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arc

An arc of lightning left her father's hand and slammed the stranger into the wall.

22190Holding out her arm, she was fascinated to see the rain arc to avoid it.

8833The shortest line joining any two points is an arc of a great circle.

6146Joan of Arc defeated the English here in 1429.

4736He emerged from the shadow world in a luxurious penthouse suite in Paris overlooking the Arc de Triomphe.

1818adjust the frequency so that it has the value of the normal time period of the circuit formed of the condenser and transformer secondary circuit, and thus it is possible to obtain condenser oscillatory discharges free from any admixture with alternating current arc. In this manner the condenser discharge can be started or stopped at pleasure, and long and short discharges made in accordance with the signals of the Morse FIG.

11107He 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.

108The 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.

1010Edith 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.

96The voyage of Lord Anson to the Pacific in 1740-1744 was of a predatory character, and he lost more than half his men from scurvy; while it is not pleasant to reflect that at the very time when the French and Spaniards were measuring an arc of the meridian at Quito, the British under Anson were pillaging along the coast of the Pacific and burning the town of Payta.

912He waved his flashlight in an arc above his head and repeated the two words, a quake in his voice.

810Duddell, " On Rapid Variations in the Current through the Direct Current Arc," Journ.

65Duddell discovered in 1900 that if a continuous current carbon arc had its carbon electrodes connected by a condenser in series with an inductance, then under certain conditions oscillations were excited in this condenser circuit which appeared to be continuous.

67She'd never left the country and couldn't help but stare in wonder at the romantically lit Arc de Triomphe.

613The document is entitled "Secrett Inventionis, proffitabill and necessary in theis dayes for defence of this Iland, and withstanding of strangers, enemies of God's truth and religion," a and the inventions consist of (1) a mirror for burning the enemies' ships at any distance, (2) a piece of artillery destroying everything round an arc of a circle, and (3) a round metal chariot, so constructed that its occupants could move it rapidly and easily, while firing out through small holes in it.

613I am going because... well, because everyone is going: and besides--I am not Joan of Arc or an Amazon.

55More effective was the electric arc. In 1892 Sir W.

44This result created a great sensation, and proved that Transatlantic electric wave telegraphy was quite feasible and not inhibited by distance, or by the earth's curvature even over an arc of a great circle 3000 m.

35Poulsen immensely improved this process by placing the arc in an atmosphere of hydrogen, coal-gas or some other nonoxidizing gas, and at the same time arranging it in a strong magnetic field.'

35They were in a burnt-out room…with the Arc de Triomphe a short distance away.

36If instead of imagining to ourselves commanders of genius leading the Russian army, we picture that army without any leaders, it could not have done anything but make a return movement toward Moscow, describing an arc in the direction where most provisions were to be found and where the country was richest.

36The earlier deposits of that sea now rise to the surface in Brittany, the Ardennes, the Montagne Noire and the Cvennes, and in all these regions they arc intensely folded.

310These layers arc secreted by the protoplasm by the direct apposition of substances on those already in existence; and they may go on increasing in thickness, both by apposition and by the intussusception of particles probably carried in through the protoplasmic fibres, which penetrate the cell-wall as long as the cell lives.

22The southern group of the Malay Archipelago, from Sumatra to Java and Timor, extends in the arc of a circle between 95° and 127° E., and from 5° to 10° S.

22To paint a Joan of Arc who lives and dies inglorious is the theme she sets herself, and through most of the novel it is perfectly executed.

24In order to produce electric oscillations in the system, the first or alternating current transformer must charge the condenser connected to its secondary terminals, but must not produce a permanent electric arc between the balls.

24Various devices have been suggested for extinguishing the arc and yet allowing the condenser oscillatory discharge to take place.

24The so-called musical arc of Duddell has been the subject of considerable investigation, and physicists are not entirely in accordance as to the true explanation of the mode of production of the oscillations.

24The electric arc is formed between cooled copper (positive) and carbon (negative) electrodes in an atmosphere of hydrogen or coal-gas.

24Across the arc is a transverse or radial magnetic field, and the electrodes are connected by an oscillatory circuit consisting of a condenser and inductance.

24As regards habit of life the vast majority of Hydromedusae arc 6 FIG.

24This consists of a few xylem elements, e a a segment of phloem, pericycle, and usually an arc of h~s endodermis, which closes round the bundle as it detaches ~

24The stereom is furnished either by cortical cells or by the tracheal elements, in a few cases by fibres which arc probably homologous with sievetubes.

24In recent apparatus, to enable it to be used on board ship, a hydrogeneous spirit is used which is fed drop by drop into the chamber in which the arc is worked.

25The municipal electric-lighting plant was in 1907 producing arc lights for $34 per arc, per year.

10The 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.

10Rev., 1904, 18, 370) in the electric arc.

10He sold Joan of Arc to the English.

10raining dials placed on the mountings where they can be read by the layers, and more accurate elevation indicators have made laying by quadrant elevation, and in certain cases giving direction by means of graduated arc and pointer, both accurate and rapid, so that once more this system of laying is coming into favour for long ranges.

