Base Sentence Examples

base
  • Despise that which is base, said his mother.

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  • Think we're safer at our base camp?

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  • He cooked bare-chested, wearing black chinos, his dark hair clasped at the base of his neck.

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  • She ran hard, spotting Yully and Charles fighting back-to-back at the base of the obelisk.

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  • It had been on the nightstand, partially hidden by the base of a lamp.

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  • She left him at the base of the stairs and ascended alone.

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  • Dean also spoke to Cece Baldwin again, just to touch base and see if she might have heard further from her mysterious benefac­tor.

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  • The men on the small base drew their weapons at the sight of Darian.

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  • A military organization may be quite correctly compared to a cone, of which the base with the largest diameter consists of the rank and file; the next higher and smaller section of the cone consists of the next higher grades of the army, and so on to the apex, the point of which will represent the commander-in-chief.

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  • The only sound was the rush of water at the base of the canyon.

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  • Katie turned the crank at the base of the bed.

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  • Alex didn't like highly spiced food, so she decided to bake Cornish game hens for the base of the meal.

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  • Through her tears the old Oak tree stood tall, the flowers at its base waving softly in the breeze.

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  • Battles raged atop the walls, on the narrow stairways, at the base of the walls.

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  • The expression of that base and cringing smile, which Pierre knew so well in his wife, revolted him.

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  • I dropped to the ground as he yanked the phone from its base and flung it across the room.

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  • There was a pointed pic at the base of its handle.

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  • She pulled her hair back in a scrunchie at the base of her neck, growing nervous once again.

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  • The dark base of the mountainous thunderheads had a greenish tinge.

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  • I didn't get to first base but you've got a spiffy uniform and a shiny badge.

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  • The two pedaled together most of the afternoon, enjoying the pine-scented air, the cool breeze that hugged the base of the mountains and the yellow sunshine of a perfect spring day.

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  • The plateau-like summit, which originally could be reached only from the south by a steep and narrow path, was rendered almost impregnable to Indian attack by a sheer cliff on the river side of the hill, a deep ravine along its eastern base and steep declivities on the other sides.

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  • The birthplaces of these persons are still known, and to this day there are sequestered villages, nestling near the western base of the Ghats, which are pointed to as being the ancestral homes of men who two centuries ago had political control over half India.

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  • Thus Raghoji Bhonsla established himself in the tracts lying underneath the southern base of the Satpura range (namely, Nagpur and Berar), overran Orissa and entered Bengal.

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  • The slopes of the Armenian highlands are clothed with fine forests, and the vine is grown at their base, while on the wide-stretching steppes the Turko-Tatars pasture cattle, horses and sheep. The lower part of the Kura valley assumes the character of a dry steppe, the rainfall not reaching 54 in.

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  • While the Martello tower owes its reputation and its widespread adoption in Great Britain to a single incident of modern warfare, the round masonry structure entered by a door raised high above the base is to be found in many lands, and is one of the earliest types of masonry fortification.

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  • They are thus the double key of The double Comte's systematization of the philosophy of all the key of sciences from mathematics to physiology, and his positive analysis of social evolution, which is the base of philo= sociology.

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  • Many ships have been wrecked on the jagged reefs which fringe their base.

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  • If you'll tell me how much you use each week, I'll replace it and we'll keep that base.

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  • It is, however, though doubtless near to the base of the Oligochaetous series, most nearly allied in the reproductive system to the Oligochaeta.

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  • Russian aggression began somewhat early in the r8th century, when Peter the Great, establishing his base at Astrakhan on the Volga, and using the Caspian for bringing up supplies and munitions of war, captured Derbent from the Persians in 1722, and Baku in the following year.

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  • The lower fort lies at the eastern base of the rock and measures about half a mile in diameter.

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  • The Goyt has its source a little farther north, at the base of the same hill, and, taking a N.N.E.

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  • In its rotunda is Jean Antoine Houdon's full-length marble statue of Washington, provided for by the Virginia General Assembly in 1784, and erected in 1796; its base bears a fine inscription written by James Madison.

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  • The greatest height of the monument is 60 ft., and the diameter of its base is 86 ft.

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  • In 1676, during " Bacon's Rebellion," a party of Virginians under Bacon's command killed about 150 Indians who were defending a fort on a hill a short distance east of the site of Richmond in the " Battle of Bloody Run," so called because the blood of the slain savages is said to have coloured the brook (or " run ") at the base of the hill.

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  • Their cones are composed of thin, rounded, closely imbricated scales, each with a more or less conspicuous bract springing from the base.

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  • The visceral hump forms a low conical dome above the subcircular foot, and standing out all round the base of this dome so as completely to overlap the head and foot, is the circular mantle-skirt.

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  • It will be remembered that, according to Spengel, the osphradium of mollusca is definitely and intimately related to the gill-plume or ctenidium, being always placed near the base of that organ; further, Spengel has shown that the nerve-supply of this olfactory organ is always derived from the visceral loop. Accord ingly, the nerve-supply FIG.

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  • Supposing the tube to be completely introverted and to commence its eversion, we then find that eversion may take place, either by a forward movement of the side of the tube near its attached base, as in the proboscis of the Nemertine worms, the pharynx of Chaetopods and the eye-tentacle of Gastropods, or by a forward movement of the inverted apex of the tube, as in the proboscis of the Rhabdocoel Planarians, and in that of Gastropods here under consideration.

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  • The head is seen in front resting on the foot and carrying a median non-retractile snout or rostrum, and a pair of cephalic tentacles at the base of each of which is an eye.

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  • The minute structure of the epithelium which clothes it, as well as the origin of the nerve which is distributed to the parabranchia, proves it to be the same organ which is found universally in molluscs at the base of each gill-plume, and tests the indrawn current of water by the sense of ?,g smell.

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  • Marine Euthyneura, the more archaic forms of which have a relatively large foot and a small visceral hump, from the base of which projects on the right side a short mantle-skirt.

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  • Its superficial extent is seen when the folds covering the shell are cut away and the shell removed; the external surface forms a triangle with its base bordering the pericardium, and its apex directed posteriorly and reaching to the lefthand posterior corner of the shell-chamber.

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  • Thus the base of the gill passes in a slanting direction across the right-hand side of the kidney, the posterior end being dorsal to the apex of the gland, and the anterior end ventral to the right-hand corner.

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  • Dorsum furnished on either side with papillae, at the base of which are ramified appendages.

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  • The head bears a single pair of contractile but not invaginable tentacles, at the base of which are the eyes.

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  • Jaw formed of folds imbricated externally and meeting at an acute angle near the base.

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  • Nelson's capture of Malta (5th of September 1800) also secured for the time a sure base for British fleets in the Mediterranean.

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  • Certainly he needed her support during that campaign; but many good judges have inclined to the belief that the whole-hearted support of Poles and Lithuanians would have been of still greater value, and that the organization of their resources might well have occupied him during the winter of 1812-1813, and would have furnished him with a new and advanced base from which to strike at the heart of Russia in the early summer of 1813.

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  • Ia, frons; b, clypeus (the pointed labrum beneath it); II, mandible; III, first maxilla; (a, base; b, sheath; c, piercer), III', inner view of sheath; IV, second maxillae forming rostrum (b, mentum; c, ligula).

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  • One tripod thus affords a firm base of support while the legs of the other tripod are brought forward to their new positions.

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  • The frost broke at the end of February 1709, and then the spring floods put an end to all active operations till May, when Charles began the siege of the fortress of Poltava, which he wished to make a base for subsequent operations while awaiting reinforcements from Sweden and Poland.

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  • Scapa Flow was preferred to the Cromarty Firth as his chief naval base by Admiral Jellicoe, but no preparations had been made and everything had to be improvised, guns being landed from the ships to strengthen the defences.

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  • The few capital ships which happened to be there put to sea, and it was recognized that the base would be unsafe until anti-submarine defences were installed.

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  • But it was now made to appear that the struthious birds in this respect resembled, not only the duck, but a great many other groups - waders, birds-of-prey, pigeons, passerines and perhaps all birds not gallinaceous - so that, according to Cuvier's view, the five points of ossification observed in the Gallinae, instead of exhibiting the normal process, exhibited one quite exceptional, and that in all other birds, so far as he had been enabled to investigate the matter, ossification of the sternum began at two points only, situated near the anterior upper margin of the side of the sternum, and gradually crept towards the keel, into which it presently extended; and, though he allowed the appearance of detached portions of calcareous matter at the base of the still cartilaginous keel in ducks at a certain age, he seemed to consider this an individual peculiarity.

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  • It must not, however, be forgotten that Justin is here speaking as the apologist of Christianity to an educated Pagan public, on whose philosophical view of life he had to base his arguments, and from whom he could not expect an intimate comprehension of the religious position of Christians.

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  • Doria seized Chioggia as a base of operations and drew his fleet inside the lagoons.

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  • The ship to which he was appointed was ordered to China, and he found opportunities during the voyage for indulging his passion for exploration, making a journey from Rio de Janeiro to the base of the Andes, and another from Bombay through India to Ceylon.

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  • In the War of 1812 Sackett's Harbor was an important strategic point for the Americans, who had here a naval station, Fort Tompkins, at the base of Navy Point, and Fort Volunteer, on the eastern side of the harbour.

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  • In 1420 the emperor Sigismund made the city the base for his unsuccessful attack on the Taborites; Kuttenberg was taken by Ziika, and after a temporary reconciliation of the warring parties was burned by the imperial troops in 1422, to prevent its falling again into the hands of the Taborites.

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  • The caudal fin is crescent-shaped, strengthened at the base by two short ridges on each side.

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  • Apt to minimize difficulties, to search for the common ground of unity in opponents, he turned aside, with a disdain which superficial critics often mistook for indifference, from the base, the violent and the common.

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  • Viscosity increases with density, but oils of the same density often vary greatly; the coefficient of expansion, on the other hand, varies inversely with the density, but bears no simple relation to the change of fluidity of the oil under the influence of heat, this being most marked in oils of paraffin base.

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  • Since, however, the steppe edge on the east is somewhat indefinite, some early Moslem and other geographers have included all the Hamad in Syria, making of the latter a blunt-headed triangle with a base some 700 m.

