# Arc sentence example

arc

- An arc of lightning left her father's hand and slammed the stranger into the wall.
- Holding out her arm, she was fascinated to see the rain arc to avoid it.
- The shortest line joining any two points is an arc of a great circle.
- Joan of Arc defeated the English here in 1429.
- Edith at first looked shocked, but almost at once, her face melted to a resigned look—a condemned maiden mounting the guillotine steps, Joan of Arc as the match ignited her pyre.Advertisement
- He hooked the light to his belt where it swung in an eerie arc, casting jumping shadows on the rock-strewn slope and yellow streaks into nothingness.
- 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.
- The municipal electric-lighting plant was in 1907 producing arc lights for $34 per arc, per year.
- The surface of the inland ice forms in a transverse section from the west to the east coast an extremely regular curve, almost approaching an arc of a wide circle, which along Nansen's route has its highest ridge somewhat nearer the east than the west coast.
- He sold Joan of Arc to the English.Advertisement
- The length of the arc of a circle, for instance, is known if the length of the chord and its distance from the middle point of the arc are known; but it may be more convenient in such a case to use a formula such as Huygens's rule than to obtain a more accurate result by means of trigonometrical tables.
- The value in terms of arc of the scale of the record can be obtained by measuring the distance between the magnet mirror and the recording drum, and in most observations it is such that a millimetre on the record represents one minute of arc. The time scale ordinarily employed is 15 mm.
- This involves a loss of accuracy because, with a spiderline micrometer, the accidental error of pointing is of the order of o I" of arc.
- The area of the complete curve is 2a 2, and the length of any arc may be expressed in the form f(1 - x 4) - i dx, an elliptic integral sometimes termed the lemniscatic integral.
- Howles, who, employing a high tension alternating arc, showed that the effectiveness depended upon the temperature.Advertisement
- Lovejoy at Niagara Falls, who passed atmospheric air, or air enriched with oxygen, about a high tension arc made as long as possible; but the company (the Atmospheric Products Company) was a failure.
- The arc is produced by leading a current of about 5000 volts equatorially between the poles of an electromagnet; this produces what is practically a disk of flame, 62 ft.
- In the process of the Badische Anilinand Soda-Fabrik, the arc, which is said to be 30 to 50 ft.
- The Rankin process, of which very little is known, produces the arc with much lower current.
- When made bishop of Orleans in 1849, he pronounced a fervid panegyric on Joan of Arc, which attracted attention in England as well as France.Advertisement
- The Château du Milieu (1lth to 15th centuries) comprises the keep, the Pavillon de 1'Horloge and the Grand Logis, in the principal apartment of which the first meeting between Joan of Arc and Charles VII.
- The military posts were drawn up in echelon along the frontier of the desert, especially along the southern slopes of the Aures, as far as Ad Majores (Besseriani), and on the Tripolitan frontier as far as Cydamus (Ghadames), forming an immense arc extending from Cyrenaica to Mauretania.
- Between the two and at the highest point of the arc, so far as morphological differentiation is concerned, stands the scorpion; near to it in the trilobite's direction (that is, on the ascending side) are Limulus and the Eurypterines - with a long gap, due to obliteration of the record, separating them from the trilobite.
- The strange nobody-crabs or Pycnogonids occupy a place on the ascending half of the arc below the Eurypterines and Limulus.
- Under these circumstances the arc to be considered is bisected at 0, and its length is proportional to the width of the slit.Advertisement
- If the slit is of 'constant width and we require the illumination at various points on the screen behind it, we must regard the arc of the curve as of constant length.
- If the slit be narrow, so that the arc is short, the intensity is constant over a wide range, and does not fall off to an important extent until the discrepancy of the extreme phases reaches about a quarter of a period.
- The toga was a piece of woollen cloth in the form of a segment of a circle, 2 the chord of the arc being about three times the height of the wearer, and the height a little less than one-half of this length.
- This will be evident if we consider that, since radii vectores of the hodograph represent velocities in the orbit, the elementary arc between two consecutive radii vectores of the hodograph represents the velocity which must be compounded with the velocity of the moving point at the beginning of any short interval of time to get the velocity at the end of that interval, that is to say, represents the change of velocity for that interval.
- Hence the elementary arc divided by the element of time is the rate of change of velocity of the moving-point, or in other words, the velocity in the hodograph is the acceleration in the orbit.Advertisement
- The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
- Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.
- The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before.
- Johnson in England Arc appear, in 1853, to have introduced the earliest practical form of furnace.
- When used for ore smelting, the reduced metal and the accompanying slag were to be caught, after leaving the arc and while still liquid, in a hearth fired with ordinary fuel.Advertisement
- At once the attractive force of the solenoid on the iron cylinder was automatically reduced, and the falling of the latter caused the negative carbon to rise, starting an arc between it and the metal in the crucible.
- A counterpoise was placed on the solenoid end of the balance beam to act against the attraction of the solenoid, the position of the counterpoise determining the length of the arc in the crucible.
- Any change in the resistance of the arc, either by lengthening, due to the sinking of the charge in the crucible, or by the burning of the carbon, affected the proportion of current flowing in the two shunt circuits, and so altered the position of the iron cylinder in the solenoid that the length of arc was, within limits, automatically regulated.
- Were it not for the use of some such device the arc would be liable to constant fluctuation and to frequent extinction.
- In the latter case the crucible, which was placed in the cavity immediately beneath the arc, was about 3 in.Advertisement
- He also arranged an experimental tubefurnace by passing a carbon tube horizontally beneath the arc ' Cf.
- The temperature of the electric furnace, whether of the arc or incandescence type, is practically limited to that at which the least easily vaporized material available for electrodes is converted into vapour.
- The arc furnaces now widely used in the manufacture of calcium carbide on a large scale are chiefly developments of the Siemens furnace.
- Godin, a member of the French commission for measuring an arc of the meridian near Quito, became professor of mathematics at San Marcos in 1750; and the botanical expeditions sent out from Spain gave further zest to scientific research.
- As the meteors have been numerously visible in five or six successive years it follows they must be pretty densely distributed along a considerable arc of their orbit.Advertisement
- There arc also remains of a well-preserved Roman theatre, close to the left bank of the river.
