In Figure 65, _E a_, _E b_, _E c_, &c., are successive representations of the radius vector. Now, if a planet sets out from _a_, and travels round the sun in the direction of _a b c_, it will move faster when nearer the sun, as at _a_, than when more remote from it, as at _m_; yet, if _a b_ and _m n_ be arcs described in equal times, then, according to the foregoing law, the space _E a b_ will be equal to the space _E m n_; and the same is true of all the other spaces described in equal times. Although the figure _E a b_ is much shorter than _E m n_, yet its greater breadth exactly counterbalances the greater length of those figures which are described by the radius vector where it is longer. THIRD LAW.--_The squares of the periodical times are as the cubes of the mean distances from the sun._ The periodical time of a body is the time it takes to complete its orbit, in its revolution about the sun. Thus the earth's periodic time is one year, and that of the planet Jupiter about twelve years. As Jupiter takes so much longer time to travel round the sun than the earth does, we might suspect that his orbit is larger than that of the earth, and of course, that he is at a greater distance from the sun; and our first thought might be, that he is probably twelve times as far off; but Kepler discovered that the distance does not increase as fast as the times increase, but that the planets which are more distant from the sun actually move slower than those which are nearer. After trying a great many proportions, he at length found that, if we take the squares of the periodic times of two planets, the greater square contains the less, just as often as the cube of the distance of the greater contains that of the less. This fact is expressed by saying, that the squares of the periodic times are to one another as the cubes of the distances.