bluuebunny/crossref_metadata_2025 huggingface dataset:
X.—On the Contact of the Loops of Epicycloidal Curves
Authors: Sang Edward
Published: January 2013

During the summer vacation, Mr Henry Perigal of London proposed to me the following problem:—

“To determine the proportions of an epicycloid of which the loops touch each other.”

The solution of this problem contains some points of interest to the general analyst, and exhibits relations between certain trigonometric formulæ and algebraic equations. I, therefore, offer an outline of it to the attention of the Royal Society.
IV.—On the Action of the Halogen Compounds of Ethyl and Amyl on some Vegetable Alkaloids
Authors: How Henry
Published: January 2013

The memoir which I have now the honour of presenting to the Society contains part of a continued investigation, of which the first results were published in a paper read, last year, before the Chemical Society of London. The nature of the materials experimented on is such, and the scope of the subject so large, as to afford nothing more to all I have at present brought to light than the name of a bare and partial outline; yet the facts I have now to adduce, of some interest in themselves, will increase that of those already made known, and prove of additional service in aiding to complete that desirable object, a knowledge of the chemical constitution of the natural bases. In the paper alluded to, I shewed that, by the action of iodide of ethyl and of methyl upon morphia and codeine, the two most prominent alkaloids of opium, new salts are produced, in which the basic molecules appear to assimilate by their chemical characters to the hypothetical metal ammonium, or its oxide rather; so that, in the system of Hofmann, these peculiar results of natural, and as yet inimitable agencies, would take rank among the nitryle bases.
VI.—Note on the Possible Density of the Luminiferous Medium and on the Mechanical Value of a Cubic Mile of Sunlight
Authors: Thomson William
Published: January 2013

That there must be a medium forming a continuous material communication throughout space to the remotest visible body is a fundamental assumption in the undulatory Theory of Light. Whether or not this medium is (as appears to me most probable) a continuation of our own atmosphere, its existence is a fact that cannot be questioned, when the overwhelming evidence in favour of the undulatory theory is considered; and the investigation of its properties in every possible way becomes an object of the greatest interest. A first question would naturally occur, What is the absolute density of the luminiferous ether in any part of space? I am not aware of any attempt having hitherto been made to answer this question, and the present state of science does not in fact afford sufficient data. It has, however, occurred to me that we may assign an inferior limit to the density of the luminiferous medium in interplanetary space by considering the mechanical value of sunlight as deduced in preceding communications to the Royal Society from Pouillet's data on solar radiation, and Joule's mechanical equivalent of the thermal unit.
VII.—On the Mechanical Energies of the Solar System
Authors: Thomson William
Published: January 2013

The mutual actions and motions of the heavenly bodies have long been regarded as the grandest phenomena of mechanical energy in nature. Their light has been seen, and their heat has been felt, without the slightest suspicion that we had thus a direct perception of mechanical energy at all. Even after it has been shewn that the almost inconceivably minute fraction of the Sun's heat and light reaching the earth is the source of energy from which all the mechanical actions of organic life, and nearly every motion of inorganic nature at its surface, are derived, the energy of this source has been scarcely thought of as a development of mechanical power.
IX.—On the Dynamical Theory of Heat. Part V. Thermo-electric Currents
Authors: Thomson William
Published: January 2013

Preliminary §§ 97–101. Fundamental Principles of General Thermo-dynamics recapitulated.

97. Mechanical action may be derived from heat, and heat may be generated by mechanical action, by means of forces either acting between contiguous parts of bodies, or due to electric excitation; but in no other way known, or even conceivable, in the present state of science. Hence Thermo-dynamics falls naturally into two Divisions, of which the subjects are respectively, the relation of heat to the forces acting between contiguous parts of bodies, and the relation of heat to electrical agency. The investigations of the conditions under which thermodynamic effects are produced, in operations of any fluid or fluids, whether gaseous or liquid, or passing from one state to the other, or to or from the solid state, and the establishment of universal relations between the physical properties of all substances in these different states, which have been given in Parts I.-V. of the present series of papers, belong to that first great Division of Thermo-dynamics—to be completed (as is intended for future communications to the Royal Society) by the extension of similar researches to the thermo-elastic properties of solids.
XVI.—Notes on some of the Buddhist Opinions and Monuments of Asia, compared with the Symbols on the Ancient Sculptured “Standing Stones” of Scotland
Authors: Wise Thomas A.
Published: January 2013

The general identity, in idea and design, of the ancient monuments of Southern and Western Europe, with those of Hindostan, is so marked, as to appear to justify the inference that races of Asiatics proceeded westward at different ages, and established themselves along the shores of the Baltic and Mediterranean Seas, and part of the Atlantic Ocean; along which route they have left characteristic monuments, which resemble those of their original country.
XIX.—Researches on the Amides of the Fatty Acids
Authors: Rowney Thomas H.
Published: January 2013

