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angle

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angle

angle Sentence Examples

  • From this angle, it's hard to tell you from the mules.

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  • It must be noticed, however, that the angle of maximum polarization would be about 76° instead of 90°.

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  • From that angle, she could see the place on the mountain.

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  • Brady muttered a curse, reached for his laser weapon, and fired at an angle at the ceiling.

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  • "You need more of an angle when you deflect," he told her.

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  • Now, madam, these triangles are equal; please note that the angle ABC...

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  • He must have thought it fruitless to pursue that angle so he moved on.

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  • If you angle your sword, the blow glances off.

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  • The angle between the rivers was now almost full.

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  • Next Spanish hides, with the tails still preserving their twist and the angle of elevation they had when the oxen that wore them were careering over the pampas of the Spanish Main--a type of all obstinacy, and evincing how almost hopeless and incurable are all constitutional vices.

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  • The planets were shown to have visible disks, and to be attended by satellites whose distance and position angle relative to the planet it was desirable to measure.

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  • The point of the angle was broken off.

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  • Above them, the headlights of the two vehicles grew more distant, finally hidden from view by their angle of descent.

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  • It doesn't take much ice to give you a bomber, a firm hold, provide you set your angle right.

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  • The 24-hour term is very variable both as regards its amplitude and its phase angle (and so [[Table Iv]].

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  • After the first several feet, the angle of the slope dropped more sharply and he was forced to move to his left to avoid falling.

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  • The end-plane of this cylinder receives the pressure of the micrometer screw, so that by turning the small drum-head the coincidence-reading of the movable web with the fixed web can be changed, and thus any given angle can be measured with different FIG.

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  • She was in a car with one of Talon's men, her crumpled body at an awkward angle jammed in the small area between the backseat and the driver's seat.

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  • The motives alike of geographical convenience and of the advantages to be gained by recognizing these movements of Roman subjects combined to urge a forward policy at Rome, and when the vigorous Vespasian had succeeded the fool-criminal Nero, a series of advances began which gradually closed up the acute angle, or at least rendered it obtuse.

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  • The angle through which the arm was moved, or, in the latter case, the angle between the two arms, was read off upon a finely graduated arc. With such means no very high accuracy was possible.

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  • I just wonder what his angle is.

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  • The slope dropped at a precarious angle, impossible to maneuver unsecured, only a few degrees from the perpendicular.

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  • This stream, the Murray, in the upper part of its course runs in a north-westerly direction, but afterwards turning southwards, almost at a right angle, expands into Lake Alexandrina on the south coast, about 60 m.

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  • She thought she knew every inch of her place, but she'd never examined it from this angle before.

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  • Kiera settled at an uncomfortable angle, the sandpapery red roofing snagging her polyester disco clothing and preventing her from sliding over the nearby edge of the three-story row house.

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  • At length the sun's rays have attained the right angle, and warm winds blow up mist and rain and melt the snowbanks, and the sun, dispersing the mist, smiles on a checkered landscape of russet and white smoking with incense, through which the traveller picks his way from islet to islet, cheered by the music of a thousand tinkling rills and rivulets whose veins are filled with the blood of winter which they are bearing off.

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  • In 1853 the Fort of the Twenty-four Hours was demolished, and in the angle specified by Haedo the skeleton of Geronimo was found.

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  • rainfall band circles across the continent through the middle of the Northern Territory, embraces the entire centre and south-west of Queensland, with the exception of the extreme south-western angle of the state, and includes the whole of the interior of New South Wales to a line about 200 m.

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  • The tenant of the air, it seemed related to the earth but by an egg hatched some time in the crevice of a crag;--or was its native nest made in the angle of a cloud, woven of the rainbow's trimmings and the sunset sky, and lined with some soft midsummer haze caught up from earth?

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  • The angle was too steep, though and the roots of the bush too shallow.

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  • From the northwest angle of Nova Scotia, viz., that angle which is formed by a line drawn due north from the source of St. Croix River to the highlands; along the said highlands which divide those rivers that empty themselves into the river St. Lawrence ...

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  • This angle, therefore, divided by the magnifying power of the telescope gives the real angular distance of the centres of a double star.

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  • Hardly had he passed an angle of the wood before a stout gentleman in a beaver cap came riding toward him on a handsome raven-black horse, accompanied by two hunt servants.

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  • The tangent at any point bisects the angle between the focal distances of the point, and the normal is equally inclined to the focal distances.

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  • I live in the angle of a leaden wall, into whose composition was poured a little alloy of bell-metal.

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  • I told her when I returned from my preparations in the cabin I'd better find my little angle quiet or she could watch her mother die before her eyes.

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  • One thing was cer­tain, Fred O'Connor would jump on this new angle like Ellery Queen!

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  • The Russians, they say, fortified this position in advance on the left of the highroad (from Moscow to Smolensk) and almost at a right angle to it, from Borodino to Utitsa, at the very place where the battle was fought.

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  • Below, he could see a displaced boulder and disturbed earth before the slope dropped off at an impossible angle into utter blackness.

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  • The angle between two objects, such as stars or the opposite limbs of the sun, was measured by directing an arm furnished with fine " sights " (in the sense of the " sights " of a rifle) first upon one of the objects and then upon the other (q.v.), or by employing an instrument having two arms, each furnished with a pair of sights, and directing one pair of sights upon one object and the second pair upon the other.

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  • The block containing his body was built into an angle of the Fort of the Twenty-four Hours, then under construction.

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  • The fact that at this stage the polarization is a maximum, when the angle through which the light is turned exceeds a right angle, is the more worthy of note, as the opposite result would probably have been expected.

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  • Not only did the Russians not fortify the position on the field of Borodino to the left of, and at a right angle to, the highroad (that is, the position on which the battle took place), but never till the twenty- fifth of August, 1812, did they think that a battle might be fought there.

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  • As regards the polarization of the dispersed light as dependent on the angle at which it is emitted, we find that although, when terms of the second order are included, the scattered light no longer vanishes in the same direction as before, the peculiarity is not lost but merely transferred to another direction.

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  • The south-western angle of the continent, bounded by a line drawn diagonally from Jurien river to Cape Riche, has an average of from 30 to 40 in.

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  • The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes.

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  • 1 It is evident from equation (13) that the angle of immersion depends solely on the speed of the ship; hence in laying a cable on an irregular bottom it is of great importance that the speed should be sufficiently low.

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  • On the east and west the ravines already mentioned afforded, in the main, a sufficient protection, so that a massive wall was unnecessary, while near the south-eastern angle a breastwork was formed by the excavation of the natural rock, 2 which in later times was honeycombed with tombs.

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  • Join CR; the angle CRQ is then the eccentric anomaly.

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  • The branches grow at a more acute angle.

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

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  • The angle between the costa and termen is the apex.

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  • When the wing is spread, its long axis is more or less at a right angle to the body axis.

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  • I) bounded by the two faces of the basal pinacoid (c) and the four faces of the prism (m); the angle between the prism-faces (mm) is 78° 23', whilst that between c and m is go.

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  • Parker in the Journal of the Royal Asiatic Society, Journal asiatique, Revue numismatique, Asiatic Quarterly, &c. (C. EL.) EPI, the French architectural term for a light finial, generally of metal, but sometimes of terra-cotta, e forming the termination of a spire or the angle of a roof.

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  • high rise at the north-west angle.

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  • Only one of the original mosaics now exists, the one over the doorway at the north-western, or St Alipio, angle.

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  • At this point, perhaps out of regard for the remains of Ziani's palace, the work seems to have been arrested for many years, but in 1424 the building was resumed and carried as far as the north-west, or judgment, angle, near St Mark's, thus completing the sea and piazzetta facades as we now see them.

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  • At the south-east angle is the "Drunkenness of Noah," at the south-west the "Fall of Man," and at the north-west the "Judgment of Solomon."

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  • Barnaba; the Palazzo Priuli at San Severo, with a remarkably graceful anglewindow, where the columnar mullion carries down the angle of the wall; the flamboyant balconies of the Palazzo Contarini Fasan; the Palazzo Bernardo on a side canal near S.

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  • The columned, round-headed windows are set in deeply between the pillars which carry the massive entablature, and this again is surmounted by a balustrade with obelisks at each angle and figures marking the line of each bay.

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  • The chief work was executed at the south-west angle, where the columns of the arcade had become so broken and distorted as to menace the safety of the whole building.

