On a sheet of paper let us mark down by a point (Fig. 68) the place occupied by the earth in relation to the sun.[77] From this point _o_, we draw a right line terminating at _a_, the sun's noon-day position (for example, on the 1st of January); the succeeding lines shall touch upon _a´ a´´_, which the sun occupies successively after the same interval of time (twenty-four hours, or the exact duration of the earth's rotation on its axis);--and let us continue after this mode until the sun has accomplished, by its own proper movement from west to east, the whole circuit of the heavens, traversing 360 degrees in the space of a year. If we ascribe to the radius _o a_ a certain length, corresponding to a definite solar diameter, the lengths of all the others, corresponding to the variations of the same diameter, will depend upon that of the first, which, for facility of calculation, we suppose to be divided into one thousand parts. [Illustration: FIG. 68.--Diagram for Kepler's Laws.] After having thus allotted to each straight line its approximate length, let us join their extremities by a curve. What do we see before us? A geometrical figure widely different from a circle, for the diameters (_i.e._, the straight lines passing through the centre) are far from being equal. The figure is an ellipse. If now we pass from the appearance to the reality, _o_ will be the sun, and _a a´ a´´_, _m m´_ will indicate the terrestrial orbit, or the points of the curve successively occupied by the earth in movement. The moveable straight lines, free at one extremity, and at the other attached to the centre of the sun, are called the _Vector heliocentric radii_. By the help of this construction, you see that the point occupied by the sun is beyond or without the centre; this eccentric point is the _focus_ of the ellipse, and the distance from this focus to the centre, its _eccentricity_. The extremity of the major axis, the nearest to the focus, is the _perihelion_, and its farthest extremity the _aphelion_. The difference of the angles formed by the vector radii indicate the inequality of the movements: to the greatest angle, the perihelion, corresponds the _maximum_ of velocity (_a a´ a´´_), just as to the smallest, or aphelion, corresponds the _minimum_ (_m m´_); the other angles mark the velocities intermediary between these two extremes. We have thus before us a series of triangles with their apices at the focus of the ellipse, and their bases on the contour of the curve. But these latter are not sufficient for the mind, whose principal function lies in seeking unity among the variety of phenomena.