If we arrange in the order of date the various apparitions of comets (hat have been recorded, and note how these bodies appear in different regions of the heavens, and how some pursue a direct and others a retrograde course; or, better, if we study their elements in a catalogue, our attention is at once arrested by the diversity of these elements, which seem connected by no relation.

It may, however, be instructive to examine, by comparing these materials, whether any law presides over the distribution of comets in time and space. We shall, therefore, give a rapid résumé of the analysis we have made with this object. We have taken the catalogue published by Mr. Watson at the end of his work on Theoretical Astronomy as the basis of our investigation.

In this catalogue, which we reproduce at the end of this work, we find 279 comets arranged in the order of their successive apparitions, from the most ancient times to the commencement of the year 1867; we have ourselves completed it for the seven following years, including also the first half of the year 1874; so that the total number of comets in the catalogue is by this means increased to 311, a number very inferior, not only to the actual number of comets, but to the number of those which have received mention in history.