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  • Akhma, over the northern end of which runs a single easy pass (Beilan) to the north-east angle of the Levant coast (Alexandretta), while at the southern end is a gap through which the Orontes turns sharply to the sea.

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  • an angle equal to that of the torsion head.

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  • If then the torsion head is provided with an index needle, and also if the movable coil is provided with an indicating point, it is possible to measure the torsional angle through which the head must be twisted to bring the movable coil back to its zero position.

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  • In these circumstances the torsional angle becomes a measure of the torque and therefore of the product of the strengths of the currents in the two coils, that is to say, of the square of the strength of the current passing through the two coils if they are joined up in series.

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  • By geometrical consideration it can be shown that the angle subtended by p, as seen from F, must be inversely as the square of its distance r.

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  • I bet he has an angle.

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  • Behind him, to the far right, I could see the front door was off its hinges, wrested to a strange angle.

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  • Technically that's true, but maybe she has an angle.

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  • He looked for signs anyone had walked through the brush and branches, pausing at intervals to squat and look at his surroundings from a different angle.

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  • C is the clamp and M the slow motion in position angle.

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  • Trapezus), a city of Asia Minor, situated on the Black Sea, near its south-eastern angle.

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  • The lower jaw is slender, nearly straight, 2-3 and without a coronoid process or inflected angle.

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  • The speed of the ship must therefore be so regulated that the angle of immersion is as great as the inclination of the steepest slope passed over.

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  • In ordinary circumstances the angle of immersion i varies between six and nine degrees.

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  • galvanometer coil so that the influence of the latter causes the mirror (through the action of the magnetic needle) to be turned through a small angle in one direction or the other according to the direction of the current through the coil.

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  • from Peschiera, where it issues from the lake at its south-eastern angle, till it joins the Po.

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  • Besides these offshoots of the Apennines there are in this part of Central Italy several detached mountains, rising almost like islands on the seashore, of which the two most remarkable are the Monte Argentaro on the coast of Tuscany near Orbetello (2087 ft.) and the Monte Circello (1771 ft.) at the angle of the Pontine Marshes, by the whole breadth of which it is separated from the Volscian Apennines.

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  • But some stems grow parallel to the surface of the soil, while the branches both of stems and roots tend to grow at a definite angle to the main axis from which they come.

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  • The angle which the earth's axis makes with the plane in which the planet revolves round the sun determines the varying seasonal distribution of solar radiation over the surface and the mathematical zones of climate.

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  • An elevation of great extent which rises at a very gentle angle from a surrounding depression is termed a " rise," one which is relatively narrow and steep-sided a " ridge," and one which is approximately equal in length and breadth but steep-sided a " plateau," whether it springs direct from a depression or from a rise.

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  • The outline of the curve of a valley's sides ultimately depends on the angle of repose of the detritus which covers them, if there has been no subsequent change, such as the passage of a glacier along the v.alley, which tends to destroy the regularity of the crosssection.

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  • This arises mostly from the angle formed by the keel with the body of the sternum, passes by a strong tendon through the foramen triosseum, and is inserted upon the upper tubercle of the humeral crest, which it rotates and abducts.

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  • The article REFLECTION explains the symmetrical arrangement of images formed by two mirrors inclined at an angle which is a sub-multiple of four right angles.

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  • In its simplest form it consists of a tube about twelve inches long containing two glass plates, extending along its whole length and inclined at an angle of 60°.

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  • in length, actuating a universal joint on the first spindle of the register; it consisted of an air-tight thin metal tube with a coned fore-end, carrying flat metal vanes set at an angle.

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  • 12) the angle of the pitch can be altered.

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  • In this case the rack had pin teeth carried in a pair of angle bars.

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  • In Great Britain the curvature is defined by stating the length of the radius, expressed in chains (i chain=66 ft.), in America by stating the angle subtended by a chord ioo ft.

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  • In this engine the two piston-rods of one side are not coupled to a common cross-head, but drive on separate cranks at an angle of 180°, the pair of 180° cranks on each side being placed at right angles.

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  • Its form is approximately that of an isosceles triangle, with the sharp angle extending into Lower California, W.

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  • Another of Yung-lo's bells is hung in a Buddhist temple outside the north-west angle of the city wall, and is covered both on the inside and outside with the Chinese texts of the Lankavatara Sutra, and the Saddharma pundarika Sutra.

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  • But he had, as Newman afterwards said of him, "struck into the movement at an angle."

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  • A distinctive feature is the position assumed in resting; Culex has a humpbacked attitude, while in Anopheles the proboscis, head and body are in a straight line, and in many species inclined at an angle to the wall, the tail sticking outwards.

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  • Near the north-west angle of the palace was a larger bath chamber, and by the N.

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  • Among the most important of these were - Lyttus or Lyctus, in the interior, south-east of Cnossus; Rhaucus, between Cnossus and Gortyna; Phaestus, in the plain of Messara, between Gortyna and the sea; Polyrrhenia, near the north-west angle of the island; Aptera, a few miles inland from the Bay of Suda; Eleutherna and Axus, on the northern slopes of Mount Ida; and Lappa, between the White Mountains and the sea.

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  • The two great rivers of China, the Hwang-ho and the Yang-tsze-kiang take their rise from the eastern face of Tibet, the former from the north-east angle, the latter from the south-east.

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  • Gulf, the Tigris, and thence westward to the north-east angle of the Levant; on the north the high land follows nearly 36° N.

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  • The southern and south-western face follows the coast closely up the Persian Gulf from the mouth of the Indus, and is formed farther west by the mountain scarp, which, rising in many points to 10,000 ft., flanks the Tigris and the Mesopotamian plains, and extends along Kurdistan and Armenia nearly to the 40th meridian; beyond which it turns along the Taurus range, and the north - eastern angle of the Mediterranean.

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  • In this line of investigation the prime importance belongs to the discovery (1) of the connexion between the refractive index and the polarizing angle, (2) of biaxial crystals, and (3) of the production of double refraction by irregular heating.

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  • These double and triple ranges, which have a general elevation of 8500-10,000 ft., stretch from the south-east angle of the Black Sea, 400 m.

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  • The anomaly is then the angle BFP which the radius vector makes with the major axis.

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  • The anomaly AFQ of Q at any moment is called the mean anomaly, and the angle QFP by which the true anomaly exceeds it at that moment is the equation of the centre.

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  • One of these is the position of the line MN through the sun at F in which the plane of the orbit cuts some fundamental plane of reference, commonly the ecliptic. This is called the line of nodes, and its position is specified by the angle which it makes with some fixed line FX in the fundamental plane.

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  • The angle from the pericentre to the actual radius vector, and the length of the latter being found, the angular distance of the planet from the node in the plane of the orbit is found by adding to the true anomaly the distance from the node to the pericentre.

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  • The best-preserved portions are at the eastern extremity, at the northern side near the ancient " royal " exit, and at the southwestern angle.

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  • TRISECTRI X, a curve which is a variety of the limacon of Pascal, and named from its property of trisecting an angle.

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  • Then OJ trisects the given angle.

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  • A diagnosis covering all the Ratitae (struthio, rhea, casuarius, dromaeus, apteryx and the allied fossils dinornis and aepyornis) would be as follows - (i) terrestrial birds without keel to the sternum, absolutely flightless; (ii) quadrate bone with a single proximal articulating knob; (iii) coracoid and scapula fused together and forming an open angle; (iv) normally without a pygostyle; (v) with an incisura ischiadica; (vi) rhamphotheca compound; (vii) without apteria or bare spaces in the plumage; (viii) with a complete copulatory organ, moved by skeletal muscles.

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  • Assuming the four valencies of the carbon atom to be directed from the centre of a regular tetrahedron towards its four corners, the angle at which they meet.

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  • Baeyer supposes that in the formation of carbon, rings " the valencies become deflected from their positions, and that the tension thus introduced may be deduced from a comparison of this angle with the angles at which the strained valencies would meet.

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  • The values in other cases are calculable from the formula RI 09° 28' - a), where a is the internal angle of the regular polygon contained by sides equal in number to the number of the carbon atoms composing the ring.

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  • Starkenburg occupies the angle between the Main and the Rhine, and in its south-eastern part includes some of the ranges of the Odenwald, the highest part being the Seidenbucher Hohe (1965 ft.).

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  • In the Phoenician alphabet it takes a form closely resembling the English W, and this when moved through an angle of 90 is the ordinary Greek sigma 2.

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  • Thus Horsell, who was the first to introduce tints the ground, however, was made until towards the close of the 18th century, when horizontal contours and hachures regulated according to the angle of inclination of all slopes, were adopted.

