In a paper published some time since, Mr Peddie takes up the following question: Given a gas whose molecules contain atoms which are held together by purely elastic forces, do there exist, even in this simplest type of multiply-atomic molecules, cases in which, when there is equilibrium of heat, the average equipartition of kinetic energy demanded by the Boltzmann-Maxwell Law does not exist?

A few months ago I received from Mr G. H. Knott three specimens of Sigillaria from the Halifax Hard Bed of Yorkshire having the structure of their steles and outer cortex well preserved.

Among the undescribed species of plants occurring in the well-known material of Calciferous sandstone age found near Pettycur, Fife, is an interesting specimen belonging to the older type of Lepidodendroid structure which has a solid primary xylem.

From time to time various methods have been employed for the examination of samples of sea-water. Of these, the four which have been received most favourably by oceanographers are:—

(1) Estimation of the total combined chlorine per unit volume of water.

(2) Determination of the relative density.

(3) Measurement of the refractive index.

(4) Determination of the specific electric conductivity.

There has been considerable discussion as to whether any physical constant of sea-water can be used to give an accurate measure of its total salinity, and from theoretical reasoning it would appear obvious that, in so complex a mixture, no physical constant can give an accurate measure of either the total amount of dissolved salts or of the chlorine present. In a paper communicated to this Society, Mr J. J. Manley showed that the optical method for distinguishing between various samples was as delicate as the relative density method, but the refractometer used was expensive and not fitted for use on board ship.

On this very important subject I have not been able to discover much published work of a quantitative description. Professor Hartig, a writer in Dingler's Polytechnic Journal, 1879, appears to have made a special study on the strengths of threads, and was able to express the results of his investigation in the algebraic formula.

The determination of the degree of twist in a folded or ply thread composed of two or more strands is an easy matter. It is merely necessary to stretch the thread between two clamps, one being fixed and the other forming the end of a bar which can be rotated about its axis. A counter is attached to indicate the number of rotations. Rotating the thread in the opposite direction to its twist ultimately brings the singles parallel to each other. This point is easily observed. If we apply this method to single yarns we are at once confronted with the difficulty that the fibres constituting the yarn cannot be reduced to exact parallelism with each other.

For purposes of comparison with the analysis of a composite sample of Red Clay recently published in the Proceedings, I have received from Sir John Murray a composite of fifty-two “terrigenous” clays, dredged up from oceanic depths ranging from 140 to 2120 fathoms. In the nomenclature of the Challenger Expedition, forty-eight of the individual samples are classified as “blue muds,” and four as “green muds.” Twenty-three of the clays were collected by the Challenger; the others were brought in from voyages of the Buccaneer, Dart, Egeria, and Rambler. The range of collection, as in the case of the “red clay,” was world-wide, and all of the great oceans are represented in the composite sample.

It has long been known that the rotative power of certain optically active salts in aqueous solution is greatly, and in some cases enormously, changed by the addition of certain non-active salts. Of late years a good deal of work has been done on this subject, and a considerable amount of data has been collected; but, generally speaking, little explanation has been obtained of the precise causes of the observed phenomena. In some cases at least the reason for this no doubt lies in the fact that in such solutions there exist complicated molecular combinations, about which it may not be easy to obtain ordinary chemical evidence. This, however, only makes it the more important that we should utilise tothe fullest extent such means of investigation as are readily available, and of these none is so good as that of optical activity.

The object of the present research was to follow, by the degeneration method, the course of the fibres proceeding from definite and limited areas of the motor cortex, and to determine to what extent there is a grouping or localisation of the fibres of the pyramidal tract at different levels in the brain and spinal cord.

The systematic study of the Hydrachnidæ, or water-mites, of Scotland appears to have been entirely neglected until within the last few years, and, so far as I am aware, the only communications dealing with Hydrachnids found in Scotland are two noted in the list of literature cited.

Of the life-history of Hydrachnids we have only a limited knowledge, and that may in time be modified as further information is acquired. At present the life-cycle appears to be in four definite stages—the egg, the larva, the nymph, and the imago. When an egg is hatched, a six-legged larva emerges, and apparently its main function is to find a suitable host to which it may attach itself.

In papers previously read before the Society, the behaviour of sulphur when heated has been the subject of investigation. It has been shown that the transition from a pale-yellow mobile liquid to a deep-brown viscous one, which occurs as the temperature rises in the neighbourhood of 160°, is due to the production from the mobile sulphur (Sλ) of another distinct variety (Sμ). The proportion of the viscous variety (Sμ) is about 4 per cent, at the melting point (114·5°). At 160° it has become 11 per cent., at 170° 19 per cent., and at the boiling point 34 per cent.

1. An account is given of a fully grown specimen of Helix pomatia, which, in addition to the normal set of reproductive organs present on the right side, possesses also on the left side a set of accessory male organs—namely, a penis and its retractor muscle, vas deferens, and flagellum. There is no trace of connection between these supernumerary organs and the ovotestis or the genital ducts of the right side.

2. The normal and supernumerary penes are equally developed and are symmetrically placed with regard to the median plane of the head.

3. The extra penis has the usual structure; it possesses a fully-developed copulatory organ and a muscular tubular introvert upon the inner sheath.