10ALIDADE (from the Arab.), the movable index of a graduated arc, used in the measurement of angles.

10The 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.

10The 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.

10The vertical through the centre of gravity of the arc AP (see fig.

10Arago, with whom he had already carried out investigations on the refractive properties of different gases, in the measurement of an arc of the meridian in Spain, and in subsequent years he was engaged in various other geodetic determinations.

11The great geographical event of the century, as regards that continent, was the measurement of an arc of the So meridian.

12The arc measured was 3° 7' 3" in length; and the work consisted of two measured bases connected by a series of triangles, one north and the other south of the equator, on the meridian of Quito.

121738, Pierre Louis Moreau de Maupertuis, Alexis Claude Clairaut, Charles Etienne Louis Camus, Pierre Charles Lemonnier and the Swedish physicist Celsius measured an arc of the meridian in Lapland.

12ln, rn, Primarily left nephridium W, Wooden arc representing and primarily right nephthe base-line of the wall ridium.

12It fuses easily in the electric arc. It oxidizes superficially when heated, but fairly rapidly when ignited in an oxidizing blowpipe flame, forming a black smoke of the oxide.

12- The shortest distance between two places on the surface of a globe is represented by the arc of a great circle.

12Ptolemy were translated into Arabic, and in 827, in the reign of the caliph Abdullah al Mamun, an arc of the meridian was measured in the plain of Mesopotamia.

12In France, in the meantime, an arc of the meridian had been measured (1669-1670) by Jean Picard, numerous longitudes had been observed between 1672 and 1680 by the same, and by Phil.

12Crookes showed that the arc brought about combination; and in 1897 Lord Rayleigh went into the process more fully.

12It appears, however, to depend upon the fact that an electric arc is not like a solid conductor.

13The chief silk-producing provinces arc Lombardy, Venetia and Piedmont.

13For the illumination of large stations by night electric arc lamps are frequently employed, but some authorities favour high-pressure incandescent gas-lighting.

13Increase in the voltage acting upon a solid conductor increases the current through it, but in the case of the electric arc an increase in current is accompanied by a fall in the difference of potential of the carbons, within certain limits, and the arc has therefore been said to possess a negative resistance.'

14Since 1890 further and more rigorous application of the telegraphic method of determining longitudes differentially with Greenwich has resulted in a slight correction (amounting to about 2" of arc) to the previous determination by the same method through Suez.

17The hilly regions of Limousin, Prigord and the Cvennes are the home of the chestnut, which in some places is still a staple food; walnuts grow on the lower levels of the central plateau and in lower Dauphin and Provence, figs and almonds in Provence, oranges and citrons on the Mediterranean coast, apricots in central France, the olive in Provcnce and the lower valleys of the Rhneand Durancc. Truffles arc found under Silk Cocoons.

116The impedance of the primary or alternator circuit is so adjusted that when both the chokers are in circuit the current flowing is not sufficient to charge the condensers; but when one choker is short-circuited the impedance is reduced so that the condenser is charged, but the alternating arc is not formed.

123Such train ferries arc common in America, especially on the Great Lakes, and exist at several places in Europe, as in the Baltic between Denmark and Sweden and Denmark and Germany, and across the Straits of Messina.

131equatorial telescope, is the first position micrometer constructed capable of measuring position angles to 1' of arc.

00This involves a loss of accuracy because, with a spiderline micrometer, the accidental error of pointing is of the order of o I" of arc.

00Elec. Eng., 1900, 30, p. 232; P. Janet, " On Duddell's Musical Arc."

00The 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.

00Howles, who, employing a high tension alternating arc, showed that the effectiveness depended upon the temperature.

00Lovejoy 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.

00The 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.

00In the process of the Badische Anilinand Soda-Fabrik, the arc, which is said to be 30 to 50 ft.

00long or more, is formed in a long tube, and the gases are sent round the arc by obliquely injecting them.

00The Rankin process, of which very little is known, produces the arc with much lower current.

00Sodium nitrite, the most commonly used salt of the acid, is generally obtained by heating the nitrate with metallic lead; by heating sodium nitrate with sulphur and sodium hydroxide, the product then being fractionally crystallized;(Read, Holliday & Sons): 3NaNO 3 +S+2NaOH = Na2S04+3NaN02+H20; by oxidizing atmospheric nitrogen in an electric arc, keeping the gases above 300° C., until absorption in alkaline hydroxide solution is effected (German Pat.

00When made bishop of Orleans in 1849, he pronounced a fervid panegyric on Joan of Arc, which attracted attention in England as well as France.

00The 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.

00The 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.

00Between 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.

00The strange nobody-crabs or Pycnogonids occupy a place on the ascending half of the arc below the Eurypterines and Limulus.

00Under these circumstances the arc to be considered is bisected at 0, and its length is proportional to the width of the slit.

00If 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.

00If 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.

