Chapter 10

SeeHistory of the Indian Administration(Bentley, 1874), edited by Lord Colchester;Minutes of Evidence taken before the Select Committee on Indian Territories(June 1852); volume i. of theCalcutta Review; theFriend of India, during the years 1842-1845; and John Hope,The House of Scindea: A Sketch(Longmans, 1863). The numerous books by and against Sir Charles Napier, on the conquest of Sind, should be consulted.

ELLERY, WILLIAM(1727-1820), American politician, a signer of the Declaration of Independence, was born in Newport, Rhode Island, on the 22nd of December 1727. He graduated from Harvard in 1747, engaged in trade, studied law, and was admitted to the bar in 1770. He was a member of the Rhode Island committee of safety in 1775-1776, and was a delegate in Congress in 1776-1781 and again in 1783-1785. Just after his first election to Congress, he was placed on the important marine committee, and he was made a member of the board of admiralty when it was established in 1779. In April 1786 he was elected commissioner of the continental loan office for the state of Rhode Island and from 1790 until his death at Newport, on the 15th of February 1820, he was collector of the customs for the district of Newport.

See Edward T. Channing, “Life of William Ellery,” in vol. 6 of Jared Sparks’sAmerican Biography(Boston and London, 1836).

ELLESMERE, FRANCIS EGERTON,1st Earl of(1800-1857), born in London on the 1st of January 1800, was the second son of the 1st duke of Sutherland. He was known by his patronymic as Lord Francis Leveson Gower until 1833, when he assumed the surname of Egerton alone, having succeeded on the death of his father to the estates which the latter inherited from the duke of Bridgewater. Educated at Eton and at Christ Church, Oxford, he entered parliament soon after attaining his majority as member for the pocket borough of Bletchingly in Surrey. He afterwards sat for Sutherlandshire and for South Lancashire, which he represented when he was elevated to the peerage as earl of Ellesmere and Viscount Brackley in 1846. In politics he was a moderate Conservative of independent views, as was shown by his supporting the proposal for establishing the university of London, by his making and carrying a motion for the endowment of the Roman Catholic clergy in Ireland, and by his advocating free trade long before Sir Robert Peel yielded on the question. Appointed a lord of the treasury in 1827, he held the post of chief secretary for Ireland from 1828 till July 1830, when he became secretary-at-war for a short time. His claims to remembrance are founded chiefly on his services to literature and the fine arts. Before he was twenty he printed for private circulation a volume of poems, which he followed up after a short interval by the publication of a translation of Goethe’s Faust, one of the earliest that appeared in England, with some translations of German lyrics and a few original poems. In 1839 he visited the Mediterranean and the Holy Land. His impressions of travel were recorded in his very agreeably writtenMediterranean Sketches(1843), and in the notes to a poem entitledThe Pilgrimage. He published several other works in prose and verse, all displaying a fine literary taste. His literary reputationsecured for him the position of rector of Aberdeen University in 1841. Lord Ellesmere was a munificent and yet discriminating patron of artists. To the splendid collection of pictures which he inherited from his great-uncle, the 3rd duke of Bridgewater, he made numerous additions, and he built a noble gallery to which the public were allowed free access. Lord Ellesmere served as president of the Royal Geographical Society and as president of the Royal Asiatic Society, and he was a trustee of the National Gallery. He died on the 18th of February 1857. He was succeeded by his son (1823-1862) as 2nd earl, and his grandson (b. 1847) as 3rd earl.

ELLESMERE, a market town in the Oswestry parliamentary division of Shropshire, England, on the main line of the Cambrian railway, 182 m. N.W. from London. Pop. of urban district (1901) 1945. It is prettily situated on the west shore of the mere or small lake from which it takes its name, while in the neighbourhood are other sheets of water, as Blake Mere, Cole Mere, White Mere, Newton Mere and Crose Mere. The church of St Mary is of various styles from Norman onward, but was partly rebuilt in 1848. The site of the castle is occupied by pleasure gardens, commanding an extensive view from high ground. The town hall contains a library and a natural history collection. The college is a large boys’ school. The town is an important agricultural centre. Ellesmere canal, a famous work of Thomas Telford, connects the Severn with the Mersey, crossing the Vale of Llangollen by an immense aqueduct, 336 yds. long and 127 ft. high.

The manor of Ellesmere (Ellesmeles) belonged before the Conquest to Earl Edwin of Mercia, and was granted by William the Conqueror to Roger, earl of Shrewsbury, whose son, Robert de Belesme, forfeited it in 1112 for treason against Henry I. In 1177 Henry II. gave it with his sister in marriage to David, son of Owen, prince of North Wales, after whose death it was retained by King John, who in 1206 granted it to his daughter Joan on her marriage with Llewellyn, prince of North Wales; it was finally surrendered to Henry III. by David, son of Llewellyn, about 1240. Ellesmere owed its early importance to its position on the Welsh borders and to its castle, which was in ruins, however, in 1349. While Ellesmere was in the hands of Joan, lady of Wales, she granted to the borough all the free customs of Breteuil. The town was governed by a bailiff appointed by a jury at one of the court leets of the lord of the manor, until a local board was formed in 1859. In 1221 Henry III. granted Llewellyn, prince of Wales, a market on Thursdays in Ellesmere. The inquisition taken in 1383 after the death of Roger le Straunge (Lord Strange), lord of Ellesmere, shows that he also held two fairs there on the feasts of St Martin and the Nativity of the Virgin Mary. By 1597 the market had been discontinued on account of the plague by which many of the inhabitants had died, and the queen granted that Sir Edward Kynaston, Kt., and thirteen others might hold a market every Thursday and a fair on the 3rd of November. Since 1792 both have been discontinued. The commerce of Ellesmere has always been chiefly agricultural.

