bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Composition of some Deep-Sea Deposits from the Mediterranean
Authors: Buchanan J. Y.
Published: June 2016

The muds, the analyses of which are reported in this paper, were collected in September 1879, during the laying of a cable between Marseilles and Algiers by the India Rubber, Gutta-Percha, and Telegraph Works Company, Limited, of Silvertown, the ship employed being the s.s. “Dacia.” The numbers of the samples are those which were affixed to them on board ship. Nos. 31 to 43 are all from localities lying near the African Coast; Nos. 45 and 46 are from positions between the African Coast and the Balearic Bank. Nos. 64 and 65 are from the Balearic Bank, and Nos. 86 to 89 are from the Gulf of Lyons. The positions and depths are collected in Table I.
On a Method of Observing and Counting the Number of Water Particles in a Fog
Authors: Aitken John
Published: June 2016

The phenomena known as haze, fog, mist, and rain are in a general way but the successive development of the same process, and the line which divides the one from the other is very indefinite. Dust in the atmosphere produces a haze, and the thickness of a haze of this kind depends principally on the amount of dust present when the relative humidity of the atmosphere is very low. But as the humidity increases the effect of the vapour increases also; the dust particles attract the water vapour which becomes deposited on them, thus increasing their size and their hazing effect, till at last when the air is nearly saturated it becomes very thick, and forms what we call a fog; when in this condition, the thickness of the atmosphere depends principally on the degree of saturation. Between the haze and the fog, however, there is no recognised distinction in kind, it is principally one of degree. After the air is saturated and the conditions are such as to tend to cause supersaturation, then a change takes place in the condensation. A few of the dust particles have water deposited on them, and after a time they grow and become little drops of water, in which the original dust nucleus bears a very small proportion to the total weight. At this stage it is still called a fog, but after more water is deposited on the small drops they grow and become what is known as mist, and when the mist drops combine and fall they are called rain-drops.
On some Relations between Magnetism and Twist. Parts II., III
Authors: Knott Cargill G.
Published: June 2016

Part II. contains a continuation of former experiments on the twists produced in the magnetic metals when they are under the combined influence of circular and longitudinal magnetisations.

It is established that a cobalt rod of rectangular section twists left-handedly when a current is passed along it in the direction of magnetisation. That is, cobalt behaves like nickel. Iron, on the other hand, twists right-handedly, until very high fields are employed. These results seem to have a close connection with the magnetic changes of length in these metals; for iron expands in moderate fields, while nickel and cobalt contract, the former always, and the latter till high fields are reached.
Chairman's Opening Address
Authors: McLaren
Published: June 2016

I find that during the past Session forty-one papers have been road. Of these, ten belong to the department of Physics, five to Mathematics, one to Chemistry, two to Geology, seven to Biology, one to Botany, four to Anatomy, three to Physiology, four to Meteorology, four to Astronomy.

Since the commencement of the past Session, eighteen Fellows have been added to our numbers. Of these, one is a Professor of Philosophy, two are University Lecturers, and six are Doctors of Medicine.
On the Relation of Miller's Trisector to the Quartic Trisectrix, with a Description of a Seven-bar Limaçonograph
Authors: Chrystal
Published: June 2016

If, instead of causing the point B of the trisector to move along an arm of the angle, we cause P, the intersection of the two edges, to move along an arm, and find the locus of the point B, we get another curve associated with the instrument.
The Condition of the Iron in the Spleen
Authors: Brodie William Brodie
Published: June 2016

Many investigations have been made as to the destruction of red blood corpuscles in the spleen, and there can be little doubt that this occurs. If the hæmoglobin set free is also destroyed in the spleen, iron in some form will be liberated. The presence of iron in the spleen has already been shown by various observers, but the exact nature of the substances with which it is combined is still a matter of doubt.The object of this investigation was, if possible, to trace the stages in the decomposition of hæmoglobin as shown by the existence of intermediate compounds, and to ascertain the chemical nature of such compounds.
Quaternion Binaries: an Extension of Quaternions to give an Eight-element System applicable to Ordinary Space
Authors: Peddie W.
Published: June 2016

In this system vectors are regarded as translators only. A special operator, R, transforms them into rotors. A second application of the operator retransforms rotors into translators. The system is essentially Hamilton's, with the removal of the restriction that vectors shall act as translators in addition, and as rotors in multiplication.
Suggested Modifications of the Sign of Equality for Use in Chemical Notation
Authors: Marshall Hugh
Published: June 2016

