of the conditions to be imposed on both parties, leases became mutual contracts, bilateral in form.

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  • The general state of the island when the Japanese assumed possession was that the plain of Giran on the eastern coast and the hill-districts were inhabited by semibarbarous folk, the western plains by Chinese of a degraded type, and that between the two there existed a traditional and continuous feud, leading to mutual displays of merciless and murderous violence.

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  • He defined structure " as the manner of the mutual linking of the atoms in the molecule," but denied that any such structure could give information as to the orientation of the atoms in space.

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  • From the former point of view the freeman, then essentially a warrior, and the slave were mutual auxiliaries, simultaneously exercising different and complementary functions - each necessary to the community.

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  • There were treaties between states for the extradition of fugitives, and contracts of mutual assurance between individuals against their loss by flight.

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  • Doubtless there was often genuine mutual affection; slaves sometimes, as in noted instances during the civil wars, showed the noblest spirit of devotion to their masters.

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  • A freedman, unless he became such by operation of law, remained client of his master, and both were bound by the mutual obligations arising out of that relation.

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  • In 1831 and 1833 Great Britain entered into an arrangement with France for a mutual right of search within certain seas, to which most of the other powers acceded; and by the Ashburton treaty (1842) with the United States provision was made for the joint maintenance of squadrons on the west coast of Africa.

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  • The birds of the genus Leucosticte seem to be more terrestrial in their habit than those of Linota, perhaps from their having been chiefly observed where trees are scarce; but it is possible that the mutual relationship of the two groups is more apparent than real.

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  • Four years later his influence brought about a truce between Hungary and the Venetians, who had agreed with Bosnia for mutual support against the Croats; and in 1353, the year of his death, his daughter Elizabeth was married to King Louis.

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  • These events and the friction caused by mutual complaints of infringements of the treaty stirred up public opinion in Turkey, and the British ambassador lent his support to the war party.

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  • The mutual slaughter of barbarians in the Levant seemed, even to George Canning, a lesser evil than a renewed Armageddon in Europe; and all the resources of diplomacy were set in motion to heal the rupture between Turkey and Russia.

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  • After the first fervour of enthusiasm had subsided the Christian nationalities in Macedonia resumed their old attitude of mutual jealousy, the insurgent bands began to reappear, and the government was in1909-1910forced to undertake the disarmament of the whole civil population of the three vilayets.

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  • The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

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  • The action between any two magnetic poles is mutual.

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  • The induction of the magnetization may be measured by observing the force required to draw apart the two portions of a divided rod or ring when held together by their mutual attraction.

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  • If each portion of the bar has an independent magnetizing coil wound tightly upon it, we have further to take into account the force due to, the mutual action of the two magnetizing coils, which assists.

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  • It is, of course, true for permanent magnets, where H = o, since then F = 27rI 2; but if the magnetization is due to electric currents, the formula is only applicable in the special case when the mutual action of the two magnets upon one another is supplemented by the electromagnetic attraction between separate magnetizing coils rigidly attached to them.2 The traction method was first employed by S.

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  • In the first experiments it was calculated from observations of the mutual induction of two conducting circuits in air and in the liquid; the results for oxygen at-182° C. were I 00287, 228 X IO-6.

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  • Soc., 1890, 48, 342) has demonstrated that it is quite unnecessary to assume either the directive force of Weber, the permanent set of Maxwell, or any kind of frictional resistance, the forces by which the molecular magnets are constrained being simply those due to their own mutual attractions and repulsions.

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  • When no current is passing through the coil and the magnetic field is of zero strength, the needles arrange themselves in positions of stable equilibrium under their mutual forces, pointing in.

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  • Ordinarily a substance composed of asymmetrical molecules is paramagnetic, but if the elementary magnets are so conditioned by their strength and concentration that mutual action between them is possible, then the substance is ferromagnetic. In all cases however it is the diamagnetic condition that is initially set up - even iron is diamagnetic - though the diamagnetism may be completely masked by the superposed paramagnetic or ferromagnetic condition.

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  • The difficulties attending the experimental investigation of the forces acting between magnetic poles have already been referred to, and indeed a rigorously exact determination of the mutual action could only be made under conditions which are in practice unattainable.

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  • Ampere's experimental and theoretical investigation of the mutual action of electric currents, and of the equivalence of a closed circuit to a polar magnet, the latter suggesting his celebrated hypothesis that molecular currents were the cause of magnetism.

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  • Prantl has professed to find the headstream of Nominalism also in Scotus Erigena; but beyond the fact that he discusses at considerable length the categories of thought and their mutual relations, occasionally using the term voces to express his meaning, Prantl appears to adduce no reasons for an assertion which directly contradicts Erigena's most fundamental doctrines.

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  • In 1849 he brought forward a proposal in parliament in favour of international arbitration, and in 1851 a motion for mutual reduction of armaments.

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  • "He is above all," he added, "in our eyes the representative of those sentiments and those cosmopolitan principles before which national frontiers and rivalries disappear; whilst essentially of his country, he was still more of his time; he knew what mutual relations could accomplish in our day for the prosperity of peoples.

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  • The long-sought cause of the "great inequality" of Jupiter and Saturn was found in the near approach to commensurability of their mean motions; it was demonstrated in two elegant theorems, independently of any except the most general considerations as to mass, that the mutual action of the planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the Jovian system were expressed in the so-called "laws of Laplace."

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  • Mutual recriminations led to a public discussion in 1535, when Tartalea completely vindicated the general applicability of his methods and exhibited the inefficiencies of that of Floridas.

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  • In Hindu law a Gandharva marriage is one contracted by mutual consent and without formality.

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  • Among the latter were the mayor of Zagreb, the poet Vojnovic, and prominent Serb, Croat and Slovene deputies of all parties, including the peasant leader Stephen Radic and the future minister Pribicevic. Their resolutions, though necessarily vague, amounted to a pledge of mutual support in the cause of unity and independence.

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  • In the 17th century the lovers of the new philosophy, the investigators of nature by means of observation and experiment, banded themselves into academies or societies for mutual support and intercourse.

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  • The occurrence of factors such as sin 4), or 2 (1cos 0), in the expression of the secondary wave has no influence upon the result of the integration, the effects of all the elements for which the factors differ appreciably from unity being destroyed by mutual interference.

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  • That all points of mutual difference shall be regulated by the friendly course of arbitration, or by what- The ever amicable way may be agreed upon by the government with Her Majesty's Government.

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  • The dispute was finally referred by mutual consent to the Hague Court of Arbitration.

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  • Thus the reciprocity of the various organs, maintained throughout the divisions of physiological labour, is not merely a mechanical stability; it is also a mutual equilibration in functions incessantly at work on chemical levels, and on those levels of still higher complexity which seem to rise as far beyond chemistry as chemistry beyond physics.

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  • In the mutual behaviour of such cells, toxins, and antitoxins, and again of microbes themselves, we may demonstrate even on the field of the microscope some of the modes of such actions, which seem to partake in great measure at any rate of a chemical quality (agglutinins, coagulins, chemotaxis).

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  • According to Thomas Moore, Lord Edward Fitzgerald was the only one of the numerous suitors of Sheridan's first wife whose attentions were received with favour; and it is certain that, whatever may have been its limits, a warm mutual affection subsisted between the two.

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  • The vortex advances with a certain velocity; and if an equal circular vortex is generated coaxially with the first, the mutual influence can be observed.

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  • The hydrodynamical equations with moving axes, taking into account the mutual gravitation of the liquid, become dp +4 p Ax+ du - vR {-wQ?

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  • The gild brothers associated in mutual defence and support, and they had to share in the payment of fines.

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  • Medieval gilds were voluntary associations formed for the mutual aid and protection of their members.

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  • When the old kin-bond or maegth was beginning to weaken or dissolve, and the state did not yet afford adequate protection to its citizens, individuals naturally united for mutual help.

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  • Prayers for the dead, attendance at funerals of gildsmen, periodical banquets, the solemn entrance oath, fines for neglect of duty and for improper conduct, contributions to a common purse, mutual assistance in distress, periodical meetings in the gildhall, - in short, all the characteristic features of the later gilds already appear in the statutes of these Anglo-Saxon fraternities.

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  • With the expansion of trade and industry the number of artisans increased, and they banded together for mutual protection.

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  • The chief of these are the following: the relation of vassal and lord; the principle that every holder of land is a tenant and not an owner, until the highest rank is reached, sometimes even the conception rules in that rank; that the tenure by which a thing of value is held is one of honourable service, not intended to be economic, but moral and political in character; the principle of mutual obligations of loyalty, protection and service binding together all the ranks of this society from the highest to the lowest; and the principle of contract between lord and tenant, as determining all rights, controlling their modification, and forming the foundation of all law.

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  • His observations led him to the view that a glacier is an imperfect fluid or a viscous body which is urged down slopes of a certain inclination by the mutual pressure of its parts, and involved him in some controversy with Tyndall and others both as to priority and to scientific principle.

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  • gravis, heavy), in physical science, that mutual action between masses of matter by virtue of which every such mass tends toward every other with a force varying directly as the product of the masses and inversely as the square of their distances apart.