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  • Thus the French survey commission of 1828 fixed the proportion of black to white at one and a half times the angle of slope; while in Austria, where steep mountains constitute an important feature, solid black has been reserved for a slope of 80°, the proportion of black to white varying from 80:o (for 50) to 8: 72 (for 5°).

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  • Instead of supposing the light to fall vertically upon the surface it is often supposed to fall obliquely, generally at an angle of 45° from the upper left-hand corner.

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  • If both places have the same latitude we have to deal with an isosceles triangle, of which two sides and the included angle are given.

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  • If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given.

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  • These orthodromic distances are of course shorter than those measured along a loxodromic line, which intersects all parallels at the same angle.

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  • angle of the town and occupying the promontory of Lochias, which shut in the Great Harbour on the east.

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  • The castle stands in the angle between the Ouse and the Foss immediately above their junction.

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  • In this manner by the end of March upwards of 200,000 men were moving towards the Elbe,' and in the first fortnight of April they were duly concentrated in the angle formed by the Elbe and Saale, threatening on the one hand Berlin, on the other Dresden and the east.

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  • The angle of the slope decreases gradually from the margin of the inland ice, where it may be I° or more, towards the interior, where it is o°.

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  • Outside the north-west angle of the castle, Richard de Clare in 1256 founded a Dominican priory, which was burnt by Glendower in 1404.

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  • The principal feature is the suppression of the direct channel of the sap, and the substitution of four, or more commonly two, mother branches, so laid to the wall that the central angle contains about 90°.

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  • The orbital planes of earth and moon are inclined to each other at an angle of 50.8 ° and at two points only in its orbit can the moon be situated in the plane of the ecliptic: the line joining these two points is called the "line of nodes."

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  • South of Resht this section is broken through at almost a right angle by the Safid Rud (White river),and along it runs the principal commercial road between the Caspian and inner Persia, Resht-Kazvin-Teheran.

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  • ELONGATION, strictly "lengthening"; in astronomy, the apparent angular distance of a heavenly body from its centre of motion, as seen from the earth; designating especially the angular distance of the planet Mercury or Venus from the sun, or the apparent angle between a satellite and its primary.

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  • His father, Wilgils, an Angle or, as Alcuin styles him, a Saxon, of Northumbria, withdrew from the world and constructed for himself a little oratory dedicated to St Andrew.

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  • Its smaller northern part is a prolongation of the southern angle of the Bohemian forest and contains as culminating points the P16cklstein (4510 ft.) and the Sternstein (3690 ft.).

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  • The angle between the optic axes varies from 70 0 -50° in muscovite and lepidolite to Io - o° in biotite and phlogopite; the latter are thus frequently practically uniaxial.

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  • GALICIA (the ancient Gallaecia or Callaecia, KaAAaucia or KaXaucia), a captaincy-general, and formerly a kingdom, countship and province, in the north-western angle of Spain; bounded on the N.

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  • Each discovery in turn was, according to the prevailing custom, announced to the learned world under the veil of an anagram - removed, in the case of the first, by the publication, early in 1656, of the little tract De Saturni luna observatio nova; but retained, as regards the second, until 1659, when in the Systema Saturnium the varying appearances of the so-called "triple planet" were clearly explained as the phases of a ring inclined at an angle of 28° to the ecliptic. Huygens was also in 1656 the first effective observer of the Orion nebula; he delineated the bright region still known by his name, and detected the multiple character of its nuclear star.

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  • Annual parallax is the angle between the direction in which a star appears from the earth and the direction in which it appears from the centre of the sun.

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  • The angle which the magnetic axis makes with the plane of the horizon is called the inclination or Along an irregular line encircling the earth in the neighbourhood of the geographical equator the needle takes up a horizontal position, and the dip is zero.

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  • Within a limited space, such as that contained in a room, the field due to the earth's magnetism is sensibly uniform, the lines of force being parallel straight lines inclined to the horizon at the angle of dip, which at Greenwich in 1910 was about 67°.

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  • an angle e with the normal, the normal component of the magnetization, I cos e, is called the surface density of the magnetism, and is generally denoted by a.

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  • The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is r, is V=M cos 0/r 2, (io) where 0 is the angle between r and the axis of the magnet.

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  • If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin 0, (17) where 0 is the angle between the axis of the magnet and the direction of the force.

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  • The potential at any point due to a magnetic shell is the product of its strength into the solid angle w subtended by its edge at the given point, or V = Fu.

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  • M/H = (d 2 -1 2) tan 0/2d, where 1 is half the length of the magnet, which is placed in the " broadside-on " position as regards a small suspended magnetic needle, d the distance between the centre of the magnet and the needle, and 0 the angle through which the needle is deflected by the magnet.

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  • Thus if the magnet is suspended horizontally by a fine wire, which, when the magnetic axis points north and south, is free from torsion, and if 0 is the angle through which the upper end of the wire must be twisted to make the magnet point east and west, then MH = CB, or M = C6/H, where C is the torsional couple for r 0.

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  • Let 0 be the angle which the standard magnet M makes with the meridian, then M'/R = sin 0, and M/R = cos 0, whence M' = M tan 0.

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  • The direction of the resultant field of force will then make, with that of H E, an angle 0, such that Hp/H E tan 0, and the suspended needle will be deflected through the same angle.

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  • The angle B is indicated by the position of the spot of light upon the scale, and the horizontal intensity of the earth's field H E is known; thus we can at once determine the value of H P, from which the magnetization I of the body under test may be calculated.

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  • The effect of the ends of the wire is, as Ewing remarks, to shear the diagram in the horizontal direction through the angle which the sloping line makes with the vertical.

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  • The curve thus constructed should be a straight line inclined to the horizontal axis at an angle 0, the tangent of which is 1.6.

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  • If a coil of insulated wire is suspended so that it is in stable equilibrium when its plane is parallel to the direction of a magnetic field, the transmission of a known electric current through the coil will cause it to be deflected through an angle which is a function of the field intensity.

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  • 23 should have a common vertex in the middle of the neck with a semi-vertical angle of 54° 44', while the condition for a uniform field is satisfied when the cones have a semivertical angle of 39° 14'; in the latter case the magnetic force in the air just outside is sensibly equal to that within the neck.

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  • A pair of cones having a semi-vertical angle of 45° were considered to combine high concentrative power with a sufficient approximation to uniformity of field.

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  • The corresponding intensity of the outside field was 24,500, but, owing to the wide angle of the cones used (about X63°), this was probably greater than the value of the magnetic force within the metal.

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  • But the application of a magnetic field at right angles to the plane of the metal causes the equipotential lines to rotate through a small angle, and the points at] which the galvanometer is connected being no longer at the same potential, a current is indicated by the galvanometer.'

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  • Maxwell (Electricity and Magnetism, § 444), recognizing that the theory in this form gave no account of residual magnetization, made the further assumption that if the deflection of the axis of the molecule exceeded a certain angle, the axis would not return to its original position when the deflecting force was removed, but would retain a permanent set.

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  • The ovary is generally two-chambered, with two inverted ovules standing side by side at the inner angle of each chamber.

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  • His investigation of the properties of amicable numbers and of the problem of trisecting an angle, are of importance.

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  • The Treaty of Trianon satisfied the most essential claims of Yugoslavia, by dividing the whole Banat (save a small Magyar triangle opposite the city of Szeged) between her and Rumania, and by assigning to her the whole Backa (except Baja and district), part of the Baranya (forming the angle between Drave and Danube) and the Medjumurje (between Drava and Mur).

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  • We conclude that a double line cannot be fairly resolved unless its components subtend an angle exceeding that subtended by the wave-length of light at a distance equal to the horizontal aperture.

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  • If the angle subtended by the components of a double line be twice that subtended by the wave-length at a distance equal to the horizontal aperture, the central bands are just clear of one another, and there is a line of absolute blackness in the middle of the combined images.

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  • From a measurement of the maximum distance the least angle between consecutive lines consistent with resolution may be deduced, and a comparison made with the rule stated above.

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  • The extreme value possible for a is a right angle, so that for the microscopic limit we have Z X o/µ (2).

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  • If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.

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  • The eye, unaided or armed with a telescope, is able to see, as points of light, stars subtending no sentsible angle.

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  • B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.