During recent years the great attention which has been paid to the study of reversible chemical actions has led to a desire for some method of specially indicating in the equations the reversibility of these actions. This is generally done by replacing the sign of equality by two parallel and oppositely-directed arrows; the use of this symbol in such cases does not only imply the reversibility of the action, it has the same value as the sign of equality in an ordinary equation. Unfortunately, there are several drawbacks to the use of this symbol: as generally printed, it is rather clumsy in appearance; the arrows, being widely separated, do not suggest the sign of equality which they replace; and further, in conjunction with formulæ, arrows are frequently employed, especially in organic chemistry, to indicate merely the stages and methods by which a substance can be produced from some other substance as starting-point. In such cases, as no attention is paid to the bye products, there is nothing of the nature of an equation involved. Numerous examples are to be seen in Richter's Organisehe Chemie, and amongst them cases in which oppositely-directed arrows, resembling the symbol employed for the equations for reversible actions, are used to indicate that each of the two substances concerned may serve as starting point for the preparation of the other, without involving equality on the two sides of the symbols. Such a double use of a symbol is highly objectionable.
Magnetic Shielding in Hollow Iron Cylinders
Authors: Russell James
Published: June 2016

This investigation deals with the shielding which exists within hollow iron cylinders when placed in a uniform transverse magnetic field. This transverse field divided by the internal magnetic field is defined as the shielding ratio. For the thin iron cylinders experimented with, it appears from various mathematical contributions to the subject that the shielding ratio minus unity may for present purposes be taken to be proportional to certain geometrical data and to the permeability (the permeability being large). By means of a rotating inductor within the shield, connected with a ballistic galvanometer, experimental determinations of the shielding ratio are made under various conditions of magnetisation; and an endeavour is also made to show how far and under what conditions these results approximate to theoretical formulas which assume the permeability to be uniform all round the shield, and the absence of retentivity and coercive force in the iron. Two iron shields were experimented with, the hysteretic constants (η) being ·0015 and ·0028 respectively.
The Plague Research Laboratory of the Government of India, Parel, Bombay
Authors: Bannerman W. B.
Published: June 2016

Before beginning the account of the present state of the Plague Research Laboratory, it may be interesting to glance rapidly at the history of Mr W. M. Haffkine, C.I.E., its originator and present Directorin-Chief.
Contributions to Scottish Mineralogy. (Part I.)
Authors: Goodchild J. G-.
Published: June 2016

The following observations are based chiefly upon the results of an exhaustive survey of the specimens in the Scottish Mineral Collection in the Edinburgh Museum of Science and Art, which were made while I was studying the material for completing The Mineralogy of Scotland. The survey has been continued since the publication of that work, in connection with the revision of the arrangement of the specimens in question. A large number of facts of interest have come to light in the course of this work. Furthermore, the forms of several hundreds of crystals in the Collection have now been determined, and freehand drawings of most of these crystals have been made, and placed alongside of the specimens to which they refer. It is proposed from time to time to lay some of the more interesting of the results arising from this work before this Society, especially as little or none of them have hitherto been published, and as the crystals, which present considerable interest, do not appear to have been previously figured.
Freezing-Point Depression in Electrolytic Solutions
Authors: Walker James , Robertson A. J.
Published: June 2016

The following research was undertaken for the purpose of determining the freezing points of solutions under conditions which would involve a different systematic error from that encountered when the ordinary method of procedure is followed; and, secondly, for the purpose of obtaining ionisation values for electrolytic solutions by the cryoscopic method which should be made by compensation as far as possible independent of any systematic error in determining the freezing points.
The Occurrence of the Sperm Whale or Cachalot in the Shetland Seas, with Notes on the Tympano-petrous Bones of Physeter, Kogia, and other Odontoceti
Authors: Turner William
Published: June 2016

In August 1901 Mr Thomas Anderson, merchant, Hillswick, to whom and to other members of whose family I have on several occasions been indebted for specimens to illustrate the Zoology of Shetland, wrote to tell me that a dead whale had been found floating near Hillswick and had been towed into Roeness Voe. It was within three miles of land when seen by the fishermen and was claimed by the Crown. From the appearance of the animal Mr Anderson thought that it was a sperm whale, and he sent me the following description, from which it was clear that he had correctly recognised it.
The Theory of Colour Vision
Authors: Peddie W.
Published: June 2016

The theories which give the best account of the facts of colour vision and colour blindness are the Young-Helmholtz theory and Hering's theory. Both are trichromatic theories, and, apart from physiological or anatomical questions, both can, by proper choice of fundamentals, be made to give a good account of the main facts. The facts of one-eyed colour blindness show that, on the Young-Helmholtz theory, colour blindness must be regarded as due to fusion of at least two fundamental sensations, but the curves of one sensation determined by observations on different eyes differ considerably among themselves, and this indicates that a broader basis for the theory may be desirable. This may be sought for in a tetrachromatic theory, but any such theory must explain the possibility of trichromatic representation of all colours. A theory proposed assumes two pairs of complementary stimulations, say R,G1 and G2,V.
On the Abdominal Viscera of Cercocebus fuliginosus and Lagothrix humboldti
Authors: Bradley O. Charnock
Published: June 2016

