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.

Dr Penard has examined and reported upon the Rhizopods and Heliozoa collected in Loch Ness at depths exceeding 250 feet. No littoral samples were sent to him, as his object was to investigate the sarcodine fauna peculiar to deep lakes. The majority of the species found in the deep collections were recognised as belonging to the fauna of the littoral region, or of the adjacent moors, only some half a dozen species or varieties being regarded as peculiar to the abyssal region.

In order to complete the list of the Sarcodina of Loch Ness, in so far as this can be done from the observations made by the Lake Survey, I now add the names of several species which were not detected in any of the collections sent to Dr Penard. Nearly all are common bog species.

Whilst examining my “tow-nettings” from the West Coast, I have met with a peculiar Decapod larva, which, so far as I know, is unlike anything previously described. In general appearance it is very like semi-adult forms of Lawifer, having an elongated “neck,” at the tip of which the eyes and antennae are carried. My specimens were obtained from two localities—1st, about half a dozen at about the same stage, from tow-nettings taken in Machrie Bay (west shore of Arran), 17th September 1886; and 2nd, about 20 specimens, some further advanced than those of the previous gathering, which were collected at a depth of 8 to 10 fathoms in the Sound of Mull, 24th August 1887. These were associated with various larval stages of Porcellana, Galathea, and other Decapods.

1. Specimens of steel cooled from high temperatures are, as regards their magnetic properties, in a “sensitive state.”

2. After magnetisation, reversal of the field reduces the susceptibility.

3. Cyclic reversals of the field between definite limits bring the magnetic quality to a definite lower value for fields lying between these limits.

4. So long as the field is not changed in sign, the “sensitive state” persists.

5. Cyclic reversals of the field between narrow limits reduce the susceptibility for fields beyond these limits, but not to its lowest possible value.

6. The rate of cooling from the high temperature—if not very rapid—has little influence on the magnitude of the effect.

7. The “sensitive state” does not wear off with time.

8. Mechanical vibration of the specimens considerably reduces the phenomenon.

9. The “sensitive state” is most pronounced in hard steels.

10. The effect is induced to a slight degree in some varieties of steel by temperatures as low as 100° C. It increases with increasing temperatures to about 700° C. Further increase in temperature has little influence.

11. Similar effects are noticeable in cast iron and in cobalt. The “sensitive state” is absent, or is present to only a very slight extent, in soft iron.

12. The effect has a maximum value for fields which give large values of μ, and tends to zero as the saturation point is approached.

The three charts which were exhibited, showing, by isobarometric lines, the mean atmospheric pressure over the globe, during January, July, and the year, were constructed from observations made at 358 places thus distributed over the earth,—167 in Europe; 51 in Asia; 22 in Africa and adjoining islands; 35 in South America, West Indian Islands, and Atlantic; 63 in North America; and 20 in Australasia and Antarctic Ocean. Of the European stations, 12 are in Scotland, 14 in England, 27 in Austria, 12 in Italy, 10 in France, 10 in the Netherlands, 9 in Norway, and 57 in the Russian empire, &c. The list might have been largely increased; thus a larger number might have been given from the 80 Scottish stations; but the 12 given were judged sufficient to represent the mean atmospheric pressure of this country.

The author gave an account of the microscopical appearances of striped muscle of the crab and lobster. The muscle of the crab and lobster is suitable for investigation because of the comparatively large size of the structural elements, and the readiness with which the sarcous matter can be fixed and otherwise prepared in different conditions. The author is entirely opposed to the opinions expressed by Melland, and more recently by Gehuchten, regarding the structure of the sarcous matter, and maintains, as he did at the International Medical Congress in 1881 (Transactions International Medical Congress, 1881, vol. i. p. 270), that the sarcous matter essentially consists of contractile fibrils, with an interstitial substance between them—an opinion previously expressed by Kölliker and others, and recently supported by Rollett.

The problem of Graduation or Adjustment, with which the present paper is concerned, may be defined as follows. Let a number u be a function of a number x: and suppose that, corresponding to the values … −3, − 2, −1, 0, 1, 2, 3 … of x, we have obtained, as a result of observation, values … u−3, u−2, u−1, u0, u1, u2, u3 … for u. Owing to errors of observation, these observed values when plotted against the corresponding values of x do not lie on a smooth curve, although for theoretical reasons we believe that they would do so if freed from errors. The problem is to determine the most probable set of “graduated” or “adjusted” values

which differ only slightly from the above observed values, and which lie on a smooth curve.

