(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).
Jeffrey 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.
The eccentricity which had characterized his opinions from the beginning of his career gradually became more marked until they developed into insanity.
Most of the orbits are remarkably eccentric ellipses, the average eccentricity being about 0.5.
The 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.
Concurrently 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.
It 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.
From 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).
It may be considered as arising from a semi-annual variation in the eccentricity of the moon's orbit and the position of its perigee.
A 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.
There 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.
After 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.
The 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.
An 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.
And 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.
He 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.
In 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.
In computing the column sections a proper allowance must be made for any eccentricity of loading.
Its 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.
Instead 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.
At 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.
The axes and eccentricity of the ellipse, and the position of the plane in which it lies.
Hipparchus 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.
The 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.
The Eccentricity of the Moon's Orbit.
Assuming 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.
The eccentricity determined in this way is more than a degree in error, owing to the effect of the evection, which was unknown to Hipparchus.
Therefore the eccentricity found by Hipparchus was only 5°, and was more than a degree less than its true value.
Euler 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.
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.
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.
This 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.
Of 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.
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 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.
Most 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.
The 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.
Although they had little or none of the eccentricity of the history, they proved almost as popular.