4. The extra vas deferens opens at one end into the penis and at the other terminates blindly in the sub-epidermal tissue; the blind end is bound to the epidermis by a short cord of connective tissue.

5. The extra flagellum is normal in size and in its internal structure.

6. The penial nerves on both sides have a corresponding course from the cerebral ganglion to their distribution on the penes. Owing to defective preservation it was impossible to determine whether the fibres of the extra penial nerve arise from the ocular nerve, as is apparently the case, or whether they really arise from the pedal ganglion, as do those of the normal penial nerve.

7. The penis opens into a short atrium which communicates with the exterior by a genital aperture of normal size and shape. This supernumerary genital aperture occupies a position on the left side exactly corresponding to that of the normal one on the right side. About 2·5 mm. posterior and slightly dorsal to it is the blind end of the vas deferens, which is situated close to the dorsal margin of the epidermal groove, which traverses the anterior portion of the animal.

8. In the duplication of the penis and its associated structures this snail presents an example of lateral homoeosis. The only comparable cases recorded in the Mollusca are a Pteropod with paired penes (see Addendum, p. 327) and a specimen of Moschites cirrosa, in which not only was the third right arm hectocotylised as usual, but the third left one also.

9. The supplementary vas deferens and the retracted penis form a U-shaped loop, both ends of which are in contact with the epidermis, and so closely resemble the corresponding structures figured by Plate in the primitive Pulmonate, Pythia scarabeus, that these organs may be described as having identical relations in the two forms, except that in the supplementary organs of Helix the vas deferens has no actual opening at its epidermal end and that it bears a flagellum which is not present in Pythia. It is suggested that the supplementary organs of Helix, having been able to develop free from the disturbing influence of the vagina, oviduct, and their accessory structures (which on the right side have been secondarily moved forwards in phylogeny), have assumed a condition closely resembling that which they would present in the ancestral form in which male and female apertures were some distance apart. The form of the extra organs (the vas deferens having a close connection at one end with the epidermis), which, it is suggested, might also be assumed by the corresponding normal organs if they were also free to develop independently of the female structures, supports the view that the present condition of the genital ducts in Helix and in other Stylommatophora, has been derived from a condition existing in the ancestral form in which the vas deferens and penis were connected with the primitive genital opening by means of a lateral groove, such as is still found in Pythia.

10. Consideration of this and of other abnormalities which have been described in the Pulmonata leads to the conclusion that the penis develops as an epidermal structure which in Helix and other Stylommatophora is closely associated with, and is secondarily carried inwards by, the invaginating atrium. In proterogynously hermaphrodite forms, especially in those in which the shell is depressed, reduced, or absent, the development of the penis rudiment may be postponed until the male elements in the gonad are further developed.

Fifty years ago, Japan was almost a mythical land to the Western world; what little was known of it was through the medium of the Dutch, who were allowed to trade in the single port of Nagasaki. What we Japanese knew of the outer world was also derived mostly from them, and from such books as were brought into the country by them. In 1853 came Commodore Perry, and demanded that we should open up our country to the commerce of the world; we were but ill prepared for such a course, but it was not in our power to resist the demand, and unwillingly enough the Shōgun's government was obliged, notwithstanding the strong opposition of the Imperial Court and of the conservative elements in the country, to contract a treaty of commerce with America, which was speedily followed by those with other nations.

This investigation was carried out for the purpose of extending to other substances an inquiry into the effect of an electric current on Young's Modulus, which was carried out by Miss Noyes on a steel wire at Cornell University, and described in the Physical Review, No. 4, vol. ii. In the investigation of Miss !Noyes, the wire under examination was heated by a coil, the current being supplied by a storage battery. To vary the method of heating, the current was also sent through the wire with the expectation that the same effects would be obtained as when the wire was heated by the coil. This, however, was found not to be the case, and Professor Nichols, under whose superintendence the investigation was carried out, in his Laboratory Manual of Physics, vol. ii. p. 293, states that an extension of the inquiry to other materials than iron would be of interest.

The elliptic functions introduced by Professor K. Weierstrass of Berlin are best known through the admirable pages of Professor H. A. Schwarz's Formeln und Lehrsätze zum Gebrauche der elliptischen Functionen, Göttingen, 1885. These pages have been translated literally into French by Dr Henri Padé, Paris, 1894. Halphen's well-known three-volumed treatise on elliptic functions is devoted almost entirely to the Weierstrassian forms. In the English language, the following references may be useful:—Whittaker, Modern Analysis; Greenhill, Elliptic Functions; Harkness and Morley, Theory of Functions; Forsyth, Theory of Functions.

Trichloromethyl-Sulphonic Chloride in ethereal solution acts readily on sodium ethylate, and the same reaction takes place when the solutions of the two substances in absolute alcohol are mixed.

The transformations of volume integrals into surface integrals, and of surface integrals into line integrals, are usually established first for a small parallelepiped and parallelogram. These elements are not, however, very convenient, or indeed altogether satisfactory, for the extension of the theorems over finite domains. If arranged in straight rows and plates, the elements cannot be fitted to a general boundary; and if they are arranged in curved rows and shells like the stones of a vault, there will be, in general, between various elements of the first order, spaces of the second not represented. This inconvenience disappears if tetrahedra and triangles are taken as elements. In Quaternions, the theorems are easily proved for such elements.