is indeed a fundamental difference between the two cases. The colleges of the Victoria University are widely separated, and appeal to the strong local feeling of powerful and independent districts. A generous rivalry may therefore exist between them without ill result. Each should be left, as they have been left, to work out their own success with as little external interference as possible. "It is sometimes argued that because the population of London largely exceeds that even of such districts as Lancashire or the West Riding, there ought to be room within it for the separate and independent institutions in which teaching of the highest type could be provided. This view ignores the importance of geographical separation, and unduly exalts that of the numerical magnitude of the population whose wants be met. If Manchester and Leeds were on are to opposite sides of the Irwell or the Aire, if they were connected by an elaborate system of overground and underground railways, then it would be more economical to concentrate, in one or the other, the higher teaching which must now perforce be given in both. The loss of time to the students in reaching the scene of their daily labours would be but imperceptibly increased, while the prestige of the colleges, great as it already is, their claims on the State, strong as they already are, would be enhanced in a proportion greater than that calculated by merely adding their separate reputations and resources. In a city of the size of London it is desirable to multiply institutions in which preparatory work of all sorts is undertaken, but I think it may be assumed as almost axiomatic that it is impossible, at present at all events, to create in one town more than one institution in which laboratories and lecture rooms and the other machinery of scientific instruction shall be provided on the large scale which the elaboration of the highest modern scientific teaching demands. In London, then, the teachers in almost all existing institutions feel the necessity for a combination of forces. They have expressed themselves as willing to be formed into battalions and regiments rather than to be left to carry on their work as isolated companies. I will not dwell on the fact that this desire could only be declared by men who were willing to risk their personal position for the public good, but I want you to observe how in this case also the work of decentralization, which began with the foundation of University College, London, has been followed and would have been far more effective had it been accompanied by a corresponding manifestation of centralizing force." With these views we heartily agree. If ever we are to have in London laboratories such as those which are to be found in Germany, it can only be if the higher teaching in each subject is concentrated in some one great central institution, and if rival colleges are allowed to combine their forces for the public good, instead of being compelled as at present to fritter them in suicidal competition. Taking it for granted that all will admit that such an ideal would be the best if it could be realized, we believe that the possibility of its realization is chiefly doubted on two grounds, to neither of which any real importance is to be attached. It has been supposed, in the first place, that those who advocate a policy of union among the London colleges think that this union must be carried out in all particulars immediately; and secondly that in order to secure this end it must be carried out by compulsion, even if the practical confiscation of the property of the existing colleges were necessary. It need hardly be said that such a statement is a parody of the views of men who have had at least as much experience as their critics (of the tone of mind of the governing bodies of great educational institutions, and who therefore would be the first to anticipate the difficulties which such demands would inevitably 'cause, No responsible body has, as far as we are aware, advocated more than the establishment of a University on a basis which would permit the union of the various colleges, in whose buildings the University teaching might at first be carried on, if the colleges were themselves willing that such a union should be effected. The advocates of union have all along been striving, not to attain an immediate and complete realization of their ideal University of London, but to prevent the Charter being drawn so as to make that realization impossible. It cannot be beyond the limits of human skill to frame a scheme which shall offer every inducement to the London colleges to effect an immediate fusion, and shall further provide that any approximation which may at first take place shall easily become closer in the future. The Victoria University does not consist of competing colleges. A federal University of London would consis of colleges which from their mere local proximity would. whether they willed it or no, be necessarily antagonistic Unless the Commissioners fairly grasp this fact and realize that they have it in their power to lay down the lines on which a great institution shall be founded in close connection with the State, which