The anatomy of the primates is responsible for a very considerable volume of contributions to morphological literature. But, quite naturally, those forms which have the closest affinity to man have been more extensively and more carefully observed than those occupying a lower position in the zoological scale. And, further, the most painstaking and accurate work has been done in connection with organs which are very specially modified in man, such, for example, as those of the nervous system. This is perfectly consistent with the desire to obtain any light, and from any source, which will facilitate the unravelling of the many problems of human structure. Moreover, the soft and flaccid viscera do not lend themselves to accurate observation so readily as do the more solid organs which retain their shape after their removal from the body. So it comes to pass that, up to quite recent times, the abdominal viscera, and more especially the hollow organs of the abdomen, such as the stomach and the intestines, have only received scant attention; or, if they have been more carefully examined, the descriptions as given prior to the introduction of modern methods cannot be held as absolutely satisfactory, because of the change of shape and disposition resulting from the removal of their natural support, to wit, the abdominal walls.
The Molecular Condition of Iron demagnetised by various Methods
Authors: Russell James
Published: June 2016

The demagnetisation of iron by decreasing reversals secures a molecular condition such that there is perfect symmetry to subsequent applications of either a positive or negative magnetising force (H). In a former communication it was shown that this symmetry is uni-directional. It is symmetry to the directional force (ab) used in the demagnetising process. During the early stages of induction iron is more permeable to a reapplication of a magnetising force in the same direction (+ or − ) as that used in the immediately preceding demagnetising process, than it is to a force (+ or − ) at right angles to that used in the immediately preceding demagnetising process. The hypothesis was advanced that on the completion of this process, a preponderance of the molecules would point towards an equatorial belt at right angles to ab. If H makes an angle other than zero with ab, the number of molecules lying in the most advantageous position, i.e., equatorially, is reduced, and the pull becomes less and less as the angle approximates to 90°.
The Theory of Continuants in the Historical Order of its Development up to 1870
Authors: Muir Thomas
Published: June 2016

The more or less disguised use of continued fractions has been traced back to the publication of Bombelli's Algebra in 1572, eighty-four years, that is to say, before the publication of Wallis’ Arithmetica Infinitorum, in which Brouncker's discovery was announced and the fractions explicitly expressed. The study of the numerators and denominators of the convergents viewed as functions of the partial denominators was first seriously undertaken by Euler in his Specimen Algorithmi Singularis of the year 1764, in which denoting by

the convergents to

he established a long series of identities, such as
Theorem regarding the Orthogonal Transformation of a Quadric
Authors: Muir Thomas
Published: June 2016

The theorem in question arises out of a consideration ol several passages in Jacobi's important memoir of 1833 or orthogonal transformation. Having determined the substitutior which simultaneously changes

and
On Deep-water Two-dimensional Waves produced by any given Initiating Disturbance
Authors: Kelvin Lord
Published: June 2016

§ 1. Consider frictionless water in a straight canal, infinitely long and infinitely deep, with vertical sides. Let it be disturbed from rest by any change of pressure on the surface, uniform in every line perpendicular to the plane sides, and left to itself under constant air pressure. It is required to find the displacement and velocity of every particle of the water at any future time. Our initial condition will be fully specified by a given normal component velocity, and a normal component displacement, at every part of the surface.
Some Field Evidence Relating to the Modes of Occurrence of Intrusive Rocks, with Some Remarks upon the Origin of Eruptive Rocks in General
Authors: Goodchild J. G.
Published: June 2016

It is commonly believed by geologists, as well as by coal miners, that the inner faces of the rocks which enclose intrusive masses were at one time in contact, and that each of these surfaces is the counterpart in form to the other, from which it has been severed by the forces to which the injection of the intrusive mass was due. In the case of a sill, for example, this belief implies that the rock floor below the sill and the roof above it were in unbroken contact at some time before the sill was intruded, and that the floor and the roof have been forced apart to a distance equal to the thickness of the intrusive mass.
On the Date of the Upheaval which caused the 25-feet Raised. Beaches in Central Scotland
Authors: Munro Robert
Published: June 2016

About forty-two years ago Mr Archibald Geikie (now Sir Archibald), then an energetic member on the staff of the Geological Survey, propounded and advocated the doctrine that the change in the relative level of sea and land, indicated by the 25-feet raised beaches which have been long known to geologists as fringing the winding shores of the firths of Central Scotland, took place subsequent to the occupation of the district by the Romans. Further researches, together with a more careful examination of the archaeological phenomena on which Sir Archibald mainly relied as evidence, convinced later observers that the facts did not justify this conclusion. Hence for some years I have been under the impression that the post-Roman theory was abandoned, not only by the general body of geologists and archaeologists, but, as I understood, by the author himself. The following statement of opinion on the subject, recently urged in the interests of the Trustees of the British Museum by a distinguished Professor of Geology, and one who has had exceptional opportunities of making himself conversant with all the factors of the problem, will, however, show how wide of the truth that impression must have been.
On the Thermal Expansion of Dilute Solutions of certain Hydroxides
Authors: Carse George A.
Published: June 2016

In a paper communicated to the Nova Scotian Institute of Natural Science,* Professor MacGregor has shown that in the case of weak aqueous solutions of certain hydroxides, the volume of a solution is less than the volume of water used in its preparation. At his suggestion I have investigated the hydroxides of sodium, barium, and strontium, to ascertain whether they exhibit this property, and how the excess of the volume of solution over the volume of constituent water varies with the temperature. From the observations made, I have also determined the thermal expansion coefficients, and found how they vary with temperature and with concentration.
Networks of the Plane in Absolute Geometry
Authors: Sommerville Duncan M. Y.
Published: June 2016