The following paper contains the details of some experiments upon the action of ammonia on the oils and fats, of which a preliminary notice was published in the Quarterly Journal of the Chemical Society of London. The production of a soapy emulsion by the action of ammonia on these substances has long been familiar to chemists, but comparatively few accurate experiments have been made upon the compounds formed. Boullay long since examined the crystalline substance obtained from olive-oil, which he called Margaramide, and mentioned that similar compounds were obtained with the other oils, although he did not examine them. More lately, M. Bouis produced ricinolamide from castor-oil, and showed that, by fusion with potash, it yielded caprylic alcohol and sebacic acid; and still more recently, he has obtained another fatty amide, which he calls Isocetamide, by the action of ammonia on the fat of the purging nut of the West Indies.
XX.—On the Volatile Bases produced by Destructive Distillation of Cinchonine
Authors: Williams C. Greville
Published: January 2013

The history of the organic bases has now become as ardent an object of study among chemists as that of the as yet far more numerous group of acids; and it is generally admitted that the information obtained has been no less important and interesting. Of all organic alkaloids, those of opium and the cinchona barks doubtless occupy the first rank, whether we regard their value as remedial agents, or the remarkable facts which have been ascertained connected with their atomic relations, and the influence exerted by the latter, upon the theory of the science.
XXI.—On the Extent to which the received Theory of Vision requires us to regard the Eye as a Camera Obscura
Authors: Wilson George
Published: January 2013

In the course of those researches on Colour-Blindness, which, at intervals, I have recently been engaged in prosecuting, I have encountered some phenomena connected with normal vision, which I am desirous to submit to the consideration of the Society. Those phenomena I have already in part detailed, in the account of the researches referred to, and I shall not, accordingly, repeat the description of them here, to a greater extent than is essential to rendering intelligible the question which I wish to submit for discussion.

I venture to assume, that without adducing a lengthened series of authorities, I may take for granted, that, on the received theory of vision, the eye of man, as well as that of most of the lower animals, is regarded as essentially realizing, during the performance of its function of sight, the condition of a darkened chamber, or camera obscura. In more precise words: the theory in question teaches, that those rays of light, which reach the eye from the objects which they render visible, and entering at its front traverse all its transparent humours and membranes, last of all pierce the retina, and after making that impression upon it which is supposed to be the most important physical element of vision, are stopped, or absorbed by the dark pigment lining the choroid coat, and suffer extinction as visible rays. The dark surface of the choroid is thus held to abolish all the light which reaches it, so that none of the luminous rays return through the retina, or retrace their course across the chamber of the eye.
XXIII.—On a Problem in Combinations
Authors: Kelland Philip
Published: January 2013

Several years ago, when discussing the question of the distribution of the stars, a problem occurred to Professor Forbes, which, simple as it is, appears to have escaped notice prior to that time. Having been consulted as to its solution, I communicated my results to Professor Forbes, who has inserted one of them in his paper printed in the Philosophical Magazine for 1850, vol. xxxvii., p. 425. But for the very ingenious application which Professor Forbes has there made of it, the problem might probably not be worth recurring to. As it is, I have thought it would not be altogether uninteresting to give the complete solution.

The Problem is as follows:—There are n dice, each of which has p faces, p being not less than n; it is required to find the number of arrangements which can be formed with them, 1°, So that no two show the same face; 2°, That no three show the same face; 3°, That no four do so, and so on.
XXVI.—Researches on Chinoline and its Homologues
Authors: Williams C. Greville
Published: January 2013

Twenty-two years have now elapsed, since Runge first published his remark, able experiments on coal naphtha, and it would, perhaps, be difficult to instance any chemical investigation which has formed the point of departure of a greater number of researches. When we consider the vast quantity of bodies which have, first and last, been obtained from coal-tar, it might appear that little more remained to be done,—that the mine was exhausted,—but so far from this being the case, the discovery of one substance has only served to pave the way for the isolation of others.

Among the bodies examined by Runge, there was one which apparently possessed comparatively few features of interest; indeed its very name (the first syllable derived from λευχός was intended to express its supposed inability to produce coloured reactions, a feature which, in the chemistry of the time, militated greatly against its claims to notice. I have used the expression “supposed inability,” because I shall show further on, that this substance is capable, under certain conditions, of affording extremely brilliant colorations. Eventually, Gerhardt, by acting on quinine, cinchonine, and strychnine, with hydrate of potash, obtained the same body. The first chemist who succeeded in procuring any of its compounds in a state of tolerable purity was Hofmann, whose analysis of the platinum salt is very nearly exact. But, at the time of that analysis, he was of opinion that the products obtained from coal and chinoline were essentially different, an opinion which he subsequently retracted. In the mean time, the alkaloid, as obtained from cinchonine was examined by Bromeis and Laurent, their results, however, not elucidating the composition of the basic fluid obtained in the manner alluded to.
XXVII.—On Fermat's Theorem
Authors: Talbot H. F.
Published: January 2013