shall concentrate under one central directing power all the educational efforts which are at present partly wasted through wa of joint action, they will have failed to make the most o a great opportunity, and will have frittered the force which, if allowed free play, are competent to do for the higher education of London all that the best friends o London can desire. THE STUDY OF ANIMAL LIFE. The Study of Animal Life. By J. Arthu Thomso M.A., F.RS.E. "University Extension Manuals (London: Murray, 1892.) THE HE chief aim of an "Extension Manual" as o "Extension lectures" is to stimulate interest and t spread information. In natural science, at any rate, it impracticable through the medium of either Extension lectures or Extension manuals, to give that training whic the student, be he specialist or generalist, can obtain on by practical work, aided by practical instruc tion. E there are a great number of people, some already busi engaged, others on the threshold of their life's work, wh possess some interest in, and some information abou those matters, with the study of which scientific men ar occupied. For them Extension lectures and manua are a great boon; and to them Mr. Thomson's work "The Study of Animal Life" may be cordially recom mended. We trust it will stimulate them, as he woul desire, to become themselves observers. The work is divided into four parts, of which the first, entitled "The Everyday Life of Animals," deals with the wealth of life, the web of life, the struggle of life, the shifts for a living, the social life of animals, the domestic life of animals, and the industries of animals. The second part, on The Powers of Life," contributed by Mr. Norman Wyld, treats of vitality, the divided labours of the body, and instinct. The third par describes "The Forms of Animal Life" and includes chapters on the life-history of animals, and their past history as read in the geological record. The fourth and last part treats of "The Evolution of Animal Life” and, besides a discussion of the influence of habits and surroundings, and of heredity, gives a sketch of the evolution of evolution theories. Appendices on the relation of animal life to human life, and on some of the best books on animal life bring the work to a conclusion. The The general arrangement of the subject-matter is, as will be seen by the above summary, well and carefully thought out, and the facts given in elucidation of the varied tendencies of organic development are skilfully marshalled and are derived from the most trustworthy sources. information given is therefore accurate and up to date. The only suggestion we have to offer in this connection is that a little more selective elimination might have been exercised. Some facts are given in so terse and condensed a form that no one but a zoologist could appreciate their value. If a considerable number of these had been struck out and the space thus gained had been utilized in expanding those that remained, the Extensionee would have been the gainer. "The Zoological Summary of the Animal Kingdom" (pp. 210-272) might by some such process have been replaced by a sketch with more life and go in it. As it stands it will, by many readers, be gracefully skipped. In such a work style is an important element. Here Mr. Thomson is often exceedingly happy. He has imagination and a feeling for the poetic aspect of nature. But his imagination and poetry need at times just a little chastening. When he tells us that in birds "the breathing powers are perfected and economized by a set of balloons around the lungs," and that their brains are not wrinkled with thought like that of mammals"; when he speaks of the sponge as "a Venice-like city of cells"; when he describes the ciliated cells of the windpipe as "lashed cells," or the embryonic membranes as "birthrobes," and when he says that in ponds subject to drought the organism often "sweats off a protective sheath which is not a shroud, and waits until the rain refreshes the pools"; in these and sundry other cases of which these are samples, one may question whether the expressions which we have underlined are justified either by special elegancy or by real helpfulness to a beginner. And this we say in no spirit of hypercriticism, but as desirous of iding the author in what is by no means an easy ask. Somewhat deeper would be our criticism of sundry expressions which are of essentially human implication and which in our opinion should not lightly be applied to animal activities. Much is said of the "love" of animals for their mates when some such phrase as "sexual appetence" would be more appropriate. For example, concerning ants we read :-" After this midsummer day's delight of love death awaits many, and sometimes most." And in the analysis of the forms of struggle for existence, we have the "struggle between rivals in love." Again, of the cuckoo it is said that, "in spite of the poets, the note of this blessed bird' must be regarded as suggestive of sin"! And again, "It is not quite correct to say that the cuckoo-mother is immoral because she shirks the duties of maternity; it is rather that she puts her young out to nurse because she is immoral." It is true