ELLICE (LAGOON) ISLANDS, an archipelago of the Pacific Ocean, lying between 5° and 11° S. and about 178° E., nearly midway between Fiji and Gilbert. It is under British protection, being annexed in 1892. It comprises a large number of low coralline islands and atolls, which are disposed in nine clusters extending over a distance of about 400 m. in the direction from N.W. to S.E. Their total area is 14 sq. m. and the population is about 2400. The chief groups, all yielding coco-nuts, pandanus fruit and yams, are Funafuti or Ellice, Nukulailai or Mitchell, Nurakita or Sophia, Nukufetau or De Peyster, Nui or Egg, Nanomana or Hudson, and Niutao or Lynx. Nearly all the natives are Christians, Protestant missions having been long established in several of the islands. Those of Nui speak the language of the Gilbert islanders, and have a tradition that they came some generations ago from that group. All the others are of Samoan speech, and their tradition that they came thirty generations back from Samoa is supported by recent research. They have an ancient spear which they believe was brought from Samoa, and they actually name the valley from which their ancestors started. A missionary visiting the Samoan valley found there a tradition of a party who put to sea never to return, and he also found the wood of which the staff was made growing plentifully in the district. Borings and soundings taken at Funafuti in 1897 indicate almost beyond doubt that the whole of this Polynesian region is an area of comparatively recent subsidence.

SeeGeographical Journal, passim; andAtoll of Funafuti: Borings into a Coral Reef(Report of Coral Reef Committee of Royal Society, London, 1904).

ELLICHPUR, orIllichpur, a town of India in the Amraoti district of Berar. Pop. (1901) 26,082. It is first mentioned authentically in the 13th century as “one of the famous cities of the Deccan.” Though tributary to the Mahommedans after 1294, it remained under Hindu administration till 1318, when it came directly under the Mahommedans. It was afterwards capital of the province of Berar at intervals until the Mogul occupation, when the seat of the provincial governor was moved to Balapur. The town retains many relics of the nawabs of Berar. It has ginning factories and a considerable trade in cotton and forest produce. It is connected by good roads with Amraoti and Chikalda. It was formerly the headquarters of the district of Ellichpur, which had an area of 2605 sq. m. and a population in 1901 of 297,403. This district, however, was merged in that of Amraoti in 1905. The civil station of Paratwada, 2 m. from the town of Ellichpur, contains the principal public buildings.

ELLIOTSON, JOHN(1791-1868), English physician, was born at Southwark, London, on the 29th of October 1791. He studied medicine first at Edinburgh and then at Cambridge, in both which places he took the degree of M.D., and subsequently in London at St Thomas’s and Guy’s hospitals. In 1831 he was elected professor of the principles and practice of physic in London University, and in 1834 he became physician to University College hospital. He was a student of phrenology and mesmerism, and his interest in the latter eventually brought him into collision with the medical committee of the hospital, a circumstance which led him, in December 1838, to resign the offices held by him there and at the university. But he continued the practice of mesmerism, holding séances in his home and editing a magazine,The Zoist, devoted to the subject, and in 1849 he founded a mesmeric hospital. He died in London on the 29th of July 1868. Elliotson was one of the first teachers in London to appreciate the value of clinical lecturing, and one of the earliest among British physicians to advocate the employment of the stethoscope. He wrote a translation of Blumenbach’sInstitutiones Physiologicae(1817);Cases of the Hydrocyanic or Prussic Acid(1820);Lectures on Diseases of the Heart(1830);Principles and Practice of Medicine(1839);Human Physiology(1840); andSurgical Operations in the Mesmeric State without Pain(1843). He was the author of numerous papers in theTransactionsof the Medico-Chirurgical Society, of which he was at one time president; and he was also a fellow both of the Royal College of Physicians and Royal Society, and founder and president of the Phrenological Society. W.M. Thackeray’sPendenniswas dedicated to him.

ELLIOTT, EBENEZER(1781-1849), English poet, the “corn-law rhymer,” was born at Masborough, near Rotherham, Yorkshire, on the 17th of March 1781. His father, who was an extreme Calvinist and a strong radical, was engaged in the iron trade. Young Ebenezer, although one of a large family, had a solitary and rather morbid childhood. He was sent to various schools, but was generally regarded as a dunce, and when he was sixteen years of age he entered his father’s foundry, working for seven years with no wages beyond a little pocket money. In a fragment of autobiography printed in theAthenaeum(12th of January 1850) he says that he was entirely self-taught, and attributes his poetic development to long country walks undertaken in search of wild flowers, and to a collection of books, including the works of Young, Barrow, Shenstone and Milton, bequeathed to his father by a poor clergyman. At seventeen he wrote hisVernal Walkin imitation of Thomson. His earlier volumes of poems, dealing with romantic themes, received little but unfriendly comment. The faults ofNight, the earliest ofthese, are pointed out in a long and friendly letter (30th of January 1819) from Robert Southey to the author.

Elliott’s wife brought him some money, which was invested in his father’s share of the iron foundry. But the affairs of the firm were then in a desperate condition, and money difficulties hastened his father’s death. Elliott lost all his money, and when he was forty years old began business again in Sheffield on a small borrowed capital. He attributed his father’s pecuniary losses and his own to the operation of the corn laws. He took an active part in the Chartist agitation, but withdrew his support when the agitation for the repeal of the corn laws was removed from the Chartist programme. The fervour of his political convictions effected a change in the style and tenor of his verse. TheCorn-Law Rhymes(3rd ed., 1831), inspired by a fierce hatred of injustice, are vigorous, simple and full of vivid description. In 1833-1835 he publishedThe Splendid Village;Corn-Law Rhymes, and other Poems(3 vols.), which included “The Village Patriarch” (1829), “The Ranter,” an unsuccessful drama, “Keronah,” and other pieces. He contributed verses from time to time toTait’s Magazineand to theSheffield and Rotherham Independent. In the meantime he had been successful in business, but he remained the sturdy champion of the poor. In 1837 he again lost a great deal of money. This misfortune was also ascribed to the corn laws. He retired in 1841 with a small fortune and settled at Great Houghton, near Barnsley, where he died on the 1st of December 1849. In 1850 appeared two volumes ofMore Prose and Verse by the Corn-Law Rhymer. Elliott lives by his determined opposition to the “bread-tax,” as he called it, and his poems on the subject are saved from the common fate of political poetry by their transparent sincerity and passionate earnestness.

