This paper is the first of three communications, in which is shewn the distinctions in the regular series of nerves arising from the spinal marrow, and the ten nerves which arise directly from the brain.

The author remarks, that unless we comprehend the reason of the perfect symmetry of the spinal nerves, as contrasted with the irregularity of the encephalic nerves, we must confess ignorance of much of the structure of the animal frame.

After a general view of the nerves arising from the base of the brain, and assigning the reason of their apparent irregularity, he enters on the investigation of the third nerve. He shews that it arises from the distinct columns of which the crus cerebri is composed, by courses of parallel filaments; and that these afterwards compose a dense structure resembling ganglion.

Dr Hope stated that it has been considered a matter of considerable importance in the reasonings of geologists and hydrographers respecting some oceanic phenomena, whether sea water obeys at all temperatures the general law of expansion by heat, and contraction by cold, or, after the manner of fresh water, observes the anomalous course of contracting by heat, and expanding by cold, during a short range of temperature near its congealing point.

In this paper the author treats of the Facialis nerve or portio dura of the seventh nerve.

He commences with a view of the Respiratory System of Nerves. Vindicating the term, he proceeds to shew that the Facialis belongs to this system, and that it possesses a double function and double origin. That this composite condition of the nerve is not, however, like the double nerves of the spine (which have a toot for motion and a root for sensation), but that its origins shew it to be connected with the column of voluntary motion and of the column of respiration.

The author here first refers to the differential barometer of the late Dr Wollaston, from which he derives his new instrument. He then describes the instrument, which, in its simplest form, consists of a glass-tube bent into the form of the letter U inverted, the one end open in the line of the arms downwards, the other has its point turned up at right angles to this line. A divided scale is placed between the tubes, having its zero point as the centre. When the instrument is used, the upper curve and arms are to be filled with oil, or any other fluid lighter than water, as far as the zero on the scale; the remaining parts of the tubes are to be filled with water.

This paper is divided into three sections, each containing a distinct investigation.

The First Section is on the Variable Polarizability of different kinds of Heat. This fact, namely, that when polarization takes place by refraction through a bundle of parallel mica plates, some kinds of heat are less completely polarized than others at the same incidence, the author proposed to establish in the second series of his researches. His investigations, however, having been considered by some persons as open to objection, and directly contrary results having been obtained by M. Melloni in his repetition of these experiments, the author was induced to investigate the subject anew and with every precaution.

Professor Nichol conceives that, as the upheaving cause is a general or cosmical phenomenon, no true or complete theory of it can be deduced from a review of its merely terrestrial actions; and in the notice read to the Society, he called the attention of geologists to a few general but important inferences, from the peculiar form of the elevations in the moon.

The author introduced his observations, by adverting to the following facts, as now ascertained and generally known concerning these elevations.

As no fewer than six of the nine nerves which arise from the brain are connected with the organ of vision, he finds it necessary to announce, not only the distinct sensibilities possessed by the organ of vision, but the motions to which it is subjected. Having shewn the connection of the voluntary motions of the eye-ball with the sensation on the retina, and the motions involuntary and for the protection of an organ so delicate and so exposed, he proceeds to shew the necessity of combinations among the muscles of the eye. As there are no direct communications between the muscles, necessarily united in action, he shews the necessity of distinct nerves, and also the necessity of their relations being established at their roots, and hence deduces the reason of the fourth and sixth nerves deviating from the others in their place and mode of origin.

The author enumerated seven different deposits, overlying the rocks of the district, and subjacent to the existing soil which supports vegetation. These he described in the following order, beginning with the lowest.

(1.) Sand and fine gravel, which in some places form beds twelve feet thick.

(2.) Boulder-clay—being a stiff black or dark brown clay, characterised by enormous boulders imbedded in it, and which is occasionally forty feet thick.

The object of this paper is to determine in what consists the difference between general Symbolical Algebra and the sciences subordinate to it, particularly Arithmetical Algebra. The view which the author takes is, that Symbolical Algebra takes cognizance only of the laws by which the symbols are combined, without considering the nature of the operations represented. The greater part of the paper is occupied in applying this definition, by shewing what are the laws to which are subject the various symbols of operations we are in the habit of using; and one or two examples are given of the advantages derivable from this way of considering the subject—particularly with respect to the connection between the arithmetical and geometrical meanings of + and −. The chief application of the theory may be said to be the elucidation of the causes of analogies between operations by no means similar in their nature.