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  • The mutual action of electrified bodies, for example, is affected by their relative or absolute motion.

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  • Her death naturally broke up the fellowship, but its members did not cease their activity and kept up what mutual correspondence was possible.

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  • But to understand these in their mutual and explanatory relations it will be necessary to exhibit the conditions under which his thought grew into consistency and system.

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  • One of these, Summa de assumpto homine, is of a theological character, dealing with the humanity of Christ; the other, Summa de matrimonio, is a legal argument, to the effect that the essential fact in marriage is neither, as Gratian maintains, the copula, nor, as Peter Lombard, consent by verba de praesenti, but mutual traditio.

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  • On the 14th of February 1783 he formed a coalition with Lord North, based as they declared on "mutual goodwill and confidence."

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  • Mutual discord first sapped the prosperity of Magna Graecia.

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  • The investigation of the mutual relations of partially miscible liquids, due to P. Alexejew, D.

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  • He thereupon resigned the superintendency, and returned to St Louis, parting with the governor of the state and his colleagues in the school with regret and mutual esteem..

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  • p. 211, Paris, 1869) proposed an equation of the form (p+po)(v - b) =RO, in which the effect of the size of the molecules is represented by subtracting a quantity b, the " covolume," from the volume occupied by the gas, and the effect of the mutual attractions of the molecules is represented by adding a quantity po, the internal pressure, to the external pressure, p. This type of equation, was more fully worked out by van der Waals, who identified the internal pressure, po, with the capillary pressure of Laplace, and assumed that it varied directly as the square of the density, and could be written a/v 2 .

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  • In the case of imperfect gases, all the available experimental evidence shows that the specific volume tends towards its ideal value, V =Re/p, in the limit, when the pressure is indefinitely reduced and the molecules are widely separated so as to eliminate the effects of their mutual actions.

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  • The loss of energy could not be greater than this on the simple kinetic theory, unless there were some evolution of latent heat of co-aggregation, due to the work done by the mutual attractions of the co-aggregating molecules.

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  • As far as the order to which he carried the approximations - which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart--the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions.

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  • All the known minor planets have the same common direction, but their orbits generally have a greater eccentricity and mutual inclination.

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  • The mutual interest of the associates led to the failure of the plot.

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  • In his domestic relations he was exemplary, and he lived on terms of mutual affection with a wide circle of friends.

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  • No other system of atoms can occupy the same region of space at the same time, because before it could do so the mutual action of the atoms would have caused a repulsion between the two systems insuperable by any force which we can command.

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  • In like manner, after the French mathematicians had attempted, with more or less ingenuity, to construct a theory of elastic solids from the hypothesis that they consist of atoms in equilibrium under the action of their mutual forces, Stokes and others showed that all the results of this hypothesis, so far at least as they agreed with facts, might be deduced from the postulate that elastic bodies exist, and from the hypothesis that the smallest portions into which we can divide them are sensibly homogeneous.

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  • The fact that a solid body in its natural state is capable both of compression and of dilatation indicates that the molecules of the body must not be supposed to be fixed rigidly in position relative to one another; the further fact that a motion of either compression or of dilatation is opposed by forces which are brought into play in the interior of the solid suggests that the position of rest is one in which the molecules are in stable equilibrium under their mutual forces.

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  • Now this is exactly the shape which we should expect to find in molecules composed of two spherical atoms distorting one another by their mutual forces, and all gases for which n=2 are diatomic.

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  • John Knox, who, after a chequered career, had come under the influence of Calvin at Geneva, returned to Scotland for a few months in 1 555, and shortly after (1557) that part of the Scottish nobility which had been won over to the new faith formed their first " covenant " for mutual protection.

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  • It was decreed that the Benedictine houses of each ecclesiastical province should henceforth be federated for the purposes of mutual help and the maintenance of discipline, and that for these ends the abbots should every third year meet in a provincial chapter (or synod), in order to pass laws binding on all and to appoint visitors who, in addition to the bishops, should canonically visit the monasteries and report on their condition in spirituals and temporals to the ensuing chapter.

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  • The organization of the Benedictine houses into provinces or chapters under this legislation interfered in the least possible degree with the Benedictine tradition of mutual independence of the houses; the provinces were loose federations of autonomous houses, the legislative power of the chapter and the canonical visitations being the only forms of external interference.

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  • Thereafter, whatever befell, the allied armies would resolutely press forward towards Paris, affording each other mutual support, and with the tremendous weight of troops at their disposal thrust back Napoleon upon his capital, force him to fight in front of it, and drive him when defeated within its works.

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  • The calculation of this last expression is simplified by noticing that we are only concerned with the mutual ratios of Xo, X 1, ...

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  • The alternative method, therefore, consists in taking a simple formula, such as the trapezoidal rule, and correcting it to suit the mutual relations of the differences.

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  • The folds, therefore, which are disposed for the purpose of making the grasp secure, vary with the relative lengths of the metacarpal bones, with the mutual relations of the sheaths of the tendons, and the edge of the palmar fascia, somewhat also with the insertion of the palmaris brevis muscle.

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  • Thus mutual oversight and care are among the duties of the members of Christ's body; while their collective inspiration, enabling them to " try the gifts of godliness " of specially endowed fellow-members, is the divine warrant in election to church office.

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  • The approximation was mutual.

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  • Under, this custom of " stated supplies " ordination may be granted to those whose ministry in a particular church is made and dissolved by no other process than a mutual agreement.

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  • There can have been little personal intercourse between them, for Haydn was rarely in the capital, and Mozart seems never to have visited Eisenstadt; but the cordiality of their relations and the mutual influence which they exercised upon one another are of the highest moment in the history of 18th-century music. " It was from Haydn that I first learned to write a quartet," said Mozart; it was from Mozart that Haydn learned the richer style and the fuller mastery of orchestral effect by which his later symphonies are distinguished.

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  • The True Word had very little influence either on the mutual relations of Church and State, or on classical literature.

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  • If the amplitudes of vibration which thus mutually interfere are moreover equal, the effect is the total mutual destruction of the vibratory motion.

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  • If a tuning-fork in vibration be turned round before the ear, four positions will be found in which A B it will be inaudible, owing to the mutual interference FIG.

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  • He believes the United States to be a unified republic, a sovereign nation; and not a federation of independent states united only for mutual benefit and protection.

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  • George William based his claim upon a treaty of mutual succession made in 1369 between his ancestor Magnus II., duke of Brunswick, and the reigning dukes of Saxe-Lauenburg.

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  • ἀντί, against, νόμος, law), literally, the mutual incompatibility, real or apparent, of two laws.

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  • 1003 et seq.); and a convention (8th of July 1899) between France and Belgium regulates, inter alia, the mutual enforcement of awards.

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  • These inauspicious beginnings, indeed, set the whole tone of the war, which was frankly one of mutual extermination.

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  • It was then, too, that his most celebrated production, the Discourses concerning Government, was concluded, in which he upholds the doctrine of the mutual compact and traverses the High Tory positions from end to end.

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  • There is a Roman Catholic Cathedral, and the city is the see of a Roman Catholic and of a Protestant Episcopal bishop. The Prudential Life Insurance Company and the Mutual Benefit Life Insurance Company have fine office buildings.

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  • Insurance is another important business, for here are the headquarters of the Prudential, the Mutual Benefit Life and the American Fire, the Firemen's and the Newark Fire Insurance companies.

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  • mutual will, since the person of this is the person of that, and the person of that the person of this."

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  • the Mushketov, Semenov, Suess, Alexander III., Bain-sarlyk - the mutual relations of which are, however, not yet definitely settled.

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  • The mutual relations of the latter, as well as the names of the several constituent chains, are equally unsettled.

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  • Gauss, that the definite results attainable by the hypothesis of mutual atomic attractions really reposed on much wider and less special principles - those, namely, connected with the modern doctrine of energy.

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  • It has been maintained since the times of the early Greek philosophers, and possibly even more remote ages, that matter is constituted of independent indestructible units, which cannot ever become divided by means of any mutual actions they can exert.

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  • It thus appears that the doctrine of atomic material constitution and the doctrine of a universal aether stand to each other in a relation of mutual support; if the scheme of physical laws is to be as precise as observation and measurement appear to make it, both doctrines are required in our efforts towards synthesis.

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  • Thus the early idea of the services, as occasions for mutual edification through the interchange of spiritual gifts, gave way in course of time to the theory that they consisted of sacred and mysterious rites by means of which communion with God is promoted.

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  • Here the Lechici, as they called themselves (a name derived from the mythical patriarch, Lech), seemed to have lived for centuries, in loosely connected communities, the simple lives of huntsmen, herdsmen and tillers of the soil, till the pressure of rapacious neighbours compelled them to combine for mutual defence.

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  • Not even the exhortations of the popes could make her score of princes unite for mutual defence against the barbarians who en vironed them.

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  • The privileges conferred upon the magnates of which these councils were composed, especially upon the magnates of Little Poland, who brought the Jagiellos to the throne, directed their policy, and grew rich upon their liberality, revolted the less favoured szlachta, or gentry, who, towards the end of the 14th century, combined for mutual defence in their sejmiki, or local diets, of which originally there were five, three in Great Poland, one in Little Poland and one in Posen-Kalisz.'

