3d Law: The squares of the periods (_i. e._ times of revolution in their orbits) of the different planets are proportional to the cubes of their mean (average) distances from the sun. The meaning of this will be best explained by an example. Suppose one planet, whose distance we know, has a period only one-eighth as long as that of another planet, whose distance we do not know. Then Kepler's third law enables us to calculate the distance of the second planet. Call the period of the first planet 1, and that of the second 8, and also call the distance of the first 1, since all we really need to know is the _relative_ distance of the second, from which its distance in miles is readily deduced by comparison with the distance of the first. Then, by the law, 1^2 : 8^2 : 1^3 : x^3 (“x” representing the unknown quantity). Now, this is simply a problem in proportion where the product of the means is equal to the product of the extremes. But 1^2 = 1, and also 1^3= 1; therefore x^3 = 8^2, and x = ∛(8^2) (the cube root of the square of 8), which is 4. Thus we see that the distance of the second planet must be four times that of the first.