The problem to divide the plane, without overlapping, into a network of regular polygons with the same length of side, has been completely worked out for the three geometries for the case in which the polygons are all of the same kind. The resulting networks are called regular
A Laboratory Apparatus for Measuring the Lateral Strains in Tension and Compression Members, with some Applications to the Measurement of the Elastic Constants of Metals
Authors: Coker E. G.
Published: June 2016

The recognition of the importance of lateral strain in the theory of elasticity, as now taught in most engineering colleges, makes it very desirable that students should make experiments upon the lateral contraction of tension specimens and the lateral extension of compression pieces with the same facility that they now determine the values of Young's modulus and the modulus of shear.
On Pennella: a Crustacean parasitic on the Finner Whale (Balænoptera musculus)
Authors: Turner William
Published: June 2016

In this memoir the author described a Pennella found attached to the back of a Balænoptera musculus, specimens of which were given to him in 1903 by Mr Chr. Castberg. The specimens were of the same species as the Pennella balænopteræ described by Koren and Danielssen in 1857, and found infesting B. rostrata. The species is a giant Copepod, and the longest examples measured about 12½ inches.
The Diameters of Twisted Threads, with an Account of the History of the Mathematical Setting of Cloths
Authors: Oliver Thomas
Published: June 2016

During the last generation the idea of reducing the “setting “of cloths to mathematical accuracy has been gradually taking hold of the minds of thinking men in the various textile trades. That this end is perfectly attainable is perhaps an open question, but there can be no doubt that the investigation of such problems must lead to a more satisfactory knowledge of the factors which determine the construction of fabrics.
A Study of Three Vegetarian Diets
Authors: Noël Paton D. , Dunlop J. C.
Published: June 2016

The recent publication of Prof. Chittenden's Physiological, Economy in Nutrition tends to establish a new standard of dietary requirements, if not for the labouring classes, at least for men, middle-aged and young, who are not undergoing continued and sustained muscular work.
I.—The Shift of the Neutral Points due to Variation of the Intensity of Mechanical Vibrations or Electric Oscillations superposed upon Cyclic Magnetisation in Iron
Authors: Russell James
Published: June 2016

When mechanical vibrations or electric oscillations are superposed at all points of a normal hysteresis loop, the induction at the cyclic extremes is increased, the residual magnetisation decreased, and those differences of magnetic condition to which hysteresis gives rise lessened. The curves delineating these changes form a continuous loop, and neutral points occur where vibrations superposed upon decreasing cyclic field produce no induction change whatever.
IV.—On a Question in Absorption Spectroscopy
Authors: Houstoun Robert A. , Russell Alexander S.
Published: June 2016

In the third volume of his Spectroscopie, p. 91, Kayser has raised the question whether on mixing two coloured solutions which do not act on one another chemically the absorption spectrum of each of the components remains unchanged. Melde thought he had discovered such an effect; he stated that when a solution of carmine in ammonia which has two sharp bands in the green, was added to a solution of potassium dichromate which absorbs the violet end of the spectrum, or to an ammoniacal solution of copper sulphate which absorbs the red end, that the carmine bands were in each case displaced towards the end absorption in question. He ascribed this to a physical action between the molecules. It was, however, pointed out by Schuster that a shift of this nature would be seen if, instead of mixing, the one solution was merely placed behind the other. Bostwick and Krüss repeated Melde's work, and came to the conclusion that there was a real shift in addition to the apparent shift pointed out by Schuster. Since then additional evidence has been adduced by Formánek and has been quoted by Kayser in the section cited above. The object of the research recorded in this paper was to investigate those cases with the most accurate means possible, and, if a shift was established, to decide if it was physical.
V.—Dissymmetrical Separations in the Zeeman Effect in Tungsten and Molybdenum
Authors: Jack Robert
Published: June 2016

It has been mentioned by Professor Voigt of Göttingen in his newly published book and by Professor Zeeman of Amsterdam in the Physikalische Zeitschrift, that I have found examples of strongly marked dissymmetry in studying the Zeeman Effect in tungsten and molybdenum. Professor Zeeman has also discovered and published such cases of dissymmetry in other elements. Not only have many examples of normal dissymmetry been found, but almost as many cases of abnormal dissymmetry. To explain those terms, normal and abnormal, let us consider that the single spectrum line is broken up, when the light is in the magnetic field, into the three components, 1, 2, 3, where the numbers begin from the component which has the shortest wave-length. In the normal dissymmetrical triplet the middle component is nearer the component on the red side than that on the violet one, i.e. for the normal type the interval 1–2 is greater than the interval 2–3, but in the abnormal dissymmetrical triplet 2 is nearer to 1 than to 3. These observations of Professor Zeeman and myself, which were made at the same time in the Universities of Amsterdam and Göttingen, having been communicated to Professor Voigt, he wrote and published in the above-mentioned book an extension to his and Professor H. A. Lorentz's theories of the Zeeman Effect. In his original theory Professor Voigt had shown that, considering the electrons as uncoupled, cases of normal dissymmetry might arise among the Zeeman triplets, this dissymmetry being accompanied by a greater intensity of the red component than the violet one. He pointed out also that the ‘absolute’ dissymmetry or the difference between the absolute displacements of the red and violet components should be independent of the magnetic field strength used to produce the Zeeman Effect. To explain the large numbers of complicated types of Zeeman Effect which have been found —in the study of the Zeeman Effect in tungsten I discovered lines with no fewer than 17 to 19 components, the largest numbers hitherto found—Professors Voigt and Lorentz made use in their theories of couplings between electrons of the same vibration frequencies.
VIII.—Temperature Observations in Loch Garry (Inverness-shire). With Notes on Currents and Seiches
Authors: Wedderburn E. M.
Published: June 2016