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  • the 20th of March 1791, concluded an alliance with Poland which engaged the two powers to guarantee each other's possessions and render mutual assistance in case either were attacked.

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  • The result was the treaty of April 1769, providing for the mutual restitution of all conquests, and for mutual aid and alliance in defensive war; it was followed by a commercial treaty in 1770 with the authorities of Bombay.

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  • Eventually Mark surprises the two under circumstances which leave no possible room for doubt as to their mutual relation; Tristan flies for his life and takes refuge with Hoel, duke of Britanny.

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  • In 1909 Hartford was the home city of six fire insurance and six life insurance companies, the principal ones being the Aetna (fire), Aetna Life, Phoenix Mutual Life, Phoenix Fire, Travelers (Life and Accident), Hartford Fire, Hartford Life, National Fire, Connecticut Fire, Connecticut General Life and Connecticut Mutual Life.

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  • The Aetna (fire), Aetna Life, Connecticut Fire, Connecticut Mutual Life, Connecticut General Life, Hartford Fire, Hartford Life, Hartford Steam Boiler Inspection and Insurance Co., 1"1"-*: ., l Fire, Orient Fire, Phoenix Mutual Life and Travelers Yies have their own homes, some of these being among _it buildings in Hartford.

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  • Among his pamphlets are A Candid Examination of the Mutual Claims of Great Britain and the Colonies (1775); Historical and Political Reflections on the Rise and Progress of the American Rebellion (1780); Cool Thoughts on the Consequences to Great Britain of American Independence (1780); and The Claim of the American Loyalists Reviewed and Maintained upon Incontrovertible Principles of Law and Justice (1788).

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  • Among his other works may be named Paroles d'un revolte (1884); La Conquete du pain (1888); L' Anarchic: sa philosophie, son ideal (1896); The State, its Part in History (1898); Fields, Factories and Workshops (1899); Memoirs of a Revolutionist (1900); Mutual Aid, a Factor of Evolution (1902); Modern Science and Anarchism (Philadelphia, 1903); The Desiccation of Asia (1904); The Orography of Asia (1904); and Russian Literature (1905).

    0
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  • In view of the number of critical conclusions and the mutual independence of many of them, " higher criticism " 1 For details see an article in the Zeitschr.

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  • They are found in various dialects of Coptic, the mutual relations of which are not Coptic. yet certain, but the only ones which are preserved with any completeness are the Bohairic, or Lower Egyptian, and Sahidic, or Upper Egyptian, though it is certain that fragments of intermediate dialects such as Middle Egyptian, Fayumic, Akhmimic and Memphitic also exist.

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  • Both were admirable civil servants, and they had a mutual admiration for each other's sterling qualities.

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    0
  • A friendship, of mutual advantage, soon sprang up between the two men, and it has been said that Scheele was Bergman's greatest discovery.

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  • The question as to the influence of Neoplatonism on the development of Christianity is not easily answered, because it is scarcely possible to get a complete view of their mutual relations.

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  • In October 1766 tutor and pupil returned home, and they ever afterwards retained strong feelings of mutual esteem.

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  • The same circumstances detertnine the variation of profits, but in an opposite direction; the increase of stock, which raises wages, tending to lower profit through the mutual competition of capitalists.

    0
    0
  • The mutual relations of palaeontology and embryology and comparative anatomy as means of determining the ancestry of animals are most interesting.

    0
    0
  • The mutual jealousies of the Gallic tribes had enabled German invaders first to gain a foothold on the left bank of the Rhine, and then to obtain a predominant position in Central Gaul.

    0
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  • Thus the " Helena " of the Simoniani descends to this world in order by means of her beauty to provoke to sensual passion and mutual strife the angels who rule the world, and thus again to deprive them of the powers of light, stolen from heaven, by means of which they rule over the world.

    0
    0
  • It seems that there was formerly a mutual interpenetration between Lenca, Sumo and Chorotega tribes.

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    0
  • The magma, or molten lava in the interior of the earth, may be regarded as a mutual solution of various mineral silicates, charged with highly-heated vapour, sometimes to the extent of supersaturation.

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  • This was based on the assumption that the medium in which the light is propagated is discontinuous and molecular in character, the molecules being subject to a mutual attraction.

    0
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  • They found alike their mutual relations and their relations to other people - and not only to people, but to all living creatures - exclusively on love, and therefore they hold all people equal and brethren.

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  • A treaty of mutual succession was made between the two families in 1713.

    0
    0
  • The "genealogical" method, as we may call it, cannot in strictness be applied to conflated MSS., as their mutual relations can rarely be with certainty disentangled.

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  • Hence, moreover, a natural substance or body as an efficient cause or force causes an effect on another, not by propagating one eternal essence of a species into the matter of the other, but so far as we really understand force, by their reciprocally preventing one another from occupying the same place at the same moment on account of the mutual resistance of any two bodies.

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  • But as the sultan grew old his numerous sons, who held each the command of a city of the empire, embittered his old age by their mutual rivalry, and the eldest, IKutb ed-din, tyrannized over his father in his own capital, exactly at the time that Frederick I.

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  • He was handicapped by the mutual jealousy of the Saxons and the Poles, and a struggle broke out in Poland which was only ended when the king promised to limit the number of his army in that country to 18,000 men.

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  • But even the final form of Jewish theology shows much vacillation as to these details, especially as regards their sequence and mutual relation, thus betraying the inadequacy of the harmonistic method by which they were derived from the Old Testament and the stormy excitement in which the Messianic idea was developed.

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  • high; the city convention hall, the chamber of commerce, the builders' exchange, the Masonic temple, two state armouries, the Prudential, Fidelity Trust, White and Mutual Life buildings, the Teck, Star and Shea's Park theatres, and the Ellicott Square building, one of the largest office structures in the world; and, in Delaware Park, the Albright art gallery, and the Buffalo Historical Society building, which was originally the New York state building erected for the Pan-American Exposition held in 1901.

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  • A few pieces of political satire show us French and English exchanging amenities on their mutual shortcomings.

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  • Mutual exhortation was practised at all the meetings for divine service, when any member who had the gift of speech (Xfipu ia) was allowed to speak.

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  • Applying the reasoning to the case of a homogeneous radiation traversing an absorbing medium, we realize that the mutual disturbances of the molecules by collision or otherwise must bring in the free period of the molecule whatever the incident radiation may be.

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  • His most successful achievement was the union with Poland for mutual defence against the Habsburgs and the Czechs.

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  • Tradition has dramatized their first meeting into the story given by Cresacre More' - that the two happened to sit opposite each other at the lord mayor's table, that they got into an argument during dinner, and that, in mutual astonishment at each other's wit and readiness, Erasmus exclaimed, " Aut tu es Morus, aut nullus," and the other replied, " Aut tu es Erasmus, aut diabolus !

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  • 17-34), or for mutual edification in prayer, praise and prophecy (1 Cor.

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  • On the other hand, under the influence of the mechanics of his day, which had hardly distinguished between inertia, or the inability of a body to change itself, and resistance or the ability of bodies to oppose one another, he concluded that, as inertia is passive, so is resistance, and refused to recognize that in collision the mutual resistance of moving bodies is a force, or active power, of changing their movements in opposite directions.

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  • Bodies then are triply extended substances, each occupying enough space to prevent mutual penetration, and by this force of mutual impenetrability or interresistance cause one another to form a joint mass with a common velocity whenever they collide.

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  • The outward expression of such a spirit is "bold confession," a glorying in that Hope, and mutual encouragement therein (iii.

    0
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  • The importance of the kindred, however, was not limited to purposes of mutual protection.

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  • At length the two parties grew weary of this state of revolution, and a regime of conciliation, the fruit of mutual concessions, was established under Clement III.

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  • Aegisthus being sent to murder Thyestes, mutual recognition took place, and Atreus was slain by the father and son, who seized the throne, and drove Agamemnon and Menelaus out of the country (Thucydides i.

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  • Assuming such a base to exist, Newton admitted at the outset the difficulty of identifying it, but pointed out that the key to the situation might be found in the identification of forces; that is to say, in the mutual character of laws of acceleration as applied to any given body and any other by whose presence its motion is influenced.

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  • In fact, experiments upon the changes of velocity of bodies, due to a mutual influence between them, bring to light a property of bodies which may be specified by a quantity proportional to their volumes in the case of bodies which are perceived by other tests to be of one homogeneous substance, but otherwise involving also another factor.

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  • When, as in the case of contact, a mutual relation is perceived between the motions of two particles, the changes of velocity are in opposite directions, and the ratio of their magnitudes determines the ratio of the masses of the particles; the motion being reckoned relative to any base which is unaffected by the change.

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  • The Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.

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  • The mutual action between two particles is specified by means of a directed quantity to which the term "force" is appropriated.

    0
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  • Thus each mutual action is associated with a pair of equal forces in opposite directions.

    0
    0
  • It is not, however, a true force in the sense of corresponding to any mutual relation between two portions of matter.