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  • To avoid the creation of induced currents, the coil frames and the base boards are constructed of slate.

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  • The American government asked the Spanish authorities of East Florida to permit an American occupation of the country in order that it might not be seized by Great Britain and made a base of military operations.

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  • On the top of the stupa was an ornament shaped like the letter T, and as the base of the stupa was above the quadrangle, the total height of the monument was between 50 and 60 ft.

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  • In the narrow sense of the word, alchemy is the pretended art of making gold and silver, or transmuting the base metals into the noble ones.

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  • Some are in Greek and demotic, and one, of peculiar interest from the chemical point of view, gives a number of receipts, in Greek, for the manipulation of base metals to form alloys which simulate gold and are intended to be used in the manufacture of imitation jewellery.

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  • The .great mass of the Gilead range is formed of Jura limestone, the base slopes being sandstone partly covered by white marls.

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  • These early fortifications of the Acropolis, ascribed to the primitive non-hellenic Pelasgi, must be distinguished from the Pelasgicum or Pelargicum, which was in all prob ab i l i ty an encircling wall, built round the base of the g citadel and furnished with nine gates from which it derived the name of Enneapylon.

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  • These difficulties are met by the assumption that the semicircular masonry formed the base of a retaining-wall which rose to a considerable height, supporting a theatre-like structure capable of seating many thousand persons.

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  • The earliest settlement on the Acropolis was doubtless soon increased by groups of dwellings at its base, inhabited by the dependents of the princes who ruled in the stronghold.

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  • A Doric colonnade with a double row of columns was found to have extended along the base of the Acropolis for a distance of 54 yds.; behind it in a chamber hewn in the rock is the sacred well mentioned by Pausanias.

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  • The Agrippeum, a covered theatre, derived its name from Vipsanius Agrippa, whose statue was set up, about 27 B.C., beneath the north wing of the Acropolis propylaea, on the high rectangular base still remaining.

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  • Since its reversion to Ottoman power (1840) the history of Marash has been varied only by Armenian troubles, largely connected with the fortunes of Zeitun, for the reduction of which place it has more than once been used as a base.

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  • The wild oat, moreover, has a long stiff awn, usually twisted near the base.

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  • Its tetramethyl-diamino derivative, which is formed by condensing formaldehyde with dimethyl-meta-aminophenol and subsequent elimination of water from the resulting diphenyl methane derivative, is the leuco base of pyronine, into which it passes by oxidation.

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  • He refused to base Judaism on speculative philosophy alone; there was a deep emotional side to his thought.

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  • Towards the river, though rich in parts, this tract of country is generally wild and desolate, but nearer the base of the hill range there is a large natural basin of fertile land which is highly cultivated.

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  • To the south of the Satpuras and extending along its base from west to east lie successively the Berar, Nagpur and Chhattisgarh plains.

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  • The search for this essence subsequently resolved itself into the desire to effect the transmutation of metals, more especially the base metals, into silver and gold.

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  • The canals of the proboscis open ultimately into a circular vessel which runs round its base.

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  • In botany, the word is applied to leaves divided into two parts near the base.

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  • The year 1784 marks the beginning of the ordnance survey, for in that year Major-General Roy measured a base line of 27,404 ft.

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  • Six additional base lines were measured up to 1849, including the Lough Foyle, in 1827-1828, and that on Salisbury Plain, in 1849.

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  • At some points the rugged cliffs, furrowed by deep ravines, approach close to the sea; elsewhere the hills leave a considerable maritime plain between their base and the shore line.

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  • It was then determined that in the further operations against the mullah the main advance should be from a base on the east coast of Italian Somaliland - the open roadstead of Obbia being chosen.

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  • The water is deep right to the base of the cliff and owing to the winds and the strength of the ocean currents, navigation is dangerous.

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  • Nine feet in diameter at the base, it tapers to eight feet at the top. The catacombs, a short distance S.W.

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  • In Sambucus and Viburnum the small white flowers are massed in heads; honey is secreted at the base of the styles and, the tube of the flower being very short, is exposed to the visits of flies and insects with short probosces.

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  • The base of a similar column has only feet in the same attitude, and probably bore the name Nereus.

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  • The village of South Hadley, or the Center, lies at the south base of Mount Holyoke, about 4 m.

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  • Its base is Roman, of mingled stone and brick work.

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  • It results from this that the horn has the appearance of a mass of agglutinated hairs, which, in the newly growing part at the base, readily fray out on destruction of the softer intermediate substance; but the fibres differ from true hairs in growing from a free papilla of the derm, and not within a follicular involution of the same.

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  • At the base there is often an arkose, composed largely of fragments of serpentine and granite derived from the ancient floor.

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  • His weakness as a philosopher is his tendency to base the laws of the universe on the experience-born, thought-produced convictions of one man - himself.

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  • In 1355 Suleiman crossed over from Aidinjik and captured the fortress of Gallipoli, which was at once converted into a Turkish stronghold; from this base Bulair, Malgara, Ipsala and Rodosto were added to the Turkish possessions.

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  • With Spain the war continued, and on the 24th of August 1574 Tunis - which had been taken by Don John of Austria in 1572 - was recaptured by the Turks, who from this new base proceeded, under Sinan Pasha and Kilij Ali, to ravage Sicily.'

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  • In this sentence it is to be noted that the council of Constance was careful not to base itself upon the former decision of the council of Pisa.

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  • The emperor now pressed on towards Friedland, where he would completely control the Russian communications with Konigsberg, their immediate base of supply, but for once the Russians outmarched him and covered their movement so successfully that for the next three days he seems to have completely lost all knowledge of his enemy's whereabouts.

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  • The French army was thus disposed almost in an equilateral triangle with sides of about 570 m., with 95,000 men at the apex at Moscow opposed to 120,000, 30,000 about Brest opposite ioo,000, and 17,000 about Drissa confronted by 40,000, whilst in the centre of the base at Smolensk lay Victor's corps, about 30,000.

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  • Calling up St Cyr, whom he had already warned to remain at Dresden with his command, he decides to fall back towards Erfurt, and go into winter quarters between that place and Magdeburg, pointing out that Dresden was of no use to him as a base and that if he does have a battle, he had much better have St Cyr and his men with him than at Dresden.

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  • Yet even so the want of complete documentary evidence upon which to base conclusions has vitiated all but the most recent of the countless monographs and histories that have appeared on the subject.

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  • Close to this stands the so-called tomb of Sitte Zobeide (Zobaida), with its octagonal base and pineapple dome, one of the most conspicuous and curious objects in the neighbourhood of Bagdad.

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  • The oxides are then converted into double sulphates which are separated from each other by repeated fractional crystallization or by fractional precipitation with ammonia or some other base.

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  • The flowers have a hollow tube at the base bearing at its free edge five sepals, an equal number of petals, usually concave or spoon-shaped, pink or white, and a great number of stamens.

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  • In the case of the peach this peculiarity is in some way connected with the presence of small glandular outgrowths on the stalk, or at the base of the leaf.

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  • The best-placed healthy young shoot produced from the wood buds at the base of the bearing branch is to be carefully preserved and in due time nailed to the wall.

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  • The gill-pores occur on each side of the dorsal aspect of the worm in a longitudinal series at the base of a shallow groove, the branchial groove.

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  • He then finally decided to attack Soult (intending subsequently to fall back through Galicia) and ordered up transports from Lisbon to Corunna and Vigo; thus changing his base from Portugal to the north-west of Spain; Blake's Spanish army, now rallying under the marquis de la Romana near Leon, was to co-operate, but was able to give little effective aid.

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  • Let us consider the case of the neutralization of a base by an acid in the light of the dissociation theory.

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  • An exactly similar process occurs when any strongly dissociated acid acts on any strongly dissociated base, so that in all such cases the heat evolution should be approximately the same.

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  • This is fully borne out by the experiments of Julius Thomsen, who found that the heat of neutralization of one gramme-molecule of a strong base by an equivalent quantity of a strong acid was nearly constant, and equal to 13,700 or 13,800 calories.

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  • This character is the base of the plan of adding glucose to wine and beer wort before fermenting, the alcohol content of the liquid after fermentation being increased.

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  • The sides of the triangle slope down abruptly towards the west, more gradually towards the east; at the base stands the cone of Ayala Hill, the last outpost of the Rudnik Mountains, which extend far away to the south; and, at the apex, a cliff of Tertiary chalk, 200 ft.

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  • To obtain the latex, deep incisions are made near the base of the tree extending up the trunk.

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  • The trees are tapped on the " herring-bone " plan and the milk collected in vessels at the base.

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  • The manufacture of overshoes and fishing boots is an analogous process, only the canvas base is more thickly coated with a highly pigmented rubber of low quality.

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  • Several low chains of mountains have their base on the lower terrace and run from south-west to north-east; they are known as the Nerchinsk Mountains in Transbaikalia, and their continuations reach the northern parts of the Gobi.4 The great plateau is fringed on the north-west by a series of lofty border-ranges, which have their southern base on the plateau and their northern at a much lower level.

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  • A typical feature of the north-eastern border of the high plateau is a succession of broad longitudinal 5 valleys along its outer base, ' The wide area between the middle Lena and the Amur, as well as the hilly tracts west of Lake Baikal, and the Yeniseisk mining region are in this condition.

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  • Anteriorly this base supports a gurrie or gutter, the pre-oral rim of which is formed by a simple lip, but the post-oral rim is composed of a closely set row of tentacles.

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  • The small arm-sinus runs along the arms of the lophophore at the base of the tentacles, and gives off a blind diverticulum into each of these.

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  • The base of a tentacle bisected in the middle line.

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  • The kidneys or nephridia open internally by wide funnel-shaped nephridiostomes and externally by small pores on each side of the mouth near the base of the arms. Each is short, gently curved and devoid of convolutions.

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  • The chitinous chaetae have their origin in special ectodermal pits, at the base of which is one large cell which is thought to secrete the chaeta, as in Chaetopods.