During the first seven months of the year 1908 I had the good fortune to be living at Invergarry in Inverness-shire, with sufficient time at my disposal to make temperature observations in Loch Garry, and, through the generosity of Sir John Murray and Mr Laurence Pullar, the funds of the Lake Survey (Pullar Trust) were put at my disposal to defray the expenses of observation. I was further fortunate in securing the services of Mr Wm. Macdonald, Mount Pleasant, Fort Augustus, who was previously boatman to the Lake Survey on Loch Ness, and who proved himself a most painstaking and eager observer, and by whom by far the greater number of the actual observations were made.
XVII.—The Electromotive Force of Iodine Concentration Cells with One Electrode saturated with Iodine
Authors: Laurie A. P.
Published: June 2016

This investigation was undertaken with the view of determining the number of free iodine ions present in saturated solutions of iodine in potassium iodide of varying strengths.
XVIII.—Cynomacrurus Piriei, Poisson abyssal nouveau recueilli par l'Expédition Antarctique Nationale Ecossaise
Authors: Dollo Louis , Bruxelles  , Traquair M. R. H.
Published: June 2016

L'existence des Macruridæ à l'intérieur du Cercle Polaire Arctique est connue depuis longtemps.

C'est Sven Lovén qui en rapporta le premier exemplaire (Macrurus berglax), de Hammerfest (Finmark), lors de la première Expédition suédoise au Spitzberg, sur l'Enigheten, en 1837.
XXIV.—Experiment with the Spark Gap of an Induction Coil
Authors: Turner Dawson
Published: June 2016

If the electrodes of an induction coil be placed at such a distance that a spark will not pass easily, then the introduction of a dielectric between the poles will greatly facilitate the sparking, provided the dielectric be placed near or against the positive pole, but will not have this effect if placed against the negative pole. Experiments were made with mica, sulphur, glass, and ebonite, etc.
XXXVII.—Mendelian Action on Differentiated Sex
Authors: Hart D. Berry
Published: June 2016

(Abstract)

It has long been known that the male and the female human genital tract contain not only organs characteristic of their sex proper, but also certain parts of the opposite sex in a less developed but yet perfectly definite form. Thus the female genital tract is made up of, not only its characteristic organs, the ovaries, tubes, uterus, etc., but also the epoophoron (parovarium) and its duct, the equivalent of the epididymis and ductus epididymis of the testis. In the same way, the human male has his characteristic sexual organs and also the appendix testis and prostatic utricle, the representatives of the fimbriated end of the Fallopian tube and of the lower end of the vaginal tract (hymen mainly, but varying).
XLIII.—On the Development of Mixed Cultures of Bacteria and Lower Fungi in Liquid and Solid Media
Authors: Westergaard Emil
Published: June 2016

An investigation was undertaken in order to ascertain to what extent and in what manner the individual species and varieties of lower fungi and bacteria present in liquid and solid media affect the simultaneous developmentof other similar organisms. The preliminary experiments were carried out with a culture of streptococcus lactis acidi, which was added in varying proportions to cow's milk immediately after milking, and gelatine plates were made at once, partly from the milk to which the cultures had been added and partly from the natural milk. The gelatine employed contained either glucose and peptone (Witte), or in addition an excess of calcium carbonate. The proportion in which the culture was added to the milk varied from 1 c.c. in 500 c.cs. of milk to one drop of the culture in half a gallon of milk. The results were in all cases practically the same, namely, thatthe plates infected with the normal milk gave an abundant development of bacteria and were in all cases rapidly liquefied, whereas the plates made from the infected milk showed a far less varied bacterial contents and a total suppression of the liquefying species.
II.—The Cooling of the Soil at Night, with Special Reference to Late Spring Frosts (II)
Authors: Franklin T. Bedford
Published: June 2016

In my previous paper to the Society on the same subject I came to the conclusion that the temperature of the surface of open cultivated soil fell rapidly at the beginning of a calm clear night until it was such a number of degrees below the temperature at the 4-in. depth as to make the upward conduction from that depth to the surface balance the radiation. After this stage was reached the surface and 4-in. temperatures fell at the same rate.

