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TRANSACTIONS OF THE ROYAL IRISH ACA. DEMY. Vols. XVII. 3 parts; XVIII., part 1: XIX.. part 2; XXII. (Polite Literature), 4 parts; XXIV., 37 Parts; XXV. (Science), parts 1-3, 5-20; XXVI. (Science), parts 1-13, 17 to 22; XXVII., 8 parts. 1833-86. 50s.

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Vol. XXVII.-New Series, Vol. VII.-Part III. APRIL, 1893.
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1.-John Struthers, M.D. Rudimentary Hind-Limb of Balanpien
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3. Charles J. Cullingworth, M.D. Anatomy of Hymen and "Posterir Commissure of the Vulva."

4.-B. C. A. Windle, M.D. Myology of Anencephalous Fetus. 5-E. W. Carlier, M.D. Histology of Hedgehog. (Plate XXI.) 6.-D. Berry Hart. M.D., and G. Lovell Gulland, M.D. Advanced Pregnancy in Macacus Rhesus. (Plate XXII.)

7-A. Eichholz, B. A. Morphology of Limb Arteries in Vertebrates. 8.-J. Tillie, M.D. Arrow Poison from New Granada.

9.-D. Hepburn, M.D. Adductor Muscles of Thumb and Great Toe 10.-J. Jackson Clarke, M.B. Temporal Bone, chiefly in Childho d 11.-B. C. A. Windle, M. D. Report on Recent Teratological Literatur 12. Sir W. Turner. Phrenic Nerve Receiving a Root of Origin fr Descendens Hypoglossi.

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By G. JOHNSTONE STONEY, M. A., D.Sc., F.R.S. Suggestion as to a Possib'e Source of the Energy Required for the Life of Bacilli, and as to the Cause of their Small Size. Price 62 No. 13.

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A Treatise on the Mathematical Theory of Elasticity. By A. E. H. Love, M.A., Fellow and Lecturer of St. John's College, Cambridge. Vol. I. (Cambridge: University Press, 1892.)


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R. LOVE'S treatise is the necessary complement to Todhunter and Pearson's History of the Theory of Elasticity," in which an abstract is given of all the most important original memoirs bearing on this subject, arranged in historical order.

But the student who wishes to make himself acquainted with the works of these original authorities, by the guidance of Todhunter and Pearson's History, will find the necessity of an acquaintance with Mr. Love's work as an introduction to the elements and to the notation of the subject of elasticity.

Mr. Love has prepared an elegant and modern artillery of analysis; and he is not afraid to fire off his guns. To pursue the simile, there is no fear of the subject being obscured in the smoke of his own guns in these days of smokeless gunpowder.

The size of the book is kept within reasonable dimensions, compared with the scale of a continental treatise, by leaving the heaviest parts of the analysis as exercises to be worked out by the trained mathematical student, to whom the work is addressed.

The author says in the preface, "I have not thought it advisable to introduce collections of examples for practice." But such collections do not exist, and the author would find it as formidable a task as that he has already carried out to attempt to construct the examples himself. In the present state of his subject any really novel example would be worthy to take rank as a new and independent theorem.

The examples which we see around us of the physical and industrial applications of the Theory of Elasticity are the best check in existence to keep the subject from becoming a mere development of pure mathematics, with such generalisations as to space of n dimensions, and based upon physical laws adopted merely because of the analytical elegance they confer, quite apart from any experimental verification.

The first five chapters are occupied with the general theory, including the analysis of strain and stress, stressstrain relations, the strength of materials, and a number of general theorems. In the analysis of strain the method of Thomson and Tait's "Natural Philosophy" has been followed, beginning with the geometrical and algebraical theory of finite homogeneous strain, deducing thence the physical state of infinitesimal strain. Hooke's law, made such a mystery of by its inventor, now becomes a necessary consequence of the expansion by Taylor's theorem of the stresses as functions of the displacements and strains, neglecting power above the first or second; and the law receives ample experimental justification in the observed isochronism of the small vibrations of elastic bodies, as exhibited by the musical notes they give out.

In the treatment of the ben ting of a beam and the torsion of acylinder in Chapter VI., Saint-Venant's method

has been followed, and the warping and distortion of the cross-section carefully investigated and illustrated in fig. 10, p. 156.