- There arc four narrow avenues connecting this remarkable body of water with the Pacific and the Japan Sea; that on the west, called Shirnonoseki Strait, has a width of 3000 yds., that on the south, known ai Hayarnoto Strait, is 8 m.
- On the south is the arc of the Luchu islands, which penetrates into Kill Shill.
- Iii the centre there is the arc of the Izu-no-Shichito islands, which is continued into Hondo along the Fossa Magna.
- In North Hondo the great Bandai arc forms the axis of the island and stretches into Yezo (HokkaidO).Advertisement
- The ordinary colloquial differs materially from its polite form, and both arc as unlike the written form as modern Italian is unlike ancient Latin.
- Suess pointed out that it was surrounded by a curved line of earth-fracture, following an arc drawn from a centre in the Lipari Islands, from Catanzaro to Etna, and so westward; within this arc he held that the crust of the earth is gradually sinking, and is in an unstable condition.
- Thus if the ellipsoid is one of revolution, and ds is an element of arc which sweeps out the element of surface dS, we have dS = 27ryds = 27rydx/ (Ts) = 27rydx/ (b y) = 2 p2 dx.
- In order that no other settlements should encroach upon his centre of government, New Castle, the northern boundary was determined by drawing an arc of a circle, 12 m.
- The differences of the readings of the screw, when converted into arc, afford the means of measuring the variations of the sun's apparent diameter.
- The screw, turned by the wheels at g', acts in a toothed arc, whence, as shown in the figure, equal and opposite motion is communicated to the slides by the jointed rods v, v.
- Acetylene is readily decomposed by heat, polymerizing under its influence to form an enormous number of organic of compounds; indeed the gas, which can itself be directly prepared from its constituents, carbon and hydrogen, under the influence of the electric arc, can be made the startingpoint for the construction of an enormous number of different organic compounds of a complex character.
- The arc is struck in a crucible into which the mixture is allowed to flow, partially filling it.
- An ingot gradually builds up from the bottom of the crucible, the carbon electrode being raised from time to time automatically or by hand to suit the diminution of resistance due to the shortening of the arc by the rising ingot.
- This takes place when in the manufacture of the carbide the material is kept too long in contact with the arc, since this overheating causes the dissociation of some of the calcium carbide and the solution of metallic calcium in the remainder.
- 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.
- But Landen's capital discovery is that of the theorem known by his name (obtained in its complete form in the memoir of 1775, and reproduced in the first volume of the Mathematical Memoirs) for the expression of the arc of an hyperbola in terms of two elliptic arcs.
- Gilles de Laval, sire de Retz (1404-1440), the comrade-in-arms of Joan of Arc and marshal of France, gave himself over to the most revolting debauchery, and was strangled and burned at Nantes.
- Skoda howitzer, which is really a mortar as defined above, direction is given by means of a pointer on the mounting and a graduated arc on the bed.
- The centroid is sometimes called the centre of volume, centre of area, or centre of arc. The proof of the existence of the centroid of a figure is the same as the proof of the existence of the centre of gravity of a body.
- They may be applied, for instance, to finding the centroid of a semicircle or of the arc of a semicircle.
- Draw the tangents at A and B, meeting at T; draw TV parallel to the axis of the parabola, meeting the arc in C and the chord in V; and M draw the tangent at C, meeting AT and BT in a and b.
- Then it may be shown that DE is parallel to AB, and that the area of the figure between chord DE and arc DE is half the sum of the areas DHA and EJB.
- Certain approximate formulae for the length of an arc of a circle are obtained by methods similar to those of §§ 71 and 79.
- 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.
- The method of § 71 then shows that, by taking a (4L 0 - L 2) as the value of the arc, we get rid of terms in 0 2.
- If we use c 1 to represent the chord of the whole arc, c 2 the chord of half the arc, and c 4 the chord of one quarter of the arc, then corresponding to (i) and (iii) of § 70 or § 79 we have a (8c 2 - c i) and4 5 (256c 4 - 40c2+ci) as approximations to the length of the arc. The first of these is Huygens's rule.
- It forms an arc of a circle of which the convexity turns slightly to the north; neither bay nor promontory breaks the regularity of its outline.
- After this disaster he issued a third Mississippi Valley novel, The Tragedy of Pudd'nhead Wilson, in 1894, and in 1896 another historical romance, Personal Recollections of Joan of Arc, wherein the maid is treated with the utmost sympathy and reverence.
- The whisper seems to creep round the gallery horizontally, not necessarily along the shorter arc, but rather along that arc towards which the whisperer faces.
- He allowed a limited number of teeth on the arc of a circle to strike against a card.
- The shortest distance between two points on a sphere is the arc of the great circle containing the points.
- The extremities of the diameter perpendicular to a small circle are called the "poles" of that circle, and the distance from the pole to the circle, measured by the arc of the great circle through the pole, is the "polar distance" of the small circle.
- A toothed arc fixed to the revolving platform or to the live ring serves to give motion to the bridge.
- The vertical distortion of the curve must not be so great that there is a very sensible difference between the length of the arc and its chord.
- From 1792 to 1799 he was occupied with the measurement of the arc of the meridian extending from Dunkirk to Barcelona, and published a detailed account of the operations in Base du systeme metrique (3 vols., 1806, 1807, 1810), for which he was awarded in 181 o the decennial prize of the Institute.
- It is situated in a plain overlooking the Arc, about a mile from the right bank of the river.
- The direction of the folds in the older series is in Iviza nearly west to east, in Majorca south-west to north-east, and in Minorca south to north, thus forming an arc convex towards the south-east.
- 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.
- Also the velocity v at the end of the arc is given by (87) ve = u e sec 0 cos n.
- It is used in the manufacture of carbon rods for arc lights, and for the negative element in the Bunsen battery.
- The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.
- A relation which is of historical interest connects the logarithmic function with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.
- Thus if a horizontal slit is illuminated by an arc lamp, and the light - rendered parallel by a collimating lens - is transmitted through the sodium tube and focused on the vertical slit of a spectroscope, the effect of the sodium vapour is to produce its refraction spec trum vertically on the slit.
- On the 24th of May 1430, Joan of Arc having been taken prisoner at Compiegne, within the limits of his diocese, Cauchon acted as her accuser, and demanded the right of judging her.