If, therefore, the temperatures of the surface and 4-in. depth and the conductivity of the layer of soil between the 4-in. depth and the surface were known from readings of electrical resistance thermometers, and the rate of radiation was calculated from the value of the relative humidity, I suggested that it might be possible to forecast the minimum soil temperature for a calm clear night as early as the previous afternoon.
IV.—Note on Mr Quilter's Photographs of Mirage
Authors:   The General Secretary
Published: June 2016

In a paper published in the Proceedings of the Royal Society of Edinburgh (vol. xxxviii, pp. 166–168), Mr Alexander G. Ramage described cases of mirage as seen on the Queensferry Road, near Edinburgh. Similar appearances have been since then observed and reported from different parts of the country, and the photographs of these by Mr G. F. Quilter, Ingatestone, are of some interest. Prints of five photographs taken by Mr Quilter were shown at the meeting of the Society held on 3rd November 1919; four were taken at one place about 100 yards’ distance from where the dry road appeared to be a pool. The camera looked along the road in a direction E.N.E., the road rising slightly towards the position where the mirage was seen. The best photographs, which were taken on 15th June 1919, at 1.30 p.m., showed certain posts on the north side of the road appearing distinctly reflected in the mirage pool. In the fifth photograph, taken at a different locality in August 1919, the shaded side of a telegraph post with neighbouring trees and a white-walled house beyond were distinctly seen as if reflected from a pool in the middle of the road. The main interest lies in the fact that the photographs bring out the phenomenon quite clearly.
IX.—On the Quaternionic System as the Algebra of the Relations of Physics and Relativity
Authors: Peddie W.
Published: June 2016

In a recently published paper (Proc. R.S., Dec. 1919) Mr W. J. Johnston makes a brilliant use of Clifford's extension of Hamilton's quaternions to the case of four (or more) variables. He proceeds, by adding a fourth independent and real unit vector and making the corresponding tensor imaginary, to modify the quaternionic ∇ so as to make it applicable to physical problems on the basis of relativity. In this respect his vectors are simply the direct extension of Hamilton's bivectors.
XVI.—A Law of Force giving Stability to the Rutherford Atom
Authors: Marshall J.
Published: June 2016

There is a large accumulation of evidence in support of Sir Ernest Rutherford's conception of atomic structure. According to this conception an uncharged atom consists of certain groupings of negative electrons rotating about a positively charged nucleus. Dr Bohr's theory of line spectra, which is based on this structure, frankly discards dynamical conditions of stability. There is no doubt, however, that this theory has been very successful in accounting for the numerical relationships between the frequencies of spectral lines.
XVIII.–The Musical Scale
Authors: Goold Joseph
Published: June 2016

I. The Tonal Order of the Chromatic Scale.

The exact ratios of the chromatic scale were first made known by Claudius Ptolemy of Alexandria about A.D. 150. We give them here as he found them, unaltered and unalterable.

It is a most remarkable fact that while the ratios of the chromatic scale have thus been known for nearly two thousand years, its mathematical symmetry and origin have remained unrecognised down to the present day.

For the concrete musical faculty is compounded of two distinct elements, physical and mathematical.

In its physical aspect (with which we are familiar), the scale is a series of notes arranged in order of pitch upwards from the tonic (or keynote).

In its mathematical aspect, the scale is a system of intervals measured symmetrically upwards and downwards from tonic and dominant as central interval (or tonal centre).

The physical order of the scale is that which we most easily appreciate, but the mathematical order is that in which it originates. The chromatic scale therefore is, primarily, not a series of notes, but a system of intervals (or tonal system).

Diagram I shows the scale in its familiar order of pitch, and it is remarkable how effectually this physical order conceals the mathematical from view.
II.—On the Equations of Motion of a Single Particle
Authors: Wedderburn J. H. M.
Published: June 2016

§ 1. When solved for the second derivatives, the Lagrangian equations of motion for a system in which there are no extraneous forces have the form

or, disregarding the parameter t,

being the second Christoffel symbol † of the matrix associated with the kinetic energy. If there are extraneous forces Fk and, denoting t by xn+1, we add to the set of equations, the equations of motion are
III.—Æther and the Quantum Theory
Authors: Allen H. Stanley
Published: June 2016

Extreme supporters of the principle of relativity find no place for an æther. Thus Lord Haldane in discussing the theory of Einstein writes: “Space, as a physical thing with unvarying geometrical properties, is to be banished, just for the same sort of reasons as the æther was banished before it. Only observable things are to be recognised as real in the new system of modern physicists.” On the other hand, many followers of Faraday and Maxwell have regarded æther as the primary real substance; all mass, momentum, or energy being mass, momentum, or energy of the æther. Without entering into a discussion of the significance of physical “reality,” we may, with most physicists, agree to use the concept of æther as giving a model, inadequate though it is at present, for the interpretation of physical phenomena.
X.—An Experimental Analysis of the Losses by Evaporation of Liquid Air contained in Vacuum Flasks
Authors: Briggs Henry
Published: June 2016