A dew bow differs from a fog bow in being formed by minute globules of water resting on the ground; but these globules may or may not have been produced by the usual process of dew formation. In the Proceedings of the Society (vol. vii., 1870), Clerk Maxwell has published a note on a bow seen on ice. With the exception of this record, we have been unable to find any distinct account of observations of the phenomenon, although no doubt it must have been occasionally observed soon after sunrise.

The peculiarity of the bows we observed was that they were seen by night, the sources of light being the gas lamps and electric lights of the city. It was on the evening of Friday, November 11, after several days of thick foggy weather. The tiny fog particles seem to have gradually settled down in the still air, the fog steadily clearing the whole time. These globules, in spite of their contact with the damp ground, must have retained their spherical form almost perfectly; for they were able to throw back to the eye, with a rainbow deviation of approximately 42°, the light incident upon them.

In the neighbourhood of every lamp where the surface of the ground had been undisturbed by traffic the bows were seen as bright streaks, which shifted position with the observer. Any disturbance of the surface, a wheelmark, a footprint, a finger drawn across the pavement, obliterated the bright streak; and it was not seen on the surface of puddles.

I am very glad to embrace the opportunity of addressing the Fellows of the Royal Society of Edinburgh, many of whose members have contributed much to our knowledge of Oceanography. For instance, your President, Lord Kelvin, besides his researches on the tides, is well known to practical seamen from his excellent compasses and sounding machines; your Secretary, Prof. Tait, is well known from his researches on the pressure errors of deep-sea thermometers; Dr Alexander Buchan has a world-wide reputation in the department of oceanic meteorology; the late Prof. Dittmar was a great authority on the chemistry of sea water. It is enough to say that Sir Wyville Thomson, Mr J. Y. Buchanan, and Sir John Murray, were members of the “Challenger” Expedition, which has given the world such valuable information about the depths of the sea.

Of course, it is not with the intention of giving to such scientific authorities a lesson that I address the Society, but if you represent scientists, I represent the seamen, and it is useful from time to time to have a talk between these two classes of men. Every scientific study should be started by the scientist, but the sooner they can associate ordinary practical men with the work the better it will be. We practical seamen are more numerous than scientists; we constantly navigate the sea, and we have more opportunities of making contributions to science than they have. Certainly, they can make their observations in a more exact way than we can, but the laws of nature—particularly those concerning Oceanography—are so imperfectly known, that there is very much to be done even by the rough hands of the ordinary seamen.

In the Quarterly Journal, No. 162, 1910, Professor A. R. Forsyth considered some of the problems arising from a homographic transformation of plane curves whose equations could be written in the form

where F is a rational integral function of z and z′, and where z = x + iy, z′ = x − iy determine the rectangular Cartesian coordinates of the plane. It was suggested that the theory could be developed algebraically by using the symbolic methods of the German school which proved so powerful in furthering the theory of binary forms.

These are stray notes on a few of the pelagic animals found in the Clyde. I noted down their occurrence whilst examining the plankton for medusæ. The records may be useful to students who intend working in the Laboratory at Millport, and should give them an idea as to the time of year at which these animals occur. They may also be useful for comparison with other years and other localities. Most of the species have been previously recorded for the Clyde, and the few which are not mentioned in the “Fauna of the Clyde,” are fairly common on the British coasts. As these notes form a kind of appendix to my Report on the Medusæ, I have curtailed this introduction to avoid repetition.

It is a great advantage and satisfaction to work from curves taken by the phonograph itself, because it is then possible to reproduce and verify by actual hearing the sound supposed to be represented by given curves. This ought always to be done, even with the phonograph, and the slightest change of timbre should be carefully noted; for the given curve represents not really the original sound, but the sound given back by the phonograph. Every plate or membrane vibrates more readily and strongly to some pitches than to others, and in a composite sound it is almost inevitable that some of its elements are recorded with more, and others with less, than their original relative force. Different vibrators hence yield quite different-looking phonograms for the same sound. In vowels it seems fortunately to happen that considerable changes in the relative force of the component vibrations may occur without altering the vowel. It is the pitch of the components which matters; and that is not altered by an efficient vibrator. Assuming a knowledge of the methods by which the record dug vertically into the phonographic cylinder is displayed horizontally for examination and analysis, we note that a satisfactory Fourierian analysis demands a sufficient number of measurements.