00The 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.

00This 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.

00Hence 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.

00The 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 '.

00Silicon hydride, SiH4, is obtained in an impure condition, as a spontaneously inflammable gas, by decomposing magnesium silicide with hydrochloric acid, or by the direct union of silicon and hydrogen in the electric arc. In the pure state it may be prepared by decomposing ethyl silicoformate in the presence of sodium (C. Friedel and A.

00ABC is a quadrant in which the line AB and the arc AC are divided into the same number of equal parts.

00Radii 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.

00The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before.

00by passing a powerful electric arc discharge through moist air and absorbing the nitric acid formed by lime.

00- Independently of the question of the application of external heating, the furnaces used in electrometallurgy may be broadly classified into (i.) arc furnaces, in which the intense heat of the electric arc is utilized, and (ii.) resistance and incandescence furnaces, in which the heat is generated by an electric current overcoming the resistance of an inferior conductor.

00Johnson in England Arc appear, in 1853, to have introduced the earliest practical form of furnace.

00When 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.

00At 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.

00A 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.

00Any 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.

00Were it not for the use of some such device the arc would be liable to constant fluctuation and to frequent extinction.

00In the latter case the crucible, which was placed in the cavity immediately beneath the arc, was about 3 in.

00He also arranged an experimental tubefurnace by passing a carbon tube horizontally beneath the arc ' Cf.

00The 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.

00The arc furnaces now widely used in the manufacture of calcium carbide on a large scale are chiefly developments of the Siemens furnace.

00Godin, 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.

00As 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.

00There arc also remains of a well-preserved Roman theatre, close to the left bank of the river.

00There 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.

00On the south is the arc of the Luchu islands, which penetrates into Kill Shill.

00Iii the centre there is the arc of the Izu-no-Shichito islands, which is continued into Hondo along the Fossa Magna.

00In North Hondo the great Bandai arc forms the axis of the island and stretches into Yezo (HokkaidO).

00The ordinary colloquial differs materially from its polite form, and both arc as unlike the written form as modern Italian is unlike ancient Latin.

0029 expedition for the measurement of the arc of the meridian in 1816-1852.

00Suess 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.

00Thus 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.

00In 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.

00The differences of the readings of the screw, when converted into arc, afford the means of measuring the variations of the sun's apparent diameter.

00focus, would correspond with 2" of arc. But, after all, this is no practical difficulty, for screws can be used to separate the lenses, and, by these screws, as in a Gascoigne micrometer, the separation of the lenses can be measured; or we can have scales for this purpose, read by microscopes, like the Troughton 1 circles of Piazzi or Pond, or those of the Carey circle, with almost any required accuracy.

00The 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.

00105-115) to determine the division error of every line on both scales with a probable error corresponding to 0 " 0092 arc.

00Acetylene 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.

00The arc is struck in a crucible into which the mixture is allowed to flow, partially filling it.

00An 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.

00It is infusible at temperatures up to 2000° C., but can be fused in the electric arc. When heated to temperature of 2 4 5° C. in a stream of chlorine gas it becomes incandescent, forming calcium chloride and liberating carbon, and it can also be made to burn in oxygen at a dull red heat, leaving behind a residue of calcium carbonate.

00This 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.

00The 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.

00But 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.

00Gilles 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.

00Skoda 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.

00sight is placed on the top of the arc. In FIG.

00Hence area Abdc=ABX arc PQ.

00The 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.

005, the volume of the element between these planes, when h is very small, is approximately h X AB X arc PQ = h.

00They may be applied, for instance, to finding the centroid of a semicircle or of the arc of a semicircle.

006) be any arc of a parabola; and suppose we require the area of the figure bounded by this arc and the chord AB.

00Draw 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.

00CV; and therefore the area of the figure bounded by AK, BL, KL and the arc AB, is KL.

00- In § 23 the area of a right trapezium has been expressed in terms of the base and the two sides; and in § 34 the area of a somewhat similar figure, the top having been replaced by an arc of a parabola, has been expressed in terms of its base and of three lengths which may be regarded as the sides of two separate figures of which it is composed.

00Then 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.

00Draw the tangents at A and B, meeting at T; and through T draw a line parallel to KA and LB, meeting the arc AB in C and the chord AB in V.

00Certain approximate formulae for the length of an arc of a circle are obtained by methods similar to those of §§ 71 and 79.

00Let 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.

00The 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.

00If 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.

00It 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.

00After 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.

00The whisper seems to creep round the gallery horizontally, not necessarily along the shorter arc, but rather along that arc towards which the whisperer faces.

00He allowed a limited number of teeth on the arc of a circle to strike against a card.

00The concentration of the various Japanese armies on one battlefield was to be made, not along the circumference of the long arc they occupied, but towards the centre.

00The shortest distance between two points on a sphere is the arc of the great circle containing the points.

00The 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.

00A toothed arc fixed to the revolving platform or to the live ring serves to give motion to the bridge.

00The arc of rotation is 82°, and the axis of rotation is 13 ft.