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  • The two plates may meet in the middle line, and leave only a small oval opening near the centre for the pedicle, as in Rhynchonella; or they may meet only near the base of the delthyrium forming the lower boundary of the circular pedicle-opening, as in Terebratula; or the right plate may remain quite distinct from the left plate, as in Terebratella.

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  • To represent the simplest perpetuant, of weight 7, we may take as base either A2B 1 B 2 or A l A 2 B2, and since Ai+Bi =o the former is equivalent to A 2 ArB 2 and the latter to A 2 B i B2; so that we have, (1 -f-aix) (1 + a2x).

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  • The leading products of the blast-furnace are argentiferous lead (base bullion), matte, slag and flue-dust (fine particles of charge and volatilized metal carried out of the furnace by the ascending gas current).

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  • It holds its own, however, when base bullion contains bismuth in appreciable amounts, as in the Pattinson process bismuth follows the lead to be cupelled, while in the Parkes process it remains with the desilverized lead which goes to market, and lead of commerce should contain little bismuth.

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  • The base bullion is imperfectly Pattinsonized, giving lead rich in silver and bismuth, which is cupelled, and lead low in silver, and especially so in bismuth, which is further desilverized by the Parkes process.

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  • The plus-silver is due to the fact that in assaying the base bullion by cupellation, the silver lost by volatilization and cupel-absorption is neglected.

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  • In the United States the cost of desilverizing a ton base bullion is about $6.

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  • From this city as their base the Arabs, under Kotaiba (Qotaiba) ibn Moslim, early in the 8th century brought under subjection Balkh, Bokhara, Ferghana and Kashgaria, and penetrated into China as far as the province of Kan-suh.

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  • The flowers, which are solitary, or rarely in pairs, at the end of slender axillary flower-stalks, are very irregular in form, with five sepals prolonged at the base, and five petals, the lowest one larger than the others and with a spur, in which collects the honey secreted by the spurs of the two adjoining stamens.

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  • Aconitine (C33H45N013, according to Dunstan; C34H47NOH, according to Freund) is a crystalline base, soluble in alcohol, but very sparingly in water; its alcoholic solution is dextrorotatory, but its salts are laevorotatory.

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  • The next four pairs of appendages (completing the mesosomatic series of six) consist, in both Scorpio and Limulus, of a base carrying each 130 to 150 blood-holding, leaf-like plates, lying on one another like the leaves of a book.

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  • The appendage carrying the gill-book stands out on the surface of the body in Limulus, and has other portions developed besides the gill-book and its base; it is fused with its fellow of the opposite side On the other hand, in Scorpio, the gill-book-bearing apFIG.

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  • The latter open at the base of the fifth pair of limbs of the Crustacean, just as the coxal glands open on the coxal joint of the fifth pair of limbs of the Arachnid.

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  • The genital pores are situate at the base of the 7th pair of limbs, and may be repeated From Parker and Haswell's Text-book after Hoek.

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  • Ventral view of a female with the appendages cut short near the base.

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  • A, Ventral view of prosoma and of anterior region of opistho soma with the appendages cut off near the base; a and b, B, Dorsal view.

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  • Ventral view with the appendages cut off at the base.

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  • Respiratory organs tracheal, opening by a pair of spiracles in the prosoma above the base of the fifth appendage on IV III I composed, at least in many cases, of eleven somites, the 1 1 th somite very small, often hidden within the loth.

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  • Orifice of coxal gland probably situated at base of coxa of 5th appendage; sternal plate of prosoma minute or absent; no prosternal element underlying the mouth.

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  • Tracheae opening by a pair of stigmata situated above and behind the base of the 4th or 5th or 6th pair of appendages.

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  • Tracheae, except in the aquatic species in which they are atrophied, opening by a pair of stigmata situated close to or above the base of the appendages of the 1st pair (mandibles).

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  • Libau formed the base; Germany furnished the supplies; the Baits (Baron Pilar, Baron Randen) undertook the leadership. The liberation was thus made dependent on the goodwill of Germany.

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    0
  • Owing to the conflict of claims which grew out of the controversy, maritime states had to moderate their demands and base their pretensions to maritime dominion on the principle that it extended seawards from land.

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  • The latter, however, made it the base of his operations against the Romans in 89, 72 and 67 B.C. Pompey made it a free city in 65, after Mithradates' fall.

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    0
  • The beds are homotaxial with the Karharbari series of India, and represent either the top of the Carboniferous or the base of the Permian of Europe.

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  • At the west end of George Street, in the centre of Charlotte Square, stands the Albert Memorial, an equestrian statue of the prince consort, with groups at each of the four angles of the base.

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  • The parish church contains the tombs of the Forresters, of old the leading family of the district, with full-length sculptured figures, and at the base of Corstorphine Hill - from one point of which (" Rest and be Thankful ") is to be had one of the best views of Edinburgh - are the seats of several well-known families.

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  • Under the protection of the hill-fort, a native settlement was established on the ridge running down to the valley at the foot of Salisbury Crags, and another hamlet, according to William Maitland (1693-1757), the earliest historian of Edinburgh, was founded in the area at the northwestern base of the rock, a district that afterwards became the parish of St Cuthbert, the oldest in the city.

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  • A conglomerate at the base contains traces of gold.

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  • C. Smith with a force of 263 men left his camp at the Umgazi,on the eastern frontier of Cape Colony, and marching overland reached Durban without opposition, and encamped, on the 4th of May, at the base of the Berea hills.

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  • Durban was soon thronged; and Pietermaritzburg, which was then practically the terminus of the Natal railway, was the base from which nearly all the expeditions to the goldfields were fitted out.

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  • The corolla is generally funnelshaped, more rarely bell-shaped or tubular; the outer face is often marked out in longitudinal areas, five well-defined areas tapering from base to apex, and marked with longitudinal striae corresponding to the middle of the petals, and alternating with five non-striated weaker triangular areas; in the bud the latter are folded inwards, the stronger areas being exposed and showing a twist to the right.

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  • These attempts at the unification of algebra, and its separation from other branches of mathematics, have usually been accompanied by an attempt to base it, as a deductive science, on certain fundamental laws or general rules; and this has tended to increase its difficulty.

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    0
  • In n = a P, a is the root or base, p is the index or logarithm, and n is the power or antilogarithm.

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  • Neuserre of the Vth Dynasty appears to have been in the shape of a stumpy obelisk on a vast scale, only the base now remains, but hieroglyphic pictures, indicate this form.

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  • A similar band of ornament runs round the top of the walls outside, and at their base is a reeded torus.

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  • There is a 15th-century Italian example in South Kensington Museum of a pilastered turret containing an oblong crystal case, the whole resting on a stemmed base, and surmounted with a cupola.

    0
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  • The rocks at the base of the slopes are granite, the upper escarpments are of sedimentary rocks.

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  • Seams of coal lie near the base, some of them exceeding 20 ft.

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  • It was used as a base by hunters and traders with the interior, and in its vicinity there gathered a number of settlers of European origin, many of them outcasts from Europe or Cape Colony.

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  • The northern part of Natal presented two faces of a triangle to the two enemies, the short base being formed by the Tugela river.

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  • It is a very weak base, salts being only formed with mineral acids, and these are dissociated by water.

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  • The family is the base of the social system in Annam and is ruled by its head, who is also priest and judge.

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  • The primary school, in which the pupils learn only Chinese writing and the precepts of Confucius, stands at the base of this system.

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  • The nitrate of this base (known as nitron) is so insoluble that nitrates may be gravimetrically estimated with its help. These bases combine with the alkyl iodides to yield quaternary ammonium salts.

    0
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  • Still in some parts of his system Sylvius shows an anxiety to base his pathology on anatomical changes.

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  • He professed to base medicine entirely on a knowledge of symptoms, regarding all investigation of the causes of symptoms as useless.

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  • Both east and west the walls of the rift-valley are close to the lake,the water in many places washing the base of the cliffs.

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  • It is desultory to a degree; it is a base libel on religion and history; it differs from its model Ariosto in being, not, as Ariosto is, a mixture of romance and burlesque, but a sometimes tedious tissue of burlesque pure and simple; and it is exposed to the objection - often and justly urged - that much of its fun depends simply on the fact that there were and are many people who believe enough in Christianity to make its jokes give pain to them and to make their disgust at such jokes piquant to others.

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  • The Nelson Column, the central feature of Trafalgar Square, is from the designs of William Railton (1843), crowned with a statue of Nelson by Baily, and has at its base four colossal lions in bronze, modelled by Sir Edwin Landseer.

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  • The Roman general Paulinus Suetonius, after marching rapidly from Wales to put down a serious insurrection, found Londinium unfitted for a base of military operations, and therefore left the place to the mercy of Boadicea, who entirely destroyed it, and killed the inhabitants.

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  • Four small boats of the mine-laying class were also dispatched, of which three (UC 14, UC 13, UC15) made their way to Constantinople, carrying important technical stores, in the summer months after an intermediate base had been established at Orak near Budrun.

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  • After replenishing at that base, Hersing sailed on the 10th for the Dardanelles, where, on the 25th and 27th he sank the battleships " Triumph " and " Majestic."

    0
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  • The object of this second operation was twofold - it would indirectly assist the offensive against Sari Bair, it would also furnish the Allies who were planted down on the outer coast of the peninsula with a much more sheltered landing place and base than Anzac Cove.

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  • Impressed by the unsatisfactory positions in which the Allied troops found themselves on the peninsula, by the impossibility of their making any progress at their existing strength, and by the risks that the army ran in remaining on such shores without any safe harbour to depend upon for base in stormy weather, Monro, after examining the situation on the spot in the closing days of Oct., declared unhesitatingly for a complete withdrawal.

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  • Monro arrived and recommended evacuation of the peninsula, the Ottoman host gathered about the Dardanelles was already decidedly stronger in point of numbers than was the army which was clinging to patches of littoral without a sheltered base.

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  • It is seen that the action is intermittent, liquid only being discharged during a down stroke, but since the driving force is that which is supplied to the piston rod, the lift is only con ditioned by the power available and by the strength of the pump. A continuous supply can be obtained by leading the delivery pipe into the base of an air chamber H, which is fitted with a discharge pipe J of such a diameter that the liquid cannot escape from it as fast as it is pumped in during a down stroke.

