night, when the planet was looked for by the help of the ephemeris I had made, revealed the truant to the observer. Three new planets found since then have supplied fresh opportunities for examining and proving the efficacy and universality of this method. "Now a good many astronomers, immediately after the rediscovery of Ceres, desired me to publish the methods which had been used in my calculations. There were, however, not a few objections which prevented me from gratifying at that moment these friendly solicitations, viz. other business, the desire of treating the matter more fully, and more especially the expectation that, by continuing to devote myself to this research, I should bring the different portions of the solution of the problem to a more perfect pitch of universality, simplicity, and elegance. As my hopes have been justified, I do not think there is any reason for repenting of my delay. For the methods which I had repeatedly applied from the beginning admitted of so many and such important variations, that scarcely a vestige of resemblance remains between the method by which formerly I had arrived at the orbit of Ceres and the practice which I deal with in this work. Although indeed it would be alien to my intention to write a complete history about all these researches which I have gradually brought to even greater perfection, yet on many occasions, especially whenever I was confronted by some particularly serious problem, I thought that the first methods which I employed ought not to be entirely suppressed. Nay, rather, in addition to the solutions of the principal problems, I have in this work followed out many questions which presented themselves to me, in the course of a long study of the motions of the heavenly bodies in conic sections, as being particularly worthy of attention, whether on account of the neatness of the analysis, or more especially by reason of their practical utility. Yet I have always given the greater care to subjects which I have made my own, merely noticing by the way well-known facts where connection of thought seemed to demand it." [Sidenote: Rediscovery of Ceres.] [Sidenote: Another planet found.]