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  • If 1 2 and 1 1 be the thicknesses traversed by the extreme rays, and a denote the width of the emergent beam, the dispersion is given by 0 Sµ 0 2 - 11)/a, or, if t i be negligible, 0 = Sµt/a (6) The condition of resolution of a double line whose components subtend an angle 0 is that 0 must exceed X/a.

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  • In another direction, making a small angle with the last, such that the projection of AB upon it amounts to a few wavelengths, it is easy to see that the mode of interference is the same as if there were no ruling.

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  • The sine of an angle can never be greater than unity; and consequently under the most favourable circumstances only 1/m 2 ir 2 of the original light can be obtained in the m u ' spectrum.

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  • If the incident rays make an angle 0 with the normal (fig.

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  • 6), and the diffracted rays make an angle ¢ (upon the same side), the relative retardation from each element of width (a+d) to the next is (a+d) (sin 9 +sin op); and this is the quantity which is to be equated to mX.

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  • Hence, if a be the width of the diffracted beam, and do the angle through which the wave-front is turned, ado = dX, or dispersion = /a ..

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  • Then, if Q be any radiant point and Q' its image (primary focus) in the spherical mirror AP, we have 1 1 2cos4) v l + u 'a ' ' where v 1 = AQ', u =AQ, a =OA, =angle of incidence QAO, equal to the angle of reflection Q'AO.

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  • This disposition is adopted in Rowland's instrument; only, in addition to the central image formed at the angle 4' =4), there are a series of spectra with various values of 4', but all disposed upon the same circle.

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  • - 47rb 2 dr (r / ' denoting the angle between r and z.

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  • For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to r and the direction of the force, and in magnitude dependent only upon the angle (43) between these two directions and upon the distance (r).

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  • The proportionality of the secondary disturbance to sin 43 is common to the present law and to that given by Stokes, but here there is no dependence upon the angle 0 between the primary and secondary rays.

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  • The typical Egyptian obelisk is an upright monolith of nearly square section, generally to diameters in height, the sides slightly convex, tapering upwards very gradually and evenly, and terminated by a pyramidion whose faces are inclined at an angle of 60°.

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  • the angle between its directions of incidence and emergence, after one, two, three or more internal reflections.

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  • I); let AD be the refracted ray, and r the angle of refraction.

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  • If the ray suffers one internal reflection at D, then it is readily seen that, if DB be the path of the reflected ray, the angle ADB equals 2r, i.e.

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  • Since the angles of incidence and refraction are connected by the relation sin i=µ sin r (Snell's Law), µ being the index of refraction of the medium, then the problem may be stated as follows: to determine the value of the angle i which makes D = 2 (i - r) +n (7r - 2r) a maximum or minimum, in which i and r are connected by the relation sin i =µ sin r, µ being a constant.

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  • For the angle i to be real, cos i must be a fraction, that is n 2 +2n>µ 2 - I, or (n+I)2>µ2.

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  • by the methods of the differential calculus or geometrically, that the deviation increases with the refractive index, the angle of incidence remaining constant.

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  • At the Louvre, Goujon, under the direction of Lescot, executed the carvings of the south-west angle of the court, the reliefs of the Escalier Henri II., and the Tribune des Cariatides, for which he received 737 livres on the 5th of September 1550.

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  • The government offices are principally in Whitehall, the fine thoroughfare which connects Parliament Square, in the angle between the Houses and the Abbey, with Trafalgar Square.

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  • Besides the forum Stukeley suggested the sites of seven other buildings - the Arx Palatina guarding the south-eastern angle of the city where the Tower now stands, the grove and temple of Diana on the site of St Paul's, &c. No traces of any of these buildings have been found, and they are therefore purely conjectural.

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  • Then, as the chronicler writes, " all the Angle race turned to him (Alfred) that were not in bondage of the Danish men."

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  • The ore is mined in the ordinary way, by pick and shovel if soft, or by the aid of powder if necessary, and the funnel-shaped bottom of the pit is maintained at such an angle that little or no shovelling is required to bring the excavated material to the shaft.

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  • The stability of a ship is investigated practically by inclining it; a weight is moved across the deck and the angle is observed of the heel produced.

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  • If the ship heels through an angle 0 or a slope of I in m, GM =GG 1 cot 8=mc(P/W), (r) and GM is called the metacentric height; and the ship must be ballasted, so that G lies below M.

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  • For if the ship turns through a small angle 0 about the line FF', then b1, b 2, the C.G.

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  • of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.

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

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  • I n a straight uniform current of fluid of density p, flowing with velocity q, the flow in units of mass per second across a plane area A, placed in the current with the normal of the plane making an angle 0 with the velocity, is oAq cos 0, the product of the density p, the area A, and q cos 0 the component velocity normal to the plane.

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  • Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point, dM/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity.

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  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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

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  • The curves 0 = constant and 4, = constant form an orthogonal system; and the interchange of 0 and 4, will give a new state of uniplanar motion, in which the velocity at every point is turned through a right angle without alteration of magnitude.

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  • if the angle of the corner is jr/n, the path is the Cotes' spiral r sin n0=na.

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

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  • (io) The velocity q is zero in a corner where the hyperbola a cuts the ellipse a; and round the ellipse a the velocity q reaches a maximum when the tangent has turned through a right angle, and then q _ (Ch 2a-C0s 2(3).

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  • Trans., 1892); and dly/yds is the component velocity across ds in a direction turned through a right angle forward.

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  • 0, 1, = -ZUa 3 sin e B/r; (13) and then =Ux(I+1a3/r2), 4=ZUa 3 cos 0/r2, -d r = Ua3 cos B, -d9=ZUa3 sin 0, so that, if the direction of motion makes an angle >G with Ox, tan (4y-0) =Z tan 0, tan =3 tan 0/(2-tan 2 e).

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  • Denoting the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.

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  • 4), and issues in a jet between two edges A and A'; the wall xA being bent at a corner B, with the external angle (3= 2Wr/n.

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  • For the 2 polygon has a right angle at a=a, a', and a zero angle at u = b, where 0 changes from o to 27/n and 1 - 2 increases by 21-rr/n; so that dSt A (b -a.b -a') a - (u -b),/ (u - a.u - a where A= tn (II) And the w polygon has a zero angle at u =o, oo, where 4, changes from o to m and back again, so that w changes by im, and du =B, where B=-.

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  • rf > a> b> o> a'> -Do; and then so that PT =c/Zir, and the curve AP is the tractrix; and the coefficient of contraction, or breadth of the jet breadth of the orifice - +i' A change of S2 and 0 into nS2 and nO will give the solution for two walls converging symmetrically to the orifice AA 1 at an angle zr/n.

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  • Thus with a' =o, a stream is split symmetrically by a wedge of angle ' zr/n as in Bobyleff's problem; and, by making a = oo, the wedge extends to infinity; then chnS2= u, sh nS2= b n u.

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  • There is no Stokes' function when the axis of the doublet at S does not pass through 0; the image system will consist of an inclined doublet at H, making an equal angle with OS as the doublet S, and of a parallel negative line doublet, extending from H to 0, of moment varying as the distance from O.

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  • The method of electrical images will enable the stream function, )' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an integer (R.

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  • well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance.

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  • Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .

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

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  • (9) c 2 Ci If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan S = ird/nd = 2 d p/u, (10) '°If a denotes the density of the metal, and if the shell has a cavity homothetic with the external ellipsoidal shape, a fraction f of the linear scale; then the volume of a round shot being sird 3, and sird 3 x of a shot x calibres long W =*ird 3 x(I -f 3)v, (20) 2 Wki 2= 61rd 3 xo(I-f 5)Q, (21) Wk22=67rd3x 2 2+0 2(I - f5)Q.

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  • of the metal, taking water as 800 times denser than air on the average, in round numbers, and formula (to) may be written n tan 6=ir, or n6=180, when 6 is a small angle, and given in degrees.

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  • Table of Rifling for Stability of an Elongated Projectile, x Calibres long, giving S the Angle of Rifling, and n the Pitch of Rifling in Calibres.

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  • The curve also permits the solution of the problems of duplicating a cube and trisecting an angle.

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  • When crystallized from water, crystals belonging to the orthorhombic system, and having a prism angle of 61 0 10', are obtained; they are often twinned on the prism planes, giving rise to pseudo-hexagonal groups resembling aragonite.

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  • During the greater part of the 19th century the ideal of ploughing was to preserve the furrow-slice unbroken, and this object was attained by the use of long mould-boards which turned the slices gently and gradually, laying them over against one another at an angle of 45°, thus providing drainage at the bottom of the furrow, and exposing the greatest possible surface to the influences of the weather.