    0
    0
  • The more complete phenomena of mutual solubility are illustrated by the case of phenol and water.

    0
    0
  • When the two components form chemical compounds with each other, the phenomena of mutual solubility become more complex.

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  • A form of edict drawn by Grotius was published by the states, recommending mutual toleration, and forbidding ministers in the pulpit from handling the disputed dogmas.

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  • Muller to include cases of mutual resemblance between two or more noxious species inhabiting the same area.

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  • Besides consideration for the mutual convenience of sovereigns and their feudatories, there were other causes which materially contributed towards bringing about those changes in The the military system of Europe which were finally accomplished in the 13th and 14th centuries.

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  • After the battle of Legnano, in 1174, although the Lombard cities failed to reap the fruit of their united action, and fell to mutual jealousy once more, Milan internally began to grow in material prosperity.

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  • Their compact, moss-like growth and general structural peculiarities are not an expression of mutual affinity, but are in adaptation to the combined cold and dryness of their habitat.

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  • Lacking often the protection of a strong ruler, the Lombard cities had been accustomed to act together for mutual defence, and in 1093 Milan, Lodi, Piacenza and Cremona formed an alliance against the emperor Henry IV., in favour of his rebellious son Conrad.

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  • They held a meeting at Bologna and raised an army, but as in 1226, the matter ended in mutual fulminations and defiances.

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  • Let us also suppose that the plates A and C are so distant from each other that there is no mutual influence, and that p' is the capacity of one of the disks when it stands alone.

    0
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  • Although Moab and Ammon were "brothers," their history was usually associated with that of Judah and Israel respectively, and naturally depended to a considerable extent upon these two and their mutual relations.

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  • There are polymers which have hardly any inter-relations other than identity in composition; on the other hand, there are others which are related by the possibility of mutual transformation; examples of this kind are cyanic acid (Cnoh) and cyanuric acid (Cnoh) 3, the latter being a solid which readily transforms into the former on heating as an easily condensable vapour; the reverse transformation may also be realized; and the polymers methylene oxide (CH 2 O) and trioxymethylene (CH20)3.

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  • The cases of mutual transformation are generally characterized by the fact that in the compound of higher molecular weight no new links of carbon with carbon are introduced, the trioxymethylene being O CH2-0 CH 2 whereas honey-sugar correg probably C C H 2 -0% sponds to CH 2 0H [[Choh Choh Choh Choh Cho]], each point representing a linking of the carbon atom to the next.

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  • In this equation a relates to molecular attraction; and it is not improbable that in isomeric molecules, containing in sum the same amount of the same atoms, those mutual attractions are approximately the same, whereas the chief difference lies in the value of b, that is, the volume occupied by the molecule itself.

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  • For what reason this volume may differ from case to case lies close at hand; in connexion with the notion of negative and positive atoms, like chlorine and hydrogen, experience tends to show that the former, as well as the latter, have a mutual repulsive power, but the former acts on the latter in the opposite sense; the necessary consequence is that, when those negative and positive groups are distributed in the molecule, its volume will be smaller than if the negative elements are heaped together.

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  • Certain investigations on isomerism which have become especially prominent in recent times bear on the possibility of the mutual transformation of isomers.

    0
    0
  • These laws have the advantage of being applicable to the mutual transformations of isomers, whatever be the nature of the deeper origin, and so bring polymerism, metamerism and polymorphism together.

    0
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  • Both formula and experiment proved that an increase of pressure of one atmosphere elevated the transition point for about o 04° The same laws apply to cases of more complicated nature, and one of them, which deserves to be pursued further, is the mutual transformation of cyanuric acid, C 3 H 3 N 3 O 3, cyanic acid, Chno, and cyamelide (Chno).; the first corresponding to prismatic sulphur, stable at higher temperatures, the last to rhombic, the equilibrium-symbol being: cyamelide 1 .?

    0
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  • A second law for these mutual transformations is that when they take place without loss of homogeneity, for example, in the liquid state, the definite transition point disappears and the change is gradual.

    0
    0
  • This best studied case shows that a number of mutual relations are to be found between the properties of two modifications when once the phenomenon of mutual transformation is accessible.

    0
    0
  • In ordinary isomers indications of mutual transformation often occur; and among these the predominant fact is that denoted as tautomerism or pseudomerism.

    0
    0
  • The phenomena were first observed without mutual transformation, aldehyde melting at - 118°, paraldehyde at 13°, the only mutual influence being a lowering of melting-point, with a minimum at - 120° in the eutectic point.

    0
    0
  • When a catalytic agent, such as sulphurous acid, is added, which produces a mutual change, the whole behaviour is different; only one meltingpoint, viz.

    0
    0
  • The next simplest case consists in the mutual interchange of two affinity units, and so on.

    0
    0
  • This conception led Kekule to his "closed-chain" or "ring" theory of the constitution of benzene which has been called the "most brilliant piece of prediction to be found in the whole range of organic chemistry," and this in turn led in particular to the elucidation of the constitution of the "aromatic compounds," and in general to new methods of chemical synthesis and decomposition, and to a deeper insight into the composition of numberless organic bodies and their mutual relations.

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  • In a letter of Jacqueline's, dated the 27th of September, an account of a visit paid by Descartes to Pascal is given, which, like the other information on the relations of the two, give strong suspicion of mutual jealousy.

    0
    0
  • After Conrads death William of Holland received a certain allegiance, especially in the north of the country, and was recognized by the Rhenish cities which had just formed a league for mutual protection, a league which for a short time gave promise of great strength and regnum.

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    0
  • The cities, notwithstanding every kind of discouragement, formed new associations for mutual defence or strengthened those which already existed.

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    0
  • At the diet of Nuremberg in 1422 and at that of Frankfort in 1427 ~igismund endeavoured to raise men and money by means of contributions from the estates, but the plan failed owing to mutual jealousies and especially to the resistance of the cities.

    0
    0
  • A series of diets between 1495 and 1499 produced only mutual recriminations, and then Maximilian met with a serious rebuff.

    0
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  • By the terms of the Final Act this diet had very wide powers for the development f7~e of the mutual relations of the governments in all ~ matters of common interest.

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    0
  • The indispensable preliminary to a really historic view of these writings is some solution of the problem of their mutual relations.

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    0
  • Syracuse repaid the debt by good service to the Peloponnesian cause, and from that time the mutual influence of Sicily and old Greece is far stronger than in earlier times.

    0
    0
  • Unless we are to believe that the Macedonian supremacy is directly traceable to the mutual weakening of the Greek cities in 431-403, it is difficult to see what lasting importance attaches to the war.

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    0
  • Under the guidance of Pericles Athens replied that she would do nothing on compulsion, but was prepared to submit difficulties to amicable arbitration on the basis of mutual concessions.

    0
    0
  • The movements of Germany from the south-east, and of France from the west and north, were thus held in check, and by securing international agreements the mutual limits of the three European powers concerned were definitely fixed.

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    0
  • That a father and his children have mutual duties implies that there are moral laws regulating their relationship; that it is the duty of a servant to obey his master within certain limits is part of a definite contract, whereby he becomes a servant engaging to do certain things for a specified wage.

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  • Though not free from defects, this edition is absolutely indispensable for the study of the chronicles and the mutual relations of the different MSS.

    0
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  • Gradually the tension between natives and foreigners relaxed, and mutual confidence was established.

    0
    0
  • There exist, besides, in Denmark several mutual loan associations (Kreditforeninger), whose business is the granting of loans on mortgage.

    0
    0
  • Nicholas preached a crusade, and endeavoured to reconcile the mutual animosities of the Italian states, but without much success.

    0
    0
  • Do not employ such physiological antagonists as pilocarpine or morphine, for the lethal actions of all these drugs exhibit not mutual antagonism but coincidence.

    0
    0
  • Naturally, a mutual confidence between a king who had conquered his kingdom and a people who had stood in arms against him was not attainable immediately, and the first six years of Christian III.'s reign were marked by a contest between the Danish Rigsraad and the German counsellors, both of whom sought to rule "the pious king" exclusively.

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  • He visited Haddington occasionally in the following years, and a strong mutual regard arose between him and Miss Welsh.

    0
    0
  • Yet, during the siege of Stirling (11th of June 1304), Bruce had entered into a secret band with Lamberton, bishop of St Andrews, for mutual aid.

    0
    0
  • Two curious customs may be noted - the institution of an honourable order bestowed by the king, called klilt; and a species of mutual aid society, sometimes confined to women, and possessing considerable political influence.

    0
    0
  • The merit of Hegel is to have indicated and to a large extent displayed the filiation and mutual limitation of our forms of thought; to have arranged them in the order of their comparative capacity to give a satisfactory expression to truth in the totality of its relations; and to have broken down the partition which in Kant separated the formal logic from the transcendental analytic, as well as the general disruption between logic and metaphysic. It must at the same time be admitted that much of the work of weaving the terms of thought, the categories, into a system has a hypothetical and tentative character, and that Hegel has rather pointed out the path which logic must follow, viz.

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  • Torn by mutual jealousy and intrigue, and forming little confederations among 1 For fuller treatment of the data see R.

