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 observation. 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 extend 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.[48] 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 ensured 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 every where resisted by the errors and prejudices which had taken a deep hold even of the strongest minds. The philosophy of Descartes was predominant throughout Europe. Appealing to the imagination, and not to the reason of mankind, it was quickly received into popular favour, and the same causes which facilitated its introduction extended its influence, and completed its dominion over the human mind. In explaining all the movements of the heavenly bodies by a system of vortices in a fluid medium diffused through the universe, Descartes had seized upon an analogy of the most alluring and deceitful kind. Those who had seen heavy bodies revolving in the eddies of a whirlpool, or in the gyrations of a vessel of water thrown into a circular motion, had no difficulty in conceiving how the planets might revolve round the sun by analogous movements.