This warping effect is well known to engineers, though hitherto generally ignored in the mathematical treatment, as impairing the sweet simplicity of a bending moment and consequent proportional curvature resulting only from the extension and compression of the fibres, thus ignoring the shearing stresses called into play. We can now begin to perceive the reason why a beam is so much stronger and stiffer than it ought to be according to the ancient theory.

In the investigation of the torsion of a cylinder, where cross-section is a rectangle, the analysis of Thomson and Tait has been closely adhered to. Dr. Ferrers, the Master of Gonville and Caius College, has made this analysis more complete and symmetrical, and has exhibited the hydrodynamical analogies more clearly, by employing a pair of Fourier series, one proceeding by sines and cosines of multiples of x, and the other of y; each series representing separately the motion or displacement corresponding to a simple shear of the rectangular section. The elliptic function interpretation of this pair of series, in which the corresponding moduli are obviously complementary, is very interesting, but has not been pursued by Mr. Love.

Now that Prof. Karl Pearson has dedicated the first part of the second volume of the History to the "Memory of Saint-Venant," the political cloud, vaguely described in M. Bertrand's recent éloge of Chasles, which overshadowed Saint-Venant's official career, is clearing off, and full tribute is beginning to be paid in France to the great advances due to him.

Lamé, too, like Saint-Venant, appears to have lived in official neglect, although his method of Curvilinear Coordinates, expounded in Chapter VII., has been a powerful analytical engine for the solution of elastical problems, and his "Théorie de l'Élasticité" is a standard text-book to the pre sent day.

The solution of the elastic deformation of a sphere, tre ated in Chapter X., is also due to Lamé. Mr. Love applies his analysis to the consideration of the effect of a flaw in the shape of a spherical cavity, and shows that in this case the engineer's factor of safety of 2 is the theoretically correct factor.

The most important application on a large scale of the analysis of the elastic deformation of a sphere is the investigation of the effective rigidity of the earth, considered as an elastic solid, under the action of its own gravitation, and slightly disturbed by the rotation and the tide-producing forces. Elaborate calculations and observations have been carried out by Prof. G. H. Darwin ; if we could observe and measure the bodily tides in the earth, an estimate of its rigidity could be obtained. Mr. Love gives the numerical results corresponding to mean rigidities equal to those of steel and glass.

Mr. Chree's valuable investigations of the strain produced by rotation in an elastic circular disc, in a sphere or an ellipsoid, are introduced here, and receive careful analysis and interpretation.

Chapter XI. treats of the vibrations of a sphere. The free vibrations have been completely worked out by Prof. Lamb. In the forced vibrations the lag or change

of phase is the interesting subject of inquiry, as showing to what extent the equilibrium theory" of the bodily tides of the earth, considered in the preceding chapter, can be adopted as a working theory.

Lord Kelvin has shown how the inertia of a pendulum appears reversed in sign if the point of support is actuated by a vertical vibration, when the forced and free periods are as two to one; but when the periods are made in the ratio of three or four to one, the equilibrium theory can be adopted. This principle has been employed recently by Sarrau and Vieille in the measurement of powder pressures by means of spring gauges; the free period of the spring is so adjusted in comparison with the period of the applied pressure, so that the vibrations of the spring do not make their appearance, and the indications of the gauge are the same as those for an equal statical pressure, steadily applied.

Valuable work in the discussion of particular problems of a somewhat general nature has been carried out by the late Prof. Belti, of Pisa, and continued by his disciple Cerruti; particularly also by M. Boussinesq, in his theory of "local perturbations" in an elastic solid bounded by a plane, as illustrated, for instance, in the deflection produced in a sheet of ice by a man standing on it; these questions occupy Chapters VIII. and IX.

The applications of conjugate functions in Chapter XII. introduce some interesting problems. The book The book concludes with the consideration of an elliptic cylinder, turned through a small angle. Something appears wanting here, as the balancing couples on the interior and exterior confocal ellipses are not brought into evidence. When the exterior ellipse becomes indefinitely large the stresses over it are evanescent, but their resultant is a finite couple. So, too, when the inner ellipse becomes the line joining the foci; in this case the Jacobian h becomes infinite at the centre, and the displacements u and

at this point require closer investigation.