It is well known that no satisfactory demonstration has ever been given of Fermat's celebrated theorem, which asserts that the equation an = bn + cn is impossible, if a, b, c, are whole numbers, and n is any whole number greater than 2. In Legendre's Théorie des Nombres, he demonstrates the cases of n = 3, n = 4, and n = 5, the latter only in his Second Supplement. In Crelle's Mathematical Journal, ix. 390, M. Dirichlet, a mathematician of Berlin, has demonstrated the case of n = 14, but I am not aware whether his demonstration is considered successful. Legendre informs us (Second Supplement, p. 3) that the Academy of Sciences, with the view of doing honour to the memory of Fermat, proposed, as the subject of one of its mathematical prizes, the demonstration of this theorem; but the Concourse, though prolonged beyond the usual term, produced no result.
III—On the Number of Dust Particles in the Atmosphere of certain Places in Great Britain and on the Continent, with Remarks on the Relation between the Amount of Dust and Meteorological Phenomena
Authors: Aitken John
Published: January 2013

In a new investigation of this kind it is always desirable to repeat the observations under as many conditions as possible. The variables are so many that with a limited experience it cannot be expected that the subject will be exhausted, or that the conclusions arrived at from early observations will be in all cases confirmed. As an opportunity offered in the beginning of 1890 for repeating the tests made the previous year on the amount of atmospheric dust at different places on the Continent, it seemed desirable that the old ground should be gone over again rather than that the investigation should be extended to new areas. The observations made in this country have also been confined to the same stations as in 1889; and in this paper I intend giving the results of a series of tests repeated at the same stations, at about the same dates, but under the conditions existing in 1890, as has already been given for 1889 in Part I. of this subject.
V.—The Lateral Sense Organs of Elasmobranchs. I. The Sensory Canals of Læmargus
Authors: Ewart J. C.
Published: January 2013

Some years ago, when studying the electrical organs of the torpedo, I was forced to the conclusion that the nerves supplying the batteries had not been accurately described, and that notwithstanding the statements in the most recent works, the first electric nerve is not derived from the trigeminus. Finding some difficulty in making out the arrangement of the cranial nerves in the greatly specialised torpedo, I directed my attention, first to the skate, and later to certain sharks, more especially to the Greenland shark (Læmargus). I had not proceeded far before I was convinced that we had still much to learn as to the anatomy of the cranial nerves of both the higher and lower vertebrates.
XII.—On the Action of the Valves of the Mammalian Heart
Authors: Paton D. Noël
Published: January 2013

Few subjects are of greater practical importance than the mode of action of the valves of the heart, inasmuch as these structures are so frequently the seat of pathological changes which produce serious disturbances throughout the whole circulatory system.

On the general principles of the mode of action of the aortic and pulmonary valves all investigators seem to be agreed. When we turn to the auriculo-ventricular valves we find that, while in some of the best known text-books their action is considered as so thoroughly investigated and completely understood as to merit no discussion, and to require only the briefest description, in others the mechanism is admitted to be imperfectly comprehended, and is described in the most obscure and indefinite manner.
XIII.—A Contribution to the Anatomy of Sutroa
Authors: Beddard Frank E.
Published: January 2013

Our knowledge of this remarkable genus of freshwater Oligochæta is at present entirely due to Dr Gustav Eisen. Within a year or two of discovering the type species, Sutroa rostrata, Dr Eisen found a second species, evidently referable to the same genus, which has been named Sutroa alpestris. Examples of both of these species have been most kindly forwarded to me by Dr Eisen; and I therefore take the opportunity of offering a few observations upon the structure of the genus, and upon its relations to other Oligochæta, as I am able, in a few matters, to supplement Dr Eisen's papers.

The account given by Eisen of Sutroa alpestris is evidently based upon a study of the living worm; it is therefore very full as regards the vascular system, but not quite so detailed where it concerns the generative organs, which are more conveniently studied by the section method. It is more especially to these organs that I desire to again draw attention.
XV.—The Skull and Visceral Skeleton of the Greenland Shark, Læmargus microcephalus
Authors: White Philip J.
Published: January 2013

Some time ago, at the request of Professor Ewart, I undertook an examination of the skull and visceral skeleton of the Greenland shark, Læmargus microcephalus. This I readily consented to do, not only because no attempt had yet been made to describe these structures in this shark, but because they claim careful consideration in view of the recent work by Professor Ewart on the cranial nerves of Elasmobranchs.

In this paper I shall endeavour, without entering into too much detail, to point out some of the more salient features of the skull and visceral skeleton of Læmargus, and to compare them with those of other Elasmobranchs where that seems necessary.