    0
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  • The so-called oil air-pumps are much more efficient; the valve difficulty is avoided, and the risk of leakage minimized; whilst in addition there is no air clearance between the piston and the base of the cylinder as in the older mechanical forms. The Fleuss pump may be taken as an example.

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  • The inlet pipe enters an elliptical vessel which communicates with the cylinder a little way up from its base, whilst at the base there is a relief tube leading into the elliptical vessel already mentioned.

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  • It may be said to spring from the head of the Taghdumbash Pamir, where it unites with the great meridional system of Sarikol stretching northwards, and the yet more impressive mountain barrier of Murtagh, the northern base of which separates China from the semi-independent territory of Kanjut.

    0
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  • Numerous derivatives of acridine are known and may be prepared by methods analogous to those used for the formation of the parent base.

    0
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  • Phenyl-acridine is the parent base of chrysaniline, which is the chief constituent of the dyestuff phosphine (a bye-product in the manufacture of rosaniline).

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  • The leg is either pulled out from the substance of the base of the bowl, or from a small lump of glass added to the base.

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  • If the section of the finished tube is to be a triangle, with the enamel and bore at the base, the molten mass is pressed into a V-shaped mould before it is pulled out.

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  • A hollow rectangular bottle is formed, the base and sides of which are converted into sheets.

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  • Bottle moulds are made of cast iron, either in two pieces, hinged together at the base or at one side, or in three pieces, one forming the body and two pieces forming the neck.

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  • They are usually in two main pieces, a base and an upper part or collar of hinged sections.

    0
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  • The alabastra have short necks, are slightly wider at the base than at the shoulder and have rounded bases.

    0
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  • A modern glassblower, when making an amphora-shaped vase, finishes the base first, fixes an iron rod to the finished base with a seal of glass, severs the vase from the blowing iron, and finishes the mouth, whilst he holds the vase by the iron attached to its base.

    0
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  • Having severed the body of the vase from the blowing iron, he heated and closed the fractured base, whilst holding the vase by means of the rod fixed in the neck.

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  • Nearly every specimen shows traces of the pressure of a tool on the outside of the neck, as well as signs of the base having been closed by melting.

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  • Occasionally a knob or excrescence, formed by the residue of the glass beyond the point at which the base has been pinched together, remains as a silent witness of the process.

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  • The absence of traces of the transition strengthens the supposition that the revolution in technique merely consisted in the discovery that it was more convenient to finish the base of a vessel before its mouth, and such a revolution would leave no trace behind.

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  • The base is double but the inner lining has an opening in the centre.

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  • The foot at first was formed by coiling a thread of glass round the base of the waist; but, subsequently, an open glass cone was joined to the base of the waist, and a glass thread was coiled upon the surface of the cone.

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  • The lower parts, inner surface of the limbs, throat, chin and upper lip are dirty white; the outside of the ears, particularly at their base, and a patch on each side of the muzzle black; the end of the tail dusky.

    0
    0
  • Let P, Q denote the normal thrust across the sides bc, ca, and R the normal thrust across the base ab.

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  • Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.

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  • In the War of 1812 Whitehall was fortified and was a base of supplies for American operations against Canada.

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  • Vines have woody climbing stems, with alternate, entire or palmately lobed leaves, provided at the base with small stipules.

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  • It lies at the northern base of the Monti Berici, on both sides of the Bacchiglione, at its confluence with the Retrone.

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  • The body, or " strobila," consists of a usually minute organ of attachment (scolex or its representative) which is imbedded in the intestinal membrane, and of a series of segments that arise from the base of the scolex and increase in size distally.

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  • It has long been known that when organic materials such as the dung and urine of animals, or even the bodies of animals and plants, are applied to the soil, the nitrogen within them becomes oxidized, and ultimately appears in the form of nitrate of lime, potash or some other base.

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  • Lime is a base and neutralizes the acid materials present in badly drained meadows and boggy pastures.

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  • After being pared off the turf is allowed to dry for a fortnight or so and is then placed in small heaps a yard or two wide at the base, a little straw or wood being put in the middle of each heap, which is then lighted.

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  • The solitary ovule springs erect from the base of the ovarian cavity.

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  • A piece of iron called the slade is bolted to the bottom of the frame, and this, running along the sole of the furrow, acts as a base to the whole implement.

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  • They consist of a so-called "frond" - a flattened green more or less oval structure which emits branches similar to itself from lateral pockets at or near the base.

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  • The Oceanic series is generally overlaid directly, and unconformably, by coral limestones; but at Bissex Hill, at the base of the coral limestones, and resting unconformably upon the Oceanic series, there is a Globigerina marl.

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  • In the male, moreover, the pincers are caliper-like and toothed at the base, whereas in the female they are untoothed and only lightly curved at the tip. These differences suggest that the pincers aid in the pairing of the sexes.

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  • Shamshan, 1700 ft., at the base of which Aden itself is built.

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  • Kuwet was not formally placed under British protection, but it was officially announced by the government on the 5th of May 1903 " that the establishment of a naval base or fortified port in the Persian Gulf by any other power would be regarded as a very grave menace to British interests which would certainly be resisted with all the means at its disposal."

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  • It is situated on the right bank of the Danube, at the base of the Wienerwald, and at the beginning of the great plain which separates the Alps from the Carpathians.

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  • It is a monacid base; the hydrochloride, C 20 H 17 N0 4 HC1, is insoluble in cold alcohol, ether and chloroform, and soluble in 500 parts of water; the acid sulphate, C 20 H 17 N0 4 H 2 SO 4, dissolves in about loo parts of water.

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  • Though the walls at the base are 13 ft.

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  • The height of the tower is 179 ft., but the ascent is easy by a stair in the wall, and the visitor hardly perceives the inclination till he reaches the top and from the lower edge of the gallery looks "down" along the shaft receding to its base.

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  • The coast, extending from the base of the Western or Maritime Cordillera to the Pacific Ocean, consists of a sandy desert crossed at intervals by rivers flowing through narrow, fertile valleys.

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  • Farther north the Misti volcano rises over the city of Arequipa in a perfect cone to a height of over 20,013 ft., and near its base are the hot sulphur and iron springs of Yura.

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  • The third division of Peru is the region of the tropical forests, at the base of the Andes, and within the basin of the Amazon.

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  • In this plant the aeration is conducted by blowing in air at the base of the condenser.

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  • The ordinary hydrated variety forms quadratic crystals and behaves as a strong base.

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  • Hence, if a prism is placed in front of the eye with its base towards the nose, a ray of light falling upon it will be bent inwards, and seem to come from a point farther out from the axis of vision.

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  • Conversely, if the base of the prism is turned towards the temple, the ray of light will seem to come from a point nearer the axis, and will induce the eye to turn inwards, to converge towards its fellow.

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  • The cavities of the hollow tentacles open into a circular canal which surrounds the oesophagus at the base of the lophophore.

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  • The fur is short, dense and rather soft to the touch, and composed of an extremely fine and close under-fur, and of longer hairs which project beyond this, each of which is very slender at the base, and expanded, flattened and glossy towards the free end.

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  • On the hind foot the nails are long, curved and pointed, and the web extends only to their base.

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  • This spur, which attains the length of nearly an inch, is traversed by a minute canal, terminating in a fine longitudinal slit near the point, and connected at its base with the duct of a large gland situated at the back part of the thigh.

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  • Making Calcutta the base of his operations, he at once identified himself with a policy which had far-reaching results.

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  • At the beginning of the Christian era, and for many previous centuries, no eruption had been known to take place from the mountain, and the volcanic nature of the locality was perhaps not even suspected by the inhabitants who planted their vineyards along its fertile slopes, and built their numerous villages and towns around its base.

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

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  • In all tsetse-flies the proboscis in the living insect is entirely concealed by the palpi, which are grooved in their inner sides and form a closely fitting sheath for the piercing organ; the base of the proboscis is expanded beneath into a large onion-shaped bulb, which is filled with muscles.

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  • Society is to be reorganized on the base of knowledge.

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  • The mind will pursue knowledge without the wasteful jar and friction of conflicting methods and mutually hostile conceptions; education will be regenerated; and society will reorganize itself on the only possible solid base - a homogeneous philosophy.

    0
    0
  • In the year 1776, General Howe sent a detachment of his army under General Henry Clinton to seize Newport as a base of operations for reducing New England, and the city was occupied by the British on the 8th of December 1776.

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  • At the base is a thermal spring, where baths have existed since the 7th century.

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  • A triple-peaked volcano in the solfatara stage, extinct at the summit, but displaying considerable activity at its base in the form of numerous fumaroles and boiling sulilhur springs.

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  • Two of the five compartments into which it is divided by walls of deeply striated volcanic ash are constantly emitting steam, while a new vent displaying great activity has been opened at the base of the cone on the south side.

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  • In the surface of the metal the workman cuts grooves wider at the base than at the top, and then hammers into them gold or silver wire.

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  • The difference between this process and ordinary inlaying is that for sumi-zogan the design to be inlaid is fully chiselled out of an independent block of metal with sides sloping so as to be broader at the base than at the top. The object which is to receive the decoration is then channelled in dimensions corresponding to those of the design block, and the latter having been fixed in the channels, the surface is ground and polished until an intimate union is obtained between the inlaid design and the metal forming its field.

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  • Tc such a depth of debasement had the ceramic art fallen in Owari, that before the happy renaissance of the past ten years, Nagoya discredited itself by employing porcelain as a base for cloisonn enamelling.

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  • The base, usually of copper, was as thin as cardboard; the cloisons, exceedingly fine and delicate, were laid on with care and accuracy; the colors were even, and the designs showed artistic judgment.

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  • The artists great difficulty is to hide the metal base completely.

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  • But to spread and fix the enamel so that neither at the rim nor in the interior shall there be any break of continuity, or any indication that the base is copper, not porcelain, demands quite exceptional skill.

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  • In other words, a suitable design is chiselled in the metal base so as to be visible through Translucid the diaphanous enamel.

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  • A gold base deeply chiselled in wave-diaper and overrun with a paste of aubergine purple is the most pleasing.

