Although there could be little doubt that the comets were retained in their orbits by the same laws which regulated the motions of the planets, yet it was difficult to put this opinion to the test of observation. The visibility of comets only in a small part of their orbits rendered it difficult to ascertain their distance and periodic times; and as their periods were probably of great length, it was impossible to correct approximate results by repeated observations. Newton, however, removed this difficulty by showing how to determine the orbit of a comet, namely, the form and position of the orbit, and the periodic time, by three observations. By applying this method to the comet of 1680 he calculated the elements of its orbit, and, from the agreement of the computed places with those which were observed, he justly inferred that the motions of comets were regulated by the same laws as those of the planetary bodies. This result was one of great importance; for as the comets enter our system in every possible direction, and at all angles with the ecliptic, and as a great part of their orbits extends far beyond the limits of the solar system, it demonstrated the existence of gravity in spaces far removed beyond the planet, and proved that the law of the inverse ratio of the squares of the distance was true in every possible direction, and at very remote distances from the centre of our system. Such is a brief view of the leading discoveries which the _Principia_ first announced to the world. The grandeur of the subjects of which it treats, the beautiful simplicity of the system which it unfolds, the clear and concise reasoning by which that system is explained, and the irresistible evidence by which it is supported might have insured it the warmest admiration of contemporary mathematicians and the most welcome reception in all the schools of philosophy throughout Europe. This, however, is not the way in which great truths are generally received. Though the astronomical discoveries of Newton were not assailed by the class of ignorant pretenders who attacked his optical writings, yet they were everywhere resisted by the errors and prejudices which had taken a deep hold even of the strongest minds.