These two laws completely prescribe the motion of a planet round the sun. The first defines the path which the planet pursues; the second describes how the velocity of the body varies at different points along its path. But Kepler added to these a third law, which enables us to compare the movements of two different planets revolving round the same sun. Before stating this law, it is necessary to explain exactly what is meant by the _mean_ distance of a planet. In its elliptic path the distance from the sun to the planet is constantly changing; but it is nevertheless easy to attach a distinct meaning to that distance which is an average of all the distances. This average is called the mean distance. The simplest way of finding the mean distance is to add the greatest of these quantities to the least, and take half the sum. We have already defined the periodic time of the planet; it is the number of days which the planet requires for the completion of a journey round its path. Kepler's third law establishes a relation between the mean distances and the periodic times of the various planets. That relation is stated in the following words:-- "_The squares of the periodic times are proportional to the cubes of the mean distances._" Kepler knew that the different planets had different periodic times; he also saw that the greater the mean distance of the planet the greater was its periodic time, and he was determined to find out the connection between the two. It was easily found that it would not be true to say that the periodic time is merely proportional to the mean distance. Were this the case, then if one planet had a distance twice as great as another, the periodic time of the former would have been double that of the latter; observation showed, however, that the periodic time of the more distant planet exceeded twice, and was indeed nearly three times, that of the other. By repeated trials, which would have exhausted the patience of one less confident in his own sagacity, and less assured of the accuracy of the observations which he sought to interpret, Kepler at length discovered the true law, and expressed it in the form we have stated. To illustrate the nature of this law, we shall take for comparison the earth and the planet Venus. If we denote the mean distance of the earth from the sun by unity then the mean distance of Venus from the sun is 0.7233. Omitting decimals beyond the first place, we can represent the periodic time of the earth as 365.3 days, and the periodic time of Venus as 224.7 days. Now the law which Kepler asserts is that the square of 365.3 is to the square of 224.7 in the same proportion as unity is to the cube of 0.7233. The reader can easily verify the truth of this identity by actual multiplication. It is, however, to be remembered that, as only four figures have been retained in the expressions of the periodic times, so only four figures are to be considered significant in making the calculations.