An article by Thomas Carlyle in theEdinburgh Review(July 1832) is the best criticism on Elliott. Carlyle was attracted by Elliott’s homely sincerity and genuine power, though he had small opinion of his political philosophy, and lamented his lack of humour and of the sense of proportion. He thought his poetry too imitative, detecting not only the truthful severity of Crabbe, but a “slight bravura dash of the fair tuneful Hemans.” His descriptions of his native county reveal close observation and a vivid perception of natural beauty.See an obituary notice in theGentleman’s Magazine(Feb. 1850). Two biographies were published in 1850, one by his son-in-law, John Watkins, and another by “January Searle” (G.S. Phillips). A new edition of his works by his son, Edwin Elliott, appeared in 1876.

See an obituary notice in theGentleman’s Magazine(Feb. 1850). Two biographies were published in 1850, one by his son-in-law, John Watkins, and another by “January Searle” (G.S. Phillips). A new edition of his works by his son, Edwin Elliott, appeared in 1876.

ELLIPSE(adapted from Gr.ἔλλειψις, a deficiency,ἐλλείπειν, to fall behind), in mathematics, a conic section, having the form of a closed oval. It admits of several definitions framed according to the aspect from which the curve is considered.In solido,i.e.as a section of a cone or cylinder, it may be defined, after Menaechmus, as the perpendicular section of an “acute-angled” cone; or, after Apollonius of Perga, as the section of any cone by a plane at a less inclination to the base than a generator; or as an oblique section of a right cylinder. Definitionsin planoare generally more useful; of these the most important are: (1) the ellipse is the conic section which has its eccentricity less than unity: this involves the notion of one directrix and one focus; (2) the ellipse is the locus of a point the sum of whose distances from two fixed points is constant: this involves the notion of two foci. Other geometrical definitions are: it is the oblique projection of a circle; the polar reciprocal of a circle for a point within it; and the conic which intersects the line at infinity in two imaginary points. Analytically it is defined by an equation of the second degree of which the highest terms represent two imaginary lines. The curve has important mechanical relations, in particular it is the orbit of a particle moving under the influence of a central force which varies inversely as the square of the distance of the particle; this is the gravitational law of force, and the curve consequently represents the orbits of the planets if only an individual planet and the sun be considered; the other planets, however, disturb this orbit (seeMechanics).

The relation of the ellipse to the other conic sections is treated in the articlesConic SectionandGeometry; in this article a summary of the properties of the curve will be given.