The experiments here described were made on behalf of the Oxygen Research Committee of the Scientific and Industrial Research Department, and the paper is given by permission of the Department. The fullest acknowledgment is due to Dr J. A. Harker, F.R.S., and to his co-workers, Professor G. W. Todd and Mr S. H. Groom, who have, in a series of able memoirs presented to the Oxygen Committee, analysed the nature of the heat-transfer from the outer atmosphere to the interior of metal vacuum bottles; but for their memoirs the writer's experiments would not have suggested themselves.
On Swan's Prism Photometer, commonly called Lummer and Brodhun's Photometer
Authors: Knott C. G.
Published: June 2016

In 1849 William Swan, subsequently Professor of Natural Philosophy in the University of St Andrews, read a paper on the “Gradual Production of Luminous Impressions on the Eye and other Phenomena of Vision” before the Royal Society of Edinburgh (see Transactions, Vol. XVI.). This paper contains some results of high interest, but I have no recollection of ever having seen it referred to in modern literature on the subject.
The Torsional Constants of Iron and Steel
Authors: Peddie W.
Published: June 2016

This paper gave details of a series of experiments made on the same iron wire as was used in experiments described in previous papers. This series was made on the wire after it had been heated to redness and allowed to cool. A linear relation was again found to hold between log. b and n, where b and n are the quantities (constant in any one experiment) symbolised in. the equation yn(x + a) = b, y being range of oscillation and x being number of oscillations of the wire which have taken place since the commencement of the experiment. It was further found that the line representing that relation passed (as did all other such lines previously obtained with this wire) through the point log. b = 2·3, n = 1. Thus the quantity provisionally called the Oscillation Constant in the preceding paper, and regarded as characteristic of the material of the wire, retains its old value even after the wire has been heated to redness.
The Examination of Sea Water by an Optical Method
Authors: Manley J. J.
Published: June 2016

In a paper communicated to the Royal Society, Mr E. T. Günther and the author gave an account of the results obtained from the examination of two samples of water taken from Lake Urmi, and amongst other determinations of a chemical and physical nature, were those of the refractive indices, which were performed with the aid of the Royal Society's large quartz prism and spectrometer, the latter reading by means of micrometers to 2″ of arc. On comparing the values obtained for the refractive indices of the two samples of water with those obtained for the relative densities, it was at once apparent that the former differentiated the two samples quite as distinctly as the latter.
On Jacobi's Expansion for the Difference-Product when the Number of Elements is Even
Authors: Muir Thomas
Published: June 2016

The character of Jacobi's expansion of this form of alternant will be more readily understood if the two simplest special cases be first considered.
On certain Aggregates of Determinant Minors
Authors: Muir Thomas
Published: June 2016

Two curious identities have been established regarding certain aggregates of minors of special determinants; the first, which concerns axisymmetric determinants, having been discovered by Kronecker in 1882, and the second, which concerns centrosymmetric determinants, having been published by me in 1888, When we come to think of the possibility of generalising these identities, it is readily seen that there are at least two lines of attack which suggest, themselves on reading the mere description of the kind of identity; for, in saying that the identities deal with “an aggregate of minor determinants of a special determinant,” we are conscious of two points of limitation in the description, the one signalised by the word “minor” and the other by the word “special.” If, therefore, an identity were obtained regarding an aggregate of which the terms were determinantsunrestricted by a family relationship, we might have one form of generalisation; and if, while retaining the family relationship, we succeeded in removing the restriction as to the form of the parent, a generalisation of a different type might be the result.
Note on the Activity of the Saliva in Diseased Conditions of the Body
Authors: Aitchison Robertson W. G.
Published: June 2016

The investigation was undertaken to find out in what way the activity of the salivary ferment varied in different diseased conditions of the body.
The Theory of Skew Determinants and Pfaffians in the Historical Order of its Development up to 1857
Authors: Muir Thomas
Published: June 2016

Sets of equations of the form

where the coefficient of xr in the sth equation differs only in sign from the coefficient of xs in the rth equation, had often made their appearance in analytical investigations before the determinant of such a set came to be considered. An instance is to be found in a memoir of Poisson's, read before the Institute in October 1809, and printed in the Journal de l'École Polytechnique, viii., pp. 266 — 344; and similar instances of an earlier date in writings of Lagrange and Laplace therein referred to. The mathematician who first referred definitely to the determinant appears to have been Jacobi.
The Total Solar Eclipse of 28th May 1900
Authors: Heath Thomas
Published: June 2016

The Scottish Expedition to observe the Total Solar Eclipse of May 28 consisted of Professor Copeland and Mr J. B. M'Pherson, Engineer to the Royal Observatory, Edinburgh, who were sent out by the Joint Eclipse Committee of the Royal and Royal Astronomical Societies; Mr Franklin-Adams, who joined the party as a volunteer observer; and myself, who had the honour of being sent out by this Society. The special object which we had set before ourselves was, of course, the attempt, if possible, to add something, however little it might be, to the sum of known facts concerning the constitution of the solar corona.
A Peculiar Set of Linear Equations
Authors: Muir Thomas
Published: June 2016

