Introductory Remarks.—The principles set forth in this paper, though now (with the exception of the first theorem) published for the first time, were communicated to the French Academy of Sciences fifteen years ago, in a memoir entitled “ De l'Equilibre intérieur d'un Corps solide, élastique, et homogène,” and marked with the motto, “ Obvia conspicimus, nubem pellente Mathesi,” the receipt of which is acknowledged in the Comptes Rendus of the 6th April 1857.

(1.) Principle of Isorrhopic Axes.—The following theorem was first published in the “Philosophical Magazine” for December 1855.

Prop. I. “Theorem. Every self-balanced system of forces applied to a connected system of points is capable of resolution into three rectangular systems of parallel self-balanced forces applied to the same points.

There are several problems of great practical importance in electro-magnetic measurements, in which the value of a quantity has to be calculated by taking the sum of the logarithms of the distances of a system of parallel wires from a given point. The calculation is in some respects analogous to that in which we find the potential at a point due to a given system of equal particles, by adding the reciprocals of the distances of the particles from the given point. There is this difference, however, that whereas the reciprocal of a line is completely defined when we know the unit of length, the logarithm of a line has no meaning till we know not only the unit of length, but the modulus of the system logarithms.

1. The lunar diurnal variation of magnetic declination as first discovered by Kreil, depended on too few observations to be free from the errors introduced by irregular disturbing causes. The independent discovery of the lunar action on the magnetic needle made afterwards by myself, was liable to the same criticism; but the agreement of the results obtained, both for the magnetic declination and the horizontal force, was sufficiently great to give a considerable value to the conclusion, that the magnetic needle obeys a diurnal law, depending on the moon's hour angle, both as to its direction and the force with which it is directed. This conclusion was farther confirmed in the discussion first made by myself, for the lunar diurnal variation of the vertical magnetic force, which gave, within an hour, the same epochs of maxima and minima as those obtained previously by me for the horizontal component.

The illustrious Cuvier, in his treatise “ Sur les Ossemens fossiles,” described and figured an imperfect skull which had been obtained, in 1804, by M. Raymond Gorsse in the department of Bouches-du-Rhône, near Fos, on the southern coast of France. It had been found on the sea-shore in the preceding year by a peasant. Cuvier recognised it to belong to an undescribed genus of cetaceans, to which he gave the name of Ziphius; and from the deep hollow which it possessed at the base of the rostrum, he named it Ziphius cavirostris. From the condition of the bones, and the general characters of the specimen, he judged it to be a fossil. Cuvier's description, though brief, and from a mutilated specimen, yet clearly states the most salient features of the skull.

The Ipecacuan plant, Cephaëlis Ipecacuanha of Achille Richard, has been cultivated in the Edinburgh Botanic Garden for upwards of forty years, but it was not propagated to any extent until 1870, when a proposal was made to attempt the cultivation of the plant in India. This suggestion was made on account of the continued destruction of the plant by the collectors in Brazil, and the risk of scarcity in the supply of this most valuable remedy for dysentery. The Secretary of State for India (His Grace the Duke of Argyll), under the recommendation of several medical officers in Bengal, authorised an attempt to propagate the plant in our Indian possessions, and with that view application was made to me and others to aid in this important undertaking. Accordingly, I at once set about the propagation of the plant in the Edinburgh Garden, with the assistance of Mr M'Nab the curator. He found that the plant could be multiplied very rapidly by dividing the annulated root, cuttings of which, though very small, give off young shoots when placed in favourable circumstances. By this means, numerous plants were produced very rapidly, and the method was also followed by the Messrs Lawson, Nurserymen, Edinburgh, who supplied a large stock of vigorous plants. Mr M'Nab drew up a report of his mode of propagation, which was printed, and distributed extensively to district officers in India and elsewhere. The paper also appeared in the Transactions of the Botanical Society of Edinburgh, vol. x. p. 318.