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  • Passau consists of the town proper, lying on the rocky tongue of land between the Danube and the Inn, and of four suburbs, Innstadt on the right bank of the Inn, Iizstadt on the left bank of the Ilz, Anger in the angle between Ilz and the Danube, and St Nikola.

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  • angle by low ranges of limestone hills.

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  • The Anophelinae have narrow bodies, and generally spotted wings, and when at rest keep body and proboscis in a straight line, often at a considerable angle with the supporting surface; in this way they can be distinguished from Culicinae, which have a humped-up thorax with which the proboscis forms an angle, and in the resting position keep the body parallel to the support.

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  • four series of "Researches on Heat," in the course of which he described the polarization of heat by tourmaline, by transmission through a bundle of thin mica plates inclined to the transmitted ray, and by reflection from the multiplied surfaces of a pile of mica plates placed at the polarizing angle, and also its circular polarization by two internal reflections in rhombs of rock-salt.

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  • a lady's hand glass) behind the lens and inclined at an angle of 45° to the horizon so as to reflect Mirror the rays of light vertically downwards, we can produce >» on a horizontal sheet of Image with Mirror paper an unperverted image FIG.

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  • a-, privative, and ywvia, an angle), the term given to the imaginary lines on the earth's surface connecting points at which the magnetic needle points to the geographical north and south.

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  • thick, and rising from the water on each side at an angle of about 35°.

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  • Trieste is situated at the northeast angle of the Adriatic Sea, on the Gulf of Trieste, and is picturesquely built on terraces at the foot of the Karst hills.

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  • It owes its development to its geographical situation in the north-east angle of the Adriatic Sea at the end of the deeply indented gulf, and to its harbour, which was more accessible to large vessels than that of Venice.

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  • The alimentary canal persists and revolves in the median plane through an angle of 180°, accompanied by part of the larval vestibule, the space formed by the retra^tion of the oral surface.

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  • From this it is easy to pass to the most widely spread Greek form, the ordinary In Corinth, however, and its colony Corcyra, in Ozolian Locris and Elis, a form < inclined at a different angle is found.

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  • The same process is then repeated in another direction, so that the new bands cross the old at an angle adapted to the nature of the design.

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  • The county is well watered by numerous streams. The principal are the Callan, the Tynan and the Tallwater, flowing into the Blackwater, which, after forming the boundary between this county and Tyrone, empties itself into the south-western angle of Lough Neagh.

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  • of the promontory of Faro (anc. Promontorium Pelorum), which forms the northeastern angle of the island, the capital of the province of Messina and the seat of an archbishop. Pop. (1850), 97,074; (1881), 126,497; (1901), 1 49,77 8; (1905), 158,812.

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  • The upper angle of it consists of rich and fertile districts, such as Murshidabad, Nadia, Jessore and the 24 Parganas.

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  • angle of the duchy of Upper Austria situated between Salzburg and Styria.

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  • even blackish, with darker cross-bands or C-shaped markings; a dark, light-edged band extends from the eye to the angle of the mouth.

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  • Hence the total solid angle round any point is 47r.

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  • The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

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  • The electric density on the sphere being uniform, the quantities of electricity on these areas are proportional to the areas, and if the electric force varies inversely as the square of the distance, the forces exerted by these two surface charges at the point in question are proportional to the solid angle of the little cone.

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  • At each point on this surface the resultant force has a certain value, and a certain direction inclined at an angle 0 to the normal to the selected surface at that point.

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  • 3), and describe through it as centre a cone of small solid angle dw cutting out of the enclosing surface in two small areas dS and dS' at distances x and x'.

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  • The normal section of the cone at that point is equal to dS cosO, and the solid angle dw is equal to dS cos0/x 2.

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  • Accordingly, since the total solid angle round a point is 47r, it follows that the total flux through the closed surface due to the single point charge q is 41rq, and what is true for one point charge is true for any collection forming a total charge Q of any form.

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  • angle some of the blocks are 7 to 82 ft.

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  • end it turned westward at an obtuse angle and extended about io ft.

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  • On the top of this system as a foundation were set several statue bases, one bearing the signature of Lysippus, which shows that the system stood there at least as early as the 4th century B.C. Some parts of it may have been taken from older buildings, but not the cornice nor the corner metope block which formed an obtuse angle.

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  • The city possesses five gates, two on the northern face, the Kutab-chak near the north-east angle of the wall, and the Malik at the re-entering angle of the Ark-i-nao; and three others in the centres of the remaining faces, the Irak gate on the west, the Kandahar gate on the south and the Kushk gate on the east face.

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  • Chaumont is picturesquely situated on an eminence between the rivers Marne and Suize in the angle formed by their confluence.

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  • a microscope cover-glass, held close to the eye and inclined at an angle of 45° to the horizon, one can See the images of objects in front, formed by reflection from the surface of the glass, and at the same time one can also see through the transparent glass.

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  • A four-sided prism of glass is constructed having one angle of 9c)°, the opposite angle of 135°, and the two remaining angles each of 672°.

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  • He found out the formula for deriving the sine of a multiple angle, knowing that of the simple angle with due regard to the periodicity of sines.

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  • His war-ships were arranged in what was called a half-moon, and was in fact an obtuse angle with his flagship, the "Brederode," at the apex.

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  • The angle between the stars and g Ursae maj.

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  • From a series of measures of the angle between Jupiter's satellites and the planet, made in June and July 1794 and in August and September 1795, Schur finds the mass of Jupiter =I / Io 4 8.55 1.45, a result which accords well within the limits of its probable error with the received value of the mass derived from modern researches.

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  • In 1812 Bessel measured with it the angle between the components of the double star 61 Cygni and observed the great comet of 1811.

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  • 5, p. iv.) he found that the index error of the scale changed systematically in different position angles by quantities which were independent of the direction of gravity relative to the position angle under measurement, but which depended solely on the direction of the measured position angle relative to a fixed radius of the object-glass.

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  • This construction would give all the advantage of the younger Dollond's object-glass micrometer, and more than its sharpness of definition, without liability to the systematic errors which may be due to want of homogeneity of the object-glass; for the lenses will not be turned with respect to each other, but, in measurement, will always have the same relation in position angle to the line joining the objects under observation.

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  • This ring is necessary in order to allow the rods to follow the micrometer heads when the position angle is changed.

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  • For this purpose the position angle of the eye-piece micrometer is set to that of the head, and the eye-piece is displaced from the axis of the tube (in the direction of the movable segment) by an amount equal to half the angle under measurement.

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  • The eye-piece is fixed in the axis, and the segments are symmetrically displaced from the axis each by an amount equal to half the angle measured.

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  • The chief objections to the method are that, as one star is in the axis of the telescope and the other displaced from it, the images are not both in focus of the eye-piece,3 and the rays from the two stars do not make the same angle with the optical axis of each segment.

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  • 4) that Bessel had indicated, by notes in his handbooks, the following points which should be kept in mind in the construction of future heliometers: (I) The segments should move in cylindrical slides; b (2) the screw should be protected from dust; 6 (3) the zero of the position circle should not be so liable to change; 7 (4) the distance of the optical centres of the segments should not change in different position angles or otherwise; 8 (5) the points of the micrometer screws should rest on ivory plates; 9 (6) there should be an apparatus for changing the screen.'° Wilhelm Struve, in describing the Pulkowa heliometer,' 1 made The distances of the optical centres of the segments from the eye-piece are in this method as I; secant of the angle under measurement.

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  • In Bessel's heliometer this would amount to a difference of o oat h of an inch when an angle of 1 ° is measured.

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  • Their slow motion in position angle, however, was not all that could be desired.

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  • The circles for position angle and declination are read by micrometer-microscopes illuminated by the lamp L; the scales are illuminated by the lamp 1.

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  • The tube V, on the contrary, is attached to the cradle, and merely forms a support for the finder Q, the handles at f and p, and the moving ring P. The latter gives quick motion in position angle; the handles at p clamp and give slow motion in position angle, those at f clamp and give slow motion in right ascension and declination.

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  • (2) That an additional motion intermediate between the quick and slow motion in position angle was necessary, because, whilst the slow motion provided by Repsolds was admirably adapted for adjusting the pointings in position angle, it was too slow for causing the images to "cross through " each other in the process of measuring distances.

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  • To remedy drawback (2) Repsolds provided for the Yale heliometer an additional handle for motion in position angle, intermediate in velocity between the original quick and slow motions.