- The dwindlings and growths of Nevada down to the present day, and to not a slight degree the general history of the settlement of the states of the Rocky Mountain region, arc a commentary on the fate of mining industries.
- In Dec. 1917 the defensive line at Aden described an arc of about 11 m.
- The figure included by two radii and an arc is a " sector," e.g.
- As far as the circlesquaring functions are concerned, it would seem that Gregory was the first (in 1670) to make known the series for the arc in terms of the tangent, the series for the tangent in terms of the arc, and the secant in terms of the arc; and in 1669 Newton showed to Isaac Barrow a little treatise in manuscript containing the series for the arc in terms of the sine, for the sine in terms of the arc, and for the cosine in terms of the arc. These discoveries 1 See Euler, ” Annotationes in locum quendam Cartesii," in Nov.
- If this be applied to the right-hand side of the identity m m m 2 m2 tan-=- - n n -3n-5n" it follows that the tangent of every arc commensurable with the radius is irrational, so that, as a particular case, an arc of 45 having its tangent rational, must be incommensurable with the radius; that is to say, 3r/4 is an incommensurable number."
- The metal as obtained in this process is lustrous and takes a polish, does not melt in the oxyhydrogen flame, but liquefies in the electric arc, and is not affected by air at ordinary temperatures.
- Especially when large gratings are employed do we find that the electric arc alone seems sufficient to give vibrations of the requisite power.
- The metals may be introduced into the arc in various ways, and in some cases where they can be obtained in sufficient quantity the metallic electrodes may be used in the place of carbon poles.
- The definition of temperature given above, though difficult in the case of a flame and perhaps still admissible in the case of an electric arc, becomes precarious when applied to the disruptive phenomena of a spark discharge.
- When, however, the time of discharge is lengthened, the conditions of the arc are more nearly approached.
- Their presence indicates the characteristic difference between the spark and the arc. The name is due to Sir Norman Lockyer, who has studied these lines and drawn the attention of astronomers to their importance in interpreting stellar spectra.
- Another much disputed spectrum is that giving the bands which appear in the electric arc; it is most frequently ascribed to cyanogen, but occasionally also to carbon vapour.
- Proposition 30 describes the construction of a curve of double curvature called by Pappus the helix on a sphere; it is described by a point moving uniformly along the arc of a great circle, which itself turns about its diameter uniformly, the point describing a quadrant and the great circle a complete revolution in the same time.
- With the exception of the fluoride, these substances are readily soluble in water and arc deliquescent.
- Even in France the English lost ground steadily after the victory of Joan of Arc before Orleans in 1429.
- The great chain of volcanoes which runs through Sumatra and Java is continued eastwards into the Moluccas, and terminates in a hooklike curve which passes through the Damar Islands to the Banda group. Outside this hook lies a concentric arc of non-volcanic islands, including Tenimber, the Lesser Kei Islands, Ceram and Buru; and beyond is still a third concentric arc extending from Taliabu to the Greater Kei Islands.
- Eruptive rocks of supposed Cretaceous age are met with in these outer islands, but Tertiary and recent volcanic lavas are confined to the innermost arc. Halmahera lies outside these arcs.
- Following the first chart of lines of equal variation compiled by Edmund Halley in 1700, charts of similar type have been published from time to time embodying recent observations and corrected for the secular change, thus providing seamen with values of the variation accurate to about 30' of arc. Possessing these data, it is easy to ascertain by observation the effects of the iron in a ship in disturbing the compass, and it will be found for the most part in every vessel that the needle is deflected from the magnetic meridian by a horizontal angle called the deviation of the compass; in some directions of the ship's head adding to the known variation of the place, in other directions subtracting from it.
- On the adjacent Borough Hill arc extensive earthworks, and the discovery of remains here and at Burnt Walls, immediately south, proves the existence of a considerable Roman station.
- Volcanic rocks are also present but they are not so extensively developed as in the islands of the Javan arc. The Permian beds consist chiefly of limestone and contain numerous fossils similar to those of the middle and upper divisions of the Productus limestone of northern India and the Artinsk stage of the Urals.
- Alumina itself is so refractory that it cannot be melted save by the oxyhydrogen blowpipe or the electric arc, and except in the molten state it is not susceptible of decomposition by any chemical reagent.
- The first successful idea of using electricity depended on the enormous heating powers of the arc. The infusibility of alumina was no longer prohibitive, for the molten oxide is easily reduced by carbon.
- That this process did not depend upon electrolysis, but was simply an instance of electrical smelting or the decomposition of an oxide by means of carbon at the temperature of the electric arc, is shown by the fact that the Cowles furnace would work with an alternating current.
- This powder, provided that it has not been too' strongly ignited, is soluble in strong acids; by ignition it becomes denser and nearly as hard as corundum; it fuses in the oxyhydrogen flame or electric arc, and on cooling it assumes a crystalline form closely resembling the mineral species.
- The folds run, in general, in the direction of the chain, and together they form an arc around the plain of Lombardy and Piedmont.
- Outside this arc lies a depression along which the waters of the upper Danube and the lower Rhone find their way towards the sea; and beyond rise the ancient crystalline masses of Bohemia, the Black Forest and the central plateau of France, together with the intervening Mesozoic beds of southern Germany and the Jura.
- Upon the outer side of the arc the central zone of crystalline rocks is flanked by Mesozoic and Tertiary belts; towards the west, indeed, the individuality of these belts is lost, to a large extent, but the rocks remain.
- The most important ones are either " arc " furnaces, i.e.
- The Heroult furnace, the best known in the arc class, and the Kjellin and Roechling-Rodenhauser fur- lc naces, the best known of the induction class, will serve as examples.
- This furnace may be used also for purifying the molten metal, but it is not so well suited as the arc furnaces for dephosphorizing.
- Electric furnaces are at an advantage over others as regards the removal of sulphur and of iron oxide from the molten steel, because their atmosphere is free from the sulphur always present in the flame of coal-fired furnaces, and almost free from oxygen, because this element is quickly absorbed by the carbon and silicon of the steel, and in the case of arc furnaces by the carbon of the electrodes themselves, and is replaced only very slowly by leakage, whereas through the Bessemer converter and the open-hearth furnace a torrent of air is always rushing.