that Mr. Thomson adds this footnote:-" The student will notice that I have occasionally used words which are not strictly accurate. I may therefore say definitely that I do not believe that we are warranted in crediting animals with moral, æsthetic, or, indeed, any conceptions." We are glad to be thus assured. But why implant notions in the text which have to be eradicated in a footnote? Does not Mr. Thomson know how easy it is to sow tares and how difficult to root them out? Mr. Norman Wyld's chapter on "Instinct" is short, but quite to the point. We hope that he may further observe and experiment in the field of comparative psychology, for he is fully alive to the peculiar difficulties of the subject, and there is a wide field before him in which the scientific workers are none too many. In criticizing Mr. Lloyd Morgan's definition of instincts as "oft-recurring or essential to the continuance of the species," Mr. Wyld says:-"This is not quite satisfactory, for many actions that are instinctive are not oftrecurring, and many are not necessary to the preservation of the species." He does not show that there are any such actions which are neither the one nor the other. We have reason for supposing that he understood Mr. Lloyd Morgan to say that instinctive actions were "oft-recurring and essential to the continuance of the species." But this he did not say. In conclusion we may repeat that "The Study of Animal Life," though by no means faultless, may be recommended to Extension students and the general reader as, in the main, accurate, readable, and suggestive. C. LL. M. VECTOR ALGEBRA. Principles of the Algebra of Vectors. By A. Macfarlane, M.A., D.Sc., LL.D., F.R.S.Edin., Professor of Physics in the University of Texas. Reprint from the Proceedings of the American Association for the Advancement of Science, Vol. XL., 1891, pp. 65-117. (Salem Press, Salem, Mass., 1891). THIS HIS is a very suggestive contribution to the foundations of the Algebra of Vectors as recently so strongly advocated in America by Prof. Willard Gibbs, and in this country by Mr. Oliver Heaviside. The extensive use of quaternions among physicists has been prevented by the fact that the meaning of a product of vectors has been made to depend on the use of a vector as a quadrantal versor, and by the fact that this method leads to the square of a vector being negative. The advocates of the new algebra define a product of vectors independently and in such way that the square of a vector is positive. Rotations are expressed by means of dyadics, or ratios between vectors and the quaternion notion of a vector being also a quad- the plane containing the two vectors. The angle is the rantal versor is not entertained at all. The author of this pamphlet devotes a portion of it to the consideration of quaternions, which he holds should form a distinct algebra by themselves, and he suggests a special notation for them. He restricts a quaternion proper to a pure number (a stretching factor) combined with a certain amount of turning. A vector, on the contrary, may be a quantity of any dimensions, possessing direction, with no suggestion of turning attached to it. He clearly shows that the objectionable minus which occurs in scalar products in quaternions arises from the attempt to use the same symbol both for a quadrantal versor and for a vector, so that the laws established for dealing with one set of quantities may hold also for the other set, or for a combination of the two. It may be worth while to notice that this minus sign of the quaternionists would disappear as an explicit symbol if they considered the second vector as being drawn from the end of the first, as AB, BC, and then took the angle ABC as being the angle between the vectors-that is to say, if, in a polygon of vectors, they were to define the angles between the successive vectors to be the internal angles of the polygon. Indeed, by many the internal angles of a polygon (or triangle) are considered as being the angles between the sides, though there is loss of real naturalness and of symmetry caused by so considering them for instance, the connection between A, B, C and a, b, c in a spherical triangle would be greatly simplified if A, B, C were to denote the external angles. However, if we consider these internal angles to be the angles considered by the quaternionists, the reason for the square of a vector being negative appears at once; for if a be the quantitative part (freed from the notion of direction) of a vector A, we have A A = a2 cos 180°, A and A being consecutive sides of the polygon which have straightened out till the internal angle between them is 180°. It may therefore be contended that the quaternionists' minus is not quite irrational in vector algebra (though it cannot be said not to be inconvenient there), and that the advantage of being able to treat a vector as a quadrantal versor without having to establish a new set of formulæ far more than compensates for the loss of symmetry. On the other hand, the advocates of vector algebra without the minus would probably reply that they have to deal with vectors which are not in any sense the same as quadrantal or any other kind