I have made preparations of the above-named structures from the heads of several specimens of Læmargus. The sharks from which the heads were taken were of various sizes, the smallest being about six feet in length, and the largest twelve. As might have been expected, the skeletal parts of these heads are very similar to each other, but I have noticed among the few specimens I have examined points of difference, which make me wish I had a larger number of preparations at my disposal, to enable me to decide the more usual conditions.
XX.—On the Particles in Fogs and Clouds
Authors: Aitken John
Published: January 2013

In May 1891 I communicated a paper to this Society “On a Method of Observing and Counting the Number of Water Particles in a Fog,” and in July of the same year a paper “On the Solid and Liquid Particles in Clouds.” One conclusion to which the observations contained in these papers pointed was, that there existed a relation between the thickness or density in clouds and fogs and the number of water particles present. Though the figures did not show that this relation was very close, yet in all the fogs and clouds tested there was a rough relation between the thickness of the air and the number of water particles observed.
XXI.—On the Path of a Rotating Spherical Projectile
Authors: Tait
Published: January 2013

The curious effects of rotation upon the path of a spherical projectile have been investigated experimentally by Robins and many others, of whom Magnus is one of the more recent. They have also been the subject of elaborate mathematical investigation, especially by Poisson, who has published a large treatise on the question. For all that, we know as yet very little more about them than Newton did in 1666, when he made his famous experiments on what we now call dispersion.
XXVIII.—On the Number of Dust Particles in the Atmosphere of Certain Places in Great Britain and on the Continent, with Remarks on the Relation between the Amount of Dust and Meteorological Phenomena
Authors: Aitken John
Published: January 2013

In the two papers previously communicated to this Society under the above title, Parts I. and II., I have given the results of my observations on the dust in the atmosphere for the years 1889 and 1890. In this paper will be given the results of similar observations I have been able to make during the years 1891, 1892 and 1893. The observations made during these last three years are similar to those made in the two previous ones; and were mostly made at the same places and at about the same dates as those already given. These five sets of observations are therefore comparable with each other, and give a fair statement of the number of dust particles in the atmosphere at the different places at the particular dates.
XXX.—Note on some Fossils from Seymour Island, in the Antarctic Regions, obtained by Dr Donald
Authors: Sharman G. , Newton E. T.
Published: January 2013

These fossils are especially interesting on account of their having been obtained from a more southerly point than any hitherto recorded. The number of specimens is nine; five of these are referable to the genus Cucullœa, one to Cytherea, one probably to Natica, and two are fragments of Coniferous Wood. With the Cytherea are other small shells which may indicate the presence of Crassatella (?) and Donax (?). Two of the pieces of Cucullœa are entirely free from matrix, while three show in their interiors a fine sandy rock which effervesces when treated with hydrochloric acid. The shells themselves have a calcedonic appearance, but, like the matrix, they effervesce strongly with acid; they are much denuded, having apparently been long exposed to the weather. The matrix within the Cytherea is coarser than that in the Cucullœa, containing, besides fragments of quartz and of a black rock, numerous fragments of shells. The Natica (?) is almost free from matrix, and is much denuded, but in some of the crevices sandy material may be seen very like the matrix of the other shells. All these genera have a wide distribution in time, and are now living, consequently they give but little clue to the age of the rocks in which they were found. Cucullœa is rare at the present day, and the few known species occur in the Mauritius, Nicobar, and China; but as a fossil it is very common and widely distributed.
II.—On a Process in the Differential Calculus, and its application to the Solution of certain Differential Equations
Authors: Kelland P.
Published: January 2013

The facilities which are afforded by the introduction of the function into certain classes of Differential expressions are well known. This function has effected the combination and generalization of Problems, which, although found to be capable of solution in particular cases, were regarded rather as isolated and exceptional forms, than as integral parts of some comprehensive expression. But the subject is far from exhausted. Some of the most important Differential Equations have never as yet been solved by a general method. The present Memoir is intended to supply this defect. The process employed differs little from that which I have previously exhibited; but the range of Problems which it embraces is much more extensive, and the Problems themselves are of a more important character.
VII.—On the Mechanical Action of Heat, especially in Gases and Vapours
Authors: Rankine William John Macquorn
Published: January 2013

The ensuing paper forms part of a series of researches respecting the consequences of an hypothesis called that of Molecular Vortices, the object of which is to deduce the laws of elasticity, and of heat as connected with elasticity, by means of the principles of mechanics, from a physical supposition consistent and connected with the theory which deduces the laws of radiant light and heat from the hypothesis of undulations. Those researches were commenced in 1842, and after having been laid aside for nearly seven years, from the want of experimental data, were resumed in consequence of the appearance of the experiments of M. Regnault on gases and vapours.