    0
    0
  • Syria could control the situation, and it in turn was influenced by the ambitions of Assyria, to whose advantage it was when the small states were rent by mutual suspicion and hostility.

    0
    0
  • The leading reaction of this process is the mutual decomposition of ammonium bicarbonate and sodium chloride: NaCI+NH 4 HCO 3 = NaHCO 3 -1-NH 4 C1.

    0
    0
  • W.) was brought into closer relations with the colonial churches than Tait was; but the healthy development of the Lambeth Conferences on the lines of mutual counsel rather than of a hasty quasi-synodic action was largely due to him.

    0
    0
  • Hyder died in 1782, and peace was finally concluded with Tippoo in 1784, on the basis of a mutual restitution of all conquests.

    0
    0
  • The old divisions of nobility, clergy and people were a maintained and their mutual rivalry encouraged; the nobles were won over by titles and by the splendour of the viceregal court, but many persons of low birth who showed talent were raised to high positions.

    0
    0
  • Ferdinand strongly resented foreign interference, and even rejected the Austrian proposal for a league of the Italian despots for mutual defence against external attacks and internal disorder.

    0
    0
  • At the same time he endeavoured to bring about a union of Aragon with Navarre, by a contract of mutual adoption between himself and the Navarrese king, Sancho, who was old enough to be his grandfather.

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  • According To The Elementary Kinetic Theory Of An Ideal Gas, The Molecules Of Which Are So Small And So Far Apart That Their Mutual Actions May Be Neglected, The Kinetic Energy Of Translation Of The Molecules Is Proportional To The Absolute Temperature, And Is Equal To 3/2 Of Pv, The Product Of The Pressure And The Volume, Per Unit Mass.

    0
    0
  • In a number of cases measures of the relative positions of the two stars, continued for many years, have shown that they are revolving about a common centre; when this is so there can be no doubt that they form a binary system, and that the two components move in elliptic orbits about the common centre of mass, controlled by their mutual gravitation.

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  • As the simple star radiates heat and contracts, it retains its angular momentum; when this is too great for the spheroidal form to persist, the star may ultimatel y separate into two components, which are driven farther and farther apart by their mutual tides.

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  • The mutual gravitation of a large number of stars crowded in a comparatively small space must be considerable, and the individual stars must move in irregular orbits under their mutual attractions.

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    0
  • It was shown by Homer Lane that a mass of gas held in equilibrium by the mutual gravitation of its parts actually grows hotter through radiating heat; the heat gained by the resulting contraction more than counterbalances that lost by radiation.

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  • Thus we are led to regard the two systems as completely intermingled, a fact which adds considerably to the difficulty of explaining the phenomena otherwise than as produced by two great systems - universes they have been called - which have come together, perhaps, by their mutual attraction, and are passing through one another.

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  • He held that in relation to the will things possess an objective fitness similar to the mutual consistency of things in the physical universe.

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  • But Abu Moslim contrived to re-awaken their mutual distrust and jealousy, and, taking advantage of the opportunity, made himself master of Merv, in Rabia II.

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  • At an annual spiritual examination of the members, there are mutual criticisms and public confessions of sin.

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  • There were, for both sides, many advantages in arranging their mutual relations on this basis.

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  • These rights, which are heritable but not transferable, protect the tenant against eviction, except for default in payment of rent, while the rent may not be enhanced except by mutual agreement or by order of a revenue court.

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  • Oppression by the throne and the official and noble classes prevailed extensively; but the weak protected themselves by the use of the Kyei, or principle of association, which developed among Koreans into powerful trading gilds, trades-unions, mutual benefit associations, money-lending guilds, &c. Nearly all traders, porters and artisans were members of guilds, powerfully bound together and strong by combined action and mutual helpfulness in time of need.

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  • Starting from the obvious antithesis of thought and that of which it is the thought, it is possible to view the ultimate relation of its term as that of mutual indifference or, secondly, as that of a correspondence such that while they retain their distinct character modification of the one implies modification of the other, or thirdly and lastly, as that of a mergence of one in the other of such a nature that the merged term, whichever it be, is fully accounted for in a complete theory of that in which it is merged.

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  • Pledges of mutual good faith and fellowship were renewed between Philip and Richard of England on the 30th of December 1189, and they both prepared to go on the crusade.

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  • This may occur by the dissolution of one of the contracting states, by the object-matter of the agreement ceasing to exist, by full performance, by performance becoming impossible, by lapse of the time for which the agreement was made, by contrarius consensus or mutual release, by " denunciation " by one party under a power reserved in the treaty.

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  • The commune (communia, communa, communio, communitas, conjuratio, confoederatio) was formed by an oath of mutual help (sacramentum, juramentum communise).

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  • A strict line of demarcation, however, remains in the mutual oath which forms the basis of the civic community in both varieties of the latter, and in the fact that the ville libre stands to its lord in the relation of vassal and not in that of an immediate possession.

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  • The word "confederation," as distinct from "federation" has been sometimes, though not universally, used to distinguish from such a federal state (Bundesstaat) a mere union of states (Staatenbund) for mutual aid, and the promotion of interests common to all (see Confederation).

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  • Gradually their statement of this position underwent serious modifications, as it became realized that neither Jewish nor Gentile Christianity was a uniform genus, but included several species, and that the apostolic leaders from the first stood for mutual understanding and unity.

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  • They have been passed though one editorial mind, and some mutual assimilation in phraseology and idea may well have resulted.

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  • lhe usual empirical law of sliding friction is that the mutual action between two plane surfaces in contact, or between a particle and a curve or surface, cannot make with the normal an angle exceeding a certain limit X called the angle of friction.

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  • Statics of a System of ParticlesWe assume that the mutual forces between the pairs of particles, whatever their nature, are subject to the Law of Action and Reaction (Newtons Third Law); i.e.

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  • For if we have an assemblage of particles whose mutual distances are small compared with the dimensions of the earth, the forces of gravity on them constitute a system of sensibly parallel forces, sensibly proportional to the respective masses.

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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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  • This, theorem, also due to Lagrange, enables us to express the mean square of the distances of the particles from the centre of mass in terms of the masses and mutual distances.

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  • These may be divided into two categories; we have first, the extraneous forces exerted on the various particles from without, and, secondly, the mutual or internal forces between the various pairs of particles.

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  • For in time t the mutual action between two particles at P and Q produces equal and opposite momenta in the line PQ, and these will have equal and opposite moments about the fixed axis.

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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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  • The statement may be extended to a system of rigid bodies, provided the mutual reactions consist of the stresses in inextensible links, or the pressures between smooth surfaces, or the reactions at rolling contacts (~ 9).

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  • The terms due to F in (33) are such as would arise from frictional resistances proportional to the absolute velocities of the particles, or to mutual forces of resistance proportional to the relative velocities; they are therefore classed as frictional or dissipative forces.

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  • Those pieces are connected at theii joints or surfaces of mutual contact, either by simple pressure and friction (as in masonry with moist mortar or without mortar), by pressure and adhesion (as in masonry with cement or with hardened mortar, and timber with glue), or by the resistance of fastenings of different kinds, whether made by means of the form of the joint (as dovetails, notches, mortices and tenons) or by separate fastening pieces (as trenails, pins, spikes, nails, holdfasts, screws, bolts, rivets, hoops, straps and sockets.

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  • Considering, in the first place, the case in which the load and the two resistances by which each piece is balanced meet in one point, which may be called the centre of load, there will be as many such points of intersection, or centres of load, as there are pieces in the structure; and the directions and positions of the resistances or mutual pressures exerted between the pieces will be represented by the sides of a polygon joining Pi h2 ~, ~ those points, as in fig.

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  • Sliding Contact (circular): Grooved Wheels.As the adhesion or friction between a pair of smooth wheels is seldom sufficient to prevent their slipping on each other, contrivances are ~ised tc increase their mutual hold.

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  • In either case the tangential force, whether effort or resistance, exerted between the band and the pulley is their mutual friction, caused by and proportional to the normal pressure between them.

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  • Stiffness of Ropes.Ropes offer a resistance to being bent, and, when bent, to being straightened again, which arises from the mutual friction of their fibres.

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  • If R1=R1, which is the case when the resistance, as well as the effort, arises from the mutual actions of the two bodies, the above becomes, E:Ei:Ei~ 8

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  • Indemnity Mutual M.

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  • But Falk retired in 1879; various mutual concessions were made which led to a gradual abrogation of the May laws.

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  • Mutual jealousies were only increased when the seculars were grouped together under an arch-priest in 1599.

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  • Hermann's revelations are mainly taken up with an attempt to show the mutual relationship of nearly all the characters he introduces.

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  • He made the acquaintance of the Spanish reformer Juan de Valdes at Rome, and got to know him as a theologian at Naples, being especially drawn to him through the appreciation expressed by Bernardino Ochino, and through their mutual friendship with the Lady Julia Gonzaga, whose spiritual adviser he became after the death of Valdes.