- A collar is provided, which when tightened on the vertical axis, otherwise free to move, holds it rigidly in position with respect to the plate PP. To this collar is attached a slow-motion screw, working against a reaction spring, by which the plate rr can be rotated through a small arc. The upper plate carrying two, three .or four verniers vv is attached to a vertical coned pillar passing through the centre of the larger pillar and rotating in it; this plate can be clamped to the lower plate by means of the screw C, and can be rotated with respect to it by the slow-motion screw d.
- In the more ancient part of Coblenz arc several buildings which have an historical interest.
- Mechain in the attempt to determine an arc of the meridian, and the greater number of the instruments employed in the task were invented by him.
- It is, however, infusible at the temperature of the electric arc, but becomes converted superficially into graphite.
- Zoliverein, with the exception of Bavaria, Wflrttemberg Baden and Alsace-Lorraine, in which countries the excise duties arc separately collected.
- The Total in Reichskanzler is the sole responsible official, In the Pacific and conducts all the affairs of the empire, with German New G the exception of such as arc of a purely military Bismarck Archrj character, anti is the intermediary between the Caroline, Pelewa emperor, the Bundesrat and the Reichstag.
- They arc empowered, subject to the limits set by the law, to regulate their own business by means of a general meeting and of elected committees.
- In 1424 he was taken prisoner by the English at Verneuil, but was released shortly afterwards, and fought with Joan of Arc at Orleans and Patay in 1429.
- Usually the under or concave edge of the arc is the more clearly defined, and adjacent to it the sky often seems darker than elsewhere.
- Frequently an arc or band is visibly composed of innumerable short rays separated by distinctly less luminous intervals.
- These rays are more or less perpendicular to the arc or band; sometimes they are very approximately parallel to one another, on other occasions they converge towards a paint.
- Not infrequently rays extend from the upper edge of an arc towards the zenith.
- Auroral Meridian.-It is a common belief that the summit of an auroral arc is to be looked for in the observer's magnetic meridian.
- Birkeland (19), who has made a special study of magnetic disturbances in the Arctic, proceeding on the hypothesis that they arise from electric currents in the atmosphere, and who has thence attempted to deduce the position and intensity of these currents, asserts that whilst in the case of many storms the data were insufficient, when it was possible to fix the position of the mean line of flow of the hypothetical current relatively to an auroral arc, he invariably found the directions coincident or nearly so.
- Of course the phenomenon might be due to actual change in the arc, but it is at least consistent with the view that arcs are of two kinds, one form constituting a layer of no great vertical depth but considerable real horizontal width, the other form having little horizontal width but considerable vertical depth, and resembling to some extent an auroral curtain.
- One end only, for example, may appear to move, as if rotating round the other; or the two ends may move in opposite directions, as if the arc were rotating about a vertical axis through its summit.
- If an auroral arc represented a definite selfluminous portion of space of small transverse dimensions at a uniform height above the ground, its height could be accurately determined by observations made with theodolites at the two ends of a measured base, provided the base were not too short compared to the height.
- On one occasion twelve observations, extending over half an hour, were made on a single arc, the calculated heights varying in a fairly regular fashion from 1 6 to 12.9 km.
- The calculated horizontal distances of this arc varied between 5 and 24 km.
- The heights calculated in this way for the under surface of the arc, have usually exceeded 100 M.; some have been much in excess of this figure.
- Heights have been calculated in various less direct ways, by observing for instance the angular altitude of the summit of an arc and the angular interval between its extremities, and then making some assumption such as that the portion visible to an observer may be treated as a circle whose centre lies over the so-called auroral pole.
- The Swedish Expedition (17) of 1899-1902, engaged in measuring an arc of the meridian in Spitsbergen, were unusually well provided spectrographically, and succeeded in taking photographs of aurora in conjunction with artificial lines-chiefly of hydrogen-which led to results claiming exceptional accuracy.
- With a period of 18 seconds, and the record-receiving paper at a distance of about 15 ft., a deflection of I millimetre of the light spot may indicate a tilting of AD part of a second of arc, or I in.
- It is possible to adjust the apparatus so that a tilt of Tolua sec. of arc, or a change of slope of t in.
- For the movement which was to lead to the deliverance of France from the English invaders, see Joan Of Arc. The siege of Orleans was raised by her efforts on the 8th of May 1429, and two months later Charles VII.
- His wife, Mrs Hertha Ayrton, whom he married in 1885, assisted him in his researches, and became known for her scientific work on the electric arc and other subjects.
- The resplendent medieval colouring of the subject, the essentially heroic character of Joan of Arc, gave Schiller an admirable opportunity for the display of his rich imagination and rhetorical gifts; and by an ingenious alteration of the historical tradition, he was able to make the drama a vehicle for his own imperturbable moral optimism.
- The arc y r is set so as to reflect the rays in the required direction.
- Fizeau he carried on a series of investigations on the intensity of the light of the sun, as compared with that of carbon in the electric arc, and of lime in the flame of the oxyhydrogen blowpipe; on the interference of heat rays, and of light rays differing greatly in lengths of path; and on the chromatic polarization of light.
- Suppose now, for the moment, that the readings of the levels k and l are identical in both observations, we have then, in the difference between the micrometer readings north and south, a measure of the difference of the two zenith distances expressed in terms of the micrometer screw; and, if the "` value of one revolution of the micrometer screw" is known in seconds of arc we have for the resulting latitude FIG.
- The value of "one revolution of the screw in seconds of arc" can be determined either by observing at transit the difference of zenith distance of two stars of known declination in terms of the micrometer screw, the instrument remaining at rest between their transits; or by measuring at known instants in terms of the screw, the change of zenith distance of a standard star of small polar distance near the time of its greatest elongation.
- For otherwise, if they had from some unknown cause the same actual motion, the apparent motion in arc would be different.
- We have no more of her work until 1429, when she broke her silence to write a song in honour of Joan of Arc. Of the circumstances of her death nothing is known but it probably took place about this time.
- In reality, the sensation and the belief arc sufficient; when I feel a sensible pressure, I cannot help believing in its reality, and therefore judging that it is real, without any tertium quid - an idea of pressure, or of existence or of pressure existing - intervening between the sensation and the belief.
