This was certainly the most extraordinary prediction ever made, for cometary investigations were then in their infancy, and Halley was the only man living who could have computed the orbit of this comet. Newton had his doubts regarding the suggestion that a comet seen on one side of the sun might be identical with another seen on the other side some weeks later, but Robert Hooke, in a letter addressed to Newton in 1679, suspected that a comet could reappear after a definite period. He declared that, if gravity decreased according to the reciprocal of the square of the distance, the path of a projectile would be an ellipse. As the year 1758 approached, one can imagine the interest aroused among astronomers, and the calculations which were made for determining as accurately as possible the disturbing effects of the larger planets within the sphere of whose influence the comet might pass. It is impossible to convey an idea of the labor involved in making the required computations of the perturbations of this comet throughout a period of two revolutions, or one hundred and fifty years. It is with a feeling of pride that the author notes the important part taken in this work by Madame Lepaute,[9] wife of one of the assistants of the great mathematician Lalande. Her work proved of inestimable value according to the following remarks made by her husband on the subject: “During six months we calculated from morning till night, sometimes even at meals; the consequence of which was that I contracted an illness which changed my constitution during the remainder of my life. The assistance rendered by Madame Lepaute was such that without her we never should have dared to undertake the enormous labour with which it was necessary to calculate the distance of each of the two planets, Jupiter and Saturn, from the comet, separately for every degree, for one hundred and fifty years.”