But it will be seen that ellipses may be of greater or less eccentricity, and the equation to centre depends on the eccentricity. This may need a word of explanation. Suppose a circular orbit. Draw the two diameters at right angles to one another; they are of equal length. Now suppose another figure in which the one diameter is longer than the other. The circumference of this figure will be an ellipse. The greater diameter is called the Major Axis, and the diameter at right angles to it is the Minor Axis. The proportion of one to the other axis determines the amount of eccentricity. Twice the eccentricity gives the equation to centre, and to reduce this to degrees and minutes of a circle it has to be multiplied by the chord of 60 degrees, which is 57°·29578. This gives the maximum equation to centre when the planet is 3 signs or 90 degrees from its aphelion, and therefore on the Minor Axis. The eccentricity of the various planets may be here stated: Mercury, 0.2055; Mars, 0.0931; Jupiter, 0.0482; Saturn, 0.9562; Uranus, 0.9467; Earth, 0.0168; Venus, 0.0068. These quantities undergo a gradual change. Thus it is found that Jupiter, Mars, and Mercury are increasing the eccentricity of their orbits, while Venus, the Earth, and Saturn are reducing it. The orbit of Venus is now almost circular, and it affords an example of the perfect astronomical paradigm. Thus by the mean motions and the equation to centre the true longitudes of the planets in their heliocentric orbits are obtained. But inasmuch as the orbits of the planets do not lie in the same plane as the Sun, but cross its apparent path at various angles of inclination, a further equation is due to reduce the orbital longitudes of the planets to the ecliptic. To further reduce these true longitudes into their geocentric equivalents, i. e., as seen from the Earth’s centre, we have to employ the angle of Parallax, which is the angle of difference as seen from two different points in space. This will vary according to the relative distances of the bodies from one another. The Moon’s longitude is always taken geocentrically. When approximate longitudes are required, the employment of a mean vector, which is equal to half the minor axis of the planet, is found convenient. For the convenience of astronomical students I may here give the constant logarithms of the values of the tangent, which, being added to the logarithm of the tangent of half the distance of the planet from the Sun in longitude, will give the tangent of the complement. LOGARITHMS Neptune, 9.97107; Uranus, 9.95479; Saturn, 9.90858; Jupiter, 9.83114; Mars, 9.32457; Venus, 9.20812; Mercury, 9.63210.