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  • On relinquishing his command, for example, he was able to do what no other man could have done with either propriety or safety: he addressed a circular letter to the governors, pointing out changes in the existing form of government which he believed to be necessary, and urging "an indissoluble union of the states under one federal head," "a regard to public justice," the adoption of a suitable military establishment for a time of peace, and the making of "those mutual concessions which are requisite to the general prosperity."

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  • Massachusetts, Plymouth, Connecticut and New Haven constituted in their early years a group of neighbouring colonies, substantially independent of the mother country, and possessing a unity of purpose and similar institutions but in need of mutual protection from the Indians, the Dutch and the French, and also needing an arbiter to whom they might refer their own disputes, especially those relating to boundaries and trade.

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  • To understand the genesis of human morality we must study the ways of sociable animals such as horses and monkeys, which give each other assistance in trouble, feel mutual affection and sympathy, and experience pleasure in doing actions that benefit the society to which they belong.

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  • Thus, in man, do sentiments of love and mutual sympathy become instinctive and, when transmitted by inheritance, innate.

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  • He showed that the attraction between the rubbed body and the test object is mutual.

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  • Ampere in this paper gave an account of his discovery that conductors conveying electric currents exercise a mutual attraction or repulsion on one another, currents flowing in the same direction in parallel conductors attracting, and those in opposite directions repelling.

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  • By a series of well-chosen experiments Ampere established the laws of this mutual action, and not only explained observed facts by a brilliant train of mathematical analysis, but predicted others subsequently experimentally realized.

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  • These experiments furnished the first elementary forms of electric motor, since it was then seen that rotatory motion could be produced in masses of metal by the mutual action of conductors conveying electric current and magnetic fields.

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  • Electric attractions and repulsions were, however, regarded as differential actions in which the mutual repulsion of the particles of electricity operated, so to speak, in antagonism to the mutual attraction of particles of matter for one another and of particles of electricity for matter.

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  • The mission failed, as the mutual jealousy of the sovereigns would not allow either to begin operations.

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  • The worship of ancestors has again and again gathered around it powerful and ethical influences, emphasizing the parental and filial relations, and strengthening the mutual obligations of communal life.

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  • In many cases a division of sentiment came to prevail on the matter of infant-baptism, and for a while mutual toleration prevailed; but mixed churches had their manifest disadvantages and separation ultimately ensued.

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  • Henry Wilde, in 1875, in depositing copper on iron printing-rollers, recognized this principle and rotated the rollers during electrolysis, thereby renewing the surfaces of metal and liquid in mutual contact, and imparting sufficient motion to the solution to prevent stratification; as an alternative he imparted motion to the electrolyte by means of propeller blades.

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  • The martyrs fell asleep in a mutual embrace.

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  • The conflicting interests and mutual jealousies of these four independent assemblies made the work of legislation exceptionally difficult.

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  • When the Riksdag met in 1760, the indignation against the Hat leaders was so violent that an impeachment seemed inevitable; but once more the superiority of their parliamentary tactics prevailed, and when, after a session of twenty months, the Riksdag was brought to a close by the mutual consent of both the exhausted factions, the Hat government was bolstered up for another four years.

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  • The external and internal conditions of the empire are in mutual reaction upon one another.

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  • That the alliance with the Turks should soon change to hostility .and mutual attack was inevitable from the nature of the case; in the second Roman war the Turkish Khan was leagued with Rome.

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  • At this time not only was there religious fanaticism at work to stir up the mutual hatred ever existing between Sunni and Shiah, but the intrigue of European courts was probably directed towards the maintenance of an hostility which deterred the sultan from aggressive operations north and west of Constantinople.

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  • Russia and Turkey, naturally hostile to one another, had taken occasion of the weakness of Persia to forget their mutual quarrels and unite to plunder the tottering kingdom of the Safawid kings.

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  • Owing, however, to the mutual jealousies and misconduct of Goring and Grenville, and the prince's own disregard and contempt of the council, his presence was in no way advantageous, and could not prevent the final overthrow of the king's forces in 1646.

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  • In the same year the writ was used to release the wife of Earl Ferrers from his custody and maltreatment, and was unsuccessfully applied for by John Wilkes to get back his wife, who was separated from him by mutual agreement.

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  • After a conflict of mutual affection, Pylades at last yields, but the letter brings about a recognition between brother and sister, and all three escape together, carrying with them the image of Artemis.

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  • issued a proclamation in favour of Portuguese traders, and in 1353 the Portuguese envoy Affonso Martins Alho signed a covenant with the merchants of London, guaranteeing mutual good faith in all commercial dealings.

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  • A further cause of dissatisfaction was the mutual jealousy of Portugal and Brazil.

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  • " The mutual independence of the two (codes) is rather to be argued from the absence of laws identically formulated, the lack of agreement in order either in the whole or in smaller portions, and the fact that of the peculiar motives and phrases of R D there is no trace in H (Lev.

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  • Among the buildings in the burned section restored since 1906, the Union Trust, Mutual Savings, Merchants Exchange, Crocker, Flood and the Call (newspaper) buildings are notable.

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  • On 6th February 1873 Bolivia entered upon a secret agreement with Peru, the ostensible object of which was the preservation of their territorial integrity and their mutual defence against exterior aggression.

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  • Instead of calculating the direction and magnitude of the resultant force on each particle arising from the action of neighbouring particles, he formed a single expression which is the aggregate of all the potentials arising from the mutual action between pairs of particles.

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  • It consists of three parts, the first depending on the action of gravity, the second on the mutual action between the particles of the fluid, and the third on the action between the particles of the fluid and the particles of a solid or fluid in contact with it.

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  • It is found by experiment that it is only very close to the bounding surface of a liquid that the forces arising from the mutual action of its parts have any resultant effect on one of its particles.

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  • The actual force between the particles arises in part from their mutual gravitation, which is inversely as the square of the distance.

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  • The pressure at any point of the liquid arises from two causes, the external pressure P to which the liquid is subjected, and the pressure arising from the mutual attraction of its molecules.

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  • The former can be found at once by calculating the mutual attraction of the parts of a large mass which lie on opposite sides of an imaginary plane interface.

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  • If we now suppose the crevasse produced by direct separation of its walls, the work necessary must be the same as before, the initial and final configurations being identical; and we recognize that the tension may be measured by half the work that must be done per unit of area against the mutual attraction in order to separate the two portions which lie upon opposite sides of an ideal plane to a distance from one another which is outside the range of the forces.

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  • If a i, a 2 represent the densities of the two infinite solids, their mutual attraction at distance z is per unit of area 21ra l a fZ '(z)dz, (30) or 27ra l 02 0(z), if we write f 4,(z)dz=0(z) (31) The work required to produce the separation in question is thus 2 7ru l a o 0 (z)dz; (32) and for the tension of a liquid of density a we have T = a f o 0 (z)dz.

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  • Thus Sir Isaac Newton placed a magnet in a floating vessel and a piece of iron in another in order to observe their mutual action, and A.

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  • The second effect is readily attributed to the mutual repulsion of the electrified drops, but the action of feeble electricity in producing apparent coherence was long unexplained.

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  • He divorced his first wife Blanche of Navarre in 1453 on the ground of "mutual impotence."

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  • Numerous spurs, striking in all directions from the Sailughem mountains, fill up the space between that range and the lowlands of Tomsk, but their mutual relations are far from being well known.

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  • There had been mutual excommunications before, but they had not resulted in permanent schisms. Now, however, the separation was final, and the ostensible cause of its finality was the introduction by the Latins of two words Filioque into the creed.'

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  • For many years he was engaged in managing various business enterprises, and became, in 1877, president of the Boston Manufacturers' Mutual Fire Insurance Company, a post which he held till his death.

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  • The Wiirzburg Conference is the name given to the meeting of representatives of the smaller German states in 1859 to devise some means of mutual support.

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  • It rested on a solid basis of mutual affection and of common studies, the different temperaments of the two scholars securing them against the disagreements of rivalry or jealousy.

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  • In contrast with the mutual friendliness and loyalty of the Pharisees, their behaviour towards one another is lacking in courtesy, and when they mix with their fellow-countrymen, they are as offhanded as if their fellows were aliens."

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  • Guizot inaugurated a different policy; by mutual confidence and friendly offices they entirely succeeded in restoring the most cordial understanding between the two governments, and the irritation which Lord Palmerston had inflamed gradually subsided.

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  • The state of Europe facilitated Murad's projects: civil war and anarchy prevailed in most of the countries of Central Europe, where the feudal system was at its last gasp, and the small Balkan states were divided by mutual jealousies.

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  • Amesbury was settled about 1644 as a separate part of Salisbury, and in 1654, by mutual agreement of the old and new "towns," became practically independent, although not legally a township until 1666 (named Amesbury, from the English town in Wilts, in 1667).

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  • The two men were bound together by a mutual respect deeper than a sympathy of tastes, and a community of spirit stronger than a similarity of opinions.

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  • Between friends the mutual promotion of virtue should be the guiding principle.

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  • Parental tenderness and care for the young are strongly marked among the lower animals, though so inferior in scope and duration to the human qualities; and the same may be said of the mutual forbearance and defence which bind together in a rudimentary social bond the families and herds of animals.