- Thus we see at once why the shadows cast by the sun or moon are in general so much less sharp than those cast by the electric arc. For, practically, at moderate distances the arc appears as a mere luminous point.
- But if we place a body at a distance of a foot or two only from the arc, the shadow cast will have as much of penumbra as if the sun had been the source.
- Evidences of shallow water conditions arc abundant; very frequently on the bedding surfaces of sandstones and other rocks we find cracks made by the sun's heat and pittings caused by the showers that fell from the Cambrian sky, and these records of the weather of this remote period are preserved as sharply and clearly as those made only to-day on our tidal reaches.
- Domremy was the birthplace of Joan of Arc, and the cottage in which'she was born still stands.
- Above the door are the arms of France and of Joan of Arc and an inscription of 1481 reading "Vive labeur; vive le roi Louys."
- Again, the locus of G is an arc of an ellipse whose centre is in the intersection of the planes; since this arc is convex upwards the equilibrium is unstable.
- Obviously OV is parallel to the tangent to the path atP, and its magnitude is ds/dt, where s is the arc. If we project OV on the co-ordinate axes (rectangular or oblique) in the usual manner, the projections u, v, w are called the component velocities parallel to the axes.
- The following table gives the period, for various amplitudes a, in terms of that of oscillation in an infinitely small arc about a vertical axis half-way between the points of attachment of the upper string.
- Such arc the phenomena of the action of a machine, arranged in the order of can sation.
- It is divided by the pitch-point I into two .partsthe arc or line of approach described by T in approaching the line of centres, and the arc or line of recess described by T after having passed the line of centres.
- Let DID be the path of contact, consisting of the arc of approach DI and the arc of recess ID.
- Make d bf=pc, cg=pc. From f, with the radiusfa, draw the circular arc ah; from g, with the radius ga, / B
- Let r1 be the radius of the large end of each, ri that of the small end, r, that of the middle; and let Ii be the sagitta, measured perpendicular to the axes, of the arc by whose revolution each of the conoids is generated, or, in other words, the bulging of the conoids in the middle of their length.
- Intermittent LinkworkClick and Ratchet.A click acting opon a ratchet-wheel or rack, which it pushes or pulls through a certain arc at each forward stroke and leaves at rest at each backward stroke, is an example of intermittent linkwork.
- It follows therefore that there arc as many possible mechanisms as there are links in the chain.
- Let Ti be the tension of the free part of the band at that side towards which it tends to draw the pulley, or from which the pulley tends to draw it; 1, the tension of the free part at the other side; T the tension of the band at any intermediate point of its arc of contact with the pulley; 0 the ratio of the length of that arc to the radius of the pulley; do the ratio of an indefinitely small element of that arc to the radius; F=TiT2 the total friction between the band and the pulley; dF the elementary portion of that friction due to the elementary arc do; f the coefficient of friction between the materials of the band and pulley.
- Then, according to a well-known principle in statics, the normal pressure at the elementary arc do is TdO, T being the mean tension of the band at that elementary arc; consequently the friction on that arc is dF =JTdo.
- Let a denote the arc of contact expressed in turns and fractions of a turn; then O=62832a 6
- In July 1808 Davy laid a request before the managers of the Royal Institution that they would set on foot a subscription for the purchase of a specially large voltaic battery; as a result he was provided with one of 2000 pairs of plates, and the first experiment performed with it was the production of the electric arc light between carbon poles.
- This invention in conjunction with an alternating current dynamo provided a new and simple form of electric arc lighting.
- He waged continual warfare against the English in Maine until the advent of Joan of Arc. He fought at Jargeau, at Meung-sur-Loire and at Patay (1429).
- In 1429 Joan of Arc made Blois her base of operations for the relief of Orleans.
- Then, so the story ran, she drew him from his indolence, continuing the work of Joan of Arc, both by nerving the king to warlike enterprises - she did apparently induce him to take part personally in the conquest of Normandy - and by surrounding him with that band of wise advisers who really administered France during her ascendancy.
- The molten metal is sea-green in colour, and at higher temperatures (in the electric arc) it vaporizes and burns with a green flame.
- Baluch, the language of Baluchistan, also very closely akin to New Persian, but especially distinguished from it in that all the old spirants arc changed into explosives, e.g.
- Orleans, the last bulwark of royalty, had been besieged since the 12th of October 1428, and was on the point of surrender when Joan of Arc appeared.
- His more important monuments are those to Admiral Courbet (1890) at Abbeville and the famous "Joan of Arc."
- Outside the arc of the mountain chain no sign of this crumpling is to be detected except in the Salt Range, and the Peninsula of India has been entirely free from folding of any importance since early Palaeozoic times, if not since the Archean period itself.
- The practical effect of the bactericidal action of solar light is the destruction of enormous quantities of germs in rivers, the atmosphere and other exposed situations, and experiments have shown that it is especially the pathogenic bacteria - anthrax, typhoid, &c. - which thus succumb to lightaction; the discovery that the electric arc is very rich in bactericidal rays led to the hope that it could be used for disinfecting purposes in hospitals, but mechanical difficulties intervene.
- Bredig's process consists in passing an electric arc between silver electrodes under water, when a brown solution is obtained.
- He co-operated in the Danish and Hanoverian measurements of an arc and trigonometrical operations (1821-1848), and wrote (1843, 1846) the two memoirs Ãœber GegenstÃnde der hÃ¶heren GeodÃsie.
- In the meantime, in June 1429, he joined Joan of Arc at Orleans, and fought in several battles under her banner, till the influence of La Tremoille forced his withdrawal from the army.
- From this it follows that when the wing rises the body falls, and vice versa - the wing describing the arc of a large circle (f f), the body (b), or the weights (w, w') representing it, describing the arc of a small circle.
- Plinlimmon (2468 ft.) is the highest of the hills, and forms a sort of hydrographic centre for the group, as from its eastern base the Severn and the Wye take their rise - the former describing a wide curve to east and south, the latter forming a chord to the arc in its southward course.
- Sir Christopher Wren, the famous architect, determined the length of the arc and its centre of gravity, and Pierre Fermat deduced the surface of the spindle generated by its revolution.