Although much literature has been published on the minute anatomy of the ovary, there are many controversial points remaining, and therefore the publication of the results of the examination of various mammalian types adds additional proof to the facts already staged by embryologists. Three years ago this work was taken up by me as a preliminary to an investigation into the distribution of the chromatic substance in cells which show malignant degenerative changes. The work has occupied so much time that the publication of the results has been necessarily delayed. In a paper on “Primary Cancer of the Ovary,” published in 1906, I stated, as the result of a somewhat limited observation on the later stages of the development of the human ovary, that the cells of the stratum granulosum were mesoblastic in origin. This view I have modified by the more thorough and extensive investigation of the present paper.

The pioneer work of Stockard and Papanicolaou (1917, 1919) forms the basis of most subsequent observations on the œstrous cycle of the guinea-pig, and their results are, in the main, accepted by later workers—Ishii (1920), Selle (1922), Nicol (1932), etc.

Ditylum Brightwelli, a marine plankton diatom, shows very peculiar osmotic relations which have recently been investigated by Gross (1939). The cells (fig. 1) consist of a central mass of protoplasm containing the nucleus and connected by a few protoplasmic strands with the peripheral plasma membrane in which are embedded numerous chromatophores. The remainder of the space inside the cell is filled with cell sap. As in other diatoms, the protoplast is enclosed by a siliceous cell wall. Gross found that Ditylum plasmolyses rapidly in isotonic and hypotonic NaCl and sugar solutions, being reduced in a few seconds to a small spherical body about one-third to one-twentieth of its original volume, similar in all respects to a resting spore. In a solution of NaCl + CaCl2, and in unbuffered artificial sea-water, plasmolysis occurs in all cells, but the process is considerably delayed and completed only after several hours. In artificial sea-water, the pH of which is adjusted to about 8, the cells remain unchanged.

This communication falls conveniently into two sections—I. dealing with the specimens obtained by H.M.SS. “Lightning” and “Porcupine,” during what may be called the pre-Challenger period of deep-sea exploration; II. concerning those dredged by the “Knight Errant” and “Triton” during the surveys of the Wyville Thomson ridge, which were conducted in the years 1880–82.

1. The gradual growth of the theory of molecular magnetism from the original suggestions of Poisson and Weber is well known. The recent great development, made by Ewing, and tested experimentally by means of models, has placed the theory on a fairly firm basis, and has made essentially secure the fundamental postulate that magnetic phenomena in material bodies are due to magnetic molecules which may possibly be regarded as free from any directional control other than that supplied by their own mutual action.

This second paper is a discussion of the surface displacements associated with plane elastic waves reflected from the boundary of the elastic solid through which they are being propagated. In my first paper on Seismic Radiations (Proc. Roy. Soc. Edin., vol. xxviii. pp. 217–230, 1908) my aim was to find a simple distribution of density and elasticity in terms of which the transmission of seismic disturbances could be described.

(1) As is well known, the first rule given for ascertaining the sign of a single term of a determinant was made known by Cramer in his Introduction à l'Analyse des Lignes Courbes algèbriques, published at Geneva in 1750. On page 658 he says—

“On donne a ces termes les signes + ou −, selon la Règle suivante. Quand un exposant est suivi dans le même terme, médiatement ou immediatement, d'un exposant plus petit que lui, j'apellerai cela un derangement. Qu'on compte, pour chaque terme, le nombre des dérangements: s'il est pair ou nul, le terme aura le signe +; s'il est impair, le terme aura le signe −. Par ex. dans le terme Z1Y2V3 il n'y a aucun dérangement: ce terme aura done le signe +. Le terme Z3Y1X2 a aussi le signe +, parce qu'il a deux derangements, 3 avant 1 & 3 avant 2. Mais le terme Z3Y2X1 qui a trois derangements, 3 avant 2, 3 avant 1, & 2 avant 1, aura le signe −.”

According to Cramer, therefore, If δ be the number of derangements in the permutation corresponding to any term, the sign of the term is (−)δ.

Instead of the word “dérangement,” Gergonne in 1813 used “inversion” in speaking of Cramer's rule: Cauchy did the same in 1841: and, consequently, the latter term or “inversion of order” has come into pretty general use. “Inverted-pair” is probably a still better expression.‡