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  • The domestic and social affections, the kindly care of the young and the old, some acknowledgment of marital and parental obligation, the duty of mutual defence in the tribe, the authority of the elders, and general respect to traditional custom as the regulator of life and duty, are more or less well marked in every savage tribe which is not disorganized and falling to pieces.

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  • The constitution states the following as the objects of the National Council: (a) To facilitate fraternal intercourse and co-operation among the Evangelical Free Churches; (b) to assist in the organization of local councils; (c) to encourage devotional fellowship and mutual counsel concerning the spiritual life and religious activities of the Churches; (d) to advocate the New Testament doctrine of the Church, and to defend the rights of the associated Churches; (e) to promote the application of the law of Christ in every relation of human life.

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  • PROBLEM OF THREE BODIES, the problem of determining the motion of three bodies moving under no influence but that of their mutual gravitation.

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  • In the Araucarian type of wood (Araucaria and Agathis) the bordered pits, which occur in two or three rows on the radial walls of the tracheids, are in mutual contact and polygonal in shape, the pits of the different rows are alternate and not on the same level; in this type of wood the annual rings are often much less distinct than in Cupressus, Pinus and other genera.

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  • Preserved from innovations by the mutual jealousy of rival potentates, as well as by the conservative temper of a pastoral population, Andorra has kept its medieval usages and institutions almost unchanged.

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  • This inferiority of the Gregorian he explained as being probably due to the mutual interference of the rays as they crossed at the principal focus before reflection at the second mirror.

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  • The treatise is conclusive evidence as to the mutual influence of Christianity and Hellenism in the 4th century.

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  • One of these experiments was an unhappy marriage - undertaken merely that he might have a salon - which, after a year's duration, was dissolved by mutual consent.

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  • For in such mixtures, the component colours appear not, but, by their mutual allaying each other constitute a midling colour."

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  • The rules of kinship largely determined status with its correlative rights and obligations, supplied the place of contract and of laws affecting the ownership, disposition and devolution of property, constituting the clan an organic, selfcontained entity, a political, social and mutual insurance copartnership. The solidarity of the clan was its most important and all-pervading characteristic. The entire territory occupied by a clan was the common and absolute property of that clan.

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  • These prophecies 1 The idea of " righteousness " (s-d-k), or loyalty, appears to have implied the mutual bonds uniting the community and its deity, see Journ.

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  • The two "coming men" became fast friends, and their mutual esteem was never disturbed.

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  • The necessity for such sacrificial furniture has been felt in most religions, and consequently we find its use widespread among races and nations which have no mutual connexion.

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  • The first, the religious, including women and laymen as well as clergy, still maintained the old ideals of purity and mutual responsibility.

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  • no account pronounce against Charless aunt; if he could not persuade Henry and Catherine tO agree on a mutual separation, he must simply pass the time and come to no conclusion.

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  • The jubilee showed conclusively that, whatever politicians might say, the ties of blood and kinship, which united the two peoples, were too close to be severed by either for some trifling cause; that the wisest heads in both nations were aware of the advantages which must arise from the closer union of the Anglo-Saxon races; and that the true interests of both countries lay in their mutual friendship. A war in which the United States was subsequently engaged with Spain cemented this feeling.

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  • Hair having a property of mutual cohesion or " felting," which depends upon a roughened scaly surface and a tendency to curl, as in domestic sheep, is called " wool."

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  • The new fortress of Megalopolis, instead of supplying a centre of national life, merely accentuated the mutual jealousy of the cities.

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  • There is more force in the charge that his Hellenic sympathies prevented him from seeing the innate weakness and mutual jealousies of the Greek states of that period, whose only hope of peace and safety lay in submitting to the protectorate of the Roman republic. But if the event proved that the liberation of Greece was a political mistake, it was a noble and generous mistake, and reflects nothing but honour on the name of Flamininus, "the liberator of the Greeks."

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  • This was a changing England, and one that Disraeli could govern on terms of mutual satisfaction; but not if the reviving "spirit of the country" ran to extremes of selfassertion.

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  • Similarly on land, the post it occupied between northern Greece and the Peloponnese materially influenced its relation to other states, both in respect of its alliances, such as that with Thessaly, towards which it was drawn by mutual hostility to Boeotia, which lay between them; and also in respect of offensive combinations of other powers, as that between Thebes and Sparta, which throughout an important part of Greek history were closely associated in their politics, through mutual dread of their powerful neighbour.

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  • francum plegium), an early English institution, consisting (as defined by Stubbs) of an association for mutual security whose members, according to Hallam, "were perpetual bail for each other."

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  • The laws, which although called the laws of Edward the Confessor were not drawn up until about 1130, contain a clause about frithborhs which decrees that in every place societies of ten men shall be formed for mutual security and reparation.

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  • The substance of the relations between the emperor and himself, he declared, rested on mutual good-will, and added: "I must lay it down most emphatically that the prerogative of the emperor's personal initiative must not be curtailed, and will not be curtailed, by any chancellor..

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  • He rested this sovereignty on virtual mutual contract on the part of the people themselves to be so governed.

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  • Truth and falsehood belong only to assertions or denials concerning ideas, that is, to our interpretations of our ideas according to their mutual relations.

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  • But there was no mutual confidence between the sovereigns, who were at that very time pursuing opposite policies with regard to Poland.

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  • Then they invaded Alsace, but their mutual jealousy prevented them from going farther.

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  • By imbuing Frenchmen with such a mutual hatred as nothing but the arm of despotic power could control the Reign of Terror rendered political liberty impossible for many years.

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  • Catching a single deer and belling it, he drives it through the wood; the other deer, whose instinct leads them to gather into herds for mutual protection against the mosquitoes, are attracted by the sound.

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  • The songs are similar to those of the Finns, and a process of mutual borrowing seems to have gone on.

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  • By the peace of Kna.red (1613) Gustavus Adolphus gave up the Swedish claim to Finmark; and in 1751 mutual renunciations brought the relations of Swedish and Norwegian (Danish) Lapland to their present position.

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  • 16 a and on their mutual relations; a science which we have not to invent, but to discover."

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  • Aristotle goes somewhat further in recognizing the moral value of friendship (c1xAia); and though he considers that in its highest form it can be realized only by the fellowship of the wise and good, he yet extends the notion so as to include the domestic affections, and takes notice of the importance of mutual kindness in binding together all human societies.

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  • Cicero, on the other hand, in his paraphrase of a Stoic treatise on external duties (De officiis), ranks the rendering of positive services to other men as a chief department of social duty; and the Stoics generally recognized the universal fellowship and natural mutual claims of human beings as such.

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  • Human law is required, not merely to determine the details for which natural law gives no intuitive guidance, but also to supply the force necessary for practically securing, among imperfect men, the observance of the most necessary rules of mutual behaviour.

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  • - The need of such independent principles was most strongly felt in the region of man's civil and political relations, especially the mutual relations of corn munities.

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  • Thus there had become current the conception of a " state of nature " in which individuals or single families lived side by side - under none other than those " natural " laws which prohibited mutual injury and interference in the free use of the goods of the earth common to all, and upheld parental authority, fidelity of wives, and the observance of compacts freely made.

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  • This conception Grotius took, and gave it additional force and solidity by using the principles of this natural law for the determination of international rights and duties, it being obvious that independent nations, in their corporate capacities, were still in that " state of nature " in their mutual relations.

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  • toleration and mutual respect amongst the various confessions; the rousing and nurture of the Christian life and of all Christian works necessary for the moral strength and prosperity of the nation.

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  • In cases involving cross actions with mutual accounts, say between an Englishman and a German, if the German constitutes himself plaintiff he must sue his opponent before the British court, and vice versa.

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  • The field we have defined is divisible into at least two parts, that of Astronomy proper, or " Astrometry," which treats of the motions, mutual relations and dimensions of the heavenly bodies; and that of Astrophysics, which treats of their physical constitution.

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  • Modern theoretical astronomy, taken in the most limited sense, is based upon Celestial Mechanics, the science by which, using purely deductive mechanical methods, the laws of motion of the heavenly bodies are derived by deductive methods from their mutual gravitation towards each other.

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  • Celestial Mechanics is, strictly speaking, that branch of applied mathematics which, by deductive processes, derives the laws of motion of the heavenly bodies from their gravitation towards each other, or from the mutual action of the parts which form them.

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  • When the subject was taken up by the continental mathematicians, using the analytical method, the question naturally arose whether the motions of three bodies under their mutual attraction could not be determined with a degree of rigour approximating to that with which Newton had solved the problem of two bodies.

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  • In the language of algebra putting m l, m2, m 3, &c. for the masses of the bodies, r1.2 r1.3 r2.3, &c. for their mutual distances apart; vi, v 2, v 3, &c., for the velocities with which they are moving at any moment; these quantities will continually satisfy the equation orbit, appear as arbitrary constants, introduced by the process of integration.

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  • - Kepler's laws do not completely express the motion of a planet around a central body, except when no force but the mutual attraction of the two bodies comes into play.

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  • With these expressions we express their mutual action, or their pull upon each other at any and every moment.