- The length of any arc may be determined by geometrical considerations or by the methods of the integral calculus.
- Bruns in 1889; measured an arc of the meridian in East Prussia in 1831-1832; and deduced for the earth in 1841 an ellipticity of 2 4 9.
- In a bundle examined in the basal portion of a leaf the bulk of the xylem is found to be centrifugal in position, but internally to the protoxylem there is a group of centripetal tracheids; higher up in the petiole the xylem is mainly centripetal, the centrifugal wood being represented by a small arc of tracheids external to the protoxylem and separated from it by a few parenchymatous elements.
- In 1436 an impostor appeared, professing to be Joan of Arc escaped from the flames, who succeeded in inducing many people to believe in her statement, but afterwards confessed her imposture.
- The sentence passed on Joan of Arc was revoked by the pope on the 7th of July 1456, and since then it has been the custom of Catholic writers to uphold the reality of her divine inspiration.
- As an historical figure, it is impossible to dogmatize concerning the personality of Joan of Arc. The modern clerical view has to some extent provoked what appears, in Anatole France's learned account, ably presented as it is, to be a retaliation, in regarding her as a clerical tool in her own day.
- Until the 19th century the history of Joan of Arc was almost entirely neglected; Voltaire's scurrilous satire La Pucelle, while indicative of the attitude of his time, may be compared with the very fair praises in the Encyclopedie.
- Of the numerous dramas and poems of which Joan of Arc has been the subject, mention can only be made of Die Jungfrau von Orleans of Schiller, and of the Joan of Arc of Southey.
- Light from an arc lamp was so directed that only that part reached the spectroscope which fell upon the flame of the burner at grazing incidence, and was thereby refracted.
- Little else is known about Monstrelet except that he was present, not at the capture of Joan of Arc, but at her subsequent interview with Philip the Good, duke of Burgundy.
- The length of the chord of the arc across the valley is about 250 ft.
- The box, I, has a hinged bottom with a projecting click finger which, as the box de - scends, plays idly over the staves of a ladder arc. When the weight is removed from the platform, the counterbalance, E, causes the finger, G, to run back to its zero position, carrying with it the finger M, and causing the click finger of the box, I, to trip open the bottom of the box and let the penny fall out.
- A circular arc, centre D and radius c/2, meets D E in K, and the perpendicular KL gives 2c sin a.
- The resistance to slipping of a flat belt on a pulley may be obtained by considering the equilibrium of a small arc of the pulley surface subtending an angle dB at the centre, and having tensions T and T+dT at its extremities.
- In architecture, a crescent is a street following the arc of a circle; the name in this sense was first used in the Royal Crescent at Bath.
- From this depth of despair the party which, with all its faults, represented the national sentiment of France was rescued by the astonishing exploits of Joan of Arc. Charles and joan Of his counsellors had no great confidence in the mission of this prophetess and champion, when she presented herself to them, promising to relieve Orleans and turn back the English.
- The natural drift of circumstances was not stayed even by the disastrous end of the career of Joan of Arc in 1430.
- If it is not so, the government is inclined to proscribe unpopular opinion, and to forget that new opinions by which the greatest benefits arc likely to be conferred are certain at first to be entertained by a very few, and are quite certain to be unpopular as soon as they come into collision with the opinions of the majority.
- The construction in fact is, join the two points in which the third circle meets the first arc, and join also the two points in which the third circle meets the second arc, and from the point of intersection of the two joining lines, let fall a perpendicular on the line joining the centre of the two circles; this perpendicular (considered as an indefinite line) is what Gaultier terms the " radical axis of the two circles "; it is a line determined by a real construction and itself always real; and by what precedes it is the line joining two (real or imaginary, as the case may be) intersections of the given circles.
- If a line S2 cut an arc aa at b, so that the two segments ab, ba lie on opposite sides of the line, then projecting the figure so that the line Sl goes off to infinity, the tangent at b is projected into the asymptote, and the arc ab is projected into a hyperbolic leg touching the asymptote at one extremity; the arc ba will at the same time be projected into a hyperbolic leg touching the same asymptote at the other extremity (and on the opposite side), but so that the two hyperbolic legs may or may not belong to one and the same branch.
- Next, if the line S2 touch at b the arc aa so that the two portions ab, ba lie on the same side of the line Sl, then projecting the figure as before, the tangent at b, that is, the line S2 itself, is projected to infinity; the arc ab is projected into a parabolic leg, and at the same time the arc ba is projected into a parabolic leg, having at infinity the same direction as the other leg, but so that the two legs may or may not belong to the same branch.
- His method was to sift out the long dark waves which are associated with the short visible waves constituting the light of the sun or of the electric arc and to concentrate the former to a focus.
- According to Tyndall, 9 0% of the radiation from the electric arc is non-luminous.
- The arc being struck in the usual way between two carbons, a concave mirror, placed close behind it, caused a large part of the radiation to be directed through an aperture in the camera and concentrated to a focus outside.
- As the upshot, the Historia coelestis, embodying the first Greenwich star-catalogue, together with the mural arc observations made 1689-1705, was issued under Edmund Halley's editorship in 1712.
- Accordingly, in conjunction with Christopher Maire, an English Jesuit, he measured an arc of two degrees between Rome and Rimini.
- The committee decided in favour of the latter and a commission was appointed to measure the arc of the meridian between Dunkirk and Mont Jany, near Barcelona.
- Applying this deviation to the measured arc, the true zenith distance of the body is found.
- Among the fruits of the strenuous career of Nicolas Louis de Lacaille were tables of the sun, in which terms depending upon planetary perturbations were, for the first time, introduced (1758); an extended acquaintance with the southern heavens; and a determination of the moon's parallax from observations made at opposite extremities of an arc of the meridian 85' in length.
- It was further investigated by John Wallis, Christiaan Huygens (who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661).
- The rate of actual rotation is substantially uniform, while the arc through which the moon moves from day to day varies.
- Not the slightest change in the direction of such a star when in this position has ever been detected, and it is certain that if any occurs it can be but a minute fraction of a second of arc. As an atmosphere equal to ours in density would produce a deviation of an important fraction of a degree, it may be said that the moon can have no atmosphere exceeding in density the b b l o o that of the earth.