It is easily seen that each of the equations of the set

remains unaltered for each of the three interchanges

and that the set as a whole is not altered by the simultaneous performance of the cyclical substitutions
The Biology and Forest Importance of Scolytus (Eccoptogaster) multistriatus (Marsh)
Authors: Stewart MacDougall R.
Published: June 2016

The Scolytidse is a family of small roundish tetramerous beetles characterised by the fact that the female beetle enters bodily the tree or plant for her egg-laying, the eggs being generally laid in little notches cut out in the sides of the mothergallery. With some species, however, the eggs are laid all together in a bunch. The grubs are whitish, wrinkled and legless, and have, brown scaly heads. The close resemblance to each other of the grubs of the various species renders the determination of the species from larval characters extremely difficult, if not impossible, but the figures or patterns presented by the mother gallery and the larval galleries in relation to it are in general so highly characteristic, that with these and the name of the host plant one can generally determine the species.
Additional Note on the Ultra-Neptunian Planet, whose existence is indicated by its action on Comets
Authors: Forbes George
Published: June 2016

The history of research in this planet is briefly as follows:—In 1879 Professor Newton enunciated the proposition that if the elliptic orbits of comets have been changed from parabolas by planetary perturbations, then the probabilities are in favour of the comet's position at the time becoming the aphelion position of the new orbit. This explains why the aphelion distances of so many comets agree with the mean distances of Jupiter and Neptune respectively.
Observations on Binary Fission in the Life-History of Ciliata
Authors: Simpson J. Y.
Published: June 2016

The simplest and most common form of reproduction amongst the Ciliata is binary fission. In this ordinary, possibly vegetative, method of reproduction the plane of division is generally perpendicular to the long axis of the creature, To this generalisation the Vorticellidse form an apparent exception, but on the view that their evident long axis really corresponds to the dorso-ventral axis of other ciliates their case falls into line with that of the rest of the sub-class. Formerly many instances of fission in the direction of the long axis were described; they may safely be considered to have been mere instances of conjugation.
IX.—A Reduction-formula for the Functions of the Second Kind connected with the Polynomials of Applied Mathematics
Authors: Humbert Pierre
Published: June 2016

In the course of an investigation regarding rotating fluids, I have had occasion to make considerable use of Legendre's function of the second kind, which, as is well known, may be expressed in the form

where Pn is Legendre's polynomial, and fn−1 a polynomial of degree n−1. Various expressions of fn−1 have been given, particularly in terms of Legendre's polynomials of lower degrees; but I found that none was satisfactory in regard to the practical computations which I had to perform.
XVIII.—The Quadratic Relations between the Determinants of a 4–by–8 Array
Authors: Muir Thomas
Published: June 2016

1. The theorem which expresses the product of two determinants as a sum of like products is the main instrument for investigating the relations between the determinants of an oblong array. It is justifiably spoken of as “Sylvester's theorem of 1839 and 1851,” although simple cases of it date back to far earlier times; for example, the case

which was brought to light by Bezout in 1779.
V.—The Decline of the Birth-Rate : Regularities Revealed by an Analysis of the Rates Observed in Certain European Countries
Authors: Barclay R. S. , Kermack W. O.
Published: June 2016

During recent decades the vital statistics of the more developed countries of the world have exhibited two outstanding features: the first is a decline in the death‐rate, and the second a similar decline in the birth‐rate, the latter setting in some time after the former. It is generally realised that, for an adequate study of the changes involved, it is necessary, not merely to consider the crude death‐ and birth‐rates—that is, the number of deaths and births respectively per 1000 inhabitants—but also to take into account the age distribution of the population. In the case of death‐rates, for instance, it is important to know the specific death‐rates for each age-group—that is to say, for example, the annual number of deaths of persons aged twenty, per 1000 individuals of that particular age. In the same way the crude birth‐rate can only be properly interpreted when analysed in reference to the age of the mothers.
VI.—The Sex Ratio of the Domestic Fowl and its Bearing upon the Sex‐linked Lethal Theory of Differential Mortality
Authors: Crew F. A. E.
Published: June 2016

Of the explanations advanced in respect of the observed inequality in the viability and longevity of the sexes in man, the sex‐linked lethal theory advocated by Lenz (1923), Gunther (1923), Geiser (1924–5), Huxley (1924), Schirmer (1929), amongst others, has attracted most support. One reason for this is undoubtedly that it is a genetic theory promulgated at a time when biological thought was being profoundly influenced by the many spectacular discoveries which had been made in this particular science.
VII.—Studies on Reproduction in the Albino Mouse. I. The Period of Gestation and the Time of Parturition
Authors: Merton Hugo
Published: June 2016

The cellular processes of ovulation, maturation and fertilisation of the ovum in the albino mouse have been the subject of repeated and exact studies, and are now sufficiently well known. The biological phenomena of propagation in the mouse,i.e.the sexual cycle, œstrus, and copulation, have likewise been described in detail, but our knowledge concerning the period of gestation and the moment of parturition is still very inadequate.