It is unfortunate, as Maxwell remarked, that we have no space functions corresponding to the conjugate functions of a plane. But by the rotation of these conjugate plane curves about an axis, Waugerin has obtained a system of space co-ordinates, suitable for application to certain surfaces of revolution, and he, Mr. Hicks, and Mr. W. D. Niven, have worked out the analysis completely for certain quadric surfaces, cones, and tores. In the questions considered in this first volume the forces which produce the elastic displacements are of moderate amount, so that the proportionality of stress to strain may be taken as true, and they act as distributed forces throughout the solid, such as gravity and the forces of inertia introduced by vibrations.

Mr. Love measures these forces per unit mass, and not per unit volume, as in Thomson and Tait's "Natural Philosophy," so that the component forces appear as pX, pY, pZ, qualified by p, the density as a factor.

Cases might arise, however, say in a dynamo, where some of the forces, the forces of inertia and gravity, would be measured per unit mass, and the others, the electromagnetic forces, per unit volume; for this reason the Thomson and Tait method of measurement appears preferable, as the factor p can be inserted where required. The difficulties of constructing a rational theory will

turn up in the second volume, when the question of elastic equilibrium of a lamina has to be considere in which the stresses are due to an applied finite press on one side of the lamina. Mr. Basset has performed. valuable service in pointing out the insufficiency of preceding methods for constructing a theory of suct important practical question as the collapse of b flues (Phil. Mag., September, 1892), and he might have added of the Bourdon gauge. We await with interest Mr. Love's contribution to this delicate and baffling pr of the Theory of Elasticity.

In the preface of the "Treatise on Solid Geometr by Frost and Wolstenholme, the authors, after thanking the proof-readers for their trouble, conclude by "expresing their regret that they have not escaped a large numbe of errors, which it will be punishment enough to them: see tabulated in an adjoining page."

Where the critic has also been a proof-reader he la himself open to this ambiguous acknowledgment, if he points out any misprints; but we are pleased to find thi: the present volume, on careful re-examination, appear to be very clearly and correctly printed.


BIOLOGY AND THE MEDICAL STUDENT. Text-book of Elementary Biology. Introductory Science Text-book Series. By H. J. Campbell, M.D. (London Swan Sonnenschein and Co. New York: Macmillan and Co., 1893.)


HIS volume of 266 pages octavo is an ultra-elementary one, subdivided into a first part of 155 pages, which deals with generalities of plant and anima. morphology and physiology, together with the principles of classification, and into a second of 111 pages devoted to the consideration of certain type organisms. With the exception of the dog-fish, which the author dismisses in four short pages, the said types are those of the examination syllabus of the Conjoint Board of the Royal Colleges of Physicians and Surgeons; and the fact that the book is the first one which has been written up to that standard invests it with a special interest. It is illustrated by 136 borrowed woodcuts, some of which are very poor and antiquated, while others are defective. Its author shows himself to be possessed of a considerable power of discretion, and his book is clear and attractive in style. It is, however, a pure comp.lation, for the most part from well-known text-books, as is only too apparent in certain gross errors transcribed, for example, that of the assertion that the Monotreme brains are "not convoluted"; its only novelty lies in the judicious introduction of concise and useful historica résumés, giving the dates, names, and achievements of epoch-making investigators. Trivial errors abound, and controversial matters of the moment are here and there dogmatically introduced, as though finally established; to wit (a) the allusion (pp. 39 and 145) to the ectoblastic origin of the segmental duct, which, so far as it may be to-day regarded as an undisputed fact, rests upon Van Wijhe's discovery of a dividing nucleus connecting it with the parent epiderma, and (3) the assumed conjugative reproduction of Amoeba (p. 160). Conversely