To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (thefocus) to its distance from a straight line (thedirectrix) is constant and is less than unity. This ratio is termed theeccentricity, and will be denoted bye. Let KX (fig. 1) be the directrix, S the focus, and X the foot of the perpendicular from S to KX. If SX be divided at A so that SA/AX = e, then A is a point on the curve. SX may be also divided externally at A′, so that SA′/A′X = e, since e is less than unity; the points A and A′ are thevertices, and the line AA′ themajor axisof the curve. It is obvious that the curve is symmetrical about AA′. If AA′ be bisected at C, and the line BCB′ be drawn perpendicular to AA′, then it is readily seen that the curve is symmetrical about this line also; since if we take S′ on AA′ so that S′A′ = SA, and a line K′X′ parallel to KX such that AX = A′X′, then the same curve will be described if we regard K′X′ and S′ as the given directrix and focus, the eccentricity remaining the same. If B and B′ be points on the curve, BB′ is theminor axisand C thecentreof the curve.Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically. The semi-major axis is generally denoted by a, and the semi-minor axis by b, and we have the relation b² = a² (1 − e²). Also a² = CS·CX,i.e.the square on the semi-major axis equals the rectangle contained by the distances of the focus and directrix from the centre; and 2a = SP + S′P, where P is any point on the curve,i.e.the sum of the focal distances of any point on the curve equals the major axis. The most important relation between the co-ordinates of a point on an ellipse is: if N be the foot of the perpendicular from a point P, then the square on PN bears a constant ratio to the product of the segments AN, NA′ of the major axis, this ratio being the square of the ratio of the minor to the major axis; symbolically PN² = AN·NA′ (CB/CA)². From this or otherwise it is readily deduced that the ordinates of an ellipse and of the circle described on the major axis are in the ratio of the minor to the major axis. This circle is termed theauxiliary circle.Of the properties of a tangent it may be noticed that the tangent at any point is equally inclined to the focal distances of that point; that the feet of the perpendiculars from the foci on any tangent always lie on the auxiliary circle, and the product of these perpendiculars is constant, and equal to the product of the distances of a focus from the two vertices. From any point without the curve two, and only two, tangents can be drawn; if OP, OP′ be two tangents from O, and S, S′ the foci, then the angles OSP, OSP′ are equal and also SOP, S′OP′. If the tangents be at right angles, then the locus of the point is a circle having the same centre as the ellipse; this is named thedirector circle.The middle points of a system of parallel chords is a straight line, and the tangent at the point where this line meets the curve is parallel to the chords. The straight line and the line through the centre parallel to the chords are namedconjugate diameters; each bisects the chords parallel to the other. An important metrical property of conjugate diameters is the sum of their squares equals the sum of the squares of the major and minor axis.In analytical geometry, the equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents an ellipse when ab > h²; if the centre of the curve be the origin, the equation is a¹x² + 2h¹xy + b¹y² = C¹, and if in addition a pair of conjugate diameters are the axes, the equation is further simplified to Ax² + By² = C. The simplest form is x²/a² + y²/b² = 1, in which the centre is the origin and the major and minor axes the axes of co-ordinates. It is obvious that the co-ordinates of any point on an ellipse may be expressed in terms of a single parameter, the abscissa being a cos φ, and the ordinate b sin φ, since on eliminating φ between x = a cos φ and y = b sin φ we obtain the equation to the ellipse. The angle φ is termed theeccentric angle, and is geometrically represented as the angle between the axis of x (the major axis of the ellipse) and the radius of a point on the auxiliary circle which has the same abscissa as the point on the ellipse.The equation to the tangent at θ is x cos θ/a + y sin θ/b = 1, and to the normal ax/cos θ − by/sin θ = a² − b².The area of the ellipse is πab, where a, b are the semi-axes; this result may be deduced by regarding the ellipse as the orthogonal projection of a circle, or by means of the calculus. The perimeter can only be expressed as a series, the analytical evaluation leading to an integral termedelliptic(seeFunction, ii.Complex). There are several approximation formulae:—S = π(a + b) makes the perimeter about 1/200th too small; s =π√(a² + b²) about 1/200th too great; 2s = π(a + b) + π√(a² + b²) is within 1/30,000 of the truth.An ellipse can generally be described to satisfy any five conditions. If five points be given, Pascal’s theorem affords a solution; if five tangents, Brianchon’s theorem is employed. The principle ofinvolution solves such constructions as: given four tangents and one point, three tangents and two points, &c. If a tangent and its point of contact be given, it is only necessary to remember that a double point on the curve is given. A focus or directrix is equal to two conditions; hence such problems as: given a focus and three points; a focus, two points and one tangent; and a focus, one point and two tangents are soluble (very conveniently by employing the principle of reciprocation). Of practical importance are the following constructions:—(1) Given the axes; (2) given the major axis and the foci; (3) given the focus, eccentricity and directrix; (4) to construct an ellipse (approximately) by means of circular arcs.(1) If the axes be given, we may avail ourselves of several constructions, (a) Let AA′, BB′ be the axes intersecting at right angles in a point C. Take a strip of paper or rule and mark off from a point P, distances Pa and Pb equal respectively to CA and CB. If now the strip be moved so that the point a is always on the minor axis, and the point b on the major axis, the point P describes the ellipse. This is known as thetrammelconstruction.(b) Let AA′, BB′ be the axes as before; describe on each as diameter a circle. Draw any number of radii of the two circles, and from the points of intersection with the major circle draw lines parallel to the minor axis, and from the points of intersection with the minor circle draw lines parallel to the major axis. The intersections of the lines drawn from corresponding points are points on the ellipse.(2) If the major axis and foci be given, there is a convenient mechanical construction based on the property that the sum of the focal distances of any point is constant and equal to the major axis. Let AA′ be the axis and S, S′ the foci. Take a piece of thread of length AA′, and fix it at its extremities by means of pins at the foci. The thread is now stretched taut by a pencil, and the pencil moved; the curve traced out is the desired ellipse.Fig. 2.(3) If the directrix, focus and eccentricity be given, we may employ the general method for constructing a conic. Let S (fig. 2) be the focus, KX the directrix, X being the foot of the perpendicular from S to the directrix. Divide SX internally at A and externally at A′, so that the ratios SA/AX and SA′/A′X are each equal to the eccentricity. Then A, A′ are the vertices of the curve. Take any point R on the directrix, and draw the lines RAM, RSN; draw SL so that the angle LSN = angle NSA′. Let P be the intersection of the line SL with the line RAM, then it can be readily shown that P is a point on the ellipse. For, draw through P a line parallel to AA′, intersecting the directrix in Q and the line RSN in T. Then since XS and QT are parallel and are intersected by the lines RK, RM, RN, we have SA/AX = TP/PQ = SP/PQ, since the angle PST = angle PTS. By varying the position of R other points can be found, and, since the curve is symmetrical about both the major and minor axes, it is obvious that any point may be reflected in both the axes, thus giving 3 additional points.(4) If the axes be given, the curve can be approximately constructed by circular arcs in the following manner:—Let AA′, BB′ be the axes; determine D the intersection of lines through B and A parallel to the major and minor axes respectively. Bisect AD at E and join EB. Then the intersection of EB and DB′ determines a point P on the (true) curve. Bisect the chord PB at G, and draw through G a line perpendicular to PB, intersecting BB′ in O. An arc with centre O and radius OB forms part of a curve. Let this arc on the reverse side to P intersect a line through O parallel to the major axis in a point H. Then HA¹ will cut the circular arc in J. Let JO intersect the major axis in O1. Then with centre O1and radius OJ = OA¹, describe an arc. By reflecting the two arcs thus described over the centre the ellipse is approximately described.

Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically. The semi-major axis is generally denoted by a, and the semi-minor axis by b, and we have the relation b² = a² (1 − e²). Also a² = CS·CX,i.e.the square on the semi-major axis equals the rectangle contained by the distances of the focus and directrix from the centre; and 2a = SP + S′P, where P is any point on the curve,i.e.the sum of the focal distances of any point on the curve equals the major axis. The most important relation between the co-ordinates of a point on an ellipse is: if N be the foot of the perpendicular from a point P, then the square on PN bears a constant ratio to the product of the segments AN, NA′ of the major axis, this ratio being the square of the ratio of the minor to the major axis; symbolically PN² = AN·NA′ (CB/CA)². From this or otherwise it is readily deduced that the ordinates of an ellipse and of the circle described on the major axis are in the ratio of the minor to the major axis. This circle is termed theauxiliary circle.