- He was taken prisoner at the siege of Montargis in 1427, and again at the battle of Rouvrai in 1429; but in September of the latter year he repulsed Joan of Arc's attack upon Paris.
- Although flowers growing on the ground or on shrubs are not conspicuous for number or beauty, there arc many fine flowering trees, such as Poinciana regia, presenting a mass of scarlet flowers; 1 The words in parentheses are the native Malagasy names.
- In Paris he advocated the measurement of an arc of the meridian in Lapland, and took part, in 1736, in the expedition organized for the purpose by the French Academy.
- Cassini, obtained employment, first in surveying the coast from Nantes to Bayonne, then, in 1 739, in remeasuring the French arc of the meridian.
- Among its results were determinations of the lunar and of the solar parallax (Mars serving as an intermediary), the first measurement of a South African arc of the meridian, and the observation of io,000 southern stars.
- The Carpathians, which, extending in the form of an arc, form the boundary between Galicia and Hungary, are divided into the West and the East Beskides, which are separated by the northern ramifications of the massif of the Tatra.
- An arc with centre 0 and radius OB forms part of a curve.
- Then with centre 0 1 and radius OJ, =OA 1, describe an arc. By reflecting the two arcs thus described over the centre the ellipse is approximately described.
- On the north there arc numerous small indentations, many of which form convenient harbours, although the current flowing along the coast from the west often leaves in the stiller water at their mouths Coaat-Unes, obstruction bars.
- Geology.Geologically the Spanish Peninsula consists of a great massif of ancient rock, bordered upon the north, east and south by zones of folding in which the Mesozoic and early Tertiary beds arc involved.
- It stretches from Gahicia arc Asturias on the north to the valley of the Guadaiquivir on tiw south, and includes the mountains of Castile, the Sierra de Toledc and the Sierra Morena.
- But other fragments stil rose above the waves, and of these the great irassif of Portugal arc western Spain was one.
- This case arises when the visual angle, under which the object appears, is approximately a minute of arc; it is due to the physiological construction of the retina, for the ends of nerve fibres, which receive the impression of light, have themselves a definite size.
- The only sources of light are sunlight or the electric arc. The limit at which sub-microscopic particles are made visible is dependent upon the specific intensity of the source of light.
- They were in a burnt-out roomâ€¦with the Arc de Triomphe a short distance away.
- Edith at first looked shocked, but almost at once, her face melted to a resigned lookâ€”a condemned maiden mounting the guillotine steps, Joan of Arc as the match ignited her pyre.
- The sub-story concludes well, but the overall arc has yet to reach apogee.
- Gas flow meter fitted Electronic HF to start the welding arc.
- The reflex arc The three types of neurones are arranged in circuits and networks, the simplest of which is the reflex arc.
- The circumzenithal arc is the most beautiful of all the halos.
- I will definitely need to use the carbon arc brazing attachment on my arc welder for some fine touches on outer wing.
- We merely replaced the arc lamp we had used until then with another arc lamp three times as strong.
- Excitation is via one or more laser sources, or via mercury arc illumination.
- The application interpreting an initial linkbase arc may choose to limit the number of steps processed in the chain.
- This is achieved by using a plasma arc, where energy is released by an electrical discharge in an inert atmosphere.
- Both carbon and alloy steels are produced in electric arc furnaces and scrap rather than molten metal is used as the base material.
- To the right of Hercules lie the arc of stars making up Corona Borealis and then Bootes with its bright star Arcturus.
- For information on other aspects of diet, including oily fish and fish oils, see the arc booklet ' Diet and Arthritis ' .
- It means the shiny arc of reflected light on a chrome bumper instead of the smith's blacking on a hammered iron rail.
- An imposing central concourse will lead to the shopping area, which will arc out in both directions.
- Focused on esthetics, Arc is a functional room for the garden which will appeal to design conscious consumers.
- The result is in the range of - pi /2 through pi /2. acos( x) arc cosine of an angle.
- As the sun climbs the upper tangent arc opens and then droops like a gull's wings.
- Metal transfer The transfer of metal across the arc from a consumable electrode to the molten pool.
- The arc booklet ' fibromyalgia ' is a useful patient aid.
- Arc furnace A steel melting furnace in which heat is generated by an arc between graphite electrodes and the metal.
- Minutes and a report of the geodetic Arc Committee containing reports by Gill and Ardagh on geodetic surveys in Africa, 1900.
- Graphics Point, line, circle and arc drawing commands in high-resolution graphics Point, line, circle and arc drawing commands in high-resolution graphics.
- Waders present included greenshank, green and wood sandpiper and snipe as well as eight black-tailed godwits on the ARC pit.
- A glaucous gull was reported from the ARC site this morning.
- The image, however, also shows a faint circular halo beneath the arc.
- Four iron hoops arc across the boat, on top of which is a roll of green canvas.
- Unlike type I systems, type II systems arc inherently inflationary.
- Sources of such energy include lasers, arc discharge lamps, and tungsten halogen bulbs.
- To see a picture of the arc lectern with reflective film click here.
- Each target may be operated in either unbalanced magnetron or cathodic arc mode.
- A series of C -terminal deletions of Rx were made at conserved motifs in the ARC domain.
- In 2002, they examined the region of the brain's hypothalamus containing the arcuate nucleus, or ARC.
- The second method is to increase the arc of the shorter oar to achieve the same cord length illustrated by the red line.
- In 1657 he became the first to find the arc length of an algebraic curve when he rectified the cubical parabola.
- The arc of jagged peaks rises steeply form the sea and dominates the skyline for miles around.
- The second part of this arc starts at the 12 o ' clock quadrant point and ends at roughly 10 o ' clock.
- Creating a new location from an arc raster file A new location can be built up from an Arc raster file.
- These were the ones that had mercury arc rectifiers.
- Mercury arc rectifiers have now been made totally obsolete by semiconductors, although there are a few still in service in old installations.
- A mercury arc rectifier consists of a pool of mercury in a vacuum tube.
- In the wheel rut 's clinging dark watch an arc of bright cloud, blue sky.
- One white streamer moved at an estimated 3,000 m.p.h. in an arc for 20 seconds.