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  • heliometer, completed in 1887 for the Royal Observatory at the Cape of Good Hope, Repsolds, on Gill's suggestion, introduced the following improvements: (a) Four different speeds of motion in position angle were provided.

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  • With similar bevel-gear and rods the tangent screw is connected to the hand-wheel, 79, by which the observer communicates the fourth or slowest motion in position angle.

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  • In observations of position angle one of the two tablets 81 can be used to record the readings.

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  • Having selected the most suitable one he directs the axis of the finder to the estimated middle point between the comet and the star, turns the finder-micrometer in position angle until the images of comet and star lie symmetrically between the parallel position wires, and then turns the micrometer screw (which moves the distance-wires symmetrically from the centre in opposite directions) till one wire bisects the comet and the other the star.

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  • Simi larly the prism may be used for the study and elim- " ination of personal errors depending on the angle made s by a double star with the vertical.

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  • Dawes found the best method for the purpose in question was to limit the aperture of the object-glass by a diaphragm having a double circular aperture, placing the line joining the centres of the circles approximately in the position angle under measurement.

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  • By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured.

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  • If p" is the refracting angle of the prism, and n the magnifying power of the eye-piece, then p"ln will be the distance observed.

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  • Calculating from sheet A I of the Prince of Monaco's Atlas of Ocean Depths,' Kriimmel obtained a mean angle of slope of 0° 2 7 ' 44" or an average fall of i in 124 for the North Atlantic between o° and 47° N., the enclosed seas being left out of account.

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  • In the same way a mean angle of slope of approximately half a degree was found for the Adriatic and the Black Sea.

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  • Hull found a mean angle of slope of 13° to 14° for the edge of the continental shelf off the west coast of Europe, and off Cape Torinana (43° 4' N.) as much as 34°.

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  • Where the French telegraph cable between Brest and New York passes from the continental shelf of the Bay of Biscay to the depths of the Atlantic the angle of slope is.

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  • Such gradients are of a truly mountainous character, the angle of slope from the Eibsee to the Zugspitze is 30°, and that from Alpiglen station to the summit of the Eiger is 42°.

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  • The Australian Shelf rises steeply as a rule from depths, of 2500 to 3000 fathoms. A broad depression with depths of from 3300 to 3500 fathoms lies to the east of the Cocos Islands and extends into the angle between the Malay Archipelago and Australia.

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  • The steep western sides of these trenches often show an angle of slope of 7°.

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  • in diameter at least must be used or the angle of vision for the reflected light is too small.

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  • Mill has shown that in the North Sea off the Firth of Forth the average depth of visibility of a disk in the winter half-year was 4; fathoms and in the summer half-year 62 fathoms, and, although the greater frequency of rough weather in winter might tend to obscure the effect, individual observations made it plain that the angle of the sun was the main factor in increasing the depth to which the disk remained visible.

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  • The use of a sliding weight is not recommended in depths much exceeding 200 fathoms on account of the time required and the risk of the line sagging at a low angle and so stopping the weight.

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  • The inner face is smooth, but the back is strengthened with angle brackets at the corners.

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  • In the working of thick seams inclined at a high angle, such as those in the south of France, and in the lignite mines of Styria and Bohemia, the method of working in horizontal slices, about i 2 or r 5 ft.

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  • thick, and dipping at an angle of 20°, is worked in the following manner.

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  • DENDERA, a village in Upper Egypt, situated in the angle of the great westward bend of the Nile opposite Kena.

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  • The ratio p is given by e"` e, where e= 2.718; µ is the coefficient of friction and 0 the angle, measured in radians,, subtended by the arc of contact between the rope and the wheel.

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  • If the angle 0 1 =0 2 =120 0, Q = (P - p) neglecting friction.

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  • Further, the inclination of the line of metal to the axis gave the gun a fixed angle of elevation varying from 1 ° in light guns to 2-1° in the heavier natures.

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  • D is the dispart sight, S the tangent sight, A'DS the clearance angle.

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  • Guns without dispart sights cannot be layed at elevations below the clearance angle.

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  • angle.

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  • Now the height to which the tangent sight has been raised in order to direct the axis on G' is evidently proportional to the tangent of the angle OMS =AXS.

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  • This angle is called the angle of elevation; OM is constant and is FIG.

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  • The formula for length of scale is, length = sighting radius X tangent of the angle of elevation.

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  • HH' = 60 X 60' the resultant angle of deflection is HFH', and this can be determined by the same formula a = h X1200 X 3, but in this case h = HH' = R R 60 60 R X 3600 a _ = i' so that if the sight is inclined to the left I° it will R X 3600 give 1' deflection for every degree of elevation.

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  • guns this angle was 2° 16'.

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  • means of measuring .the angle of sight.

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  • added to the angle of elevation if the target is above the gun, and subtracted if vice versa.

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  • If now the telescope be directed on the target and this level be brought to the centre of its run, the angle of sight can be read - if afterwards any range ordered is put on the sight and the gun truly layed, this bubble will be found in the centre of its run - so that if thereafter the target becomes obscured the gun can be relayed by elevating till the bubble is in the centre of its run, or at a completely concealed target the angle of sight can, if the range and difference of level are known or can be measured from somewhere near the gun, be put on by means of the micrometer screw, and the gun subsequently layed by putting the range in yards or degrees on the sight drum and elevating or depressing till the bubble is central.

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  • -- of elevation Horizontal -__Target line of sight Horizontal line of sigkkt v Angle of elevation Angle of sight --------- Target Horizontal line Scott's sight.

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  • with a level and a clamp; the level is fixed at the correct angle for drift; if the sight (as is especially liable to be artillery the case on steep hillsides) is tilted away from the angle sights.

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  • In smooth-bore days the term mortar meant a piece of ordnance of a peculiar shape resting on a bed at a fixed angle of quadrant elevation of 45°.

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  • Range is reduced by increasing the angle of elevation (by clinometer) or by using reduced charges.

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  • In coast defence artillery, owing to the fact that the guns are on fixed mountings at a constant height (except for rise and fall of tide) above the horizontal plane on which their targets move, and that consequently the angle of sight and quadrant elevation for every range can be calculated, developments in sights, in a measure, gave way to improved means of giving quadrant elevation.

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  • There must be two sets of elevating gears, one which brings the axis of the gun and the sights together on to the target, thus finding the angle of sight and also pointing the axis of the gun at the target, and a second by which, independent of the sight which remains fixed, the elevation due to the range can be given to the gun and read by means of a pointer and dial marked in yards for range.

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  • 19) represent a gun at height BD above water-level DC, elevated to such an angle that a shot would strike the water at C. Draw EB parallel to DC. It is clear that under these conditions, if a tangent sight AF be raised to a height F representing the elevation due to the range BC, the object C will be on the line of sight.

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  • Then ABF = angle of elevation; EFB =quadrant angle; BCD=angle of sight; EBF=ABF - ABE; and since ABE = BCD, it also equals ABF - BCD.

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  • BCDcanalwaysbe cal culated from the formula, angle of sight in minutes - (in feet) X 1146 R (in yards) (h = height of gun above sea-level; R =range).

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  • The sights themselves fit into sockets cut at the proper angle for drift, and are raised in their sockets the requisite amount for the range by means of a small hand-wheel; they are thus non-recoiling sights.

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  • A circular piece of this paper is folded twice upon itself so as to form a quadrant, one of the folds is pulled out, and the cone thus obtained is supported in a glass or porcelain funnel having an apical angle of 60°.

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  • In Hippotragus the stout and thickly ringed horns rise vertically from a ridge above the eyes at an obtuse angle to the plane of the lower part of the face, and then sweep backwards in a bold curve; while there are tufts of long white hairs near the eyes.

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  • If a .JP solid circle be fixed in any one position and a tube be pivoted on its centre so as to move; and if the line C D be drawn upon the circle pointing towards any object Q in the heavens which lies in the plane of the circle, by turn ing the tube A B towards any other object P in the plane of the circle, the angle B 0 D will be the angle subtended by the two objects P and Q at the eye.

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  • The conception of the right angle is strengthened, by contrast, by the use of bricks in the form of a rhombus.

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  • formulae, not involving the conception of an angle as generated by rotation, belong to this stage; the additional geometrical idea involved being that of the proportionality of the sides of similar triangles.

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  • The treatment of an angle as generated by rotation, the investigation of the relations between trigonometrical ratios and circular measure, the application of interpolation to trigonometrical tables, and the general use of graphical methods to represent continuous variation, all imply an analytical onlook, and must therefore be deferred to this stage.

