The papers contained in this fourth and last volume are too diverse in character to admit of such a complete arrangement according to subjects, as was made in the earlier volumes. I begin, however, with three papers on Periodic Orbits, a subject which has played a very important part in the recent developments of dynamical astronomy. The middle one of the three is by Mr Hough, and it is reproduced, by his permission, as explaining the sequence of ideas which led from the first to the third paper.

The proprietors of the Encyklopädie der mathematischen Wissenschaften have kindly allowed me to print here the English text of the article ‘Die Bewegung der Hydrosphäre.’ It is the long paper entitled ‘The Tides,’ which forms Part II. The section on the dynamical theory of the tides is by Mr Hough, but I wrote the rest. According to my general scheme this paper would naturally have belonged to the group of papers contained in Vol. I, but it was published after the appearance of that volume. The same remark also applies to the two recent papers on tides contained in Part IV.

Part III consists of miscellaneous papers arranged in chronological order. Some of them are obviously of slight value and are reproduced merely for the sake of completeness.