the weights or quantities of matter in different planets are in the subduplicate ratio of the same distances, as has been already proved; so that with every increase of distance a planet has more matter and therefore is moved more slowly, and accumulates more time in its revolution, requiring already, as it did, more time by reason of the length of the way. The third and fourth causes compensate each other in a comparison of different planets; the simple and subduplicate proportion compound the sesquiplicate proportion, which therefore is the ratio of the periodic times." The only part of this "explanation" that is true is that the paths are in the simple ratio of the distances, the "proof" so confidently claimed being of the circular kind commonly known as "begging the question". It was reserved for Newton to establish the Laws of Motion, to find the law of force that would constrain a planet to obey Kepler's first and second Laws, and to prove that it must therefore also obey the third. CHAPTER VI. CLOSING YEARS. Soon after its publication Kepler's "Epitome" was placed along with the book of Copernicus, on the list of books prohibited by the Congregation of the Index at Rome, and he feared that this might prevent the publication or sale of his books in Austria also, but was told that though Galileo's violence was getting him into trouble, there would be no difficulty in obtaining permission for learned men to read any prohibited books, and that he (Kepler) need fear nothing so long as he remained quiet. In his various works on Comets, he adhered to the opinion that they travelled in straight lines with varying velocity. He suggested that comets come from the remotest parts of ether, as whales and monsters from the depth of the sea, and that perhaps they are something of the nature of silkworms, and are wasted and consumed in spinning their own tails. Napier's invention of logarithms at once attracted Kepler's attention. He must have regretted that the discovery was not made early enough to save him a vast amount of labour in computations, but he managed to find time to compute some logarithm tables for himself, though he does not seem to have understood quite what Napier had done, and though with his usual honesty he gave full credit to the Scottish baron for his invention.