it is refreshing to find that in this, a most elementary work, the pulmonary sacs of spiders are alluded to as "fantracheæ" (p. 105) and the lung hooks of scorpions as "chambered trachea" (p. 112). The author distinguishes between more general matter printed in large type, and more detailed set up in smaller, pointing out in his preface that "in reading the book for the first time the student is advised . . . to read only" the former. The fact that in some cases a knowledge of the details in question is indispensable for the appreciation of the broader statements laid down for first reading, somewhat detracts from the utility of the method employed; and in at least one case (two top paragraphs of p. 7) the sentences are so worded that the exclusion of the smaller type involves error and confusion of ideas. One of the most characteristic features of the work is its marked brevity. "A general review of the Mammalia" is essayed in eleven pages, while the " Infusoria" are despatched in one line and a word (but a cross reference to the Vorticella described in full in a subsequent chapter). No wonder then, that for want of due qualification, descriptions of things and conditions in reality individual and special should serve for those general and of broad application (as, for example, the assertion that the spiders as an order have an unsegmented cephalo-thorax, and that "all cells resemble each other when they are first formed "), and that negative characters should be occasionally employed for diagnostic purposes, to the exclusion of others of a positive and more forcible nature but requiring a more detailed declaration (cf. the treatment of the limbs of Primates). Some of the more lengthy descriptions are, nevertheless, inadequate and unfortunate, notably that of the sponges, which are defined (p. 85) as "the connecting link between unicellular animals on the one hand and multicellular animals on the other," and whose complex structure is illustrated by a diagram unlike anything in nature. In dealing with the vertebrate reproductive system and cloaca, the author has so mixed up details and definitions that his statements are misleading, contradictory, and in part erroneous (cf. pp. 155 and 264, and 135, 153, 252, and 256). In dealing with the lower plants, the existence of sieve-tubes in the marine algæ (Macrocystis) might with advantage be alluded to as an all-important elementary fact, and the definitions of the Thallophyta and the Pteridophyta might well be modified accordingly. Minor errors and deficiencies, such as the implied absence of sensory cells in the hydra, the too-frequent employment of the adjective "horny " in allusion to structures having no such constitution (cf. especially pp. 102 and 192), the confusion between the "wing' and patagium, and the definition of important orders and families in terms which in their scantiness convey no adequate meaning, will doubtless be duly corrected and made good. This notwithstanding, the book has many good points, and its clearness of style is a high recommendation; its greater subdivision, if amplified and supplemented by way of introduction of great groups not even named in the present edition (e.g. the Brachiopoda and Polyzoa), might be worked up into a generally serviceable volume.

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The lesser subdivision of the volume chiefly merits attention for having been avowedly compiled for the



examinees of the conjoint medical board above alluded The programme is as follows:---Amoeba (5 pp.), Yeast Plant (3 pp.), Protococcus and Gloeocapsa (6 pp.), Bacteria (6 pp.), Vorticella (7 pp.), Gregarinæ (5 pp.), Hydra (9 pp.), the Liver Fluke (11 pp.), Tape Worms (21 pp.), Nematoda (12 pp.), the Leech (11 pp), General Review of the Mammalia (11 pp.) 107 pp. in all, of which 66 are devoted to animal parasites-a veritable diet of worms! We know not upon what principles this régime has been prescribed; but when it is considered that the doctrine of phagocytosis, which has of recent years done more than all else to advance and revolutionise medical science, is the direct outcome of comparative biological inquiry, and that its founder is a non-medical man, we confess to a feeling of astonishment. The programme itself savours of the "Technical Education " bogie of our times, than which no greater deception has ever existed. The principles of an elementary scientific training must be the same for the medical man and the mechanician, the philosopher and the plumber. Natural laws and ultimate principles are for all time and unalterable; and experience shows that the medical student whose elementary biological training embraces a comprehensive structural analysis of some small mammal (if of no lower vertebrate in addition) together with the principles of comparative morphology, working from the tree thus surveyed as a whole through the scattered leaves of his surgical, anatomy, emerges a thinking man, rather than a mere pedant, as has been so often the case in the past. The chief value of biological science to the medical student is unquestionably educational. To sink this all-important aspect of his scientific training, in preference for a mere dabbling in helminthology, as we venture to think has been done in the case before us, is to neglect one of the surest safeguards for the future, and to ignore the dictates of common sense based upon experience. The attitude is indicative of a retrogressive return to the days when medicine was the only channel of approach to science, and to that order of things, the lingering relicts of which, still hovering over certain of our English-speaking Universities, to-day bar the way to the employment of all but medical graduates as responsible teachers of science in certain of their medical departments. The time is fast dawning, when in London and other great centres, the preliminary scientific training of the medical student must of necessity be imparted either in central institutions devoted to the purpose, or in no less special ones attached to the medical schools themselves. This work, if it is to be done properly and to the credit of the nation, must clearly be entrusted to trained specialists, whose business it shall be to keep abreast of the times; and by such men the text-books of the future will have to be written. The principles which have called forth the volume now under review, on the other hand, favour a professional monopoly, under which the medical practitioner will tend to usurp the functions of the trained non-medical educationalist, to the detriment of his own calling and the reversion to a well-nigh obsolete constitution. Indications of the exercise of this monopoly are abroad; but we shall be much surprised if, in the bidding for the medical student now rife, it obtains a foothold.

G. B. H.

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