The following memorandum was communicated at the former Meeting of the Society.

“On the 2d September 1839, M. Arago communicated to the Academy of Sciences a letter by M. Melloni, containing some very interesting experiments on the transmission of Radiant Heat. M. Melloni finds, that rock-salt (which is well known to transmit rays from every source with equal facility) acquires, by being smoked, the power of transmitting most easily heat of low temperature, or that kind of heat stopped in greatest proportion by glass, alum, and (according to M. Melloni) every other substance. The experiments contained in the Third Series of my Researches on Heat, shew that this is equivalent to saying, that substances in general allow only the more refrangible rays to pass; and as M. Melloni had been led by his previous experiments to the same conclusion, his statement amounts to this, that, whilst rock-salt presents the analogy of white glass, by transmitting all rays in equal proportions, every substance hitherto examined acts on the calorific rays as violet or blue glass does on light, absorbing the rays of least refrangibility, and transmitting only the others.

The instance produced was a case which had occurred in the Infirmary, in which the anterior roots of the nerves arising from the cauda equina were engaged in a tumour, and the consequence during life, was the loss of muscular power, sensibility remaining unaffected.

“The author prefaced his remarks by a short history of Bills of Exchange, and other kinds of paper currency; in which he pointed out the economy and convenience of a well regulated paper circulation.

“The means usually employed to diminish the facilities to forgery are—

“1. Colouring the paper, or the pulp of which it is manufactured, by various vegetable and mineral substances, either singly or combined. The best attempts of this sort have been imitated by a clever hand and a pencil.

“In the preceding memoir on this subject, the author had confined himself to the fundamental operations leading to the differential co-efficients of various functions. In the present paper, he offers an illustration of the entrance of such coefficients into the analysis of physical and geometrical problems. Having first established a general theorm, connecting finite integrals of a certain form with fractional and negative differentials, the author adapts it to represent the integrals actually occurring in several problems. By this means he wishes to shew that the theory of General Differential Coefficients will at some future period become a powerful instrument in the hands of analysts, by furnishing them with results comprehended under general forms, and thus opening another section of the science of comprehensive memory.’

“The author commenced with some remarks on the various causes by which the actions of plants and of their products on the animal body may be modified, and on the great vagueness and uncertainty of the information at present possessed in regard to the influence of those causes which seem to arise in peculiar circumstances of vegetation, more especially climate, weather, soil, and the progress of vegetation. He then stated the sources of information on these points, namely, the curative or therapeutic action of drugs on man,—their effects on the healthy functions both of man and animals, either as medicines or as poisons,—their sensible qualities,—and their chemical analysis; and he assigned reasons for discarding the first of these from the inquiry, and for trusting, in a great measure, to the criterions derived from sensible qualities,—from the effects of poisons on the lower animals,—and from chemical analysis.

“This is a rare and interesting species of Clavagella, now inhabiting the shores of Naples, presented by Sir Thomas Brisbane.

‘When that part of Lamarck's work on Invertebrata, which contained the class Conchiferœ, appeared in 1818, among the order Tubicolœ;, he introduced the genus Clavagella, of which he describes four species only, and they are all fossil. Even at the conclusion of his great work, in 1822, he appears not to have known any living species.

“When visiting the ancient volanoes of the Haut Vivarais, the author was led to make some inquiries relative to the fall of this remarkable meteor, which took place in broad day-light, almost in the midst of the scattered hamlet of Libounez, near Juvinas, and which was witnessed by many persons, some of whom still survive, and gave the account which the author presented.

“The stone fell on the 15th June 1821, at 4½ P. M.; sky clear, and wind north. A long roll was heard, then an explosion like that of a cannon, five minutes before the stone fell. It touched the ground within a few feet of several men who were digging potatoes within a small enclosure.

“The author referred in this paper to the experience of Baron Larrey; also to operations performed by Baron Dupuytren and M. Roux, who, in removing the arm at the shoulder-joint, heard the air drawn in, and witnessed the effect in the instant death of their patients.

“He noticed the experiments made by the Academie Royal de Medicine, and conceived that they regarded too exclusively the influence of the heart and lungs. He explained the phenomenon to be owing to the elevation of the muscles of the neck, by which the atmospheric pressure was taken off, and the air drawn into the open vein.

“This mineral occurs in small crystals embedded in prehnite, at Bishoptown, in Renfrewshire. It had been long supposed to be a variety of zinc-blende; but was first distinguished from that mineral by Lord Greenock. Two small crystals of it, sent to the author for chemical examination by Professor Jameson, appeared to be six-sided pyramids, and had a wine-yellow colour, conchoidal fracture, splendent and vitreous lustre, hardness about that of calcareous spar, orange-red streak, and considerable transparency.

“It has been noticed as a curious fact, first, it is believed, by Mr Whitwell, that all parallelograms seen obliquely appear distorted when magnified by a telescope. The effect is to render the space between the upper and lower parallel lines apparently greater as the distance increases,—thus annihilating the usual convergence to a vanishing point, or even reproducing it in an opposite direction. It is hardly necessary to add, that this Inversion of common perspective is only apparent; a fact conclusively established by measuring the angles subtended by the two extremities of a signboard or a row of windows, when the angle evidently diminishes with distance.

This bed lies from 200 to 300 feet above the level of the sea, an arm of which extends to that town, but no shells are to be found upon its shores. It covers a space of several square miles, and is coated with soil, which in many places has been removed, the shells being taken to mend the roads, as well as for building purposes, and for manure. Such openings upon the surface are frequent on the hill just above the town, on the road to Gottenburg; but a mile or two on that to Wennersburg, and to the left, there is a large vertical opening, exposing to view from thirty to forty feet of the bed's depth, its entire depth being as yet unknown.

“The author commences with some remarks on the degree of accuracy attainable by portable magnetic apparatus, and particularly by the use of dipping needles of moderate dimensions. A six-inch needle by Robinson of London, belonging to the Society, together with the Hansteen apparatus for horizontal intensity, were the chief instruments employed by him in a tour through Germany in 1837, in which (though magnetic investigations did not form his primary object), he endeavoured to obtain the approximate value of the elements of dip and intensity for several important stations, and also to carry out into the Eastern Alps the investigations he had already, in 1832, conducted in Switzerland.