On one of these occasions, whilst carefully gauging the recesses of Gemini, he espied a bright speck which was unregistered in the chart, and which at first he took for a small star that had escaped being entered in the catalogue. But the observation of a few separate nights soon made it manifest that the star was rapidly changing its position with regard to the adjacent stars, and the astronomer’s heart began to leap at the thought that the renown of the discovery of a new planet would be associated with his name. Redoubling his attention, he soon satisfied himself that what he saw was not a planet; the rapidity of its displacement rather forced him to the conjecture that it must be a comet, and this opinion was soon strengthened by the appearance of a coma, and subsequently confirmed, as the body approached the sun, by the development of a tail. A comet! The discovery was fatal to all further progress in the triangulation. However conscientiously the assistant on the Spanish coast might look to the kindling of the beacon, Rosette had no glances to spare for that direction; he had no eyes except for the one object of his notice, no thoughts apart from that one quarter of the firmament. A comet! No time must be lost in calculating its elements. Now, in order to calculate the elements of a comet, it is always deemed the safest mode of procedure to assume the orbit to be a parabola. Ordinarily, comets are conspicuous at their perihelia, as being their shortest distances from the sun, which is the focus of their orbit, and inasmuch as a parabola is but an ellipse with its axis indefinitely produced, for some short portion of its pathway the orbit may be indifferently considered either one or the other; but in this particular case the professor was right in adopting the supposition of its being parabolic. Just as in a circle, it is necessary to know three points to determine the circumference; so in ascertaining the elements of a comet, three different positions must be observed before what astronomers call its “ephemeris” can be established. But Professor Rosette did not content himself with three positions; taking advantage of every rift in the fog he made ten, twenty, thirty observations both in right ascension and in declination, and succeeded in working out with the most minute accuracy the five elements of the comet which was evidently advancing with astounding rapidity towards the earth. These elements were: 1. The inclination of the plane of the cometary orbit to the plane of the ecliptic, an angle which is generally considerable, but in this case the planes were proved to coincide. 2. The position of the ascending node, or the point where the comet crossed the terrestrial orbit. These two elements being obtained, the position in space of the comet’s orbit was determined. 3. The direction of the axis major of the orbit, which was found by calculating the longitude of the comet’s perihelion.