of versors, and that the imaginary completeness gained does not in any degree whatever compensate for the loss of naturalness and loss of symmetry involved in the minus. The author differs from Prof. Gibbs and Mr. Heaviside in the mode in which he defines the product of two vectors, as he considers the complete product formed on the understanding that the multiplication shall obey the distributive law. He then finds that this complete product consists of a non-directed part, and of a directed or vector part, the former consisting of the product of the two quantities into the cosine of the angle between them, and the latter of the product of the two quantities into the sine of the same angle, having as axis the normal to angle through which the first vector (occurring on th left-hand side of the product) would have to turn to make its direction coincide with that of the second. Prof. Gibbs and Mr. Heaviside, on the contrary, define the scalar product and the vector product as if they we entirely distinct and independent quantities. Finally the same result is attained, but Prof. Macfarlane's me of introducing these partial products as arising natura from applying the distributive law of multiplication we.. seem to have an advantage from the point of view of a student. Prof. Macfarlane dwells emphatically on the importanc of considering dimensions of vectors, as well as the direction, and to emphasize this he separates his vector. not into tensor and unit-vector, but into quantity an direction. Thus in the equation X = xi, x is the quar tity, and i denotes the axis. Hence the equation jk =: is not a violation of dimensions, but is merely a conven tion as to the interpretation of a composite direction. a convention, moreover, which could only be adopted i space of three dimensions, and is the statement that the plane in which j and k lie has its orientation sufficient indicated by the normal direction i, with the further convention that the angle from j to k shall be considered positive. The author's notation is novel, and forms a very important feature in his treatment of the subject. The scalar product of AB, which is ab cos (ab),he calls cos (AB and the vector product he calls Sin AB, its magnitude. irrespective of direction, being denoted by sin AB Possibly an improvement in this latter would be to denote it by sin ab, and then the capital letter in the complete vector would become unnecessary. The particular symbol used to denote a scalar or a vector product is a matter of secondary importance, b is a matter which must sooner or later be settled if vector algebra is to come into general use. Lord Kelvin is a opinion that a function-symbol should be written with no less than three letters, and Prof, Macfarlane's notation obeys that law, and is moreover easy to work with, bu is incomplete, being applicable to products of tw vectors only. Mr. Heaviside uses no prefix at all to a scalar product, but considers that AB means the scala product. He uses the quaternionic expression VAB fr the vector product. Prof. Gibbs uses no prefix for either but denotes the scalar product by A. B, and the vecto product by AXB. The three-lettered prefix seems the clearest in both cases to denote the special product intended, and the symbols cos and sin are more or les suggestive. In forming a product of three vectors, Prof. Macfarlane makes the convention that ABC shall mean (AB)C, the combination commencing on the left. In his notat this product expands into (cos AB + Sin ABC cos (cos AB. C+ Sin AB. C) + Sin (cos AB. C+ Sin AB.C =cos (Sin AB. C) + Sin (cos AB. C) + Sin (Sin AB. C) =vol ABC+C. cos AB+ Sin (Sin AB. C) which finally becomes =vol ABC+C cos AB+B cos AC-A cos BC; where vol (ABC) denotes the volume of the parallelopiped of which ABC are three adjacent edges. The only obection to this name lies in its suggesting that A, B, C are linear vectors. Here appears the defect in the author's cos and sin notation, in that it cannot be applied to the products of hree vectors, or at least that the special reason for its use has disappeared, and the author does not suggest -o applying it. But there is a certain perspicuity attained by this very imitation of the cos and sin notation to the products of only two vectors, inasmuch as there can be no ambiguity n the meaning of an expression in which they occur, even f brackets are omitted or placed differently. Indeed, instead of cos (Sin AB. C) the author writes cos (Sin AB)C, which seems a curious use of the bracket. But cos Sin AB. C, or preferably cos C Sin AB, is just as explicit, and even cos Sin ABC, though wrong to write as being puzzling, can only have the same meaning. The author concludes with short sections on dyads and matrices, on scalar- and vector-differentiation, including scalar-differentiation of a quaternion. On the last page are a series of propositions relating to the addition of scalar and vector quantities situate at, or passing through, specified points. The pamphlet is confined solely to statements of principles and the section devoted to dyads and matrices is very condensed, so that it is not in any sense a textbook for students. It is rather a synopsis of the subject, with