    0
    0
  • A still higher achievement is to apply to the chiselled base designs executed in colored enamels, finally covering the whole with translucid paste.

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    0
  • In the male flowers, which are numerous, the stamens are sixteen in number and arranged in pairs; the female flowers are solitary, with traces of stamens, and a smooth ovary with one ovule in each of the eight cells - the ovary is surmounted by four styles, which are hairy at the base.

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  • The fruit-stalk is very short, bearing a subglobose fruit an inch or rather more in diameter, of an orange-yellow colour, and with a sweetish astringent pulp. It is surrounded at the base by the persistent calyxlobes, which increase in size as the fruit ripens.

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  • The highly finished monoliths are all representations of a many-storeyed castle, with an altar at the base of each.

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  • Baker City lies in the valley of Powder river, at the base of the Blue Mountains, and has an elevation of about 3440 ft.

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  • But towards its southern base, resting on the sea, the country sinks into a series of great swamps, intercepted by a network of innumerable channels.

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    0
  • Characterized by possessing only a few teeth, on the posterior part of the maxillaries, on the palatines and Coronelline Nymphophidium, the same effect is reached by two prominences at the base of the skull.

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  • The poison-fangs are "solenoglyphous," perforated, having a wide hole on the anterior side at the base, in connexion with the duct of the large, paired, poison-glands, the presence of which adds considerably to the characteristic broadness of the head.

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  • If now we cut the freezing-point surface by planes parallel to the base ABC we get curves giving us all the alloys whose freezing-point is the same; these isothermals can be projected on to the plane of the triangle and are seen as dotted lines in fig.

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    0
  • Born of a family of priest-physicians, and inheriting all its traditions and prejudices, Hippocrates was the first to cast superstition aside, and to base the practice of medicine on the principles of inductive philosophy.

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  • In January 1865 Sherman marched northwards again, once more abandoning his base, towards Petersburg, where Grant and Lee were waging a war of giants.

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  • Its base was in Venetia, and its point was advanced to the Tiber.

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  • The second process depends upon the fact that, if chlorine be led into the molten alloy, the base metals and the silver are converted into chlorides.

    0
    0
  • It is especially suitable to gold containing little silver and base metals - a character of Australian gold - but it yields to the sulphuric acid and electrolytic methods in point of economy.

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    0
  • But Kunze thinks that it was not used as a base of operations against Eutyches because there is some evidence that Monophysites were willing to accept it.

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    0
  • The events preceding the peace of Utrecht, which he regarded as preparing the way for a base desertion of our allies, greatly troubled the last months of Shaftesbury's life.

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  • A base on which stood a statue of Herodes' wife, Regilla, was found close to the facade, inscribed with fulsome praise, stating that the statue was "set up by order of the Sisyphaean Senate at the outpouring of the streams."

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  • At their base they are provided with stipules, which are also modified to form the scales investing the winter buds.

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  • When ripe the two carpels separate in the form of two valves and liberate a large number of seeds, each provided at the base with a tuft of silky hairs, and containing a straight embryo without any investing albumen.

    0
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  • The tuft of hairs at the base facilitates rapid dispersion of the seed, early germination of which is rendered desirable owing to its tenuity.

    0
    0
  • The battle in 1408, which was fought along the base of the cliffs here between the Savages of the Ards and the Irish, is described in Sir Samuel Ferguson's "Hibernian Nights Entertainment."

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  • The geological formations thus exposed show that the plateaus are composed of a base of eruptive material, overlaid by enormous deposits of reddish sandstones, conglomerates and quartzites, exposed in parts to a depth of 2000 feet.

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  • In one group, represented by Cereus, they consist of a tube, more or less elongated, on the outer surface of which, towards the base, are developed small and at first inconspicuous scales, which gradually 0000 FIG.

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    0
  • At the base of the tube, in both groups, the ovary becomes developed into a fleshy (often edible) fruit, that produced by the Opuntia being known as the prickly pear or Indian fig.

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    0
  • The plants are nearly allied to Cereus, differing chiefly in the floriferous portion developing these longer and more attenuated hair-like spines, which surround the base of the flowers and form a dense woolly head or cephalium.

    0
    0
  • They differ from all the forms already noticed in being shrubby and epiphytal in habit, and in having the branches compressed and dilated so as to resemble thick fleshy leaves, with a strong median axis and rounded woody base.

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    0
  • The fortifications consist of the upper fortress, on a lofty serpentine rock rising abruptly from the plain on three sides, and of the lower fortress at the northern base of the rock.

    0
    0
  • Sharp, however, the hypopharynx is present in all Hymenoptera as a distinct structure at the base of the " tongue," which must be regarded as representing the fused laciniae of the second maxillae.

    0
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  • But the most natural division is obtained by the separation of the saw-flies as a primitive sub-order, characterized by the imperfect union of the first abdominal segment with the thorax, and by the broad base of the abdomen, so that there is no median constriction or " waist," and by the presence of thoracic legs - usually also of abdominal pro-legs - in the larva.

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  • This section includes a number of families characterized by the backward extension of the prothorax to the tegulae and distinguished from the ants by the absence of " nodes " at the base of the abdomen.

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  • Cradock preferred to fight and take the chance of inflicting injury on the German squadron, which was far from any base of refitment and repair.

    0
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  • In the adult there is a pair of such glands opening ventrally on the hindmost thoracic segment, or at the base of the abdomen; but in the young insect the glands are situated dorsally and open to the exterior on a variable number of the abdominal terga.

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  • It contains incomparable studies of the Florentine housewife and her husband, a grave business-like citizen, who falls into the senile folly of a base intrigue.

    0
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  • But the two substances were generally confounded as "fixed alkali" (carbonate of ammonia being "volatile alkali"), till Duhamel du Monceau in 1736 established the fact that common salt and the ashes of seaplants contain the same base as is found in natural deposits of soda salts ("mineral alkali"), and that this body is different from the "vegetable alkali" obtained by incinerating land plants or wood (pot-ashes).

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  • At the base of this account lies the Babylonian myth' of the birth of the sun-god Marduk, his escape from the dragon who knows him to be his destined destroyer, and the persecution of Marduk's mother by the dragon.

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  • The town, with wide streets and picturesque promenades, is finely situated on a promontory, the base of which is washed on the south by the Cousin, on the east and west by small streams. Its chief building, the church of St Lazare, dates from the 12th century.

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  • Billwiller introduced the idea of sucking air into the flame at or just below the burner tip, and at this juncture the Naphey or Dolan burner was introduced in America, the principle employed being to use two small and widely separated jets instead of the two openings of the union jet burner, and to make each a minute bunsen, the acetylene dragging in from the base of the nipple enough air to surround and protect it while burning from contact with the steatite.

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  • Apparatus is added to some dynamometers by means of which a curve showing the variations of P on a distance base is drawn automatically, the area of the diagram representing the work done; with others, integrating apparatus is combined, from which the work done during a given interval may be read off directly.

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  • It is to be noticed that each number is the sum of the numbers immediately 35 above and to the left of it; and 35 that the numbers along a line, termed a base, which cuts off an equal number of units along the top row and column are the co efficients in the binomial expansion of (I+x) r - 1, where r represents the number of units cut off.

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  • The first or typical palm-squirrel, Funambulus palmarum, inhabits Madras, has but three light stripes on the back, and shows a rufous band on the under-side of the base of the tail.

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  • It forms the base for all punitive expeditions to the Tochi Valley and Waziri frontier.

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  • The base of the abomasum is turned to the omasum.

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  • In 1871 the Danish parliament (Riksdag) passed a law defining the political position of Iceland in the Danish monarchy, which, though never recognized as valid by the Icelanders, became de facto the base of the political relations of Iceland and Denmark.

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  • The other comprises the Myxosporidia, Actinomyxidia, Sarcosporidia and Haplosporidia, the parasites included in the last named order being of comparatively simple structure, and probably near the base of this section.

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  • The bishop, who attended the Conqueror's funeral, joined in the great rising against William Rufus next year (1088), making Bristol, with which (as Domesday shows) he was closely connected and where he had built a strong castle, his base of operations.

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  • For the water supply the Aztecs used the main causeway through their city as a dam to separate the fresh water from the hills from the brackish water of Texcoco, and obtained drinking water from a spring at the base of the hill of Chapultepec. The Spaniards added three other springs to the supply and constructed two long aqueducts to bring it into the city.

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  • The air, the waters and the land were their base of supplies, and cannibalism, it is admitted, was widespread.

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  • The pattern is that of a true sight, that is to say, the base plate is capable of movement about two axes, one parallel to and the other at right angles to the axis of the gun, and has cross spirit-levels and a graduated elevating drum and independent deflection scale, so that compensation for level of wheels can be given and quadrant elevation.

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  • If of the first class, it should be situated at the base of operations and supply, secure from attack, not too near a frontier, and placed so as to draw in readily the resources of the country.

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  • The story goes that a Mahratta chief at length succeeded in scaling the precipice and in carrying off the horse, and although the thief was captured before reaching the base of the hill, the spell was broken and the fort, when next attacked, fell.

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  • Pits are present in the forehead of the skull, and the horns are ringed for part of their length, with a compressed base; their form being often lyrate,.

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  • Almost the only characters they possess in common are the short and spike-like horns of the bucks, which are ringed at the base, with smooth tips, and the large size of the face-gland, which opens by a circular aperture.

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  • The horns are generally rather small, upright, ringed at the base,.

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  • His information showed that Wellington held the western half of Belgium from the Brussels-Charleroi road to the Scheldt, that his base of operations was Ostend, and that his headquarters were at Brussels.

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  • They turned out to be stragglers; but their capture for a time helped to confirm the idea, prevalent in the French army, that Blucher was drawing off towards his base.

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  • In the upper or northern tarai, along the base of the hills, the Mechs form the principal ethnical feature.

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  • That the area of a parallelogram is equal to the area of a rectangle on the same base and between the same parallels, or that the volume of a cone is one-third that of a cylinder on the same base and of the same height, may be established by a proof which is admitted to be rigorous, or be accepted in good faith without proof, and yet fail to be a matter of conviction, even though there may be a clear conception of the relative lengths of the diagonal and the side of a square or of the relative contents of two vessels of different shapes.