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  • (iii) Right-angled triangle: sides a and b, enclosing the right angle.

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  • (v) Triangle: one side a, distant h from the opposite angle.

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  • If, for instance, the data for the triangle are sides a and b, enclosing an angle C, the area is lab sih C.

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  • The revolution need not be complete, but may be through any angle.

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    0
  • Also, let angle ABC =7r - 0, angle BCD =ir - 4, angle between BC and AD = G.

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  • Hence, if the angle which the tangent at the extremity of the ordinate u 0 makes with the axis of x is denoted by fie, we have area from uo to u1= 2h(uo + ui) - -- i i h 2 (tan y l - tan t u 2 = Wu ' + u2) - 1 Tih 2 (tan 4,2 - tan um-1 t0 26 m, - 2 h(um-1 + um) i h (tan 4, m - and thence, by summation, A =C I - i i h 2 (tan - tan 1,1/o).

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  • Let a be the radius of a circle, and 0 (circular measure) the unknown angle subtended by an arc. Then, if we divide 0 into m equal parts, and L 1 denotes the sum of the corresponding chords, so that L i =2ma sin (0/2m), the true length of the arc is L1 +a9 3 - 5 + ..., where cp. =B/2m.

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  • The tangent of the angle of deflection 0 of this needle measured from its position, when the shunt coil is disconnected, is equal to the ratio of the voltage of the dynamo to the current through the insulator.

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  • In the other gap are pivoted two coils wound on an iron core and connected at nearly a right angle to each other.

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  • a point which divides a line, or a line which divides an angle, into two equal parts; in crystallography it denotes the bisector of the angle between the optic axes.

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  • Kb(30s, a cube), in geometry, a solid bounded by six equal squares, so placed that the angle between any pair of adjacent faces is a right angle.

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  • It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."

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  • Although Hippocrates could not determine the proportionals, his statement of the problem in this form was a great advance, for it was perceived that the problem of trisecting an angle was reducible to a similar form which, in the language of algebraic geometry, is to solve geometrically a cubic equation.

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  • According to Proclus, a man named Hippias, probably Hippias of Elis (c. 460 B.C.), trisected an angle with a mechanical curve, named the quadratrix.

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  • A small stream called the Crkvina enters the Vrbas from the north-east and in the angle thus formed stand the citadel and barracks, with the 16th-century Ferhadiya Jamia, largest and most beautiful of more than 40 mosques in the city.

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  • from angle to angle.

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  • 12 represent a horizontal section of the dome through the source P. Let OPA be the radius through P. Let PQ represent a ray of sound making the angle B with the tangent at A.

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  • A ray making an angle less than 0 with the tangent will, with its reflections, touch a larger circle.

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  • the direction of the wave in the first medium), and the normal to the surface separating the two media, at the point in which the incident ray meets it; (2) The sine of the angle between the normal and the incident ray bears to the sine of the angle between the normal and the refracted ray a ratio which is constant for the same pair of media.

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  • It further follows, as in the analogous case of light, that there is a certain angle termed the critical angle, whose sine is found by dividing the less by the greater velocity, such that all rays of sound meeting the surface separating two different bodies will not pass onward, but suffer total reflection back into the first body, if the.

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  • if the angle of incidence exceeds the limiting angle.

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  • the limiting angle for these media may be easily shown to be slightly above 152°.

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  • 13), the angle POM being greater than 1 5z°, will not pass into the water at all, but suffer total reflection.

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  • So also there is on the whole none in that direction leaving at P. Let the tangent at P make angle 4) with AB.

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  • If 0 is the angle of twist, the angular velocity is d0/dt.

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  • longitudo, " length"), the angle which the terrestrial meridian from the pole through a point on the earth's surface makes with some standard meridian, commonly that of Greenwich.

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  • The west and south-west half of Saxony is more or less occupied by the ramifications and subsidiary groups of this range, one of which is known from its position as the Central Saxon chain, and another lower group still farther north as the Oschatz group. The south-east angle of Saxony is occupied by the mountains of Upper Lusatia (highest summit 2600 ft.), which form the link between the Erzgebirge and Riesengebirge in the great Sudetic chain.

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  • If r, r i be the radii of two spheres, d the distance between the centres, and 0 the angle at which they intersect, then d2=r2+ r12 2rr l cos ¢ hence 2rr 1 cos =d2r2 - r22.

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  • The bascules rotate through an angle of 82°, and their rear ends in the bascule chambers of the piers carry 365 tons of counterweight, the total weight of each being 1070 tons.

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  • It consists of a pair of tubular girders with solid or plate sides stiffened by angle irons, one line of rails passing through each tube.

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  • The anchors are built up of steel plates and angle bars, and are buried in a large mass of concrete.

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  • Soft steel is used for rivets always, and sometimes for the whole superstructure of a bridge, but medium steel more generally for the plates, angle bars, &c., the weight of the bridge being then reduced by about 7% for a given factor of safety.

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  • R=wx (I+x2/4Y2) Let i be the angle between the tangent at any point having the co-ordinates x and y measured from the vertex, then 3..

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  • The county is roughly triangular in form, London lying at the apex of the western angle, the North Foreland at that of the eastern and Dungeness at that of the southern.

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  • CALAH (so in the Bible; Kalah in the Assyrian inscriptions), an ancient city situated in the angle formed by the Tigris and the upper Zab, 19 m.

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  • In 1845 began the marked influx of Germans, which lasted in large degree up to 1860; they first limited themselves to the district "Over the Rhine" (the Rhine being the Miami & Erie Canal), in the angle north-east of the junction of Canal and Sycamore streets, but gradually spread throughout the city, although this "Over the Rhine" is still most typically German.

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  • The factor T becomes of importance in long range high angle fire, where the shot reaches the higher attenuated strata of the atmosphere; on the other hand, we must take about 800 in a calculation of shooting under water.

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  • The last function A, called the altitude function, will be explained when high angle fire is considered.

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  • vertical above B, the angle S at a range of R yds.

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  • is given by sin S=h/3R, (41) or, for a small angle, expressed in minutes, taking the radian as 3438', (42) S = 1146h/R.

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  • So also the angle /3 must be increased by S to obtain the angle at which the shot strikes a horizontal plane - the water, for instance.

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  • - Determine by calculation with the abridged ballistic table the remaining velocity v, the time of flight t, angle of elevation 0, and descent 13 of this 6-in.

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  • It is found that the alteration of the tangent elevation is almost insensible, but the quadrant elevation requires the addition or subtraction of the angle of sight.

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  • High Angle and Curved Fire.-" High angle fire," as defined officially, " is fire at elevations greater than r 5°," and " curved fire is fire from howitzers at all angles of elevation not exceeding 15°."

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  • Replacing then the angle i on the right-hand side of equations (54) - (56) by some mean value, t, we introduce Siacci's pseudovelocity u defined by (59) u = q sec, t, so that u is a quasi-component parallel to the mean direction of the tangent, say the direction of the chord of the arc.

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  • The equations (66) - (71) are Siacci's, slightly modified by General Mayevski; and now in the numerical applications to high angle fire we can still employ the ballistic table for direct fire.

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  • Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

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  • In the long range high angle fire the shot ascends to such a height that the correction for the tenuity of the air becomes important, and the curvature 4)-8 of an arc should be so chosen that 4)y 0, the height ascended, should be limited to about moo ft., equivalent to a fall of I inch in the barometer or 3% diminution in the tenuity factor T.

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  • Siacci's altitude-function is useful in direct fire, for giving immediately the angle of elevation 4, required for a given range of R yds.

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  • or X ft., between limits V and v of the velocity, and also the angle of descent 0.

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  • - 1 or, as (88) and (90) may be written for small angles, (91) sin 20.=2C [I (V) - oS j, (92) sin 20 =2C [O S - I (v)] To simplify the work, so as to look out the value of sin 20 without the intermediate calculation of the remaining velocity v, a doubleentry table has been devised by Captain Braccialini Scipione =S (U) - S (u), = I (U) - I (u); mean angle (70), (Problemi del Tiro, Roma, 1883), and adapted to yd., ft., in.

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  • After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

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  • To the west of Parr's Ridge the surface for the most part slopes gently down to the east bank of the Monocacy river (which flows nearly at a right angle with the streams east of the Ridge), and then from the opposite bank rises rapidly toward the Catoctin Mountain; but just above the mouth of the Monocacy on the east side of the valley is Sugar Loaf Mountain, which makes a steep ascent of 1250 ft.