the introduction of a special notation which the author has found useful. A text-book of vector algebra, with examples showing its application to problems in geometry, mechanics, and general physics, and contrasting the method with the Cartesian method of treating the same problems, is much needed, as many physicists are becoming interested in the new algebra, owing in great measure to Mr. O. Heaviside's able exposition of its principles and applications in the Electrician and else where. THE LAKE OF GENEVA. Le Léman: Monographie Limnologique. F. A. Forel. Tome Premier. (Lausanne: F. Rouge, 189-.) PROF. FOREL has been for some years occupied in studying the Lake of Geneva, and has now published the first instalment of the fruits of his labours. The work, when finished, is intended to be a complete monograph of the history of a single lake, and will be a most important contribution to an interesting branch of physical geography. In the present volume the geography, the hydrography, the geology, the climatology, and the hydrology of Lake Léman are discussed, after some introductory matter relating to the instruments employed in sounding with other preliminaries. But, though only a single volume, he work embraces so many questions that we must, for want of space, confine our notice mainly to one, which, of late years, has attracted the most attention, at any rate n this country, viz. What has been the origin of the ake basin? Was it formed by the old Rhone glacier or n some other way? The especial value of Prof. Forel's nemoir is the number of new facts which it brings to Dear on the problem thus propounded. The Lake of Geneva, however it may have been caused, is more modern than the middle of the Miocene period: "Le lac n'existait pas encore, la vallée du Léman n'était pas même indiquée quand la mer helvétienne déposait les mollasses d'Epalinges et du Mont." Its slopes, and almost certainly its bed, are covered with glacial deposits, of later date than the formation of its basin. Terraces around its shore indicate that its waters once reached a higher level, the greatest elevation which can be identified with certainty, being about 30m.above the present surface. The next pause was at 1om.; after that the lake sank (the fall always being rapid) to its present level. Traces of still higher terraces are to be found on the north shore, but as these neither can be identified on the opposite side, nor correspond with any natural barrier in the course of the Rhone below the lake. Prof. Forel doubts whether they indicate old levels of its waters. Lake Léman consists of two basins. The first and larger extends from the embouchure of the Rhone to the narrow of Promenthoux. At the east end the slope of the cone of alluvium deposited by the Rhone in no part exceeds 25°. First comes a zone of very shallow water off the actual shore line; to this succeeds a more rapid slope, which gradually eases off as it descends. The current of the Rhone has made and maintains a well marked channel in this mass of detritus, and the contour lines are affected down to 250m. At the embouchure of the Dranse, on the south shore, another alluvial cone has is much smaller, and does not perceptibly affect the been deposited. This, however, is rather steeper, but it course of the subaqueous contour lines below about 200m. On the north side of the basin the slope varies. Under the walls of Chillon the descent is rapid, amounting to 137 in 100; it is nearly the same near St. Gingolph on the opposite shore, doubtless indicating submerged crags; but it is generally more moderate. West of Vevay it is about one in four, whence it changes gradually to one in ten opposite to Ouchy. West of this port the descent is still more gentle, and so it continues round the western end of the basin, the lip of the latter being 75m. below the surface. The contours of the south side correspond generally with those of the north, and the form of the basin is evidently related to the geology of the district, being narrower and steeper among the harder rocks at the eastern end. The deepest part is a large rudely triangular area, the apex pointing towards the west, and the base lying roughly north and south, extending from almost opposite to the embouchure of the Dranse to near Lutry. All this area is an almost level plain, for it is wholly below the 300m. contour line, but the greatest depth obtained was only 309'7m. The Petit Lac may be described as a comparatively narrow and shallow trough, rising very slowly from a depth of about 70 to 50 metres, and then gradually mounting to the embouchure of the Rhone, its bed being slightly interrupted by five small shallow basins, which roughly speaking, have a linear arrangement, but, their floors only sink four or six yards at most below the general level. The lake to some extent is still held up by the huge mass of gravel brought down by the Arve, through which the two rivers have now cut their channels on either side of the plateau of La Bâtie below Geneva. But it is in the main a true rock basin, though its bed no doubt is concealed beneath glacial deposits and the finer mud brought down by rivers. This alluvium has been studied by