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eccentricity

It is therefore a conic section having its eccentricity equal to unity.

2625His whole kingdom was to be unified; Judaism was an eccentricity and as such doomed to extinction.

1517All the known minor planets have the same common direction, but their orbits generally have a greater eccentricity and mutual inclination.

1416All the known minor planets have the same common direction, but their orbits generally have a greater eccentricity and mutual inclination.

1416Most of the orbits are remarkably eccentric ellipses, the average eccentricity being about 0.5.

1113Most of the orbits are remarkably eccentric ellipses, the average eccentricity being about 0.5.

1113Jeffrey naturally declined to appoint a man who, in spite of some mathematical knowledge, had no special qualification, and administered a general lecture upon Carlyle's arrogance and eccentricity which left a permanent sense of injury.

69This ratio is termed the eccentricity, and will be denoted by e.

610The result of the latter inequality is brought out when it is sought to determine the eccentricity of the orbit from the observations near the time of the first and last quarter.

53Its mean distance from the sun is 1.46 times i that of the earth; but, besides, the eccentricity of its orbit is large (0.22), so that at the most favourable opportunity it can come within one-seventh of the distance of the sun.

43The eccentricity determined in this way is more than a degree in error, owing to the effect of the evection, which was unknown to Hipparchus.

43We put e for the eccentricity of the ellipse, represented P, by the ratio M CF: CA.

47The eccentricity which had characterized his opinions from the beginning of his career gradually became more marked until they developed into insanity.

47We put e for the eccentricity of the ellipse, represented P, by the ratio M CF: CA.

47Therefore the eccentricity found by Hipparchus was only 5°, and was more than a degree less than its true value.

33eccentricity 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.

33Metrical 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.

33Elliptic orbits, and a parabolic orbit considered as the special case when the eccentricity of the ellipse is 1, are almost the only ones the astronomer has to consider, and our attention will therefore be confined to them in the present article.

35The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit.

35Concurrently with the growth of this unrest Rudolph had become increasingly subject to attacks of depression and eccentricity, which were so serious as to amount almost to insanity.

35the axes and eccentricity of the ellipse, and the position of the plane in which it lies.

35It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.

36The centre of the eccentric is its connected point; and its eccentricity, or the distance from that centre to the axis of the shaft, is its crank-arm.

37The Eccentricity of the Moon's Orbit.

37Most of the elements are small numerical fractions: e, the eccentricity of the moon's orbit, about 0.055; e', the eccentricity of the earth's orbit, about o 017: y, the sine of half the inclination of the moon's orbit, about 0.046; m, the ratio of the mean motions of the moon and earth, about 0.075.

22Euler conceived the idea of starting with a preliminary solution of the problem in which the orbit of the moon should be supposed to lie in the ecliptic, and to have no eccentricity, while that of the sun was circular.

22line 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.

22Of practical importance are the following constructions: - (I) 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.

22This ratio, known as the eccentricity, determines the nature of the curve; if it be greater than unity, the conic is a hyperbola; if equal to unity, a parabola; and if less than unity, an ellipse.

22In computing the column sections a proper allowance must be made for any eccentricity of loading.

24It may be considered as arising from a semi-annual variation in the eccentricity of the moon's orbit and the position of its perigee.

25as the conic having an eccentricity greater than unity, is a convenient starting-point for the Euclidian investigation.

26In the case of very tall exposed buildings of small depth, the vertical load on the columns due to wind pressure in the opposite side of the building must be computed and allowed for, and in case the lower columns are without lateral support their bending moment must be sufficient to resist the lateral pressure due to wind and eccentricity of loading.

26He first brought the revolutions of our satellite within the domain of Kepler's laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus.

29He first brought the revolutions of our satellite within the domain of Kepler's laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus.

29Assuming the mean motion of the moon to be known and the perigee to be fixed, three eclipses, observed in different points of the orbit, would give as many true longitudes of the moon, which longitudes could be employed to determine three unknown quantities - the mean longitude at a given epoch, the eccentricity, and the position of the perigee.

14With the latest accepted diminution of the eccentricity, the coefficient is 5.91".

16A large eccentricity also produces an unsymmetrical light variation, the minimum occurring at a time not midway between two maxima; stars of this character are called Cepheid variables, after the typical star S Cephei.

18After seeing to the publication of this instalment of Tristram and of another set of sermons - more pronouncedly Shandean in their eccentricity - he quitted England again in the summer of 1765, and tavelled in Italy as far as Naples.

18An eccentric may be made capable of having its eccentricity altered by means of an adjusting screw, so as to vary the extent of the reciprocating motion which it communicates.

18and eccentricity I

19This marriage may have done something to increase Granville's reputation for eccentricity.

00From the time of his first introduction to Tycho he had devoted himself to the investigation of the orbit of Mars, which, on account of its relatively large eccentricity, had always been especially recalcitrant to theory, and the results appeared in Astronomia nova ainoXayrgrii, seu Physica coelestis tradita commentariis de motibus stellae Martis (Prague, 1609).

00In manner he was simple, direct, void of the least affectation, and entirely free from awkwardness, oddity or eccentricity.

