new object assiduously till February 11th, when he became dangerously ill; but he had written, on January 23rd, to Oriani of Milan, and to Bode at Berlin on the following day. These letters, however, did not reach the recipients (in those days of leisurely postal service) until April 5th and March 20th respectively; and we can imagine the mixed feelings with which Bode heard that the discovery which he had contemplated for fifteen years, and for which he was just about to organise a diligent search, was thus curiously snatched from him. [Sidenote: Hegel's forecast.] More curious still must have seemed the intelligence to a young philosopher of Jena named Hegel, who has since become famous, but who had just imperilled his future reputation by publishing a dissertation proving conclusively that the number of the planets could not be greater than seven, and pouring scorn on the projected search of the half-dozen enthusiasts who were proposing to find a new planet merely to fill up a gap in a numerical series. [Sidenote: The planet lost again.] The sensation caused by the news of the discovery was intensified by anxiety lest the new planet should already have been lost; for it had meanwhile travelled too close to the sun for further observation, and the only material available for calculating its orbit, and so predicting its place in the heavens at future dates, was afforded by the few observations made by Piazzi. Was it possible to calculate the orbit from such slender material? It would take too long to explain fully the enormous difficulty of this problem, but some notion of it may be obtained, by those unacquainted with mathematics, from a rough analogy. If we are given a portion of a circle, we can, with the help of a pair of compasses, complete the circle: we can find the centre from which the arc is struck, either by geometrical methods, or by a few experimental trials, and then fill in the rest of the circumference. If the arc given is large we can do this with certainty and accuracy; but if the arc is small it is difficult to make quite sure of the centre, and our drawing may not be quite accurate. Now the arc which had been described by the tiny planet during Piazzi's observations was only three degrees; and if any one will kindly take out his watch and look at the minute marks round the dial, three degrees is just _half_ a single minute space. If the rest of the dial were obliterated, and only this small arc left, would he feel much confidence in restoring the obliterated portion? This problem gives some idea of the difficulties to be encountered, but only even then a very imperfect one. [Sidenote: Gauss shows how to find it.]