- Continue to use quartz tungsten halogen curing lights as plasma arc curing lights appear to confer no clinical advantage at the present time.
- Between 1968 and 1974 there was a rising arc of labor unrest.
- The voltage waveform shows a complete absence of any beat envelope following the initiation of an arc to ground.
- There are other more specialist arc welding processes such as spot welding or seam welding which work without a filler.
- X 5 mm., the sides of this square being parallel spider webs 4" of arc apart; the size of the square is reckoned from centre to centre of these double webs.
- Each of the two micrometer screws X and Y moves a system of six parallel webs, placed 4" of arc apart from each other.
- Pure amorphous boron is a chestnut-coloured powder of specific gravity 2.45; it sublimes in the electric arc, is totally unaffected by air at ordinary temperatures, and burns on strong ignition with production of the oxide B 2 0 3 and the nitride BN.
- This Antoine de Chabannes, count of Dammartin in right of his wife, fought under the standard of Joan of Arc, became a leader of the Ecorcheurs, took part in the war of the public weal against Louis XI., and then fought for him against the Burgundians.
- Fleming devised a method which has practical advantages in both preventing the arc and permitting the oscillatory currents to be controlled so as to make electric wave signals.
- Monstrosities.A large class of cases of departure from the normal form, depending on different and often obscure causes, may be grouped together under this heading; most of them arc of the kind termed Teretological, and it is difficult to decide how far they should be regarded as pathological if we insist that a disease threatens the existence of the plant, since many of these malformationse.g.
- Each arc was measured with every precaution and a multitude of observations.
- He also wrote a suggestion for reform in the administration of justice entitled Libellus de optimo ordine forenses lites audiendi et deferendi; an Apologia, written to answer the charges brought against him by Louis XI.; a Breviloquium, or allegorical account of his own misfortunes; a Peregrinatio; a defence of Joan of Arc entitled Opinio et consilium super processu et condemnatione Johanne, dicte Puelle, and other miscellaneous writings.
- This defect appears most strongly in his treatment of Joan of Arc; and the attack on Agnes Sorel seems to have been dictated by the dauphin (afterwards Louis XI.), then a refugee in Burgundy, of whom he was afterwards to become a severe critic. He was not, however, misled, as his more picturesque predecessor Froissart had been, by feudal and chivalric tradition into misconception of the radical injustice of the English cause in France; and except in isolated instances where Burgundian interests were at stake, he did full justice to the patriotism of Frenchmen.
- The ChÃ¢teau du Milieu (1lth to 15th centuries) comprises the keep, the Pavillon de 1'Horloge and the Grand Logis, in the principal apartment of which the first meeting between Joan of Arc and Charles VII.
- Hence, in accordance with the rule for compounding vector quantities, the resultant vibration at B, due to any finite part of the primary wave, is represented in amplitude and phase by the chord joining the extremities of the corresponding arc (U2-0.1).
- Minor improvements in tangent sights certainly were made, notably an automatic clamp, but quadrant elevation was mainly used, and in the case of guns equipped with position-finders (see Range-Finder) the guns could be layed for direction by means, of a graduated arc on the emplacement and a pointer on the mounting.
- If we bisect AB and CD in P and Q respectively, and describe the arc PQ of a circle with centre 0, the length of this arc is 2(b+a)0; and b - a =AB.
- The data for the area ADQ are a series of values of u corresponding to equidifferent values of x; if we denote by y the distance of a point on the arc AD from QD, we can from the series of values of u construct a series of values of y corresponding to equidifferent values of u, and thus find the area of ADQ, treating QD as the base.
- This proposition is the basis of the "great circle sailing" of navigators, and the arc of the great circle is called the "rhumbline" or "loxodromic curve."
- The Indians on reservations and in Indian schools include members of the Yankton, Yanktonai, Oglala, Brule, Sisseton, Wahpeton, Flandreau, Sioux, Blackfeet, Miniconjou, Sans Arc and Ute tribes, on the Standing Rock and Cheyenne River reservations in the north of the state, the Lower Brule and Crow Creek reservations in the central part, and the Pine Ridge and Rosebud reservations in the south.
- During the Revolution, he was one of the three members of the council established to introduce the decimal system, and he was also a member of the commission appointed to determine the length of the metre, for which purpose the calculations, &c., connected with the arc of the meridian from Barcelona to Dunkirk were revised.
- But, as originally pointed out by Euler, the difficulty can be turned if we notice that in the ordinary trajectory of practice the quantities i, cos i, and sec i vary so slowly that they may be replaced by their mean values,, t, cos 7 7, and sec r t, especially if the trajectory, when considerable, is divided up in the calculation into arcs of small curvature, the curvature of an arc being defined as the angle between the tangents or normals at the ends of the arc.
- Treating this final velocity v e and angle 0 as the initial velocity vo and angle 4) of the next arc, the calculation proceeds as before (fig.
- Ingalls, U.S.A., for approximating to a high angle trajectory in a single arc, which assumes that the mean density of the air may be taken as the density at two-thirds of the estimated height of the vertex; the rule is founded on the fact that in an unresisted parabolic trajectory the average height of the shot is two-thirds the height of the vertex, as illustrated in a jet of water, or in a stream of bullets from a Maxim gun.
- Of the makers of paper boxes, of shirts, collars and cuffs, of hosiery and knitting mill operatives, of glove-makers, silk mill operatives and book-binders they are more than half; so also of other textile workers, excluding wool and cotton mill operatives (these last the second largest group of women workers in manufactures), in which occupations males arc in a slight excess.
- The length of a parabolic arc can be obtained by the methods of the infinitesimal calculus; the curve is directly quadrable, the area of any portion between two ordinates being two thirds of the circumscribing parallelogram.
- The arc Cs is graduated, and is set so that the angle COD equals the complement of the sun's declination.
- His "Triumph of the Republic" (1881-1886), a vast quadriga for the Arc de Triomphe, Paris, is perhaps more amazingly full of life than others of his works, all of which reveal this quality of vitality in superlative degree.
- He co-operated in the Danish and Hanoverian measurements of an arc and trigonometrical operations (1821-1848), and wrote (1843, 1846) the two memoirs ÃƒÅ“ber GegenstÃƒnde der hÃƒ¶heren GeodÃƒsie.