0072 with arcs of the length 1,, l2, l3, &c., and with the radii r1, r 2, &c. (note, for a length 2l 1 at each end the radius will be infinite, and the curve must end with a straight line tangent to the last arc), then let v be the measured deflection of this curve from the straight line, and V the actual deflection of the bridge; we have V = av/b, approximately.

00The 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.

00The chief commodities of trade arc coal, grain, lumber, flour and various products of the city's own manufactories.

00From 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.

00Lalande's Astronomie (1792), and republished in an improved form by the bureau of longitudes in 1817; Methodes analytiques pour la determination d'un arc du meridien (1799); Tables du soleil (publiees par le bureau des longitudes) (1806); Rapport historique sur les progres des sciences mathematiques depuis l'an 1789 (181o); A brege d'astronomie (1813); Astronomic theorique et pratique (1814); &c.

00It is situated in a plain overlooking the Arc, about a mile from the right bank of the river.

00The 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.

00Replacing 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.

00di g d tan i g dt - v cos i ' and now (53) dx d 2 y dy d2xdx Cif dt 2 dt dt2 _ - _ gdt' and this, in conjunction with (46) dy _ d y tan i = dx dt/dt' (47)di d 2 d d 2 x dx sec 2 idt = (ctt d t - at dt2) I (dt), reduces to (48) Integrating from any initial pseudo-velocity U, (60) du t _ C U uf(u) x= C cos n f u (u) y=C sin n ff (a); and supposing the inclination i to change from 0, to 8 radians over the arc.

00The difficulty is avoided by the use of Siacci's altitude-function A or A(u), by which y/x can be calculated without introducing sin n or tan n, but in which n occurs only in the form cos n or sec n, which varies very slowly for moderate values of n, so that n need not be calculated with any great regard for accuracy, the arithmetic mean 1(0+0) of ¢ and B being near enough for n over any arc 4)-8 of moderate extent.

00Now 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.

00Now calculate the pseudo-velocity uo from =v 95 cos 4) sec n, and then, from the given values of 0 and 8, calculate u e from either of the formulae of (72) or (73): (82) I (u 9) - I (u0) tan 0 - tan 8 C sec n (83) D(ue) =D (uq5) 4)°-B° cos n' Then with the suffix notation to denote the beginning and end of the arc 0-0, mt e = C[Tum) - T (u0)], 5 ((x x9 1l 0.

00Also the velocity v at the end of the arc is given by (87) ve = u e sec 0 cos n.

00In 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.

00It is used in the manufacture of carbon rods for arc lights, and for the negative element in the Bunsen battery.

00The element carbon unites directly with hydrogen to form acetylene when an electric arc is passed between carbon poles in an atmosphere of hydrogen (M.

00arc tOe por:e in fp:crc: fo: t h er o io the l'ympottt of hcren.

00Ztc ffeb arc rho' that trtourne:fo: they f ha.ib% cotttfo:teb. ?.?lc?ctiart the tttcre: fo: 4 ieyfha!!

00lcifeb arc they which iitffrcperfitucicrt rigiycirefiic4 fafc:fo:ttseraiet4ctynOotttofhcrcn.

004c men fOatfrcryteyou/anbper(ccutc you/ artb O at f at f iy f:ayc ail of a e 141.'101 a i lay'tlrt you 1,-.r fly cioyc+t all arc u)youre rc roHr =' FIG.

00The 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.

00A 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.

00Thus 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.

00He had commenced them with a survey of Livonia (1816-1819), which was followed by the measurement of an arc of meridian of more than 31° in the Baltic provinces of Russia (Beschreibung der Breitengradmessung in den Ostseeprovinzen Russlands, 2 vols.

00This work was afterwards extended by Struve and General Tenner into a measurement of a meridional arc from the north coast of Norway to Ismail on the Danube (Arc du meridien de 25° 20' entre le Danube et la Mer Glaciale, 2 vols.

00On 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.

00The 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.

00In Dec. 1917 the defensive line at Aden described an arc of about 11 m.

002), is termed an " arc "; and the plane figure enclosed by a chord and arc, e.g.

00The figure included by two radii and an arc is a " sector," e.g.

00Arc and Sector.

00- 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.

00Exact formulae are: - Arc =a0, where 8 may be given directly, or indirectly by the relation c=2a sin 28.

00Area of sector =100 = z radius X arc.

00Approximate formulae are: - Arc=3(8c 2 - c) (Huygen's formula); arc = s (c - 40c, +256c4).

00distance of mid-point of arc from chord.

00Approximate formulae are: - Area = 15 (6c+ 8c 2)h; = 11,/ (c2+h42) h; = i, (7 c +3 a) h, a being the true length of the arc.

007 angled at C, ADB is the semicircle described on AB as diameter, AEB the circular arc described with centre C and radius CA= CB.

009): ACB being a semicircle whose centre is 0, and AC the arc to be rectified, he produced AB to D, making BD equal to the radius, joined DC, 1 Vieta, Opera math.

