From M. Lefort's opening sentence it appears that he had only recently received the copy of my remarks which had been posted to him on 22d December. Perhaps on this account M. Lefort has been hurried in the perusal of my paper, and so has fallen into several mistakes as to my meaning. These will be apparent to any one who peruses the writings, and I shall pass them over entirely, confining myself to the very few points which are essential to the subject in hand. The only extraneous matter to which I shall allude is this, that while M. Lefort has obviously and justly been desirous of upholding the dignity of the Grandes Tables du Cadastre, he has, in the true spirit of an inquirer after truth, clearly and faithfully exhibited even those points which press most sorely on his own position.

This note contains the results of experiments we have made on the electric resistance of solutions by a method brought under the notice of this Society by Messrs Ewing and M'Gregor, and described in their paper printed in the Transactions, vol. 27, page 51. Our results, so far as they have gone, are as follows :—

1. Resistance of solutions of sodium-chloride, and potassium-chloride, varying in strength from ·002 grains to 4 and 5 grains to 25 cubic inches of water. In these weak solutions the polarization was very little and easily got rid of, and the results satisfactory.

In the following paper I propose to investigate expressions for the vector of the following six points of a spherical triangle :—

(1.) Pole of inscribed circle.

(2.) (3.) (4.) Poles of escribed circles.

(5.) Pole of circumscribed circle.

(6.) The orthocentre or intersection of arcs drawn perpendicularly from angles upon the opposite sides.

These vectors will all be found in terms of the vector of the corners of the triangle drawn from the centre of the sphere.

The subject of comparative philology has always interested scholars, but latterly the study has been carried on in a more scientific manner, and I may also say with more success, than at any former period. One great object in prosecuting the study is to detect the various disguises which words radically the same are apt to assume in different languages or dialects. The great scholars of two centuries ago were fully alive to the importance of this inquiry, and although they sometimes indulged in too great a latitude of conjecture, there is scarcely an etymological affinity now generally admitted of which traces and indications are not plainly to be found in the works of those learned men, and more particularly in the writings of Salmasius, the greatest of them all.

Pour faire un usage intelligent destables des fonctions irrationelles en général, et des tables de logarithmes en particulier, il est indispensable de conaître les formules fondamentales de l'interpolation, et de savoir se rendre compte du degré d'approximation que l'on peut obtenir dans les différénts cas. Je traite dans ce mémoire ces deux points qui sont à peine indiqués dans la plupart des ouvrages élémentaires, et qui sont complètement omis dans les introductions les plus développées à des tables d'ailleurs très estimables.

This was a preliminary notice of the results of a series of experiments devised to test the part played by water-vapour in the production of atmospheric electricity. While water is in the form of vapour it must be electrified by contact with the gases of the atmosphere—as they are by contact with one another. Precipitation of vapour in a receiver, whether produced by cold or by exhaustion, was found to be steadily accompanied with a disengagement of electricity. Further experiments are to be made with receivers of very great capacity.

Upwards of three years ago the author laid a paper before two members of the Scottish Meteorological Society. The question taken up was, why horizontal movement takes off vertical pressure; and the conclusion arrived at was, that every such horizontal current, owing to its passage over a resisting surface, and by means of rapid upper currents, caused removal of air and lifting, and thereby diminished pressure. It was inferred that the barometer which represented this was consequently an “effect” and not a cause of wind.

These experiments were suggested by observations on the different lengths of time required, under different circumstances, for telegraph cables to assume the temperature of the water in which they were submerged. The method employed was that known as “Angström's,” which has already been described by Prof. Tait (Proc. K. S. E. 1872–73 p. 55–61); the manner of the application of the method being, however, somewhat modified in these experiments, we will give a short description of it.

The paper commences with an account of various methods of producing very perfect exhaustion of a receiver, especially that recently devised by the authors, in which the absorbent power of charcoal is made use of. An attempt is made to calculate the amount of exhaustion thus producible.

The following paper is a continuation of a former brief one, communicated to the Society, and printed in the Proceedings, on the change of electric resistance of iron due to change of temperature. In a note appended to Prof. Tait's paper on a “First Approximation to a Thermo-electric Diagram” (Trans. R.S.E., 1872–73), attention was drawn to the curious phenomenon observed by Gore, that at a temperature about dull red heat, iron wire undergoes sudden changes in length, and also to the further discovery by Prof. Barrett, that if the wire be cooling, a sudden reglow occurs simultaneously with these changes. These phenomena seemed to be connected with other known physical changes which take place in iron at this critical temperature, such as the loss of its magnetic properties, the remarkable bend of the iron line in the thermo-electric diagram, and the interesting alteration in the rate of change of electric resistance with respect to change of temperature, observable in iron at the same dull red heat. The following experiments were made mainly with the view of more thoroughly investigating this last peculiarity.