Here it will be seen that the two series of numbers, in the upper and lower row respectively, agree completely for as many decimal places as are given, except in the cases of the two outer planets, where the lower numbers are slightly in excess of the upper. For this discrepancy Newton afterwards assigned a reason (chapter IX., § 186), but with the somewhat imperfect knowledge of the times of revolution and distances which Kepler possessed the discrepancy was barely capable of detection, and he was therefore justified—from his standpoint—in speaking of the law as “precise.”[92] [Illustration: FIG. 62.—The “music of the spheres,” according to Kepler. From the _Harmony of the World_.] It should be noticed further that Kepler’s law requires no knowledge of the actual distances of the several planets from the sun, but only of their relative distances, _i.e._ the number of times farther off from the sun or nearer to the sun any planet is than any other. In other words, it is necessary to have or to be able to construct a map of the solar system correct in its _proportions_, but it is quite unnecessary for this purpose to know the _scale_ of the map. Although the _Harmony of the World_ is a large book, there is scarcely anything of value in it except what has already been given. A good deal of space is occupied with repetitions of the earlier speculations contained in the _Mysterium Cosmographicum_, and most of the rest is filled with worthless analogies between the proportions of the solar system and the relations between various musical scales. He is bold enough to write down in black and white the “music of the spheres” (in the form shewn in fig. 62), while the nonsense which he was capable of writing may be further illustrated by the remark which occurs in the same part of the book: “The Earth sings the notes M I, F A, M I, so that you may guess from them that in this abode of ours MIsery (_miseria_) and FAmine (_fames_) prevail.”