00and produced it to meet the tangent at A in E; and then his assertion (not established by him) was that AE was nearly equal to the arc AC, the error being in defect.

00II) whose centre is 0, AC its chord, and HK the tangent drawn at the middle point of the arc and bounded by OA, OC produced, then, according to Archimedes, AMC AC. In modern trigonometrical notation the propositions to be compared stand as follows: 2 tan 20 >2 sin 28 (Archimedes); tan 10+2 sin 3B>0> 3 sin B (Snell).

00As 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.

00If 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."

00the Debonair was deposed in 833; and at the siege of the town in 1430 Joan of Arc was taken prisoner by the English.

00and England (1451), and undertook, ex officio, the revision of the trial of Joan of Arc; he afterwards reformed the statutes of the university of Paris.

00The 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.

00Especially when large gratings are employed do we find that the electric arc alone seems sufficient to give vibrations of the requisite power.

00The 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.

00The 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.

00(f) The relative intensity of lines in the spark taken from metallic poles may be altered by the insertion of greater or smaller capacities, similarly the relative intensities are different in arc and spark spectra.

00When, however, the time of discharge is lengthened, the conditions of the arc are more nearly approached.

00Their 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.

00Another 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.

00Proposition 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.

00With the exception of the fluoride, these substances are readily soluble in water and arc deliquescent.

00Even in France the English lost ground steadily after the victory of Joan of Arc before Orleans in 1429.

00The 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.

00Eruptive 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.

00the temperature of the sun and of the electric spark, others again with electro-photometry and the chemistry of the electric arc. With Professor J.

00Following 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.

00The arc contained between any two points is 11° 15'.

00on Lake Erie, on the east where the Delaware river with two large bends separates it from New York and New Jersey, and in the south-east where the arc of a circle which was described with a 12-m.

00With a battery of five Grove cells and a Ruhmkorff coil of medium size, a somewhat short spark, or arc, of about 5 mm.

00On 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.

00Volcanic 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.

00Alumina 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.

00The 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.

00That 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.

00This 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.

00Col de Gebroulaz (Arc Valley to Moutiers Tarentaise), snow (W) ï¿½ Col de Monei (Cogne to Locana), snow (E) Col du Grand Paradis (Ceresole to the Val Savaranche), snow (E)..

00in 1875 only); Operations geodesiques et astronomiques pour la mesure d'un arc du parallele moyen (2 vols., 1825-1827); H.

00The folds run, in general, in the direction of the chain, and together they form an arc around the plain of Lombardy and Piedmont.

00Outside 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.

00Upon 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.

00The most important ones are either " arc " furnaces, i.e.

00The 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.

00This furnace may be used also for purifying the molten metal, but it is not so well suited as the arc furnaces for dephosphorizing.

00Electric 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.

00A 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.

00In the more ancient part of Coblenz arc several buildings which have an historical interest.

00Mechain 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.

00It is, however, infusible at the temperature of the electric arc, but becomes converted superficially into graphite.

00Zoliverein, with the exception of Bavaria, Wflrttemberg Baden and Alsace-Lorraine, in which countries the excise duties arc separately collected.

00The 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.

00They 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.

00In 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.

00Usually the under or concave edge of the arc is the more clearly defined, and adjacent to it the sky often seems darker than elsewhere.

00Frequently an arc or band is visibly composed of innumerable short rays separated by distinctly less luminous intervals.

00These 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.

00Not infrequently rays extend from the upper edge of an arc towards the zenith.

004 .-Auroral Curtain Below An Arc.

00Auroral Meridian.-It is a common belief that the summit of an auroral arc is to be looked for in the observer's magnetic meridian.

00Birkeland (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.

00Of 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.

00Dividing the whole number of arcs, 156, whose angular velocities were measured into three numerically equal groups, according to their altitude, the following were the results in minutes of arc per second of time (or degrees per minute of time): - Each group contained auroras which appeared stationary.

00One 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.

00If 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.

00On 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.

00The calculated horizontal distances of this arc varied between 5 and 24 km.

00The 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.

00Heights 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.

00The 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.

00With 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.

00It is possible to adjust the apparatus so that a tilt of Tolua sec. of arc, or a change of slope of t in.

00For 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.

00was crowned at Reims. Charles's intimate counsellors, La Tremoille and Regnault de Chartres, archbishop of Reims, saw their profits menaced by the triumphs of Joan of Arc, and accordingly the court put every difficulty in the way of her military career, and received the news of her capture before Compiegne (1430) with indifference.

00had resolved on the rehabilitation of Joan of Arc, thus rendering a tardy recognition of her services.

00His 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.

00The 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.

00The arc y r is set so as to reflect the rays in the required direction.

00Fizeau 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.

00In 1849 he contributed to the Comptes Rendus a description of an electromagnetic regulator for the electric arc lamp, and, in conjunction with H.