Of the properties of a tangent it may be noticed that the tangent at any point is equally inclined to the focal distances of that point; that the feet of the perpendiculars from the foci on any tangent always lie on the auxiliary circle, and the product of these perpendiculars is constant, and equal to the product of the distances of a focus from the two vertices. From any point without the curve two, and only two, tangents can be drawn; if OP, OP′ be two tangents from O, and S, S′ the foci, then the angles OSP, OSP′ are equal and also SOP, S′OP′. If the tangents be at right angles, then the locus of the point is a circle having the same centre as the ellipse; this is named thedirector circle.

The middle points of a system of parallel chords is a straight line, and the tangent at the point where this line meets the curve is parallel to the chords. The straight line and the line through the centre parallel to the chords are namedconjugate diameters; each bisects the chords parallel to the other. An important metrical property of conjugate diameters is the sum of their squares equals the sum of the squares of the major and minor axis.

In analytical geometry, the equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents an ellipse when ab > h²; if the centre of the curve be the origin, the equation is a¹x² + 2h¹xy + b¹y² = C¹, and if in addition a pair of conjugate diameters are the axes, the equation is further simplified to Ax² + By² = C. The simplest form is x²/a² + y²/b² = 1, in which the centre is the origin and the major and minor axes the axes of co-ordinates. It is obvious that the co-ordinates of any point on an ellipse may be expressed in terms of a single parameter, the abscissa being a cos φ, and the ordinate b sin φ, since on eliminating φ between x = a cos φ and y = b sin φ we obtain the equation to the ellipse. The angle φ is termed theeccentric angle, and is geometrically represented as the angle between the axis of x (the major axis of the ellipse) and the radius of a point on the auxiliary circle which has the same abscissa as the point on the ellipse.

The equation to the tangent at θ is x cos θ/a + y sin θ/b = 1, and to the normal ax/cos θ − by/sin θ = a² − b².

The area of the ellipse is πab, where a, b are the semi-axes; this result may be deduced by regarding the ellipse as the orthogonal projection of a circle, or by means of the calculus. The perimeter can only be expressed as a series, the analytical evaluation leading to an integral termedelliptic(seeFunction, ii.Complex). There are several approximation formulae:—S = π(a + b) makes the perimeter about 1/200th too small; s =π√(a² + b²) about 1/200th too great; 2s = π(a + b) + π√(a² + b²) is within 1/30,000 of the truth.

An ellipse can generally be described to satisfy any five conditions. If five points be given, Pascal’s theorem affords a solution; if five tangents, Brianchon’s theorem is employed. The principle ofinvolution solves such constructions as: given four tangents and one point, three tangents and two points, &c. If a tangent and its point of contact be given, it is only necessary to remember that a double point on the curve is given. A focus or directrix is equal to two conditions; hence such problems as: given a focus and three points; a focus, two points and one tangent; and a focus, one point and two tangents are soluble (very conveniently by employing the principle of reciprocation). Of practical importance are the following constructions:—(1) Given the axes; (2) given the major axis and the foci; (3) given the focus, eccentricity and directrix; (4) to construct an ellipse (approximately) by means of circular arcs.

(1) If the axes be given, we may avail ourselves of several constructions, (a) Let AA′, BB′ be the axes intersecting at right angles in a point C. Take a strip of paper or rule and mark off from a point P, distances Pa and Pb equal respectively to CA and CB. If now the strip be moved so that the point a is always on the minor axis, and the point b on the major axis, the point P describes the ellipse. This is known as thetrammelconstruction.

(b) Let AA′, BB′ be the axes as before; describe on each as diameter a circle. Draw any number of radii of the two circles, and from the points of intersection with the major circle draw lines parallel to the minor axis, and from the points of intersection with the minor circle draw lines parallel to the major axis. The intersections of the lines drawn from corresponding points are points on the ellipse.

(2) If the major axis and foci be given, there is a convenient mechanical construction based on the property that the sum of the focal distances of any point is constant and equal to the major axis. Let AA′ be the axis and S, S′ the foci. Take a piece of thread of length AA′, and fix it at its extremities by means of pins at the foci. The thread is now stretched taut by a pencil, and the pencil moved; the curve traced out is the desired ellipse.

(3) If the directrix, focus and eccentricity be given, we may employ the general method for constructing a conic. Let S (fig. 2) be the focus, KX the directrix, X being the foot of the perpendicular from S to the directrix. Divide SX internally at A and externally at A′, so that the ratios SA/AX and SA′/A′X are each equal to the eccentricity. Then A, A′ are the vertices of the curve. Take any point R on the directrix, and draw the lines RAM, RSN; draw SL so that the angle LSN = angle NSA′. Let P be the intersection of the line SL with the line RAM, then it can be readily shown that P is a point on the ellipse. For, draw through P a line parallel to AA′, intersecting the directrix in Q and the line RSN in T. Then since XS and QT are parallel and are intersected by the lines RK, RM, RN, we have SA/AX = TP/PQ = SP/PQ, since the angle PST = angle PTS. By varying the position of R other points can be found, and, since the curve is symmetrical about both the major and minor axes, it is obvious that any point may be reflected in both the axes, thus giving 3 additional points.

(4) If the axes be given, the curve can be approximately constructed by circular arcs in the following manner:—Let AA′, BB′ be the axes; determine D the intersection of lines through B and A parallel to the major and minor axes respectively. Bisect AD at E and join EB. Then the intersection of EB and DB′ determines a point P on the (true) curve. Bisect the chord PB at G, and draw through G a line perpendicular to PB, intersecting BB′ in O. An arc with centre O and radius OB forms part of a curve. Let this arc on the reverse side to P intersect a line through O parallel to the major axis in a point H. Then HA¹ will cut the circular arc in J. Let JO intersect the major axis in O1. Then with centre O1and radius OJ = OA¹, describe an arc. By reflecting the two arcs thus described over the centre the ellipse is approximately described.