00Divide SX internally at A and externally at A', so that the ratios SA/AX and SA'/A'X are each equal to the eccentricity.

00In the case of the circle, the centre is the focus, and the line at infinity the directrix; we therefore see that a circle is a conic of zero eccentricity.

00eccentricity of the orbit really be maintained over billions of years?

00eccentricity of the earth 's orbit around the sun.

00eccentricity of an ellipse is a measure of how fat (or thin) it is.

00changing the eccentricity enables orbits of planets and comets to be compared.

00Our current best orbit has an eccentricity of about 0.537.

00Once upon a time the Kings Road encompassed and celebrated the eccentricity that so defined England.

00The lower two frames show eccentricity, or how elliptical their orbits are.

00However, a modest orbital eccentricity is plainly not incompatible with life.

00We wanted something that reflected the spirit of English eccentricity.

00Nor can one deny that there has been considerable eccentricity in his treatment of his son.

00Giraffe Manor, Kenya, bastion of British eccentricity.

00A new enthusiastic young writer joins the staff of jaded hacks each with their own eccentricity.

00eccentricity climate cycles.

00eccentricity values are found to be either complex or negative.

00At this eccentricity, three midget bipolar cells synapse with the midget ganglion cell.

00THE SPIRIT OF THE man celebrates the mettle of a man whose footballing achievements and eccentricity endeared him to a nation.

00At this eccentricity, three midget bipolar cells synapse with the midget ganglion cell.

00as the conic having an eccentricity greater than unity, is a convenient starting-point for the Euclidian investigation.

00His whole kingdom was to be unified; Judaism was an eccentricity and as such doomed to extinction.

00This marriage may have done something to increase Granville's reputation for eccentricity.

00Elliptic orbits, and a parabolic orbit considered as the special case when the eccentricity of the ellipse is 1, are almost the only ones the astronomer has to consider, and our attention will therefore be confined to them in the present article.

00Although some of his quatrains are purely mystic and pantheistic, most of them bear quite another stamp; they are the breviary of a radical freethinker, who protests in the most forcible manner both against the narrowness, bigotry and uncompromising austerity of the orthodox ulema and the eccentricity, hypocrisy and wild ravings of advanced Sufis, whom he successfully combats with their own weapons, using the whole mystic terminology simply to ridicule mysticism itself.

00The magnetization at any point inside the ellipsoid will then be I = HN (29) where N=47r (e2t) (-2-eloI- e - t), e being the eccentricity (see Maxwell's Treatise, § 438).

00The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit.

00He was much struck by English manners, was deeply penetrated by English toleration for personal freethought and eccentricity, and gained some thousands of pounds from an authorized English edition of the Henriade, dedicated to the queen.

00(x2+3,2) If the ellipsoid is one of revolution round the major axis a (prolate) and of eccentricity e, then the above formula reduces to I I l og e (I +e) C - tae Whereas if it is an ellipsoid of revolution round the minor axis b (oblate), we have I sin - tae C2 - ae (9).

00Concurrently with the growth of this unrest Rudolph had become increasingly subject to attacks of depression and eccentricity, which were so serious as to amount almost to insanity.

00It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.

00The eccentricity which had characterized his opinions from the beginning of his career gradually became more marked until they developed into insanity.

00From the time of his first introduction to Tycho he had devoted himself to the investigation of the orbit of Mars, which, on account of its relatively large eccentricity, had always been especially recalcitrant to theory, and the results appeared in Astronomia nova ainoXayrgrii, seu Physica coelestis tradita commentariis de motibus stellae Martis (Prague, 1609).

00In manner he was simple, direct, void of the least affectation, and entirely free from awkwardness, oddity or eccentricity.

00It may be considered as arising from a semi-annual variation in the eccentricity of the moon's orbit and the position of its perigee.

00Jeffrey naturally declined to appoint a man who, in spite of some mathematical knowledge, had no special qualification, and administered a general lecture upon Carlyle's arrogance and eccentricity which left a permanent sense of injury.

00It is therefore a conic section having its eccentricity equal to unity.

00A large eccentricity also produces an unsymmetrical light variation, the minimum occurring at a time not midway between two maxima; stars of this character are called Cepheid variables, after the typical star S Cephei.

00There is a very striking relation between the eccentricity and the period of a system; in general the binaries of longest period have the greatest eccentricities.

00Although they had little or none of the eccentricity of the history, they proved almost as popular.

00After seeing to the publication of this instalment of Tristram and of another set of sermons - more pronouncedly Shandean in their eccentricity - he quitted England again in the summer of 1765, and tavelled in Italy as far as Naples.

00and eccentricity I

00The centre of the eccentric is its connected point; and its eccentricity, or the distance from that centre to the axis of the shaft, is its crank-arm.

00An eccentric may be made capable of having its eccentricity altered by means of an adjusting screw, so as to vary the extent of the reciprocating motion which it communicates.

00And when he heaps suspicion, not on Christian dogmas, but on beliefs of which the resemblance to Christian tenets is sufficiently patent, the real aim is so transparent that his method seems to partake rather of the nature of literary eccentricity than of polemical artifice; yet by this disingenuous indirectness he gave his argument that savour of duplicity which ever after clung to the popular conception of deism.