The investigation which I have now to describe, relates to the mutual conversion of heat and mechanical power by means of the expansion and contraction of gases and vapours.
IX.—On the Power and Economy of Single-Acting Expansive Steam-Engines, being a Supplement to the Fourth Section of a Paper On the Mechanical Action of Heat
Authors: Rankine William John Macquorn
Published: January 2013

(34.) The objects of this paper are twofold: First, To compare the results of the formulæ and tables relative to the power of the steam-engine, which have been deduced from the Dynamical Theory of Heat, with those of experiments on the actual duty of a large Cornish engine at various rates of expansion; and, Secondly, To investigate and explain the method of determining the rate of expansion, and, consequently, the dimensions and proportions of a Cornish engine, which, with a given maximum pressure of steam in the cylinder, at a given velocity, shall perform a given amount of work at the least possible pecuniary cost, taking into account the expense of fuel, and the interest of the capital required for the construction of the engine.
XII.—The Development of the Müllerian Duct of Amphibians
Authors: Wilson Gregg
Published: January 2013

Last summer I began an investigation of the Müllerian duct of Amphibians at the suggestion of Professor Wiedersheim, to whom I am indebted for most kind advice during the progress of my work, as well as for all the material that I have made use of in the course of it.

I have been able to examine stages in the development of the duct in Rana esculenta, Triton alpestris, Salamandra atra and S. maculosa, Siredon pisciformis (Axolotl), and Desmognathus; but I have paid special attention to Salamandra atra and Axolotl, which have not yet been studied in this connection. The Urodeles are easier to work with than the Anura, owing to the comparatively early formation of the Anlage of the Müllerian duct; and I have found Axolotl to be particularly instructive, as the pronephros and segmental duct persist during the early stages of the formation of the Müllerian duct.

I propose in this paper to describe what I have observed in various stages of the development of these two forms, and to compare the results thus arrived at with the appearances described in the published works on the subject.
XVII.—The ς′ of Diophantus
Authors: Thompson D'Arcy Wentworth
Published: January 2013

The Arithmetical, or, as we should say, Algebraic, Problems of Diophantus involve a single unknown quantity, symbolised by ς′ or ς°′. The number for which this symbol stands is described as πλῆθος μονάδων ἄλογον, and is spoken of as ὁ ἀόριστος ἀριθμός, the undefined number, or simply as ὁ ἀριθμός, the number, par excellence, of the problem in question.

By all commentators, with but one exception so far as I know, the ς′ of Diophantus is taken as an abbreviation of ἀριθμός, and I find the same statement made unquestioningly in the standard Palæography of Gardthausen. The mathematicians, while expressing no doubt as to the fact, show, however, in some cases, a clear enough perception of the difficulty of accounting for such an abbreviation, and are not all agreed as to its more precise origin. Nesselmann, Cantor, and most others, treat the ς as the final letter of ἀριθμός: Heath, who devotes many pages to a discussion of the subject, puts forward, as an alternative and preferable hypothesis, a suggestion that the ς may be a corrupt cursive abbreviation of the two first letters αρ of the same word.
XIX.—On the Cranial Nerves ofChimæra monstrosa (Linn. 1754);with a Discussion of the Lateral Line System, and of the Morphology of theChorda tympani
Authors: Cole Frank J.
Published: January 2013

This investigation first commenced in the examination of a few special points which had arisen in connection with Professor Ewart's investigations on the Cranial Nerves and Lateral Sense Organs of Elasmobranchs. As this examination revealed facts of more interest than was expected, it occurred to me to investigate very thoroughly the whole of the cranial nerves of this animal, and to publish the results as a continuation of the work already alluded to. The research turned out to be much easier and more interesting than I had anticipated, and, as regards its cranial nerves at any rate,Chimærais unrivalled among vertebrates, first, for the ease with which its nerves may be dissected, and second, for the almost ideal results that are to be obtained. The endless perplexity and mystification produced by the study of the trigeminal and facial nerves of the cartilaginous fishes,—dispelled to a very great extent, it is true, by the researches of Marshall and Spencer,—would probably have never arisen if Stannius had made a careful examination of the roots of the 5th and 7th nerves of hisChimæra. This, however, he omitted to do in the very form—in fact, as far as we know, the only form—which would have repaid the investigation ; and hence the embryologist stepped in and made a discovery that the anatomist had just, and only just, failed to grasp. The more important facts, therefore, relating to the cranial nerves of the Holocephali are, it is claimed, here recorded for the first time.
XXIV.—On the p-discriminant of a Differential Equation of the First Order, and on Certain Points in the General Theory of Envelopes connected therewith
Authors: Chrystal
Published: January 2013

The theory of the singular solutions of differential equations of the first order, even in the interesting and suggestive form due to Professor Cayley (Mess. Math., ii., 1872), as given in English text-books, is defective, inasmuch as it gives no indication as to what are normal and what are abnormal phenomena. Moreover, Cayley added an appendix to his theory regarding the circumstances under which a singular solution exists, which is misleading so far as the theory of differential equations is concerned, if not altogether erroneous.

The main purpose of the following notes is to throw light on the point last mentioned by means of a number of examples. I have also taken the opportunity to furnish simple demonstrations of several well-known theorems regarding the p-discriminant which do not find a place in the current English text-books.
XXXIV.—On the Total Solar Eclipse of 1851
Authors: Smyth C. Piazzi
Published: January 2013

Eclipses are still, as they have ever been, very important phenomena for the astronomical observer; partly on account of the crucial test which they afford for the examination of the truth of the theory and calculation of the motions, real and apparent, of the Sun and Moon, partly also for the special opportunities which they furnish of inquiring into some of the arcana of the physical characteristics of those bodies.