00distant from Epinal; from the lower Moselle to Girancourt the works are grouped principally about Uxegney and Sarchey; from Girancourt to the upper river and Fort de la Mouche a long ridge extends in an arc, and on this south-western section the principal defence is Fort Ticha and its annexes.

00part of France was in English hands; when he was five years old, Joan of Arc appeared; he was just six when his father was crowned at Reims. But his boyhood was spent apart from these stirring events, in the castle of Loches, where his father visited him rarely.

00is = 1 1 of arc. An excellent mounting of type B, made by T.

00arranged, and are all necessary for the quick and easy working raised and lowered nearly in an arc of a circle of which the point of intersection of the polar and declination axes is the centre.

00Suppose 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.

00- Zenith Telescope (by Warner & SwaseY) 4 - 2{(n -)+(Sn+ss)I, where - t 5 is the difference of the micrometer readings converted into arc - it being assumed that increased micrometer readings correspond with increased zenith distance of the star.

00The 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.

00C. Chandler in 1884 constructed an equal altitude instrument on this principle, which he called the almucantar, and he found that after disturbance the telescope recovered its original zenith distance within j i of a second of arc. R.

00For otherwise, if they had from some unknown cause the same actual motion, the apparent motion in arc would be different.

00We 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.

00In 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.

00Thus 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.

00But 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.

00Evidences 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.

00Domremy was the birthplace of Joan of Arc, and the cottage in which'she was born still stands.

00Above the door are the arms of France and of Joan of Arc and an inscription of 1481 reading "Vive labeur; vive le roi Louys."

00The three conditions of equilibrium arc therefore ~(X) = o, ~(Y) = o, ~(xY yX) = o.

00Again, 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.

00If the chain be uniform we have W = ws, where s is the arc AP: hence ws=To tan ~.

00Obviously 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.

00The 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.

00Such arc the phenomena of the action of a machine, arranged in the order of can sation.

00Then, for every possible pair of points of contact, the two following equations must be simultaneously fulfilled: Sum of radii, CiUi+C2U2==C1T,+C,Ti = constant; arc, T2U2 = TiUi.

00To illustrate this subject, it may be mentioned that an ellipse rotating about one focus rolls completely round in outside gearing with an equal and similar ellipse also rotating about one focus, the distance between the axes of rotation being equal to the major axis of the ellipses, and the velocity ratio varying from to I ~eccentricitY an hyperbola rotating about its further focus rolls in inside gearing, through a limited arc, with an equal and similar hyperbola rotating about its nearer focus, the distance between the axes of rotation being equal to the axis of the hypereccentricity + I

00It 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.

00Let DID be the path of contact, consisting of the arc of approach DI and the arc of recess ID.

00Nearly Epicycloidal Teeth: Williss Method.To facilitate the drawing of epicycloidal teeth in practice, Willis showed how to approximate to their figure by means of two circular arcsone concave, for the flank, and the other convex, for the faceand each having for its radius the mean radius of curvature of the epicycloidal arc. \Villiss formulae are founded on the following properties of epicycloids Let R be the radius of the pitch-circle; r that of the describing circle; 8 the angle made by the normal TI to the epicycloid at a given point T, with a tangent-to the circle at Ithat is, the obliquity of the action at T.

00Make d bf=pc, cg=pc. From f, with the radiusfa, draw the circular arc ah; from g, with the radius ga, / B

00draw the circular arc ak.

00Let 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.

00The radii at the middle and end being thus ~ietermined, make the generating curve an arc either of a circle or of a parabola.

00and if these ends be not in one straight line with that axis, then S, L R, and L+R, are the three sides of a triangle, having the angle opposite S at that axis; so that, if 0 be the supplement of the arc between the dead-points, Si=2(L2+Ri)_2(Li_R~ cos0,)

00Intermittent 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.

00While the stroke of A is ACa, extending to equal distances on either side of C, and equal to twice the chord of the arc Dd, the stroke of B is only equal to twice the sagitta; and thus A is guided through a comparatively long stroke by the sliding of B through a comparatively short stroke, and by rotatory motions at the joints C, D, B.

00It follows therefore that there arc as many possible mechanisms as there are links in the chain.

00u1=T~-+-~-);u2=Tf\+ also, let 0 be the obliquity of the action; then the times occupied by the approach and recess arc respectively Ci Ci -

00Let 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.

00Then, 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.

00Now that friction is also the difference between the tensions of the band at the two ends of the elementary arc, or dT =dF =fTdO; which equation, being integrated throughout the entire arc of contact, gives the following formulae:

00Let a denote the arc of contact expressed in turns and fractions of a turn; then O=62832a 6

00In 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.

00This invention in conjunction with an alternating current dynamo provided a new and simple form of electric arc lighting.

00The various improvements in electric illuminants, such as the Nernst oxide lamp, the tantalum and osmium incandescent lamps, and improved forms of arc lamp, enclosed, inverted and flame arcs, are described under Lighting: Electric. Between 1890 and 1900, electric traction advanced rapidly in the United States of America but more slowly in England.