Prof. Forel, but into the matter we are unable to enter. Both the origin of lake basins in general and of that of Léman in particular are carefully discussed by Prof. Forel. He examines, only to reject as attended by insuperable difficulties, the hypothesis that it was excavated by the old glacier of the Rhone. He shows that the subaqueous portion corresponds in its general features with a river valley, and is only a prolongation of that of the Rhone. This valley was first defined at a very early period in the uprising of the Alps; its excavation progressed with their growth; it was practically completed at a time when they were higher, perhaps by some 1000 m., than at present. Then the lake was formed by a general subsidence of the mountain region, the lowland remaining comparatively unaffected. The movements of the parts depressed may have been to some extent differential; but this, in Prof. Forel's opinion, is not a necessary assumption. To us, however, it appears that it would be very difficult to explain the rock barrier at St. Maurice between the upper and lower plains without some amount of differential movement. Prof. Forel's view, of course, is not novel; for it has been long maintained in England as a general explanation of the greater Alpine lakes by a few geologists, who never bowed the knee to the glacial Baal With their writings, however, Prof. Forel does not appear to be acquainted, though they appeared in publications generally accessible. The remainder of the present volume is occupied by a discussion of the temperature, rainfall, and general hydrology of the Lake Léman region. It is full of interesting facts and discussions, which we would gladly notice did space permit. The book is well printed, and contains many illustrations, together with a large map of the lake on which the subaqueous contours are depicted. If the book were less diffuse its scientific value would have been greater, but Prof. Forel pleads in excuse that he aimed at writing a volume which would be also acceptable to the general public, or in other words, would combine meat for men with milk for babes. As a comprehensive history of a lake is a great desideratum, it would be ungracious to find fault with Prof. Forel's very natural desire to secure a large number of readers and of purchasers. T. G. BONNEY. OUR BOOK SHELF. Horn Measurements and Weights of the Great Game of the World, being a Record for the use of Sportsmen and Naturalists. By Rowland Ward, F.Z.S. (London: Published by the Author, 1892.) IN these days, when every one is striving to "beat the record," it is only right that sportsmen should have clearly put before them the results already arrived at as regards the size of the trophies and the weight of game-animals already obtained by their brother Nimrods. No one is in so good a position to do this as Mr. Rowland Ward, to whose well-known "jungle" in Piccadilly all the leading shooters of the present day send their "heads" to be mounted and their "skins" to be stuffed. It is, however, much to be regretted that Mr. Ward did not take into his councils some brother "F.Z.S." more versed in scientific knowledge than himself when he pre pared this volume, or at any rate did not have the proc sheets revised by some zoologist with a good knowledge of the Mammalia. The consequence of this want of fore sight is that the nomenclature and localities upon wha the importance of the records entirely depends are in a very confused state, and in many cases quite erroneots Take the Deer (Cervida), for instance. Of this fami a very correct and accessible list, drawn up by the late Sir Victor Brooke, has been published in the "Procee ings" of the Zoological Society for 1878, which Mr. Wart would have done well to follow. But we find under the Sambur (Cervus aristotelis) a head from "Java," where this species certainly does not occur, recorded in the list Next to this (p. 10) comes the "Central and South Indian Sambur, Rusa hippelaphus" (whatever this may be), but three out of the four specimens assigned to it are from Nepal! On the other hand, several heads from Java are attributed (p 22) to Cervus rusa, which is merely synonym of Cervus hippelaphus. The heads of the large Deer of the Caucasus obtained by Mr. St. George Littiedale are assigned (p. 28) to the Red Deer (Cervus elaphus). But we have good reason to know that they really belong to the Persian Deer C maral), quite a different species. Looking over the list of Antelopes, we find similar errors prevalent, though perhaps not quite to so great as extent. The specimens of the Chiru (Panthalops hodgsoni) are assigned to "India," whereas this Antelope is only met with in the snow-fields of Ladakh and Tibet. Nor can the "Takin" (Budorcas taxicolor) be properly stated to be from "India." It occurs only in the Mishm Hills on the frontiers of Assam. These and many like mistakes are the more serious as Mr. Ward's volume is well got up, nicely illustrated, and likely to be frequently used by the sporting naturalist But the statements contained in it cannot be relied upon for scientific accuracy. 66 Der Peloponnes. Versuch einer Landeskunde au Traité Encyclopédique de Photographie. By Charles |