For the former purpose, a partial eclipse will serve almost as well as a total one; while the continued improvement of the observation of meridian passages is now raising these daily measures fully to the importance of the other occasional phenomena, as a test of the theory. But for inquiry into the physics of the Sun, a perfectly total eclipse of that body is necessary; revelations may then happily be procured, which no observation of any other phenomena at any other time, can hope to afford any suspicion of.
XL.—On the Mechanical Action of Heat
Authors: Rankine William John Macquorn
Published: January 2013

Section VI.—A Review of the Fundamental Principles of the Mechanical Theory of Heat; with Remarks on the Thermic Phenomena of Currents of Elastic Fluids, as illustrating those Principles.

(Article 46.) I have been induced to write this Section, in continuation of a paper on the Mechanical Action of Heat, by the publication (in the Philosophical Magazine for December 1852, Supplementary Number) of a series of experiments by Mr Joule and Professor William Thomson, on the Thermal Effects experienced by Air in rushing through small Apertures. Although those authors express an intention to continue the experiments on a large scale, so as to obtain more precise results; yet the results already obtained are sufficient to constitute the first step towards the experimental determination of that most important function in the theory of the mechanical action of heat, which has received the name of Carnot's Function.
V.—On the Fossil Flora of the Yorkshire Coal Field. (Second Paper.)
Authors: Kidston Robert
Published: January 2013

Among the specimens from the Yorkshire Coal Field which have been collected by Mr W. Hemingway, Barnsley, and submitted to me for examination at various times, are the remains of several cones which are referable to the genus Sigillariostrobus, Schimper.

Notwithstanding the great frequency of the genus Sigillaria in the Coal Measures, and especially in the Middle Coal Measures, examples of their fructification are very rare. This is the more remarkable, as specimens of Sigillaria, showing cone scars, though not common, are occasionally met with. Possibly, however, the apparent rarity of Sigillarian cones is due, in part, to our inability at present to distinguish them in all cases from cones generally placed under the name of Lepidostrobus, which latter genus there is every reason to believe comprises cones that belong to several genera of Lycopods.
IX.—On the Definite Integralwith Extended Tables of Values
Authors: Burgess Jas.
Published: January 2013

1. The integral occurs so frequently in various branches of research that, as far back as 1783, Laplace suggested that it would be useful to tabulate its values for successive ranges of integration. It is employed in investigations on the theories of refraction, conduction of heat, of errors of observation, of probabilities, etc. These are familiar to physicists and need not be dwelt upon.
X.—The Relations between the Coaxial Minors of a Determinant of the Fourth Order
Authors: Muir Thomas
Published: January 2013

1. The existence of relations between the coaxial minors of a determinant was first discovered by MacMahon in 1893. The whole literature of the subject is comprised in three papers, viz.:—

MacMahon, Phil. Trans., clxxxv. pp. 111–160.

Muir, Phil. Mag., 5th series, xli. pp. 537–541.

Nanson, Phil. Mag., 5th series, xliv. pp. 362–367.

My present object is to continue the investigation of the relations in question, and more particularly to draw attention to an explicit expression for a determinant of the 4th order in terms of its own coaxial minors. At the outset some fresh considerations regarding determinants in general will be found useful.
IV.—On the Convection of Heat by Air Currents
Authors: Mitchell A. Crichton
Published: January 2013

1. The present paper deals with a, series of experiments made in the Physical Laboratory, Edinburgh University, from January to October 1899, with the object of determining the convective loss of heat from a cooling body owing to the action of currents of air.
XX.—A Bathymetrical and Geological Study of the Lakes of Snowdonia and Eastern Carnarvonshire
Authors: Jehu T. J.
Published: January 2013

The study of lakes has received more attention on the Continent than it has in our own country. The inland waters of France and Switzerland have been most carefully surveyed, and in America accurate soundings of many of the lakes have been made by the Geological Surveys. But until recent years this work has been almost altogether neglected in Britain; the Government had considered it to be outside the function of the Ordnance Survey, and though of importance to geological research, it has not been undertaken by the Geological Survey. The absence of adequate knowledge concerning the forms of the basins occupied by the lakes has been a serious obstacle to the geological inquiry as to the mode of origin of these basins. But recently, in the English Lake District and in Scotland, this obstacle has been removed to a great extent through the work of geographers, who have carried out a very complete bathymetrical survey of many of the lakes of those regions; and the importance of this work has been recognised by geologists. But in North Wales not only had no attempt been made to ascertain the configuration of the lake-beds, but in many cases even the depths of the lakes remained unknown.
XIII.—Continuants resolvable into Linear Factors
Authors: Muir Thomas
Published: January 2013