00He 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).

00In 1429 Joan of Arc made Blois her base of operations for the relief of Orleans.

00Then, 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.

00The molten metal is sea-green in colour, and at higher temperatures (in the electric arc) it vaporizes and burns with a green flame.

00Baluch, 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.

00Some scholarl attribute it to the Iranian family; others prefer to regard it as a separate and independent member of the Indo-European group. Many words that at first sight seem to prove its Iranian origin arc only adopted from the Persian.8 (K.

00Orleans, 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.

00His more important monuments are those to Admiral Courbet (1890) at Abbeville and the famous "Joan of Arc."

00Outside 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.

00The regular form of the Himalaya, constituting an arc of a true circle, appears to indicate that the whole chain has been pushed forward as one mass upon a gigantic thrust-plane; but, if so, the dip of the plane must be low, for a line drawn along the southern foot of the Himalaya would coincide with the outcrop of a plane inclined to the surface at an angle of about 14°.

0017, except that two slit-like openings of equal length allowed the light to pass, and that the light was that of the electric arc passed through a quartz prism and casting a powerful spectrum on the plate.

00The 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.

00On the morning of the 23rd it was formed in an arc facing S.

00Bredig's process consists in passing an electric arc between silver electrodes under water, when a brown solution is obtained.

00He 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.

00In 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.

00From 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.

00Plinlimmon (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.

00Sir 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.

00The length of any arc may be determined by geometrical considerations or by the methods of the integral calculus.

00corners, and sweeping in a vast arc over 6 degrees of latitude and 58 degrees of longitude.

00Bruns 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.

00In 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.

00JOAN OF ARC, more properly Jeanneton Darc, afterwards known in France as Jeanne D'Arc 1 (1411-1431), the " Maid of Orleans," was born between 1410 and 1412, the daughter of Jacques Darc, peasant proprietor, of Domremy, a small village in the Vosges, partly in Champagne and partly in Lorraine, and of his wife Isabeau, of the village of Vouthon, who from having made a pilgrimage to Rome had received the usual surname of Romee.

00In 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.

00The 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.

00As 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.

00Until 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.

00The attempt to establish the reality of the " revelations " and consequently to obtain the canonization of Joan of Arc led the Catholic party in France to publish lives (such as Sepet's, 1869) in support of their claims. Excellent works worth special mention are: Simeon Luce, Jeanne d'Arc a Domremy; L.

00Of 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.

00In connexion with this subject it may be mentioned that the highest measured temperature produced terrestrially, that of the arc, is about 3500° to 4000° abs.

00Dyson has measured some eight hundred lines in the lower chromosphere and identified them with emission spectra of the following elements: hydrogen, helium, carbon with the cyanogen band, sodium, magnesium, aluminium, silicon, calcium, scandium, titanium, vanadium, chromium, manganese, iron, zinc, strontium, yttrium, zirconium, barium, lanthanum, cerium, neodymium, ytterbium, lead, europium, besides a few doubtful identifications; it is a curious fact that the agreement is with the spark spectra of these elements, where the photosphere shows exclusively or more definitely the arc lines, which are generally attributed to a lower temperature.

00Recent experiments on arc spectra at pressures up to 100 atmospheres by W.

00Light 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.

00Little 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.

00and the chord of the arc 515 ft.

00The length of the chord of the arc across the valley is about 250 ft.

00The 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.

00A circular arc, centre D and radius c/2, meets D E in K, and the perpendicular KL gives 2c sin a.

00The 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.

005 offend the context, spiritual 'Etudes historiques, Essai sur Disc. arc. (Paris 1902).

00In 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.

00There is to be no taxation without the consent of the Great Council of the Realmwhich is to consist of all barons, who arc to be summoned by individual units, and of all smaller tenalitsin-chief, who are to be ~aiied not by separate letters, but by a general notice published by the sberiff~ It has beep pointed out thatthis provides no representation for sub-tenants or the rest of the nation, so that we are still far from the ideal of a repre~ sentative parliament.

00From 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.

00The natural drift of circumstances was not stayed even by the disastrous end of the career of Joan of Arc in 1430.

00If 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.

00The 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.

00If 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.

00Next, 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.

00His 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.

00According to Tyndall, 9 0% of the radiation from the electric arc is non-luminous.

00The 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.

00As 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.

00Accordingly, in conjunction with Christopher Maire, an English Jesuit, he measured an arc of two degrees between Rome and Rimini.

00The 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.

00Applying this deviation to the measured arc, the true zenith distance of the body is found.

00Knowing Alexandria and Syene to be situated 5000 stadia apart on the same meridian, he found the sun to be 7° 12' south of the zenith at the northern extremity of this arc when it was vertically overhead at the southern extremity, and he hence inferred a value of 252,000 stadia for the entire circumference of the globe.

00Among 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.

00It 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).

00The Tian-shan consists almost everywhere of " sheaves " of parallel ranges, having their strike predominantly east and west, with deflexions to the W.S.W., west of Khan-tengri and to the E.S.E., east of 92° E., thus describing as it were a wide flattened arc open to the south.