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  • This is the process adopted, for instance, for comparison of the area of a parallelogram with that of a rectangle on the same base and of the same height.

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  • It would be possible to regard this form of the figure as the general one; the figure considered in (i) would then represent the special case in which the two end-pieces of the broken line are at right angles to the base.

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  • Then the figure is (usually) the sum of two trapezoids F on base AE, and its area can be calculated as in § 24.

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  • Take any base X'X, and draw lines at right angles to this base through all the angular points of the figure.

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  • Then, if we take ordinates Kb, Lg, Mc, Nd, Pf, equal to B'B, GG', C'C, D'D, FF', the figure abgcdfe will be the equivalent trapezoid, and any ordinate drawn from the base to the a LM N P e X top of this trapezoid will be equal to the portion of this ordinate (produced) which falls within the original figure.

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  • This formula holds for the general case in which the base is a trapezium; the wedge being thus formed by cutting a triangular prism by any two planes.

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  • Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.

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  • This would involve p and q; but, for our purposes, the data are the sides pa+q and pb+q and the base b - a, and the expression of the integral in terms of these data would require certain eliminations.

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  • Either or both of the bounding ordinates may be zero; the top, in that case, meets the base at that extremity.

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  • The corresponding solid figure, in its most general form, is such as would be constructed to represent the relation of a magnitude E to two magnitudes F and G of which it is a function; it would stand on a plane base, and be comprised within a cylindrical boundary whose cross-section might be of any shape.

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  • We are not concerned with figures of this general kind, but only with cases in which the base is a rectangle.

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  • A briquette may therefore be defined as a solid figure bounded by a pair of parallel planes, another pair of parallel planes at right angles to these, a base at right angles to these four planes (and therefore rectangular), and a top which is a surface of any form, but such that every ordinate from the base cuts it in one point and one point only.

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

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  • The " mid-ordinate " is the ordinate from the middle point of the base, i.e.

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  • In the case of the briquette the position of the foot of the ordinate u is expressed by co-ordinates x, y, referred to a pair of axes parallel to a pair of sides of the base of the briquette.

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  • If the lengths of these sides are H and K, the coordinates of the angles of the base - i.e.

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  • If this is done for every possible value of x, there will be a series of ordinates tracing out a trapezette with base along OX.

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  • The top is then a parabola whose axis is at right angles to the base; and the area can therefore (§ 34) be expressed in terms of the two bounding ordinates and the midordinate.

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  • Thus we find from (i) that Simpson's second formula, for the case where the top is a parabola (with axis, as before, at right angles to the base) and there are three strips of breadth h, may be replaced by area = 8h(3u i + 2U 1 + 3us).

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  • In the case of a pyramid, of height h, the area of the section by a plane parallel to the base and at distance x from the vertex is clearly x 2 /h 2 X area of base.

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  • To extend these methods to a briquette, where the ordinate u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the ordinate of a trapezette.

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  • The most simple case is that in which the trapezette tapers out in such a way that the curve forming its top has very close contact, at its extremities, with the base; in other words, the differential coefficients u', u", u"',.

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  • The formulae of § 82 can be extended to the case of a briquette whose top has close contact with the base all along its boundary; the data being the volumes of the minor briquettes formed by the planes x =x0, x = x i,

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  • These lines isolate certain swellings or monticuli, the largest of which is (I) the ball of the thumb, called the mountain of Venus; (2) that at the base of the index finger is the mountain of Jupiter; (3) at the root of the middle finger is the mountain of Saturn, while those at the bases of ring and little finger are respectively the mountains of the (4) Sun and (5) of Mercury.

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  • They may be obtained by heating a monometallic orthophosphate of a fixed base, or a dimetallic orthophosphate of one fixed and one volatile base, e.g.

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  • Bands of black nodules, highly phosphatic, are found at the top of the Bala limestone in North Wales; beds of concretions occur in the Jurassic series; and important deposits are known in the Cretaceous strata, especially in the Lower Greensand and at the base of the Gault.

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  • The Cambridge Greensand, rich in phosphatic nodules, occurs at the base of the Chalk Marl.

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  • At the base of the Red Crag in East Anglia, and occasionally at the base of the other Pliocene Crags, there is a " nodule bed," consisting of phosphatic nodules, with rolled teeth and bones, which were formerly worked as " coprolites " for the preparation of artificial manure.

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  • Since this plateau region is a northward extension of the Alleghany plateau, which skirts the western base of the Appalachian mountains, it rises as the mountains are approached.

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  • It was a settled point of British military policy throughout the war to hold New York City, and from it, as a base, to establish a line of fortified posts along the Hudson by means of which communication might be maintained with another base on Lake Champlain.

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  • Thus in the air-pump experiment, before exhaustion it travels through the glass of the receiver and the base plate.

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  • It consists of a cylindrical chest of brass, the base of which is pierced at its centre with an opening in which is fixed a brass tube projecting outwards, and Siren of intended for supplying the cavity of the cylinder with Cagniard de compressed air or other gas, or even liquid.

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  • The most important example of this type is the tuning-fork, which may be regarded as consisting of two parallel bars clamped together at the base.

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  • When the velocity of the jet is gradually increased there is a certain range of velocity for which the jet is unstable, so that any deviation from the straight rush-out tends to increase as the jet moves up. If then the jet is just on the point of instability, and is subjected as its base to alternations of motion, the sinuosities impressed on the jet become larger and larger as it flows out, and the flame is as it were folded on itself.

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  • Dalny, the commercial harbour, was seized without fighting, and a month was spent in preparing a base Nogi's there.

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  • A strong machicolated and turreted wall surrounds the rock, running along its base on the south, ascending halfway up the cliff on the north, on which side it stands close to the abbey wall, and again descending on the west.

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  • Round the base is a flagged pathway surrounded by a stone railing and entered at the four points of the compass by gateways some 18 ft.

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  • The Contrat social, as its title implies, endeavours to base all government on the consent, direct or implied, of the governed, and indulges in much ingenious argument to get rid of the practical inconveniences of such a suggestion.

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  • The Thanet beds resting on chalk form a narrow outcrop rising into cliffs at Pegwell Bay and Reculver, and consist (1) of a constant base bed of clayey greenish sand, seldom more than 5 ft.

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  • This is succeeded by an outcrop of the Lower Greensand - including the Folkestone, Sandgate and Hythe beds with the thin Atherfield Clay at the base - which extends across the country from west to east with a breadth of from 2 to 7 m., and rises into the picturesque elevations of the Ragstone hills.

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  • It has the properties of a monacid base and contains the methylamino group, NCH3.

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  • Tt is a monacid base which is readily soluble in solutions of the cans' is alkalis.

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  • General Stuart's victory at Maida (July 3) shook Joseph's throne to its base; but the surrender of Gaeta soon enabled Massena to march southwards and subdue Calabria.

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  • Crete now became the base of operations against the Greeks.

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  • But the guerilla tactics of the wily klepht were powerless against Ibrahim, who marched northward, and, avoiding Nauplia for the present, seized Tripolitsa, and made this the base from which his columns marched to devastate the country far and wide.

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  • The Senonian series is represented by the White Limestone, a hardened chalk with flints, which is often glauconitic and conglomeratic at the base.

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  • An event happened which gave him a base of operations, and enabled him to mask his schemes against the emperor.

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  • From 1792 to 1799 he was occupied with the measurement of the arc of the meridian extending from Dunkirk to Barcelona, and published a detailed account of the operations in Base du systeme metrique (3 vols., 1806, 1807, 1810), for which he was awarded in 181 o the decennial prize of the Institute.

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  • They have from very early times been resorted to as a means of staining the hair of a dark colour, and they are the base of the tattooing dye of the Somali women.3 The gall-making Hymenoptera include, besides the Cynipidae proper, certain species of the genus Eurytoma (Isosoma, Walsh) and family Chalcididae, 'e.g.'

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  • There are three original documents at its base.

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  • Judged by the florists' rules, they are either good or bad in form, and pure or stained (white or yellow) at the base; the badly formed and stained flowers are thrown away, while the good and pure are grown on, these being known as "breeder" tulips.

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  • The least stain at the base of the flower, technically called the "bottom," would render a tulip comparatively valueless.

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  • The profits of trade had value in his eyes only as means to these ends, and settlements were important chiefly as a base of discovery.

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  • At the base of the monument are muskets used by United States soldiers in that war and guns captured at Cerro Gordo.

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  • The material is sometimes won by the aid of channelling machines which make a series of cuts at right angles to each other in the face of the rock; a block is then broken off at its base by wedges forced into the cuts, and its removal permits access to other blocks.

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  • The part of Maryland within the Piedmont Plateau extends west from the Fall Line to the base of Catoctin Mountain, or the west border of Frederick county, and has an area of about 2500 sq.

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  • When that state was reduced to order, the Potomac became the front, and, later, the base, of the Northern armies.

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  • As against the civilian enemy the navy strangled commerce; its military preponderance nipped in the bud every successive attempt of the Confederates to create a fleet (for each new vessel as it emerged from the estuary or harbour in which it had been built, was destroyed or driven back), while at any given point a secure base was available for the far-ranging operations of the Union armies.

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  • Two days later McClellan's advanced troops fought a sharp combat at Williamsburg and the Army of the Potomac rendezvoused on the Chickahominy with its base at White House on the Pamunkey (May 7).

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  • Lee soon cut the communication with White House, but McClellan changed his base and retreated towards Harrison's Landing on the James river.

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  • At Bruinsburg, beyond Pemberton's reach, a landing was made on the eastern bank and, without any base of supplies or line of retreat, Grant embarked upon a campaign which made him in the end master of the prize.

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  • Long forward strides of the Napoleonic type were rarely attempted; "changes of base" were indeed made across country, and over considerable distances, as by Sherman in 1864, but ordinarily either the base and the objective were connected by rail or water, or else every forward step was, after the manner of Marlborough's time, organized as a separate campaign.

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  • From time immemorial, indeed, this coast has had an evil reputation among mariners, quite apart from the pirates who for centuries made it the base of their depredations.

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  • The form is that of a truncated cone, placed on a cylindrical base, 196 ft.