(1) It is known that a continuant whose three diagonals are formed of certain equidifferent progressions is resolvable into linear factors, the earliest specimens placed on record being those of Sylvester and Painvin. The object of the present paper is to show that there are continuants of quite a different type which are also so resolvable, and to expound a general mode of investigating the subject.
XIV.—The Igneous Geology of the Bathgate and Linlithgow Hills
Authors: Falconer J. D.
Published: January 2013

The Bathgate and Linlithgow Hills occupy a well-defined belt of rising ground stretching S.S.W.–N.N.E. from Bathgate to Bo'ness, and included in the marginal portions of sheets 31 and 32 of the 1-in. maps of the Ordnance and Geological Surveys. Throughout the range the steeper slopes face the west, while the eastern flanks are deeply buried in drift. The glaciated contours are well seen from the east, and the sky-line is in several places deeply indented by glacial grooves. The physical geography is throughout intimately dependent upon the geological structure, but the latter is simplicity itself when contrasted with the complicated structure of the shale-fields to the east. Alternating zones of volcanic and sedimentary rocks strike parallel with the direction of elongation of the range from Bathgate to Bonnytoun Hill, and these are cut by a later connected series of dykes and sills of intrusive igneous rock. The latter, as a rule, are more resistant than the lavas, and form the more prominent features of the landscape, while the sedimentary intercalations may frequently be traced, even where no rock is visible, by the trough-like depressions which have been hollowed out of them between the zones of lava.
XXVI.—Magnetic Shielding in Hollow Iron Cylinders and Superposed Inductions in Iron
Authors: Russell James
Published: January 2013

§ 1. The shielding effect which exists within hollow iron spheres and cylinders, when placed in a uniform magnetic field, has been previously investigated. Poisson, Stefan, Maxwell, and among others, and more recently, Professors Rücker and Du Bois, have contributed to the subject. If

and the ratio of n to R be the order 1 to 100, it appears that the following expressions may be taken as sufficiently correct:
XXX.—The Lower Devonian Fishes of Gemünden
Authors: Traquair R. H.
Published: January 2013

Gemünden is situated in Rhenish Prussia, about eighteen miles to the west and slightly also to the south of Bingen, in the district known as the “Hunsrück,” and the rock in which the fishes to be described in this memoir occur is called the “Hunsrück Slates.”

These Hunsrück slates belong to the Lower Devonian of the Rhenish area, and the position assigned to them by German geologists is as follows:—

The above table is quoted from Kayser and Lake's Text-book of Comparative Geology, as is also the following brief statement regarding the Hunsrück slates themselves.
XXXII.—The Canonbie Coalfield: its Geological Structure and Relations to the Carboniferous Rocks of the North of England and Central Scotland
Authors: Peach B. N. , Horne J.
Published: January 2013

The Canonbie Coalfield occupies a small tract of ground between the Liddel Water and the river Esk in the south-east part of the county of Dumfries. Though of limited extent, the coalfield has aroused considerable interest, due partly to the important series of plants obtained from the beds, and partly to the questions bearing on the correlation of the Carboniferous rocks of the Scottish Border with those in the North of England and Central Scotland.
XI.—On a Case of Colour Blindness. Part I.
Authors: Peddie Wm.
Published: January 2013

The case under consideration was brought to my notice while I was attempting to arrange a colour match by the well-known disc method. The colour was somewhat like lilac, though rather more red. A number of onlookers—including the gentleman whom I afterwards found to be colour-blind, and whom I shall in this paper denote as Mr A.—pronounced the match fairly satisfactory. Mr A. subsequently remarked to me that he sometimes had a difficulty in distinguishing greens and blues. He said, also, that he had, though much less frequently, a difficulty with reds. This condition is so abnormal that I at once handed him a direct vision spectroscope and asked him to name the colours which he saw in succession from one end of the spectrum to the other. He said that red was the first. “And after the red?” I asked; “green,” he said: “and after the green?”; “blue.” And when asked what followed the blue, he said that the rest of the spectrum was blue throughout the whole extent. When asked if he saw white light between the red and green colours, he was very undecided, but said that he did not think he would call it white—it might be yellow.
XXII.—The Emblem of the Crab in Relation to the sign Cancer
Authors: Thompson D'Arcy Wentworth
Published: January 2013

This paper deals with a leisure-time study of mine, from which I once before drew the subject of an essay for this Society. The representations of animal form in Ancient Art interest me chiefly in so far as they present to us a problem involving an unsolved question as to the whole spirit and motive with which such representations were designed. We may see expressed in them merely a tendency to portray familiar objects in appropriate associations, to use the fish, or the crab, or the cuttle-fish as the device of an habitation of fishermen or resort of mariners, or to employ those creatures and others—the ox, the sheep, and the goat, the lion, the wolf, and the eagle—as the more fanciful appanage of divinities whose imaginary attributes were the attributes of the sea, the plain, the mountain or the sky. But we err, in my opinion, if we fail to recognise in this antiquated symbolism a deeper intention, whose spirit is rather Oriental than Western, archaic than modern. I believe these representations for the most part to have been associated with specific notions or beliefs of astronomical or astrological science, of religion or superstition.
XXVIII.—Contributions to the Craniology of the People of the Empire of India. Part I. The Hill Tribes of the North-East Frontier and the People of Burma
Authors: Turner Wm.
Published: January 2013