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  • Hence the position of the plane of the orbit of each planet is continually changing in consequence of their mutual action.

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  • The result of these repetitions is that, during a number of revolutions, the special mutual actions of the two planets at these three points of their orbits repeat themselves, while the actions corresponding to the three intermediate arcs are wanting.

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  • Thus it happens that if the mutual actions are balanced through a period of a few revolutions only there is a small residuum of forces corresponding to the three regions in question, which repeats itself in the same way, and which, if it continued indefinitely, would entirely change the forms of the two orbits.

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  • The action of the sun alone would completely throw them out of these planes as each satellite orbit would rotate independently; but the effect of the mutual action is to keep all of the planes in close coincidence with the plane of the planet's equator.

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  • It consisted, first, in the identification, by strict numerical comparisons, of terrestrial gravity with the mutual attraction of the heavenly bodies; secondly, in the following out of its mechanical consequences throughout the solar system.

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  • The descriptive branch found its principle of development in the growing powers of the telescope, and had little to do with mathematical theory; which, on the contrary, was closely allied, by relations of mutual helpfulness, with practical astronomy, or " astrometry."

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  • And here, to their great mutual advantage, the old and the new astronomies meet and join forces.

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  • The mutual relations and exact orographical connexions of several of the ranges east and north of the Khan-tengri group are not yet elucidated.

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  • Laws resulted from the combination of men who agreed for mutual protection to surrender individual freedom of action.

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  • Though it is quite obvious that the theory of a social contract (or compact, as it is also called) contains a considerable element of truth - that loose associations for mutual protection preceded any elaborate idea or structure of law, and that government cannot be based exclusively on force - yet it is open to the equally obvious objection that the very idea of contract belongs to a more advanced stage in human development than the hypothesis itself demands.

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  • The Triple Alliance of 1882 between Germany, Austria and Italy was ostensibly directed to the preservation of European peace against any possible aggressive action of France or Russia; and this led in turn, some ten years later, to the Dual Alliance between Russia and France, for mutual support in case of any hostile action of the other powers.

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  • They must respect the rights of all the cities, and thus promote unity based on mutual confidence.

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  • Throughout the domain of knowledge the two forms are found in constant mutual relations, another proof of the fundamental unity of thought and being or of the objectivity of knowledge.

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  • Besides substituting Hungarian for Austrian sovereignty, it provided that the diet and the ban should control local affairs, subject to the Croatian minister in the Hungarian cabinet, and that Croatia-Slavonia should pay 55% of its revenue to Hungary for mutual and imperial expenses, but should be represented in the Hungarian parliament by thirty-six delegates, and should continue to use Serbo-Croatian as the official language.

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  • The mutual love of these two, proceeding from the relation they hold to one another, symbolizes the Holy Spirit.

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  • In 1870 negotiations were opened between France and Great Britain on the basis of a mutual exchange of territories in West Africa.

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  • A knowledge of being and existences (concrete, not abstract) and their mutual relations, is necessary as the beginning of philosophy.

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  • Among the western Baluba, or Bashilange, a remarkable politico-religious revolution took place at a comparatively recent date, initiated by a secret society termed Bena Riamba or " Sons of Hemp," and resulted in the subordination of the old fetishism to a cult of hemp, in accordance with which all hemp-smokers consider themselves brothers, and the duty of mutual hospitality, &c., is acknowledged.

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  • There was no trace of a political idea in these disputes; the mutual hatred of two women aggravated jealousy to the point of causing terrible civil wars from 561 to 613, and these finally created a national conflict which resulted in the dismemberment of the Frankish empire.

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  • The - This, the first document in the vulgar tongue in the bur,Q~ oath, history of France and Germany, was merely a mutual contract of protection for the two armies, which nevertheless did not risk another battle.

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  • Any deprivation or supersession of the count might impoverish, dispossess or ruin the vassals of the entire county; so that all, vassals or officials, small and great, feeling their danger, united their efforts, and lent each other mutual assistance against the permanent menace of an overweening monarchy.

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  • The idea of public authority had been replaced by one Dismemthat was simpler and therefore better fitted for a half- berinent of civilized societythat of dependence of the weak on the kingthe strong, voluntarily entered on by means of mutual dow.

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  • Neither did he love his brother, Gaston of Orleans, and the feeling was mutual; for the latter, remaining for twenty years heir-presumptive to a crown which he could neither defend nor seize, posed as the beloved prince in all the conspiracies against Richelieu, and issued from them each time as a Judas.

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  • Arago, 'who summed up the results of a searching series of experiments in the following laws of the interference of polarized light: (r) Under the same conditions in which two streams of common light interfere, two streams polarized at right angles are without mutual influence.

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  • By these momentous inductions the geometrical theory of the solar system was perfected, and a hitherto unimagined symmetry was perceived to regulate the mutual relations of its members.

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  • Expulsion was impossible and combination only attainable by mutual agreement, and that was never secured.

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  • It derives its celebrity ffom the demonstration by Laplace that to whatever mutual actions all the bodies of a system may be subjected, the position of this plane remains invariable.

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  • A research into the mutual perturbations of Jupiter and Saturn secured for him the prize of the Berlin Academy in 1830, and a memoir on cometary disturbances was crowned by the Paris Academy in 1850.

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  • Zamoyski was at first in favour of a member of the Báthory family, with which he was united by ties of amity and mutual interest; but on becoming convinced of the impossibility of any such candidature, he pronounced for a native Pole, or for whichever foreign prince might be found most profitable to Poland.

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  • They are deeply separated by religious differences, and their mutual jealousies, their inordinate vanity, English Miles 0 5 io 20 30 40 50 Railways Capitals of Vilayets &c. C Longitude East 42 of Greenwich their versatility and their cosmopolitan character must always be an obstacle to the realization of the dreams of the nationalists.

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  • By mutual consent no allusion was made to the death of the Wangs.

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  • The custom by which neighbouring churches sought mutual aid and advice, prepared the way for the Presbyterian system of church government, which was established by an ecclesiastical assembly held at Saybrook in 1708, the church constitution there framed being known as the " Saybrook Platform."

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  • In 1445 an old feud with the archbishop of Magdeburg was settled, and in 1457 a treaty of mutual succession was made with the houses of Saxony and Hesse.

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  • But the ultimate conception of understanding, that of the world of objects, quantitatively determined, and standing in relation of mutual reciprocity to one another, is not a final ground of explanation.

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  • His brother is Anteros, the god of mutual love, who punishes those who do not return the love of others, without which Eros could not thrive; he is sometimes described as the opponent of Eros.

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  • He certainly had Destiny's approval - and the admiration appeared to be mutual.

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  • That their feelings for each other were mutual, she had no doubt.

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  • Mary liked him, and the feelings were obviously mutual.

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  • Life would be filled with mutual concessions I thought as I tucked my tee shirt into a bottom drawer.

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  • We agreed on our mutual commitment.

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  • Yes, they admitted it appeared a large volume of tips bore mutual similarities.

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  • We five hirelings, as dissimilar as snowflakes, are tripping over one another in an effort to display mutual accommodation.

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  • By mutual agreement, announced to Howie by our silence, no discussion about Julie took place unless initiated by Howie himself.

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  • By mutual agreement with both Daniel Brennan and Merrill Cooms, our conversations are reduced to an occasional call, for security sake.

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  • We both managed a smile at our mutual concern.

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  • "The FBI is all over the place," he said after our mutual greeting.

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  • We both have a mutual problem.

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  • Certainly. It's not as if they don't have a mutual interest in this business.

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  • They chatted further about general matters—mutual friends, and from Weller, some advice on campaigning.

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  • Cynthia was the first to comment but Dean at first dismissed her concerns as mutual nervousness.

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  • While Dean distrusted the Dawkins, given their mutual animosity toward one another, any collective effort on their part—on any project—seemed questionable, if not impossible.

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  • By mutual agreement, Alex had final say in decisions, but they were supposed to discuss it first.

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  • While the two maintained mutual respect, Jake Weller appeared unsettled in Dean's presence, a combination of insecurity over Dean's more extensive experience and memories of past encounters that had pushed the lawman into compromising situations.

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  • After a few moments of mutual silence, both men rose and returned to their rooms.

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  • After mutual love-you's, he hung up.

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  • When they arrived in Ouray there was a mutual understanding all that lay between them had not been discussed.

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  • I want mutual trust and love.

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  • Obviously there was a mutual physical attraction between them, but that was all.

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  • Although Ethel and Fred had never met, that didn't stop them from developing a strong mutual dislike, fueled via telephone mes­sages and third-party comments.

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  • Both told childhood tales, stories of happy memories, each prompting the memory of yet another incident to their mutual delight.

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  • Why hadn't she ever thought about their mutual love of animals?

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  • Marriage was based on mutual respect.

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  • Was it wishful thinking, or was there a mutual attraction between them?

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  • Could it have been mutual?

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  • The feeling is mutual.

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  • The job interview especially is a moment of mutual acquaintance.

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  • Despite amiable companions, continually endeavoring to bestow mutual pleasure, I was now alone.

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  • This also gives us a great opportunity to leverage synergies from our successful mutual fund business in India.

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