In this paper the author institutes an examination of the various methods of conceiving and constructing the conic sections, the different standards of comparison to which they have been referred, and the means by which their properties have been developed and expressed in the ancient and modern schools of mathematics. He finds that the constitution of the curves in plano by means of their remarkable properties, and the demonstration of their other properties from the constitution so obtained; have been noticed by Eutocius in the 6th century, and by him referred to Apollonius, although the formal adoption of the plane method is generally referred to a recent date.

These observations were made, at Professor Forbes's suggestion, at the expense of the British Association. They are still continued, and the present notice contains only a first approximation to the solution of the problems which they are intended to give.

The chief aim of the experiments is to ascertain the progress of Solar Heat in the Crust of the Globe, and has no immediate reference to the question of central heat; the depth to which the experiments extend being inadequate to afford decisive results on that head.

The object of the paper was to examine into the present state of our knowledge of this subject, for the purpose of ascertaining its defects, and indicating the manner in which they were to be remedied.

Although it appears to any one who examines only a single authority on the constitution of vapour, that its laws are sufficiently definite, yet on comparing together all the authorities we possess on this subject, or even the best of them, we find such discrepancies both in the general expressions of the law, and in the experiments themselves upon which they rest, as are highly discreditable to mechanical science, and far exceed the limits of error usually admitted in similar departments of experimental science. Between 32° and 212°, the difference between Dr Dalton's experiments and Dr Ure's amounts to more than three-tenths of an inch of mercury. Between the experiments of the Institute of France and of the Franklin Institute,—the latest and most extensive series of experiments,—there is a difference at the eleventh atmosphere of more than 6° in temperature, and about 20 inches of mercury in the pressure of the vapour.

In laying the results of these observations before the Society, it was thought necessary to make a few remarks in explanation of the manner in which they were made.

The instrument consists of a fixed japanned cylinder, on which the points of the compass are marked, and a moveable portion, which revolves freely round the cylinder as the wind changes; the circular disk of a fly kept opposite to the wind by a weathercock vane, is made to revolve with a velocity proportional to that of the wind. The motion thus produced is diminished by means of endless screws, working in a pair of toothed-wheels, and carried down to a pencil, which, in its descent, rubs on the surface of the cylinder, and traces a broad line, whose length is proportional to the velocity of the wind, and the time during which it blows from any one direction taken jointly. The compartment of the cylinder on which the marks are made indicates the direction of the wind.

The watering-place of Kissingen is situated in north latitude 49° 50′ east longitude, 9° 50′ from Greenwich, 60 English miles east of Frankfort. Long before it was frequented for medical purposes, its salt springs were turned to profitable account. Of these there are several, but the one recently enlarged by boring, known under the name of the Runde Brunnen, is much more remarkable than the others, on account of its Copiousness, its Temperature, its discharge of Carbonic Acid Gas in vast quantity, and its extraordinary phenomenon of Intermission.

The fine Map of Sweden by Hissenger shews that the greatest part of that kingdom, to beyond the 61° N. Lat., may be characterized as a vast gneiss formation, skirted on the SW. and NE. by extensive detrital or alluvial formations.

The gneiss is interspersed with considerable tracts of granite, especially in the province of Ostergottland, and here and there exhibits small portions of hornblende-rock, porphyry, quartz-rock, mica-slate, and primary sandstone; but these rocks scarcely form any considerable tracts, and the scarcity of mica-slate is rather remarkable in a gneiss country.

This notice is occasioned by a passage in the fifth volume of the Transactions of the British Association, page 251, in which Professor Challis claims for himself the merit of having been the first who deduced from mechanical principles the anomalous emergence of a floating body from a fluid at high velocities, and where he adduces Mr Russell's experiments in support of the method of reasoning he has there adopted. Previous to the publication of his paper, Mr Russell had given the theoretical explanation of the phenomenon, and had also adduced experiments in support of that explanation at the meeting of the British Association in Edinburgh.

The author accidentally remarked, that the colour of the Sun seen through vapour issuing from the safety-valve of a locomotive engine is deep red, exactly similar to that which a column of smoke or a smoked glass gives to it.

He next noticed that this colorific character of steam extended but a short way beyond the orifice, and that it gradually became more opake, and perfectly white like noon-day clouds, both for transmitted and reflected light. At moderate thicknesses, in this state, its opacity is complete.