For a number of years I have been collecting specimens and conducting an investigation into the craniological characters of the native inhabitants of our great Indian Empire, and several hundred skulls have now been under examination, and almost all have been measured. The sources to which I have been indebted for material are in part the collection of crania belonging to the Henderson Trustees, long known as the Edinburgh Phrenological Museum, and now deposited by the Trustees in the Anatomical Museum of the University; in part, a few specimens belonging to the University collected by my predecessors in office; in part, the valuable series of Indian crania belonging to the Indian Museum, Calcutta, which through the intercession of Dr John Anderson, F.R.S., the former Director, the Trustees of that Museum, with great liberality, most courteously permitted me to have the loan of for purposes of study; and lastly, a number of crania which have been forwarded to me by friends and former pupils, engaged in the public service in India, to whom I take this opportunity of expressing my indebtedness for the valuable material which I have received from them.
XXXII.—Report on Fossil Fishes collected by the Geological Survey of Scotland in the Silurian Rocks of the South of Scotland
Authors: Traquair Ramsay H.
Published: January 2013

In the autumn of last year (1897), Sir A. Geikie, F.R.S., Director-General of the Geological Survey, kindly placed in my hands for description an important collection of fossil fish-remains from the Silurian rocks of the Lesmahagow district, which had been made by Messrs Macconochie and Tait, collectors to the Survey. I accordingly prepared a brief report on these fishes, which was included by the Director-General in hisSummary of Progressfor that year.

The collection was, however, considerably increased by additional work on the part of Mr Tait in the spring of the present year (1898). Many better and more complete specimens were procured, and I was able to define one new genus and species, which had previously been represented only by undeterminable fragments. The results gained by the examination of the entire collection I now propose, with Sir Archibald Geikie's sanction, to lay before this Society in detailed form.
IX.—On the Structure of the British Nemerteans, and some New British Annelids
Authors: M'Intosh W. Carmichael
Published: January 2013

The anatomy of the soft worms variously arranged under the Nemertean Order has, even in recent times, not been carried out with that completeness necessary for their thorough elucidation, a state of matters partly due to the confounding of the structure of one family with another, and predicating of the series what investigation has but proved in one group. Few British comparative anatomists have paid much attention to these animals; indeed, Dr George Johnston, Mr Harry Goodsir and Dr Thomas Williams, are the only three who have left researches of any moment on the subject. The observations of the first-mentioned naturalist were made many years ago, with the aid of inferior instruments, and, though conscientious enough, are very meagre and unsatisfactory; and those of Dr Williams, while also showing the defects just noted, bear evident traces of imagination. Mr H. Goodsir's interpretation of structures was, from his limited observations, likewise very erroneous. On the Continent, again, the investigators have been more numerous, and a long list of distinguished names attest the interest which the subject has received at their hands.
XXIII.—On the Internal Structure of Sigillaria elegans of Brongniart's “Histoire des végétaux fossiles”
Authors: Kidston Robert
Published: January 2013

Before giving a description of the specimen which forms the subject of this communication, it seems desirable that a brief summary of the literature dealing with the internal structure of Sigillaria, and some general remarks on the classification of the genus, should be given.

More for the purpose of convenience than on scientific grounds, the genus Sigillaria is usually divided into four groups. These groups were originally supposed by their founders to be of generic value, but experience has shown that the characters on which they were founded are more or less common to all four divisions, and in some cases the distinctive divisional characters even occur on the same specimen.
XXIV.—On the Structure of the Series of Line- and Band-Spectra
Authors: Halm J.
Published: January 2013

In a preliminary note read before the Society on July 4, 1904, I drew attention to the fact that a number of line-series, forming a group which includes the first series of Hydrogen, can be represented by an equation of the form

where v denotes the wave-frequency of any line of the series, v∞ that of the so-called “tail” of the series (m = ∞), and a1, b1 constants depending on the nature of the emitting substance; the frequencies of successive lines being obtained by substituting successive integers for m. We see at once that this equation is a generalisation of Balmek's formula, into which it is transformed by equating b1 to zero. In the same note I also pointed out the existence of another group represented by an equation of the same form, if (m + ½) is substituted for m. As a special case (b1 = 0) this group contains the second Hydrogen series discovered by Professor Pickering in the spectrum of ζ Puppis. Subsequent investigations convinced me, however, that, although a considerable number of line-series may be classified into these two groups, there are numerous instances where the more general formula

must be employed, in which μ represents various fractional numbers.