By approaching very near to a large planet, a comet may have its orbit entirely changed. This fact is strikingly exemplified in the history of the comet of 1770. At its appearance in 1770, its orbit was found to be an ellipse, requiring for a complete revolution only five and a half years; and the wonder was, that it had not been seen before, since it was a very large and bright comet. Astronomers suspected that its path had been changed, and that it had been recently compelled to move in this short ellipse, by the disturbing force of Jupiter and his satellites. The French Institute, therefore, offered a high prize for the most complete investigation of the elements of this comet, taking into account any circumstances which could possibly have produced an alteration in its course. By tracing back the movements of this comet, for some years previous to 1770, it was found that, at the beginning of 1767, it had entered considerably within the sphere of Jupiter's attraction. Calculating the amount of this attraction from the known proximity of the two bodies, it was found what must have been its orbit previous to the time when it became subject to the disturbing action of Jupiter. It was therefore evident why, as long as it continued to circulate in an orbit so far from the centre of the system, it was never visible from the earth. In January, 1767, Jupiter and the comet happened to be very near to one another, and as both were moving in the same direction, and nearly in the same plane, they remained in the neighborhood of each other for several months, the planet being between the comet and the sun. The consequence was, that the comet's orbit was changed into a smaller ellipse, in which its revolution was accomplished in five and a half years. But as it approached the sun, in 1779, it happened again to fall in with Jupiter. It was in the month of June that the attraction of the planet began to have a sensible effect; and it was not until the month of October following, that they were finally separated. At the time of their nearest approach, in August, Jupiter was distant from the comet only 1/491 of its distance from the sun, and exerted an attraction upon it two hundred and twenty-five times greater than that of the sun. By reason of this powerful attraction, Jupiter being further from the sun than the comet, the latter was drawn out into a new orbit, which even at its perihelion came no nearer to the sun than the planet Ceres. In this third orbit, the comet requires about twenty years to accomplish its revolution; and being at so great a distance from the earth, it is invisible, and will for ever remain so unless, in the course of ages, it may undergo new perturbations, and move again in some smaller orbit, as before. With the foregoing leading facts respecting comets in view, I will now explain to you a few things equally remarkable respecting their _motions_.