00He is perhaps apt to attach an exaggerated importance to some of the authorities which he was the first to bring to light, to see a general tendency in what may only be the expression of an individual eccentricity, to rely too much on ambassadors' reports which may have been written for some special end, to enter too fully into the details of diplomatic correspondence.

00In the case of very tall exposed buildings of small depth, the vertical load on the columns due to wind pressure in the opposite side of the building must be computed and allowed for, and in case the lower columns are without lateral support their bending moment must be sufficient to resist the lateral pressure due to wind and eccentricity of loading.

00In computing the column sections a proper allowance must be made for any eccentricity of loading.

00Its mean distance from the sun is 1.46 times i that of the earth; but, besides, the eccentricity of its orbit is large (0.22), so that at the most favourable opportunity it can come within one-seventh of the distance of the sun.

00Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the parallax, or the inclination of the lunar orbit.

00At the other extreme we know that innumerable swarms of minute bodies, probably little more than particles, move round the sun in orbits of every degree of eccentricity, making themselves known to us only in the exceptional cases when they strike the earth's atmosphere.

00the axes and eccentricity of the ellipse, and the position of the plane in which it lies.

00Hipparchus fixed the chief data of astronomy - the lengths of the tropical and sidereal years, of the various months, and of the synodic periods of the five planets; determined the obliquity of the ecliptic and of the moon's path, the place of the sun's apogee, the eccentricity of his orbit, and the moon's horizontal parallax; all with approximate accuracy.

00The discovery, just one hundred years after the publication of Newton's Principia, of its dependence upon the slowly varying eccentricity of the earth's orbit signalized the removal of the last conspicuous obstacle to admitting the unqualified validity of the law of gravitation.

00The eccentricity of the ellipse is in the general average about 0.055, whence the moon is commonly more than i' further from the earth at apogee than at perigee.

00The Eccentricity of the Moon's Orbit.

00Assuming the mean motion of the moon to be known and the perigee to be fixed, three eclipses, observed in different points of the orbit, would give as many true longitudes of the moon, which longitudes could be employed to determine three unknown quantities - the mean longitude at a given epoch, the eccentricity, and the position of the perigee.

00The eccentricity determined in this way is more than a degree in error, owing to the effect of the evection, which was unknown to Hipparchus.

00The result of the latter inequality is brought out when it is sought to determine the eccentricity of the orbit from the observations near the time of the first and last quarter.

00Therefore the eccentricity found by Hipparchus was only 5Ã‚°, and was more than a degree less than its true value.

00Most of the elements are small numerical fractions: e, the eccentricity of the moon's orbit, about 0.055; e', the eccentricity of the earth's orbit, about o 017: y, the sine of half the inclination of the moon's orbit, about 0.046; m, the ratio of the mean motions of the moon and earth, about 0.075.

00Euler conceived the idea of starting with a preliminary solution of the problem in which the orbit of the moon should be supposed to lie in the ecliptic, and to have no eccentricity, while that of the sun was circular.

00With the latest accepted diminution of the eccentricity, the coefficient is 5.91".

00eccentricity 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.

00This ratio is termed the eccentricity, and will be denoted by e.

00line 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.

00Metrical 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.

00Of practical importance are the following constructions: - (I) 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.

00(3) If the directrix, focus and eccentricity be given, we may employ the general method for constructing a conic. Let S (fig.

00Divide SX internally at A and externally at A', so that the ratios SA/AX and SA'/A'X are each equal to the eccentricity.

00This ratio, known as the eccentricity, determines the nature of the curve; if it be greater than unity, the conic is a hyperbola; if equal to unity, a parabola; and if less than unity, an ellipse.

00In the case of the circle, the centre is the focus, and the line at infinity the directrix; we therefore see that a circle is a conic of zero eccentricity.

00He seems to find that perfect blend of yesteryear and eccentricity in sunglasses that makes him stand out even more than usual in movies and in public appearances.

00It's okay to express your eccentricity and imagination, but keep in mind if you are employee or student, your style may become cause for concern.

00Some of the symptoms may be dismissed as social awkwardness or eccentricity.

00At the other extreme we know that innumerable swarms of minute bodies, probably little more than particles, move round the sun in orbits of every degree of eccentricity, making themselves known to us only in the exceptional cases when they strike the earth's atmosphere.

02There is a very striking relation between the eccentricity and the period of a system; in general the binaries of longest period have the greatest eccentricities.

04He is perhaps apt to attach an exaggerated importance to some of the authorities which he was the first to bring to light, to see a general tendency in what may only be the expression of an individual eccentricity, to rely too much on ambassadors' reports which may have been written for some special end, to enter too fully into the details of diplomatic correspondence.

04Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the parallax, or the inclination of the lunar orbit.

04The discovery, just one hundred years after the publication of Newton's Principia, of its dependence upon the slowly varying eccentricity of the earth's orbit signalized the removal of the last conspicuous obstacle to admitting the unqualified validity of the law of gravitation.

05Although they had little or none of the eccentricity of the history, they proved almost as popular.

010

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