The third book contains the practical application of the propositions in the two earlier books to the solar system. I need not describe this in detail. In order to justify this application, Newton commenced by laying down four rules which have since been accepted as binding in scientific investigations. These, as given in the third edition, are to the following effect: (1) We are not to assume more causes than are sufficient and necessary for the explanation of observed facts. (2) Hence, as far as possible, similar effects must be assigned to the same cause; for instance, the fall of stones in Europe and America. (3) Properties common to all bodies within reach of our experiments are to be assumed as pertaining to all bodies; for instance, extension. (4) Propositions in science obtained by a wide induction are to be regarded as exactly or approximately true, until phenomena or experiments show that they may be corrected or are liable to exceptions. The substance of these rules is now accepted as the basis of scientific investigation. Their formal enunciation here serves as a landmark in the history of thought. As soon as the Copernican view of the solar system was accepted, it was natural for men to seek to explain the reason why the planets moved as they did. Descartes, in 1644, had suggested that the explanation might be found in the existence of vortices in space. This conjecture, although based on arbitrary assumptions, and in fact untenable, played an important part in the history of the subject, for it accustomed men to think that planetary phenomena might be explicable by the same laws as are found to be true on the earth. That this was so was established by Newton in his _Principia_, where all the motions of the solar system were made to depend on one assumption as to the law of attraction. The question whether this law could itself be deduced from some more fundamental assumption was raised by Newton, but he could not devise a satisfactory hypothesis. It has been discussed again and again since his time, and the problem is still unsolved. Newton's conclusions were immediately accepted in Britain, and very rapidly by the leading mathematicians in Europe: indeed Huygens came expressly from Holland in order to make the personal acquaintance of a writer whose work promised to revolutionize the history of science. The refutation of the Cartesian hypothesis ran, however, counter to the sentiments and wishes of a certain number of philosophers, and some few years elapsed before the truth of the gravitation theory was universally admitted, but it would be ungracious to dwell further on this. In Britain the work exercised a profound influence in philosophy as well as in science, and educated men of all schools of thought acquainted themselves with the general line of Newton's reasoning and his deductions.