Were the earth's path a circle, having the sun in the centre, the sun would always appear to be at the same distance from us; that is, the radius of the orbit, or _radius vector_, (the name given to a line drawn from the centre of the sun to the orbit of any planet,) would always be of the same length. But the earth's distance from the sun is constantly varying, which shows that its orbit is not a circle. We learn the true figure of the orbit, by ascertaining the _relative distances_ of the earth from the sun, at various periods of the year. These distances all being laid down in a diagram, according to their respective lengths, the extremities, on being connected, give us our first idea of the shape of the orbit, which appears of an oval form, and at least resembles an ellipse; and, on further trial, we find that it has the properties of an ellipse. Thus, let E, Fig. 32, be the place of the earth, and _a_, _b_, _c_, &c., successive positions of the sun; the _relative_ lengths of the lines E _a_, E _b_, &c., being known, on connecting the points _a_, _b_, _c_, &c., the resulting figure indicates the true figure of the earth's orbit. These relative distances are found in two different ways; first, _by changes in the sun's apparent diameter_, and, secondly, _by variations in his angular velocity_. The same object appears to us smaller in proportion as it is more distant; and if we see a heavenly body varying in size, at different times, we infer that it is at different distances from us; that when largest, it is nearest to us, and when smallest, furthest off. Now, when the sun's diameter is accurately measured by instruments, it is found to vary from day to day; being, when greatest, more than thirty-two minutes and a half, and when smallest, only thirty-one minutes and a half,--differing, in all, about seventy-five seconds. When the diameter is greatest, which happens in January, we know that the sun is nearest to us; and when the diameter is least, which occurs in July, we infer that the sun is at the greatest distance from us. The point where the earth, or any planet, in its revolution, is nearest the sun, is called its _perihelion_; the point where it is furthest from the sun, its _aphelion_. Suppose, then, that, about the first of January, when the diameter of the sun is greatest, we draw a line, E _a_, Fig. 32, to represent it, and afterwards, every ten days, draw other lines, E _b_, E _c_, &c.; increasing in the same ratio as the apparent diameters of the sun decrease. These lines must be drawn at such a distance from each other, that the triangles, E _a b_, E _b c_, &c., shall be all equal to each other, for a reason that will be explained hereafter. On connecting the extremities of these lines, we shall obtain the figure of the earth's orbit.