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  • The columns encircling the cylindrical portion are stunted and much broader at the base than the top; the capitals are Doric. Many of the columns, 60 in number, have been much damaged.

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  • Respiration is conducted by the general surface, by the branchial lamina (external branch) of the feet, and the vesicular appendage (when present) at the base of this branch.

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  • The Gymnomera, with a carapace too small to cover the feet, which are all prehensile, are divided also into two tribes, the Onychopoda, in which the four pairs of feet have a toothed maxillary process at the base, and the Haplopoda, in which there are six pairs of feet, without such a process.

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  • Considering the imprisonment of the ostracod body within the valves, it is more surprising that the Asteropidae and Cypridinidae should have a pair of compound and sometimes large eyes, in addition to the e median organ at the base of I the " frontal tentacle," than 6 that other members of the group should be limited to P that median organ of sight, or have no eyes at all.

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  • The question, therefore, is whether we ought not to base our text on the versions and ecclesiastical quotations rather than on the extant Greek MSS.

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  • Norman or transitional work appears in the base of both towers, of which the southern also shows Early English and Decorated work, while the northern is chiefly Perpendicular.

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  • McClellandescribed this flight to the James as a change of base, but his resolve to abandon the attitude of an invader was formed when General Lee in the middle of June had caused Stuart's cavalry to reconnoitre the flanks and rear of McClellan's army, and had summoned corps from the Shenandoah Valley.

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  • The fixed coil is called the current coil, and the movable coil is called the potential coil, and each of these coils has its ends brought to separate terminals on the base of the instrument.

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  • The Rio Grande de Tarcoles rises close to the Ochomogo Pass and the sources of the Reventazon, at the base of Irazu; and the headwaters of these two streams indicate precisely the depression in the central plateau which severs the northern from the southern mountains.

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  • A secondary standard measure for dry goods is the bushel of 1824, containing 8 imperial gallons, represented by a hollow bronze cylinder having a plane base, its internal diameter bring double its depth.

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  • Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot.

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  • In Persia (24) the series on the same base was --

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  • It was also a base of operations in the exploration and conquest of the interior.

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  • It is a secondary base, but its constitution is uncertain.

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  • For the purpose of thus simplifying the operations of arithmetic, the base is taken to be Io, and use is made of tables of logarithms in which the values of x, the logarithm, corresponding to values of m, the number, are tabulated.

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  • Thus in arithmetical calculations if the base is not expressed it is understood to be io, so that log m denotes log n m; but in analytical formulae it is understood to be e.

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  • The logarithms to base io of the first twelve numbers to 7 places of decimals are log 1 =0.0000000 log 5 log 2 = 0.3010300 log 6 log 3 =0.477 121 3 log 7 log 4 =0.6020600 log 8 The meaning of these results is that The integral part of a logarithm is called the index or characteristic, and the fractional part the mantissa.

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  • When the base is to, the logarithms of all numbers in which the digits are the same, no matter where the decimal point may be, have the same mantissa; thus, for example, log 2.5613 =0-4084604, log 25.613 =1.4084604, log 2561300 = 6.4084604, &c.

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  • The fact that when the base is io the mantissa of the logarithm is independent of the position of the decimal point in the number affords the chief reason for the choice of io as base.

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  • The explanation of this property of the base io is evident, for a change in the position of the decimal points amounts to multiplication or division by some power of 10, and this corresponds to the addition or subtraction of some integer in the case of the logarithm, the mantissa therefore remaining intact.

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  • In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.

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  • The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the modulus of the system whose base is b with respect to the system whose base is a.

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  • The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.

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  • Napier's logarithms are not the logarithms now termed Napierian or hyperbolic, that is to say, logarithms to the base e where e= 2.7182818 ...; the relation between N (a sine) and L its logarithm, as defined in the Canonis Descriptio, being N=10 7 e L/Ip7, so that (ignoring the factors re, the effect of which is to render sines and logarithms integral to 7 figures), the base is C".

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  • If 1 denotes the logarithm to base e (that is, the so-called "Napierian " or hyperbolic logarithm) and L denotes, as above, " Napier's " logarithm, the connexion between 1 and L is expressed by L = r o 7 loge 10 7 - 10 7 / or e t = I 07e-L/Ia7 Napier's work (which will henceforth in this article be referred to as the Descriptio) immediately on its appearance in 1614 attracted the attention of perhaps the two most eminent English mathematicians then living - Edward Wright and Henry Briggs.

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  • It now remains to refer in more detail to the invention itself and to examine the claims of Napier and Briggs to the capital improvement involved in the change from Napier's original logarithms to logarithms to the base ro.

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  • Passing now to the invention of common or decimal logarithms, that is, to the transition from the logarithms originally invented by Napier to logarithms to the base io, the first allusion to a change of system occurs in the "Admonitio " on the last page of the Descriptio (1614), the concluding paragraph of which is " Verum si huius inventi usum eruditis gratum fore intellexero, dabo fortasse brevi (Deo aspirante) rationem ac methodum aut hunc canonem emendandi, aut emendatiorem de novo condendi, ut ita plurium Logistarum diligentia,limatior tandem et accuratior, quam unius opera fieri potuit, in lucem prodeat.

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  • Napier gives logarithms to base e ', Byrgius gives antilogarithms to base (I.coo')='a.

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  • In the same year (1620) Napier's Descriptio (1614) and Constructio (1619) were reprinted by Bartholomew Vincent at Lyons and issued together.5 Napier calculated no logarithms of numbers, and, as already stated, the logarithms invented by him were not to base e.

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  • The first logarithms to the base e were published by John Speidell in his New Logarithmes (London, 1619), which contains hYPerbolic log sines, tangents and secants for every minute of the quadrant to 5 places of decimals.

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  • Also, although logarithms have been spoken of as to the base e, &c., it is to be noticed that neither Napier nor Briggs, nor any of their successors till long afterwards, had any idea of connecting logarithms with exponents.

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  • Recent discoveries of vertebrates are of the same significance, the most primitive fishes being traced to the Ordovician or base of the Silurian, 2 which proves that we shall discover more 2 Professor Bashford Dean doubts the fish characters of these Ordovic Rocky Mountain forms. Frech admits their fish character but considers the rocks infaulted Devonic.

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  • He forsook the base and rococo forms he found rooted in Germany, and, reverting to the best historic examples, fashioned a purer Renaissance.

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  • The stomach may be situated in the disk, or may be drawn out into the base of the manubrium, so that the disk is occupied only by the radial canals.

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  • They were pyramids on a square or oblong base, rising in successive terraces to a small summit-platform.

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  • The triangle is here an irregular one, consisting of a narrow base to which one end of the string was fixed, while the second side, forming a slightly obtuse angle with the base, consisted of a wide and slightly curved sound-board pierced with holes through which the other end of the strings passed, being either knotted or wound round pegs.

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  • The Wycliffite authorship of the Commentaries on the Gospels, on which the learned editors base their argument, is, however, unsupported by any evidence beyond the fact that the writer of the Prologue to Matthew urges in strong language " the propriety of translating Scripture for the use of the laity."

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  • Cavite has long been the principal naval base of the Philippine Islands, and one of the four Spanish penitentiaries in the Islands was here.

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  • Some such document, we know, must lie at the base of our Synoptic Gospels, and it is quite possible that it may have been known to and used by Papias.

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  • As much more than one-half of the population and resources of the colonists lay north of Chesapeake Bay - New England alone having an estimated population of over 700,000 persons - it was only a question as to what point in this area should be made the future base of operations.

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  • There he found British v detachments, 2000 strong, composed of troops whom Clinton had sent down separately under Generals Benedict Arnold and William Phillips to establish a base in the Chesapeake, as a diversion in favour of the operations of Cornwallis in the Carolinas.

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  • From the very beginning of his reign Eric's morbid fear of the upper classes drove him to give his absolute confidence to a man of base origin and bad character, though, it must be admitted, of superior ability.

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  • The horns are rather flat at the base and not unfrequently corrugated; they rise vertically from the head, curving to the rear, and are more or less laterally inclined.

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  • The horns are large in the male, and of moderate size in the female, flat at the base and inclining outwards.

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  • The horns are black, slightly twisted and very short, flat at the base, pointed at the tips, and recumbent on the head.

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  • Prospect, at the base of which there is a vein of pyrrhotite, with small quantities of nickel and copper.

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  • Round the base of it were probably disposed groups of statuary.

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  • Both bear their round or ovoid male catkins at the ends of the slender terminal branchlets; the ovoid cones, either terminal or on short lateral twigs, have thick woody scales dilated at the extremity, with a broad disk depressed in the centre and usually furnished with a short spine; at the base of the scales are from three to seven ovules, which become reversed or partially so by compression, ripening into small angular seed with a narrow wing-like expansion.

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  • The bark, of nearly the same tint as that of the redwood, is extremely thick and is channelled towards the base with vertical furrows; at the root the ridges often stand out in buttress-like projections.

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  • The peculiar nature of the action between iodine and chlorine in aqueous solution has led to the suggestion that the product is a base, i.e.

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  • The salts, known as the iodates, can be prepared by the action of the acid on a base, or sometimes by the oxidation of iodine in the presence of a base.

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  • The city occupies an irregular tract of land gradually descending from the base of Mt.

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  • The direction of the great volcanic cones, which rise in an irregular line above it, is not identical with the main axis of the Sierra itself, except near the Mexican frontier, but has a more southerly trend, especially towards Salvador; here the base of many of the igneous peaks rests among the southern foothills of the range.

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  • It is a tertiary base, and has also the properties of an acid and an alcohol.

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  • This subdivision is already necessary in Maryland, where the mountain belt is represented by the Blue Ridge, which is rather a narrow upland belt than a ridge proper where the Potomac cuts across it; while the piedmont belt, relieved by occasional monadnocks stretches from the eastern base of the Blue Ridge to the coastal plain, into which it merges.

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  • The Great Plains.A broad stretch of country underlaid by nearly horizontal strata extends westward from the 97th meridian to the base of the Rocky Mountains, a distance of from 300 to 500 in., and northward from the Mexican, boundary far into Canada.