ELLIPSOID, a quadric surface whose sections are ellipses. Analytically, it has for its equation x²/a² + y²/b² + z²/c² = 1, a, b, c being its axes; the name is also given to the solid contained by this surface (seeGeometry:Analytical). The solids and surfaces of revolution of the ellipse are sometimes termed ellipsoids, but it is advisable to use the name spheroid (q.v.).

The ellipsoid appears in the mathematical investigation of physical properties of media in which the particular property varies in three directions within the media; such properties are the elasticity, giving rise to the strain ellipsoid, thermal expansion, ellipsoid of expansion, thermal conduction, refractive index (seeCrystallography), &c. In mechanics, the ellipsoid of gyration or inertia is such that the perpendicular from the centre to a tangent plane is equal to the radius of gyration of the given body about the perpendicular as axis; the “momental ellipsoid,” also termed the “inverse ellipsoid of inertia” or Poinsot’s ellipsoid, has the perpendicular inversely proportional to the radius of gyration; the “equimomental ellipsoid” is such that its moments of inertia about all axes are the same as those of a given body. (SeeMechanics.)

ELLIPTICITY, in astronomy, deviation from a circular or spherical form; applied to the elliptic orbits of heavenly bodies, or the spheroidal form of such bodies. (See alsoCompression.)

ELLIS(originallySharpe),ALEXANDER JOHN(1814-1890), English philologist, mathematician, musician and writer on phonetics, was born at Hoxton on the 14th of June 1814. He was educated at Shrewsbury, Eton, and Trinity College, Cambridge, and took his degree in high mathematical honours. He was connected with many learned societies as member or president, and was governor of University College, London. He was the first in England to reduce the study of phonetics to a science. His most important work, to which the greater part of his life was devoted, isOn Early English Pronunciation, with special reference to Shakespeare and Chaucer(1869-1889), in five parts, which he intended to supplement by a sixth, containing an abstract of the whole, an account of the views and criticisms of other inquirers in the same field, and a complete index, but ill-health prevented him from carrying out his intention. He had long been associated with Isaac Pitman in his attempts to reform English spelling, and publishedA Plea for Phonotypy and Phonography(1845) andA Plea for Phonetic Spelling(1848); and contributed the articles on “Phonetics” and “Speech-sounds” to the 9th edition of theEncy. Brit.He translated (with considerable additions) Helmholtz’sSensations of Tone as a physiological Basis for the Theory of Music(2nd ed., 1885); and was the author of several smaller works on music, chiefly in connexion with his favourite subject phonetics. He died in London on the 28th of October 1890.

ELLIS, GEORGE(1753-1815), English author, was born in London in 1753. Educated at Westminster school and at Trinity College, Cambridge, he began his literary career by some satirical verses on Bath society published in 1777, andPoetical Tales, by “Sir Gregory Gander,” in 1778. He contributed to theRolliadand theProbationary Odespolitical satires directed against Pitt’s administration. He was employed in diplomatic business at the Hague in 1784; and in 1797 he accompanied Lord Malmesbury to Lille as secretary to the embassy. On his return he was introduced to Pitt, and the episode of theRolliad, which had not been forgotten, was explained. He found continued scope for his powers as a political caricaturist in the columns of theAnti-Jacobin, a weekly paper which he founded in connexion with George Canning and William Gifford. For some years before theAnti-Jacobinwas started Ellis had been working in the congenial field of Early English literature, in which he was one of the first to arouse interest. The first edition of hisSpecimens of the Early English Poetsappeared in 1790; and this was followed bySpecimens of Early English Metrical Romances(1805). He also edited Gregory Lewis Way’s translation of selectFabliauxin 1796. Ellis was an intimate friend of Sir Walter Scott, who styled him “the first converser I ever saw,” and dedicated to him the fifth canto ofMarmion. Some of the correspondence between them is to be found in Lockhart’sLife. He died on the 10th of April 1815. The monument erected to his memory in the parish church of Gunning Hill, Berks, bears a fine inscription by Canning.

ELLIS, SIR HENRY(1777-1869), English antiquary, was born in London on the 29th of November 1777. He was educated at Merchant Taylors’ school, and at St John’s College, Oxford, of which he was elected a fellow. After having held for a few months a sub-librarianship in the Bodleian, he was in 1800 appointed to a similar post in the British Museum. In 1827 he became chief librarian, and held that post until 1856, when he resigned on account of advancing age. In 1832 William IV. made him a knight of Hanover, and in the following year he received an English knighthood. He died on the 15th of January 1869. Sir Henry Ellis’s life was one of very considerable literary activity. His first work of importance was the preparation of a new edition of Brand’sPopular Antiquities, which appeared in 1813. In 1816 he was selected by the commissioners of publicrecords to write the introduction to Domesday Book, a task which he discharged with much learning, though several of his views have not stood the test of later criticism. HisOriginal Letters Illustrative of English History(first series, 1824; second series, 1827; third series, 1846) are compiled chiefly from manuscripts in the British Museum and the State Paper Office, and have been of considerable service to historical writers. To the Library of Entertaining Knowledge he contributed four volumes on the Elgin and Townley Marbles. Sir Henry was for many years a director and joint-secretary of the Society of Antiquaries.

ELLIS, ROBINSON(1834- ), English classical scholar, was born at Barming, near Maidstone, on the 5th of September 1834. He was educated at Elizabeth College, Guernsey, Rugby, and Balliol College, Oxford. In 1858 he became fellow of Trinity College, Oxford, and in 1870 professor of Latin at University College, London. In 1876 he returned to Oxford, where from 1883 to 1893 he held the university readership in Latin. In 1893 he succeeded Henry Nettleship as professor. His chief work has been on Catullus, whom he began to study in 1859. His firstCommentary on Catullus(1876) aroused great interest, and called forth a flood of criticism. In 1889 appeared a second and enlarged edition, which placed its author in the first rank of authorities on Catullus. Professor Ellis quotes largely from the early Italian commentators, maintaining that the land where the Renaissance originated had done more for scholarship than is commonly recognized. He has supplemented his critical work by a translation (1871, dedicated to Tennyson) of the poems in the metres of the originals. Another author to whom Professor Ellis has devoted many years’ study is Manilius, the astrological poet. In 1891 he publishedNoctes Manilianae, a series of dissertations on theAstronomica, with emendations. He has also treated Avianus, Velleius Paterculus and the Christian poet Orientius, whom he edited for the ViennaCorpus Scriptorum Ecclesiasticorum. He edited theIbisof Ovid, theAetnaof the younger Lucilius, and contributed to theAnecdota Oxoniensiavarious unedited Bodleian and other manuscripts. In 1907 he publishedAppendix Vergiliana(an edition of the minor poems); in 1908The Annalist Licinianus.