00The absolute direction of the line of nodes changes but slowly as the earth and moon revolve; cerse"uently, in the case shown in the figure, the line M7 /Ma M6 of nodes will pass through the sun after the earth has passed through an arc nearly equal to the angle M 1 N.

00The rate of actual rotation is substantially uniform, while the arc through which the moon moves from day to day varies.

00Not 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.

00He 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.

00Although 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.

00In 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.

00Cassini, obtained employment, first in surveying the coast from Nantes to Bayonne, then, in 1 739, in remeasuring the French arc of the meridian.

00Among 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.

00The 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.

00government of Bedford, disgust at the iniquitous treaty of Troyes, the monarchist loyalty of many of the warriors, the still deeper sentiment felt by men like Alain Chartier towards Dame France, and the great misery that there was in the kingdom of France; all these suddenly became incarnate in the person of Joan of Arc, a young peasant of Domrmy in Lorraine.

00was already sighing for the easy life of Touraine, and recurring to that policy of truce which was so strongly urged by his counsellors, and so keenly irritating to the clear-sighted Joan of Arc. A check before Paris allowed the jealousy of La Trmoille to waste the heroine for eight months on operations of secondary importance, until the day when she was captured by the Burgundians under the walls of Compigne, and sold by them to the English.

00An arc with centre 0 and radius OB forms part of a curve.

00Let this arc on the reverse side to P intersect a line through 0 parallel to the major axis in a point H.

00Then HA' will cut the circular arc in J.

00Then 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.

00On 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.

00Geology.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.

00It 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.

00But other fragments stil rose above the waves, and of these the great irassif of Portugal arc western Spain was one.

00This 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.

00The 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.

00His first work was a poem on Joan of Arc (1804); but he wrote at the same time a Grammaire general synthetique, which attracted the attention of J.

00They were in a burnt-out roomâ€¦with the Arc de Triomphe a short distance away.

00Edith 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.

00actuate attribute on the arc.

00aghast at the thought of Solar Arc Directions.

00The sub-story concludes well, but the overall arc has yet to reach apogee.

00arc of infinity featured Amsterdam.

00Gas flow meter fitted Electronic HF to start the welding arc.

00The supralateral arc, like the related circumzenithal arc, only forms at solar altitudes below 32° .

00The reflex arc The three types of neurones are arranged in circuits and networks, the simplest of which is the reflex arc.

00The circumzenithal arc is the most beautiful of all the halos.

00XDrawArc draws a single circular or elliptical arc draws a single circular or elliptical arc, and XDrawArcs draws multiple circular or elliptical arcs.

00arc rectifier.

00I will definitely need to use the carbon arc brazing attachment on my arc welder for some fine touches on outer wing.

00arching theme of the two studies is how much arc magmatism contributes to continental growth.

00arc furnace and a high frequency furnace.

00arc it are on hand every hour of the day, every day of the year.

00We merely replaced the arc lamp we had used until then with another arc lamp three times as strong.

00Excitation is via one or more laser sources, or via mercury arc illumination.

00The application interpreting an initial linkbase arc may choose to limit the number of steps processed in the chain.

00This is achieved by using a plasma arc, where energy is released by an electrical discharge in an inert atmosphere.

00Details of the initial story arc, for example.

00Both carbon and alloy steels are produced in electric arc furnaces and scrap rather than molten metal is used as the base material.

00arc lamps of such energy include lasers, arc discharge lamps, and tungsten halogen bulbs.

00To the right of Hercules lie the arc of stars making up Corona Borealis and then Bootes with its bright star Arcturus.

00arcuate nucleus, or ARC.

00ballpoint (pen)he tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second.

00blast furnace process or an electric arc process.

00For information on other aspects of diet, including oily fish and fish oils, see the arc booklet ' Diet and Arthritis ' .

00It means the shiny arc of reflected light on a chrome bumper instead of the smith's blacking on a hammered iron rail.

00clapper strike a fresh arc of the sound bow.

00An imposing central concourse will lead to the shopping area, which will arc out in both directions.

00cone search radius is 1 arc minute.

00Focused on esthetics, Arc is a functional room for the garden which will appeal to design conscious consumers.

00heavy duty inbuilt contactor to start and stop the welding arc.

00coordinate of the upper left corner of the arc.

00corporation arc used is superior to as the bill your blood glucose.

00Math Returns the arc cosine of an angle, in the range of 0.0 through pi.

00The result is in the range of - pi /2 through pi /2. acos( x) arc cosine of an angle.

00As the sun climbs the upper tangent arc opens and then droops like a gull's wings.

00electric furnaced alloy steels are produced in electric arc furnaces and scrap rather than molten metal is used as the base material.

00electric furnacecan produce over 100,000 tons per annum in two 90 ton electric arc furnaces.

00Metal transfer The transfer of metal across the arc from a consumable electrode to the molten pool.

0