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  • The present altitude of the plains near the mountain base is 4000 ft.

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  • Along the eastern side of the Front Range in Colorado most of the upturned stratified formations have been so well worn down that, except for a few low piedmont ridges, their even surface may now be included with that of the plains, and the crystalline core of the range is exposed almost to the mountain base.

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  • In this central region, however, it is only by way of exception that the cirques were so far enlarged by retrogressive glacial erosion as to sharpen the preglacial dome-like summits into acute peaks; and in no case did glacial action here extend down to the plains at the eastern base of the mountains; but the widened, trough-like glaciated valleys frequently descend to the level of the elevated intermont basins, where moraines were deployed forward on the basin floor.

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  • Another consequence of revived erosion is seen in the occurrence of great landslides, where the removal of weak (Permian) clays has sapped the face of the Vermilion Cliffs (Triassic sandstone), so that huge slices of the cliff face have slid down and forward a mile or two, all shattered into a confused tumult of forms for a score or more of miles along the cliff base.

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  • In the new altitude of the mountain mass, its steep eastern face has been deeply carved with short canyons; and on the western slope an excellent beginning of dissection has been made in the erosion of many narrow valleys, whose greatest depth lies between their headwaters which still flow on the highland surface, and their mouths at the low western base of the range.

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  • Several of the ranges ascend abruptly from the sea; their base is cut back in high cliffs; the Sierra Santa Lucia, south of San Francisco, is a range of this kind; its seaward slope is almost uninhabitable.

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  • In all but a few places where their relations are known, the Proterozoic rocks are unconformable beneath the Palaeozoic Where conformity exists the separation is made on the basis of fossils, it having been agreed that the oldest rocks carrying the Olenellus fauna are to be regarded as the base of the Cambrian system.

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  • The site of these mountains had been, for the most part, an area of deposition throughout the Palaeozoic era, and the body of sediments which had gathered here at the western base of Appalachia, by the close of the Pennsylvanian period, was very great.

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  • The Dakota formation is largely sandstone, which gives rise to hogbacks where it has been tilted, indurated and exposed to erosion along the eastern base of the Rocky Mountains.

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  • The Fort Union stage, when the deposition was widespread about the eastern base of the northern part of the Rocky Mountains, and at some points in Colorado (Telluride formation) and New Mexico (Puerco beds), where volcanic ejecta entered largely into the formation.

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  • The Arid Transition life-zone comprises the western part of the Dakotas, north-eastern Montana, and irregular areas in Washington, Oregon, Idaho, Wyoming, California, Nevada, Utah, Colorado, Arizona, New Mexico and western Texas, covering for the most part the eastern base of the Cascade and Sierra Nevada Mountains and the higher parts of the Great Basin and the plateaus.

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  • The initial settlement of the Pacific coast following the discovery of gold in California in 1848, and of the eastern base of the Rocky Mountains after the discovery of gold in 2859, ifiustrates the same factor.

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  • The grade of precious ores hafidled has generally and greatly decreased in recent yearsaccording to the census data of 1880 and 1902, disregarding all base metallic contentsfrom an average commerical value of $29.07 to one of $8.29; nevertheless the product of gold and silver has greatly increased.

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  • Since 1825 the total product of lead refined from domestic ores and domestic base bullion was, up to the close of 1908, 7,091,548 short tons.

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  • Considerable quantities of foreign ores and base bullion are also refined in the United States.

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  • The base court nearest to the outer wall contained the buildings belonging to the functions of the body as agriculturists and employers of labour.

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  • This inner gate conducted into the base court (T), round which were placed the barns, stables, cow-sheds, &c. On the eastern side stood the dormitory of the lay brothers, fratres conversi (G), detached from the cloister, with cellars and storehouses below.

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  • It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

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  • Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (Archimedes, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary Euclidean construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.

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  • In 1873 Charles Hermite proved that the base of the Napierian logarithms cannot be a root of a rational algebraical equation of any degree.3 To prove the same proposition regarding 7r is to prove that a Euclidean construction for circle-quadrature is impossible.

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  • When hardened in situ its shape is that of a right-angled, triangular prism showing five surfaces - superior, anterior, inferior, posterior and right lateral which represents the base of the prism.

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  • At the southern base of the hill stands the fine mansion of Trumbland House.

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  • A pair of pedal otocysts, and a pair of osphradia at the base of the gills, appear to be always present.

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  • Portion of the axis of the left ctenidium which is fused with the base of the foot, the two dotted lines indicating the origins of the two rows of gill-filaments.

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  • Rudimentary cephalic eyes occur in the Mytilidae and in Avicula at the base of the first filament of the inner gill, each consisting of a I pigmented epithelial fossa containing a cuticular lens.

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  • They are relatively shorter and broader insects than the Embiidae with large prothorax and long wings, which have a transverse line of weakness at the base and are usually shed after the nuptial flight.

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  • At the base of each wing projects a dorsal lobe - the jugumand the neuration is predominantly longitudinal, resembling so closely that of the lower Lepidoptera (q.v.) that a nearer relationship of the Trichoptera to that order than to any group of the old Linnean Neuroptera is certain.

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  • The upper half or body of the uterus is somewhat triangular with its base upward, and has an anterior surface which is moderately flat, and a posterior convex.

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  • The base of the triangle is upward, and at each lateral angle one of the Fallopian tubes opens.

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  • The prostate is partly a muscular and partly a glandular structure, situated just below the bladder and traversed by the urethra; it is of a somewhat conical form with the base upward in contact with the bladder.

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  • He treated his most respectable supporters with base ingratitude, reserved his favour for unscrupulous adventurers, and gave a free rein to the licence of his mercenaries.

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  • This having been effected, Gilgal became the base for a series of operations in which the united tribes took part.

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  • Near the base of the ctenidium is a patch of sensory epithelium innervated from the branchial nerve, forming a sense-organ called the osphradium, whose function is to test the water entering the branchial cavity.

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  • They may also be obtained by the molecular rearrangement of the diazoamines, when these are warmed with the parent base and its hydrochloride.

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  • Reinders (Ber., 1896, 29, p. 1369), who found that the reaction is monomolecular, and that the velocity constant of the reaction is proportional to the amount of the hydrochloride of the base present and also to the temperature, but is independent of the concentration of the diazoamine.

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  • In most species there are three circumvallate papillae at the base, and the apical portion is generally covered with small, thread-like papillae, some of which in the porcupines become greatly enlarged, forming toothed spines.

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  • To the east this gives way to the broad level plain of Marwat, which in favourable years presents a uniform expanse of rich cultivation extending from Lakki to the base of the Shekh Budin hills.

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  • Thus one of the most common spectra is that seen at the base of every candle and in every Bunsen burner.

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  • The old town of Gwalior, which is of considerable size, but irregularly built, and extremely dirty, lies at the eastern base of the rock.

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  • The area of the surface included between this curve and its base is found - the first known instance of a quadrature of a curved surface.

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  • It is frequently armed with spines, hooks or stylets, and is further complicated by the addition of a nutritive secretion (the prostate gland) which may open at its base or pass separately by a special duct to the exterior.

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  • The coronation of a woman was in the eyes of the Russian people a scandalous innovation, and the proposed coronation was doubly scandalous in view of the base and disreputable origin of Catherine herself.

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  • All the islands are of volcanic origin, and have been built up by the eruptive process from a base about 15,000 ft.

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  • Mauna Loa (" Great Mountain "), on the S., is by far the largest volcano in the world; from a base measuring at sea-level about 75 m.

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  • During the Sicilian campaigns of Athens Corcyra served as a base for supplies; after a third abortive rising of the oligarchs in 410 it practically withdrew from the war.

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  • In 31 B.C. it served Octavian (Augustus) as a base against Antony.

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  • From the base of London and Colchester three corps continued the conquest.

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  • The opposite or alternate leaves have a pair of small stipules at the base of the stalk and a palminerved blade.

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  • Such statements as that a body moves in a straight line, and that it has a certain velocity, have no meaning unless the base, relative to which the motion is to be reckoned, is defined.

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  • Accordingly, in the extension of Galileo's results for the purpose of a universal theory, the establishment of a suitable base of reference is the first step to be taken.

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  • Newton assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.

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  • He used the term "absolute motion" for motion relative to such a base.

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  • Many writers on the subject distinguish such a base as "fixed."

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  • The name "Newtonian base" will be used in this article.

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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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  • Suppose two small smooth spherical bodies which can be regarded as particles to be brought into collision, so that the velocity of each, relative to any base which is unaffected by the collision, is suddenly changed.

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  • The additions of velocity which the two bodies receive respectively, relative to such a base, are in opposite directions, and if the bodies are alike their magnitudes are equal.

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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 Newtonian base deserves some further consideration.

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  • In the treatment of the relative motions of a limited system, we may use a confessedly provisional base, though it may be necessary to introduce corrections, either exact or approximate, to take account either of the existence of bodies outside the system, or of the rotation of the base employed relative to a more correct one.

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  • The earth, which is commonly employed as a base for terrestrial motions, is not a very close approximation to being a Newtonian base.

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  • A more considerable defect is due to the earth having a diurnal rotation relative to a Newtonian base, and this is never wholly ignored.

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  • Take a base attached to the centre of the earth, but without this diurnal rotation.

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  • A small body hanging by a string, at rest relatively to the earth, moves relatively to this base uniformly in a circle; that is to say, with constant acceleration directed towards the earth's axis.

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  • Foucault's pendulum is another example of motion relative to the earth which exhibits the fact that the earth is not a Newtonian base.

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  • For the study of the relative motions of the solar system, a provisional base established for that system by itself, bodies outside it being disregarded,' is a very good one.

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  • No correction for any defect in it has been found necessary; moreover, no rotation of the base relative to the directions of the stars without proper motion has been detected.

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  • He then turned west, followed the base of the south Tsaidam range as far as the Naichi Gol, where he entered the southern mountainous region forming the northern borderland of Tibet.

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  • Her opposition to the reform of the Polish government was plainly due to a wish to preserve an excuse for further spoliation, but her conduct was less cruel and base than that of Prussia.

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  • It has an alkaline reaction, and is a tertiary monacid base.

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