ELLIS, WILLIAM(1794-1872), English Nonconformist missionary, was born in London on the 29th of August 1794. His boyhood and youth were spent at Wisbeach, where he worked as a market-gardener. In 1814 he offered himself to the London Missionary Society, and was accepted. During a year’s training he acquired some knowledge of theology and of various practical arts, such as printing and bookbinding. He sailed for the South Sea Islands in January 1816, and remained in Polynesia, occupying various stations in succession, until 1824, when he was compelled to return home on account of the state of his wife’s health. Though the period of his residence in the islands was thus comparatively short, his labours were very fruitful, contributing perhaps as much as those of any other missionary to bring about the extraordinary improvement in the religious, moral and social condition of the Pacific Archipelago that took place during the 19th century. Besides promoting the spiritual object of his mission, he introduced many other aids to the improvement of the condition of the people. His gardening experience enabled him successfully to acclimatize many species of tropical fruits and plants, and he set up and worked the first printing press in the South Seas. Returning home by way of the United States, where he advocated his work, Ellis was for some years employed as a travelling agent of the London Missionary Society, and in 1832 was appointed foreign secretary to the society, an office which he held for seven years. In 1837 he married his second wife, Sarah Stickney, a writer and teacher of some note in her generation. In 1841 he went to live at Hoddesdon, Herts, and ministered to a small Congregational church there. On behalf of the London Missionary Society he paid three visits to Madagascar (1853-1857), inquiring into the prospects for resuming the work that had been suspended by Queen Ranavolona’s hostility. A further visit was paid in 1863. Ellis wrote accounts of all his travels, and Southey’s praise (in theQuarterly Review) of hisPolynesian Researches(2 vols., 1829) finds many echoes. He was a fearless, upright and tactful man, and a keen observer of nature. He died on the 25th of June 1872.

ELLISTON, ROBERT WILLIAM(1774-1831), English actor, was born in London on the 7th of April 1774, the son of a watchmaker. He was educated at St Paul’s school, but ran away from home and made his first appearance on the stage as Tressel inRichard III.at Bath in 1791. Here he was later seen as Romeo, and in other leading parts, both comic and tragic, and he repeated his successes in London from 1796. He acted at Drury Lane from 1804 to 1809, and again from 1812; and from 1819 he was the lessee of the house, presenting Kean, Mme Vestris and Macready. Ill-health and misfortune culminated in his bankruptcy in 1826, when he made his last appearance at Drury Lane as Falstaff. But as lessee of the Surrey theatre he acted almost up to his death, which was hastened by intemperance. Leigh Hunt compared him favourably with Garrick; Byron thought him inimitable in high comedy; Macready praised his versatility. Elliston was the author ofThe Venetian Outlaw(1805), and, with Francis Godolphin Waldron, ofNo Prelude(1803), in both of which plays he appeared.

ELLORA, a village of India in the native state of Hyderabad, near the city of Daulatabad, famous for its rock temples, which are among the finest in India. They are first mentioned by Ma′sudi, the Arabic geographer of the 10th century, but merely as a celebrated place of pilgrimage. The caves differ from those of Ajanta in consequence of their being excavated in the sloping sides of a hill and not in a nearly perpendicular cliff. They extend along the face of the hill for a mile and a quarter, and are divided into three distinct series, the Buddhist, the Brahmanical and the Jain, and are arranged almost chronologically. The most splendid of the whole series is the Kailas, a perfect Dravidian temple, complete in all its parts, characterized by Fergusson as one of the most wonderful and interesting monuments of architectural art in India. It is not a mere interior chamber cut in the rock, but is a model of a complete temple such as might have been erected on the plain. In other words, the rock has been cut away externally as well as internally. First the great sunken court measuring 276 ft. by 154 ft. was hewn out of the solid trap-rock of the hillside, leaving the rock mass of the temple wholly detached in a cloistered court like a colossal boulder, save that a rock bridge once connected the upper storey of the temple with the upper row of galleried chambers surrounding three sides of the court. Colossal elephants and obelisks stand on either side of the open mandapam, or pavilion, containing the sacred bull; and beyond rises the monolithic Dravidian temple to Siva, 90 ft. in height, hollowed into vestibule, chamber and image-cells, all lavishly carved. Time and earthquakes have weathered and broken away bits of the great monument, and Moslem zealots strove to destroy the carved figures, but these defects are hardly noticed. The temple was built by Krishna I., Rashtrakuta, king of Malkhed in 760-783.

ELLORE, a town of British India, in the Kistna district of Madras, on the East Coast railway, 303 m. from Madras. Pop. (1901) 33,521. The two canal systems of the Godavari and the Kistna deltas meet here. There are manufactures of cotton and saltpetre, and an important Church of England high school. Ellore was formerly a military station, and the capital of the Northern Circars. At Pedda Vegi to the north of it are extensive ruins, which are believed to be remains of the Buddhist kingdom of Vengi. From these the Mahommedans, after their conquest of the district in 1470, obtained material for building a fort at Ellore.