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  • They required humouring, and their march discipline was very elastic. But in battle the "thinking bayonets" resolutely obeyed orders, even though it were to attack a Marye's Hill, or a "Bloody Angle," for they had undertaken their task and would carry it through unflinchingly.

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  • The district of Ballia, constituted in 1879, occupies an angle at the junction of the Gogra with the Ganges, being bordered by two districts of Behar.

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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 willows are cut at the first indication of the sap rising and "couched" in rotten peelings and soil at a slight angle, the butts being on the ground, which should be strewn with damp straw from a manure heap. The tops are covered lightly with rotted peelings and by periodical application of water, fermentation is induced at the bottom, heat is engendered, the leaves force their way through the covering and peeling may begin.

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  • The angle of difference between these deviations is called the dispersion for those rays.

    0
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  • This quantity may readily be expressed in terms of the refractive indices for the three colours, for if A is the angle of the prism (supposed small) bc=(/1c - I)A, bD =(/ AD - OA, F - I)A, where µc, A n, µ F are the respective indices of refraction.

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  • It is more useful than (1), as the refractive indices may be measured with a prism of any convenient angle.

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  • If the increase of the angle of refraction were proportional to the diminution of wave-length for a prism of any material, the resulting spectrum would also be normal.

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  • In studying the dispersion of the aniline dyes, a prism with a very small refracting angle is made of two glass plates slightly inclined to each other and enclosing a very thin wedge of the dye, which is either melted between the plates, or is in the form of a solution retained in position by surface-tension.

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  • Only very thin layers are sufficiently transparent to show the dispersion near or within an absorption band, and a large refracting angle is not required, the dispersion usually being very considerable.

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  • Those genera, like Paradoxides, Olenus, Asaphus, Phillipsia and others, in which this groove cuts the posterior edge of the head-shield on the inner side of its angle are referred to the Opisthoparia; those, like Dalmanites and Phacops, in which it cuts the lateral border in front of the posterior angle, belong to the Proparia.

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  • But in certain genera, like Conocoryphe, Calymmene and Triarthrus, it cuts the margin of the head-shield so close to the posterior angle that the distinction between the two groups practically breaks down.

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  • into an acute angle enclosed on the N.E.

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  • At one angle, a square pillared projection contains the marble fountain or monks' lavatory, evidently the work of Moslem sculptors.

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  • angle of an irregular trapezium of land which lay between the rivers Husur (Khausar, Choser) on the N.W., Gomal on the N.E.

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  • The prior's group "entered at the south-east angle of the green court, placed near the most sacred part of the cathedral, as befitting the distinguished ecclesiastics or nobility who were assigned to him."

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  • Extending from the south-east angle of the main group of buildings are the walls and foundations of a secondary group of considerable extent.

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  • angle of the nave.

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  • The earliest form of shutter weir, known as a bear-trap, introduced in the United States in 1818, and subsequently erected across the Marne in France, consists of two wooden gates, each turning on a horizontal axis laid across the apron, inclined towards one another and abutting together at an angle in the centre when the weir is closed; the up-stream one serves as the weir, and the down-stream one forms its support, and both fall flat upon the apron for opening the weir.'

    0
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  • - N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in areal co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.

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  • =ordi- The escribed circle opposite the angle A is - sqr +(s - c)rp Hates.

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  • - Data: radius=a; 0= circular measure of angle subtended at centre by arc; c = chord of arc; c 2 = chord of semi-arc; c 4 = chord of quarter-arc.

    0
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  • 2-}-cos B It is readily shown that the latter gives the best approximation to 0; but, while the former requires for its application a knowledge of the trigonometrical ratios of only one angle (in other words, the ratios of the sides of only one right-angled triangle), the latter requires the same for two angles, 0 and 3B.

    0
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  • The right and left hepatic ducts, while still in the transverse fissure, unite into a single duct which joins the cystic duct from the gall bladder at an acute angle.

    0
    0
  • The polar clock, devised for use in place of a sun-dial, applies the fact that the plane of polarization of sky light is always 90° from the position of the sun; hence by measuring the azimuthal angle of the plane, even when the sun is below the horizon, correct apparent solar time may be obtained.

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  • Excavations have revealed one street and the north-west angle of the town walls, while the local museum contains over 2000 inscriptions, besides statues and other antiquities.

    0
    0
  • Mactridae.-External gill-plate directed ventrally; siphons united, invested by a chitinous sheath; foot long, bent at an angle, without byssus.

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  • of Andria, was constructed by Frederick II., who frequently resided here; it is an octagonal building in two storeys with octagonal towers at each angle, and was further surrounded by three outer walls.

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

    0
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  • On making a mesial vertical section of the uterus the cavity is seen as a mere slit which is bent about its middle to form an angle the opening of which is forward.

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    0
  • In addition to this, its long axis forms a marked angle with that of the vagina, so that the whole uterus is bent forward or anteverted.

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  • The round ligament is a cord of unstriped muscle which runs from the lateral angle of its own side of the uterus forward to the internal abdominal ring, and so through the inguinal canal to the upper part of the labium majus.

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  • in length, curved at the small end into a right angle, and terminating in a small round orifice, which is applied to the flame, while the larger end is applied to the mouth.

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  • SANCTI SPIRITUS, an old Cuban city in Santa Clara province, situated on a sandy plain in an angle of the Yayabo river, which winds through the city.

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  • angle of the Federal District (Districto Federal) formerly known as the Neutral Municipality (Municipio Neutro), an independent district or commune with an area of 538 sq.

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  • angle of the Praga da Republica, and the library building of the Gabinete Portuguez da Leitura with its exquisite " Manuelino " façade of Lisbon marble.

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  • The second section, Castoroidea, of the present group includes only the family Castoridae, represented by the beavers, which are large aquatic rodents characterized by their massive skulls, devoid of post-orbital processes, with the angle of the lower jaw rounded, the molars rootless or semi-rooted, with re-entering enamel-folds, and one pair of premolars above and below.

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  • The angle FIG.

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  • The upper lip is cleft, the jugal lacks an inferior angle, the fore part of the skull is short and broad; the cheek-teeth are partially rooted, with external and internal enamel-folds, the soles of the feet are smooth, there are six pairs of teats, the clavicles are imperfect and the tail is not prehensile.

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  • The jugal is without an inferior angle, and extends forwards to the lachrymal; the palate is contracted in front and deeply emarginate behind; the incisors are short, and the molars divided by continuous folds into transverse plates; and the two halves of the lower jaw are welded together in front.

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  • Associated with this is the strength and sharpness of the lower jaw, the prominence and anterior pcsition of the masseteric ridge, and the depth of the ramus from the alveolar line to the angle.

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  • If the bearer be stationary, rain-drops will traverse the tube without touching its sides; if, however, the person be walking, the tube must be inclined at an angle varying as his velocity in order that the rain may traverse the tube centrally.

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  • Hence for the rain to centrally traverse the tube, this must be inclined at an angle BAD to the vertical; this angle is conveniently termed the aberration due to these two motions.

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  • the angle between the March and September positions, being 40".

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  • The rest of the book treats of the trisection of an angle, and the solution of more general problems of the same kind by means of the quadratrix and spiral.

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  • biveau, a joiner's instrument), the inclination of one surface of a solid body to another; also, any angle othef than a right angle, and particularly, in joinery, the angle to which a piece of timber has to be cut.

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  • The mechanic's instrument known as a bevel consists of a rule with two arms so jointed as to be adjustable to any angle.

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  • The measurement of the declination involves two separate observations, namely, the determination of (a) the magnetic meridian and (b) the geographical meridian, the angle between the two being the declination.

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  • This arrangement is not very convenient, as it is difficult to protect the mirror from accidental displacement, so that the angle between the geometrical and magnetic axes may vary.

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  • The method of measuring the horizontal component which is almost exclusively used, both in fixed observatories and in the field, consists in observing the period of a freely suspended magnet, and then obtaining the angle through which an auxiliary suspended magnet is deflected by the magnet used in the first part of the experiment.

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  • What is known as the method of sines is used, for since the axes of the two magnets are always at right angles when the mirror magnet is in its zero position, the ratio M/H is proportional to the sine of the angle between the magnetic axis of the mirror magnet and the magnetic - = meridian.

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  • The difference between the two sets of readings gives twice the angle which the magnetic axis of the mirror magnet makes with the magnetic meridian.

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  • Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting m