Present Memoir Research Articles

Ueber das System der Nagethiere; eine phylogenetische Studie

THIS separately published memoir, with its own pagination, is an excerpt from the Nova Acta of the Royal Society of Upsala. It is not too lengthy for the due treatment of the subject, and it is very copiously, illustrated. Dr. Tullberg has performed a useful piece of work in bringing together the bulk of what is known about the rodents into one comprehensive monograph; his proceeding might be well imitated for other orders, in view of enormous and increasing literature. The present memoir, however, is not a compilation in any sense of that word. The first part, which is rather more than one-half, consists of a series of descriptions of a large number of species of rodents examined by the author. These descriptions are quite full, and deal with external, as well as internal, characters. In some of the facts there detailed, we observe that the author is at variance with the statements of others. For example, he does not distinguish the two genera of Lemmings, which are a little apt to be confused, by the occurrence or non-occurrence of fur upon the soles of the feet. At this moment we are unable to confirm or to dispute his correction of current statements. The list of literature is an abundant one; but the author seems to have overlooked Mr. Beddard's paper upon the rodent brain, and Mr. Parson's account of the anatomy of the little known Cape Jumping Hare, Pedetes. Perhaps the MS. of the work was in type before the appearance of the last of these papers. The scheme of classification adopted by the author will not commend itself to all. The Sciuromorpha and Myomorpha of many are associated into a tribe, Sciurognathi, which is contrasted with the only other tribe of “simplicidentate” rodents, viz. Hystricognathi. The genus Pedetes, to which we have referred, is placed in the former, a view which we do not share. We would also follow Mr. Thomas and regard the genus Bathyergus as belonging to the Myomorpha, and not to the “porcupiny” rodents, where Dr. Tullberg places it. The criticisms, however, do not affect the general merits of this important contribution to our knowledge of the mammalia. Ueber das System der Nagethiere; eine phylogenetische Studie. Von Tycho Tullberg. Pp. v + 514; 56 plates. (Upsala: Berling, 1899.)

Scientific Serials

American Journal of Mathematics, vol. xxi. No. 4, October. —Memoir on the substitution-groups whose degree does not exceed eight, by Dr. G. A. Miller (pp. 287–338), is an exhaustive piece of work, amply furnished with bibliographical notes. The author's aim is to give enough of the general theory of group construction to find all the possible groups whose degree does not exceed eight without any tentative processes. The earliest work that gives considerable attention to substitution-groups is stated to be that by Ruffini, entitled “Teoria generale delle equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al quarto” (1799). The author has won his spurs in this field, and the present memoir shows a thorough mastery of his subject. There is a good table of contents appended.—On a class of equations of transformation, by J. Westknd. In this paper the writer discusses those equations whose roots are the n + 1 values of

VII. Mathematical contributions to the theory of evolution.— IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlation

(1) In earlier memoirs by one of the present authors, methods have been discussed for the calculation of the constants ( a ) of variation, normal or skew, ( b ) of correla­tion, when normal. The subject of skew correlation would now naturally present itself, but although several important conclusions with regard to skew correlation have been worked out, there are still difficulties which impede the completion of the memoir on that topic. Meanwhile Mr. G. U. Yule has shown that the constants of normal correlation are significant, if not completely descriptive, even in the case of skew correlation. It seems desirable to take, some what out of its natural order, the subject of the present memoir, partly because the formulæ involved have been once or twice cited and several times used in memoirs by one of the present writers, and partly because the need of such formulæ seems to have been disregarded by various authors in some what too readily drawing conclusions from statistical data. Differences in the constants of variation or of correlation have been not infrequently asserted to be significant or non-significant of class or of type, or of race differences, without a due investigation of whether those differences are, from the standpoint of mathematical statistics, greater or less than the probable errors of the differences. Not withstanding that every artificial or even random selection of a group out of a community changes not only the amount of variation, but the amount of correlation of the organs of its members as com pared with those of the primitive group, it has been supposed that correlation might be a racial constant, and the approximate constancy of coefficients of correlation of the same organs in allied species has been used as a valid argument. In the like manner differences in variation have been used as an argument for the activity of natural selection without a discussion of the probable errors of those differences. In dealing with variation and correlation we find the distribution described by certain curves or surfaces fully determined when certain constants are known. These are the so-called constants of variation and correlation, the number of which may run up from two to a very considerable figure in the case of a complex of organs. If we deal with a complex of organs in two groups containing, say, n and n ' individuals, we can only ascertain whether there is a significant or insignificant difference between those groups by measuring the extent to which the differences of corresponding constants exceed the probable errors of those differences. The probable error of a difference can at once be found by taking the square root of the sum of the squares of the probable errors of the quantities forming the difference. Hence the first step towards determining the significance of a group difference— i. e ., towards ascertaining whether it is really a class, race, or type difference— is to calculate the probable errors of the constants of variation and correlation of the individual groups. This will be the object of our first general theorem.

II. Studies in the morphology of spore-producing members.—III. Marattiaceæ

In the two Memoirs of this Series already published, I have dealt with the sporebearing members of the Equisetineæ, of the Lycopodineæ (including Psilotaceæ and Isoeteæ), and of the Ophioglossaceæ. We must now take up the case of the remaining class of Pteridophyta, viz., the Filicineæ. Of the two sub-classes into which it is divided, I propose to leave the Hydropterideae for the present on one side, and discuss first the sub-class of homosporous Ferns. In a previous paper (‘Annals of Botany,' vol. 5, p. 109), I have advanced what appear to me to be good reasons for the opinion that the Eusporangiate Ferns represent a more primitive type than the Leptosporangiate. Accordingly, I propose first to take into our detailed consideration the sori of the Marattiaceæ, and it is to them that the present Memoir will be devoted.

A RESEARCH UPON ANÆSTHESIA

THE CONCLUSIONS WHICH HAVE BEEN REACHED BY THE SERIES OF EXPERIMENTS RECORDED IN THE PRESENT MEMOIR ARE: First. Lowered arterial pressure has a comparatively feeble effect upon the respiration, but when the pressure falls sufficiently, respiratory depression does occur. Second. Even excessive lowering of blood pressure primarily stimulates the vaso-motor centre, the sensibility of the centre being evidently necessary to the automatic regulation of the circulation. Third. The circulation recovers itself more slowly after profound etherization than after a like chloroform narcosis. Fourth. It is possible for ether as well as chloroform to produce death some hours after the cessation of its administration, at a time when the cerebrum has long freed itself from distinct evidences of the narcotic, so that consciousness and intellectual action have been restored. In applying these conclusions to the subject of practical anaesthesia it is evident that the depression of the circulation produced by chloroform has effect upon the respiratory centres only when the pressure has fallen very low, and whilst it may be a factor in the production of respiratory failure during chloroformization, the failure must be chiefly due to the direct influence exercised by the drug upon the respiratory centres. Clinical experience shows that nausea and general depression are more pronounced after the use of ether than after the use of chloroform, a difference which is strongly insisted upon by the advocates of chloroform as an important agent in favor of that anaesthetic. Our research confirms clinical observation, and experimentally shows that the depression of the circulation produced by ether is more permanent than that caused by chloroform; the reason probably being the large amount of ether which is necessary to produce profound narcosis, with lowering of the arterial pressure; an amount so large that it can neither be burned up in the system nor yet eliminated in the time which would be necessary for the much smaller amount of chloroform to be gotten rid of after chloroformization.

VII. Mathematical contributions to the theory of evolution.—III. Regression, heredity, and panmixia

There are few branches of the Theory of Evolution which appear to the mathematical statistician so much in need of exact treatment as those of Regression, Heredity, and Panmixia. Round the notion of panmixia much obscurity has accumulated, owing to the want of precise definition and quantitative measurement. The problems of regression and heredity have been dealt with by Mr. Francis Galton in his epochmaking work on ‘Natural Inheritance,’ but, although he has shown exact methods of dealing, both experimentally and mathematically, with the problems of inheritance, it does not appear that mathematicians have hitherto developed his treatment, or that biologists and medical men have yet fully appreciated that he has really shown how many of the problems which perplex them may receive at any rate a partial answer. A considerable portion of the present memoir will be devoted to the expansion and fuller development of Mr. Galton’s ideas, particularly their application to the problem of bi-parental inheritance . At the same time I shall endeavour to point out how the results apply to some current biological and medical problems. In the first place, we must definitely free our minds, in the present state of our knowledge of the mechanism of inheritance and reproduction, of any hope of reaching a mathematical relation expressing the degree of correlation between individual parent and individual offspring. The causes in any individual case of inheritance are far too complex to admit of exact treatment; and up to the present the classification of the circumstances under which greater or less degrees of correlation between special groups of parents and offspring may be expected has made but little progress. This is largely owing to a certain prevalence of almost metaphysical speculation as to the causes of heredity, which has usurped the place of that careful collection and elaborate experiment by which alone sufficient data might have been accumulated, with a view to ultimately narrowing and specialising the circumstances under which correlation was measured. We must proceed from inheritance in the mass to inheritance in narrower and narrwoer classes, rather than attempt to build up general rules on the observation of individual instances. Shortly, we must proceed by the method of statistics, rather than by the consideration of typical cases. It may seem discouraging to the medical practitioner, with the problem before him of inheritance in a particular family, to be told that nothing but averages, means, and probabilities with regard to large classes can as yet be scientifically dealt with ; but the very nature of the distribution of variation, whether healthy or morhid, seems to indicate that we are dealing with that sphere of indefinitely numerous small causes, which in so many other instances has shown itself only amenable to the calculus of chance, and not to any analysis of the individual instance. On the other hand, the mathematical theory wall be of assistance to the medical man by answering, inter alia, in its discussion of regression the problem as to the average effect upon the offspring of given degrees of morbid variation in the parents. It may enable the physician, in many cases, to state a belief based on a high degree of probability, if it offers no ground for dogma in individual cases. One of the most noteworthy results of Mr. Francis Galton’s researches is his discovery of the mode in which a population actually reproduces itself by regression and fraternal variation. It is with some expansion and fuller mathematical treatment of these ideas that this memoir commences.

An Improved Method for the Microscopic Investigation of Crystals

A MEMOIR of considerable importance to all who are interested in the microscopic determination of the characters of crystals, is contributed by Prof. Klein to the Silzungsberichte of the Berlin Akademie der Wissenschaften for January 31, 1895. The two essential points of the communication are that a form of stage goniometer is described, which permits of the most complete examination of many of the principal zones of the crystal with one and the same setting of the crystal upon its holder, and that the crystal is immersed during the observations in a liquid whose refractive index is about the mean of the refractive indices of the crystal. The idea of the “Universaldrehapparat,” as the new stage goniometer is termed, appears to have suggested itself almost simultaneously to Prof. Klein and to Herr von Federow, for the former described an earlier form of it in the Sitzungsberichte of April 1891, while the latter published a description of an “Universaltischen” for the microscope in the Zeitschrift für Krystallographie of May in the same year. Herr von Federow had previously contributed to the Zeitschrift a remarkable memoir concerning a theodolitic universal goniometer, and the application of the principle of that instrument to the microscope goniometer followed naturally therefrom. The present memoir of Prof. Klein affords so admirable a description of the improved instrument, which has been constructed for him by the well-known Berlin crystallographical optician, Herr Fuess, and likewise of the mode of employing it in connection with the immersion method, that readers of NATURE may find a brief account of it not uninteresting. Unfortunately this description cannot well be illustrated, as Prof. Klein's illustrations are photographic reproductions which are unsuitable for further reproduction.

XVI.—On the Fossil Plants of the Kilmarnock, Galston, and Kilwinning Coal Fields, Ayrshire

The tract of land embraced in the area from which the fossils have been derived, that form the subject of the present Memoir, extends in an easterly direction from Saltcoats to Newmilns, a distance of about 19 miles. At both extremities, the Coal Measures narrow down to under half a mile wide at Saltcoats, and about a mile broad at Newmilns. The greatest width is found towards the centre of the field, where in a northeast and south-west direction it is over 12 miles broad.

V.—Antiquities of the Bronze Age found in the Heathery Burn Cave, county Durham

The purpose of the present memoir is to place on record an account of what, in many respects, is one of the most valuable discoveries ever made in Britain of weapons, implements, ornaments, and other things belonging to the Bronze Age. Discoveries of objects of that period have usually consisted of a single article or more accidentally lost, of hoards of founders or vendors, secreted for one reason or another, and of the various sepulchral remains which have been found in barrows, cairns, or other places of burial. These all are of greater or less importance as illustrating the condition and habits of life of the people of that time, and the stage of cultivation and civilization to which they had attained. But the discovery with which this account is concerned possesses a very much higher value than that of any hoard of however great a number of articles, or of any series of objects which relate to a section only of daily life and occupation. It gives us, though perhaps in a lesser degree, much the same information that the lake dwellings of Switzerland and other countries have so abundantly supplied. “We possess, in fact, in the discovery about to be described a record in the very things themselves of the entire equipment of a family as it was possessed by them when they perished in their home, as I believe, by a sudden and unforseen catastrophe.

The Development of the Genital Organs, Ovoid Gland, Axial and Aboral Sinuses in Am-phiura squamata; together with some Remarks on Ludwig’s Haemal System in this Ophiurid

ABSTRACT The work which forms the subject of the present memoir was carried on at the Zoological Station at Naples during the six months from October, 1891, till April, 1892.

Art. XV.—The Mines of the Northern Etbai or of Northern Æthiopia. With a Map, Water-colour Drawings and Photographs by the Scientific Expedition to the Northern Etbai

By the Scientific Expedition to the Northern Etbai, despatched by his Highness the Khedive in the beginning of the year, that part of the eastern desert of Egypt which lies south of a line between Kina and Kosair and reaches rather below the twenty-fourth parallel of latitude, was rapidly examined and surveyed. The map is in the hands of the engraver of the Royal Geographical Society; the geology exhibited in a map and sections is before the Geological Society; and a map of the antiquities is attached to the present memoir. The country embraces an area of 23,000 square miles of mountain and desert, and is called by the inhabitants the Northern Etbai.

The Development of the Oviduct in the Frog

ABSTRACT The investigation which forms the subject of the present memoir was commenced in July, 1890, at Mr. Sedgwick’s suggestion. A collection of tadpoles, which were preserved in the Morphological Laboratory, Cambridge, was first examined without result. None of them showed any trace of the oviduct, though in some cases both pairs of limbs were well developed. Through the kindness of Mr. Sedgwick I was enabled to procure a considerable number of Frogs, in which the tail was being absorbed or had just vanished; and amongst these I found all the necessary stages for my work.

II. Memoir on the symmetrical functions of the roots of systems of equations

The object of the present memoir is the extension to systems of algebraical quantities of the new theory of symmetric functions which has been developed by the author in regard to a single system in Volume 11 and succeeding volumes of the ‘American Journal of Mathematics.’ In the theory of the single system the conceptions and symbolism are to a large extent arithmetical, and are based upon the properties of single integral numbers and their partitions into single integral parts. In this sense the theory may be regarded as being unipartite. In the present generalisation to the case of m systems of quantities the fundamental ideas proceed, not from a single number, but from a collection of m single numbers. In regard to number, weight, degree, part, and suffix, the collection of m numbers invariably replaces the single number of the theory of the single system. In this view the theory of the m systems is m -partite.

The Fossil Mammals of North American1

THIS important contribution to our knowledge of the extinct mammals of the United States is the joint production of Profs. W. B. Scott and H. F. Osborn, of the Geological Museum at Princeton College, to whom we are already indebted for much valuable work on the subject. The present memoir is of more than ordinary importance, since the authors have endeavoured to complete our knowledge of forms already more or less fully described, rather than to add fresh burdens to the memory by recording a host of so-called new species and genera founded upon specimens which are not sufficiently characteristic to prove their distinctness from forms already described. Indeed, they have taken the opposite course, and endeavoured to show how the number of such species and genera may be reduced; not shrinking, as the manner of some is, from relegating when necessary some of the terms proposed by themselves to the rank of synonyms. This line of work, we are assured, is the one now urgently called for, as it is almost certain that the number of names which have been already proposed must, if properly defined and correlated, really include by far the greater proportion of the animals of the better known formations.

The Labyrinthodonts of Swabia2

SWABIA, it need scarcely be said, lies to the southeast of Stuttgart—the classic ground of the Triassic Labyrinthodonts of Germany—and since it contains the same Triassic deposits, we should naturally expect to find therein the same species of this group of Amphibians. The present memoir, remarkable alike for the splendid plates with which it is illustrated, and for the care with which the specimens have been described, is devoted to making known to the scientific world the magnificent collection of Labyrinthodont remains which have been from time to time obtained from the Swabian and Würtemberg deposits, and are now preserved in the Museums at Stuttgart, Tübingen, and Munich. Of the seventeen plates with which this work is illustrated, a large proportion are folded ones of very considerable size, while all are especially noticeable for their beauty of execution. They appear to have been printed by some special process from photographs, the finely-preserved specimens of skulls standing out with wonderful clearness from a black background. Even more noteworthy than the unrivalled execution of the plates is the perfection and beauty of the specimens themselves; and we would especially direct attention to the magnificent skull of Metopias, represented in plates xii. and xiii. of the work before us, as being the finest Labyrinthodont specimen that has ever come under our notice.

Some Results of Archean Studies

Conflicts of Opinion in this Field The present memoir is simply a synopsis of facts observed by the author, with a few obvious inferences, touching the structure and classification of the older rocks of the Northwest. Citations will be made from other investigators where the facts or opinions appear to throw important light on the problems which the author has studied. The motive for offering this presentation of the results of personal studies exists in the vague and conflicting state of opinion respecting the older rocks. This concerns not only their genesis and geological history, but their constitution and characters and even their sequence and mode of mechanical relation to each other. On the one hand, there are geologists of reputation who maintain that most granitic and gneissic rocks have originated directly from a state of molten fluidity; and this view is extended even to the so-called crystalline schists and . . .

V. On the organisation of the fossil plants of the coal-measures.—Part XVI

During the last twenty years many single examples of vegetable forms from Carboniferous rocks have come into my possession, which were obviously different from any hitherto described. But I have carefully abstained from publishing such specimens until examples of each multiplied in my cabinet, enabling me to determine how far their apparently distinctive features were constant, and not merely individual, variations. Many such imperfectly known forms still occupy a drawer in my cabinet; but in the present Memoir I propose to describe several of which examples have accumulated so far as to enable me to speak with reasonable certainty as to their specific distinctiveness. In several of my previous memoirs I have from time to time called attention to a curious development of a medulla in the centre of the axial vascular bundle, especially of the Lepidodendra. This was especially done in the Memoir, Part III., when describing the Burntisland Lepidodendron , to which, as was also the case with the Arran form (Part X.), I have not yet ventured to give a specific name.

II. A class of functional invariants

The investigations herein contained are indirectly connected with some results in an earlier memoir. In that memoir functions called quotient-derivatives are obtained in the form of certain combinations of differential coefficients of a quantity y dependent on a single independent variable x ; and they are there shown to possess the property of invariance for isolated homographic transformations of the dependent and the independent variables. It is evident, however, from their form that they do not constitute the complete aggregate of irreducible invariants for the case of a single independent variable; and the deduction of this aggregate and an investigation of the relation in which they stand to a particular class of reciprocants were made in a subsequent paper. The present memoir is a continuation of the theory of functional invariants, the invariants herein considered being constituted by combinations of the differential coefficients of a function of more than one independent variable which are such that, when the independent variables are transformed, each combination is reproduced save as to a factor depending on the transformations to which the variables are subjected. The transformations, in the case of which any detailed results are given, are of the general homographic type; and the investigations are limited to invariantive derivatives of a function of two independent variables only, a limitation introduced partly for the sake of conciseness. The characteristic properties, such as the symmetry of the invariants and the forms of the simultaneous linear partial differential equations satisfied by them, can in the case of more than two independent variables be inferred from the properties actually given; but many of the deductions made are necessarily proper to functions of only two independent variables. In the matter of notation it is convenient here to state that the independent variables are denoted by x and y , and the dependent variable by The general differential coefficient ∂ m+n z/∂x m ∂y n is represented by z m, n ; but frequently the following modifications for the notation of particular coefficients are made, viz.

On a Tornaria found in British Seas

Before 1888 no specimen of Tornaria, the well-known pelagic larva of Balanoglossus, had been taken off the English Coast. But on August 9th of the past year Mr. Weldon, using the surface net near the Eddystone Lighthouse, took several young specimens of Tornaria, and subsequently the same gentleman, during a cruise of a week's duration towards the end of August, captured many larger and more mature specimens of the same larva. Other specimens were taken by us up to September 21st, and in the month of August, Mr. Rupert Vallentin found several specimens in the vicinity of Falmouth.The specimens taken on these occasions form the subject of the present memoir, and their anatomy is detailed at some length, both because of the interest attached to a form bitherto unknown to England, and because it is in some respects of morphological importance.The specimens taken by us came from the offing, and were not taken within four miles of theshore; Mr. Vallentin's Tornaria were found close to the shore at Falmouth. As he was able to bring his back alive and preserve them at leisure in his laboratory, they are better preserved than those taken by us, since we were obliged to preserve our catch in a somewhatrough manner out at sea. An examination of Mr. Vallentin's specimens leaves me no doubt that the larva is Tornaria Kröohnii, aspecies found in the Mediterranean. The different forms of Tornariahave not been with certainty referred to their adult forms, but T. Kröohnii must belong to one of the Mediterranean species of Balanoglossus, that is to say, to B. Kowalevsltii, B. minutus, or B. claviger, species which have not hitherto been recorded from the English Channel, unless we suppose that the larva of B. salmoneus v. sarniensis, which occurs in the Channel Islands andat Roscoff, is identical with Tornaria Kröohnii.

6. Investigations on the Malpighian Tubes and the “Hepatic Cells” of the Araneina; and also on the Diverticula of the Asteridea

The present memoir is a continuation of those already published by one of us, on the physiology of the Invertebrata.