ELLSWORTH, OLIVER(1745-1807), American statesman and jurist, was born at Windsor, Connecticut, on the 29th of April 1745. He studied at Yale and Princeton, graduating from the latter in 1766, studied theology for a year, then law, and began to practise at Hartford in 1771. He was state’s attorney for Hartford county from 1777 to 1785, and achieved extraordinary success at the bar, amassing what was for his day a large fortune. From 1773 to 1775 he represented the town of Windsor in the general assembly of Connecticut, and in the latter year became a member of the important commission known as the “Pay Table,” which supervised the colony’s expendituresfor military purposes during the War of Independence. In 1779 he again sat in the assembly, this time representing Hartford. From 1777 to 1783 he was a member of the Continental Congress, and in this body he served on three important committees, the marine committee, the board of treasury, and the committee of appeals, the predecessors respectively of the navy and treasury departments and the Supreme Court under the Federal Constitution. From 1780 to 1785 he was a member of the governor’s council of Connecticut, which, with the lower house before 1784 and alone from 1784 to 1807, constituted a supreme court of errors; and from 1785 to 1789 he was a judge of the state superior court. In 1787, with Roger Sherman and William Samuel Johnson (1727-1819), he was one of Connecticut’s delegates to the constitutional convention at Philadelphia, in which his services were numerous and important. In particular, when disagreement seemed inevitable on the question of representation, he, with Roger Sherman, proposed what is known as the “Connecticut Compromise,” by which the Federal legislature was made to consist of two houses, the upper having equal representation from each state, the lower being chosen on the basis of population. Ellsworth also made a determined stand against a national paper currency. Being compelled to leave the convention before its adjournment, he did not sign the instrument, but used his influence to secure its ratification by his native state. From 1789 to 1796 he was one of the first senators from Connecticut under the new Constitution. In the senate he was looked upon as President Washington’s personal spokesman and as the leader of the Administration party. His most important service to his country was without a doubt in connexion with the establishment of the Federal judiciary. As chairman of the committee having the matter in charge, he drafted the bill by the enactment of which the system of Federal courts, almost as it is to-day, was established. He also took a leading part in the senate in securing the passage of laws for funding the national debt, assuming the state debts and establishing a United States bank. It was Ellsworth who suggested to Washington the sending of John Jay to England to negotiate a new treaty with Great Britain, and he probably did more than any other man to induce the senate, despite widespread and violent opposition, to ratify that treaty when negotiated. By President Washington’s appointment he became chief justice of the Supreme Court of the United States in March 1796, and in 1799 President John Adams sent him, with William Vans Murray (1762-1803) and William R. Davie (1756-1820), to negotiate a new treaty with France. It was largely through the influence of Ellsworth, who took the principal part in the negotiations, that Napoleon consented to a convention, of the 30th of September 1800, which secured for citizens of the United States their ships captured by France but not yet condemned as prizes, provided for freedom of commerce between the two nations, stipulated that “free ships shall give a freedom to goods,” and contained provisions favourable to neutral commerce. While he was abroad, failing health compelled him (1800) to resign the chief-justiceship, and after some months in England he returned to America in 1801. In 1803 he was again elected to the governor’s council, and in 1807, on the reorganization of the Connecticut judiciary, was appointed chief justice of the new Supreme Court. He never took office, however, but died at his home in Windsor on the 27th of November 1807.

See W.G. Brown’sOliver Ellsworth(New York, 1905), an excellent biography. There is also an appreciative account of Ellsworth’s life and work in H.C. Lodge’sA Fighting Frigate, and Other Essays and Addresses(New York, 1902), which contains in an appendix an interesting letter by Senator George F. Hoar concerning Ellsworth’s work in the constitutional convention.

ELLSWORTH, a city, port of entry and the county seat of Hancock county, Maine, U.S.A., at the head of navigation on the Union river (and about 3¾ m. from its mouth), about 30 m. S.E. of Bangor. Pop. (1890) 4804; (1900) 4297 (189 foreign-born); (1910) 3549. It is served by the Maine Central railway. The fall of the river, about 85 ft. in 2 m., furnishes good water-power, and the city has various manufactures, including lumber, shoes, woollens, sails, carriages and foundry and machine shop products, besides a large lumber trade. Shipbuilding was formerly important. There is a large United States fish hatchery here. The city is the port of entry for the Frenchman’s Bay customs district, but its foreign trade is unimportant. Ellsworth was first settled in 1763 and for some time was called New Bowdoin; but when it was incorporated as a town in 1800 the present name was adopted in honour of Oliver Ellsworth. A city charter was secured in 1869.

ELLWANGEN, a town of Germany in the kingdom of Württemberg, on the Jagst, 12 m. S.S.E. from Crailsheim on the railway to Goldshöfe. Pop. 5000. It is romantically situated between two hills, one crowned by the castle of Hohen-Ellwangen, built in 1354 and now used as an agricultural college, and the other, the Schönenberg, by the pilgrimage church of Our Lady of Loreto, in the Jesuit style of architecture. The town possesses one Evangelical and five Roman Catholic churches, among the latter the Stiftskirche, the old abbey church, a Romanesque building dating from 1124, and the Gothic St Wolfgangskirche. The classical and modern schools (Gymnasium and Realschule) occupy the buildings of a suppressed Jesuit college. The industries include the making of parchment covers, of envelopes, of wooden hafts and handles for tools, &c., and tanneries. There are also a wool-market and a horse-market, the latter famous in Germany.

The Benedictine abbey of Ellwangen is said to have been founded in 764 by Herulf, bishop of Langres; there is, however, no record of it before 814. In 1460 the abbey was converted, with the consent of Pope Pius II., into aRitterstift(college or institution for noble pensioners) under a secular provost, who, in 1555, was raised to the dignity of a prince of the Empire. The provostship was secularized in 1803 and its territories were assigned to Württemberg. The town of Ellwangen, which grew up round the abbey and received the status of a town about the middle of the 14th century, was until 1803 the capital of the provostship.

Back to Index Next