tions which were founded by our forefathers for their especial benefit.

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Hitherto we have been dwelling on the disadvantages of the present system. It is time to turn to the great and unquestionable advantages it offers. It may be true that the colleges supply a fair amount of mathematics, a very little Latin and Greek, and a miserable amount of prelections on Paley's Evidences" and the "Greek Testament," by way of retaining some faint pretence of furnishing a religious education. But we are reminded, and with justice, that if the intellectual pabulum provided is scanty, neither do four out of five who enter the college walls resort thither in search of this. They are sent there, that by the society of young men of equal birth and position, by the frank, high-bred tone of the intercourse, by the undefinable atmosphere of the place, they may receive the finishing touches in the training of an English gentleman. Without stopping to inquire how far this meets the original views of the founders, we may at once admit that the existence of such places of culture is of incalculable service to the development of the young men of the nation, and that their value would be grievously impaired by any modification of the collegiate system. A man might come up to the university, take lodgings for himself in some quiet street, attend the lectures of the most eminent professors, place himself under the guidance of an experienced and able private tutor, and take at last a brilliant degree, without mixing in the least with the real life of the place, without making any of those acquaintances which are so pleasant at the time, so valuable in after life. But suppose a man comes up and enters at a college; he may have been educated privately, or at some small school, so that he has few or no introductions, but the undergraduates of higher standing, who have rooms on the same staircase, will call upon him, and be ready to help him in any way they can; others he will meet at dinner in the common hall, in chapel, or at lecture, and thus he will soon have formed many acquaintances, some of which will ripen into the friendships which are the charm of college days. At the same time, it must be admitted that this very facility of making acquaintances often proves a grievous hindrance to steady work, and thus becomes a disadvantage rather than an advantage. A man may have some slight knowlege of one of his fellow-collegians who is a boating-man, and he, under the influence of the restlessness produced by training, will come wandering into the rooms of his acquaintance, in the midst of the morning's work, and discuss at great length the chance of Emmanuel for the fours, or the fitness of "six" for his place in the 'Varsity boat. After him, perhaps, may enter

another acquaintance, who is devoted to the Union, and who will recapitulate the heads of his speech there the night before, so taking another good half hour from the differential calculus or Eschylus. Hence it comes that no small proportion of reading men prefer to go out of college into lodgings during their last year, that they may be able to study with the fewer distractions. It requires no small amount of resolution to prevent this great advantage of college life from becoming a serious disadvantage.

There is just one other point on which the collegiate system deserves our commendation. It nourishes a feeling of intense patriotism, if we may be allowed the expression, like that which has always animated the citizens of small states, making them willing to do anything for their dear little home. At Oxford, where there is one style of gown common to all undergraduates, and where migrations are frequent, there is, perhaps, less of this strong college feeling than at Cambridge; but in both our great universities it is a marked feature, and, on the whole, a considerable advantage. It serves as a strong link between those of the college, by the multitude of small clubs and societies that are thus formed; it encourages those habits of self-government on which much of our English freedom is justly reputed to be based; and it produces a healthy emulation between the various parts of the university, which contributes largely to the wellbeing of the whole. Of course there are attendant evils-petty jealousies, a tendency to prefer in university elections a member of the same college to another candidate who may be better suited for the post, and a want of catholic sympathies. But, on the whole, the advantages seem to us to outweigh the evils.

It would appear, then, that for those who have abundant means and strong resolution, a college life is far preferable to a university education unaccompanied by this; while in the case of students of narrower means and less firm principles, the present system is open to grave objections. What conclusions should be drawn from these facts we may, perhaps, endeavour to point out on some other occasion.

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Reviews.

Elementary Mensuration, for the use of Schools. By SEPTIMUS TEBAY, M.A. Macmillan & Co.

WE hope there are not many schools where it is thought necessary to teach mensuration pure and simple as set forth in this little book. If by mensuration is to be understood, as seems customary, simply a collection of rules whereby lengths areas and volumes may be calculated, we can hardly regard it as a very important educational engine. The book seems a very good and useful one, it is simply its title that startles us, since we are in the habit of expecting in books intended for the use of schools, at any rate attempts to give reasons for the faith that is in us, whereas here we find only rules which the schoolboy must receive simply as articles of faith; as for example on page 8, where a rule is given for constructing an arch of given height and span, but no indication of a reason given for any of the steps taken. Among those who have to deal practically with the matters of which this book treats, there are, it is to be presumed, always a large proportion who do not care to learn more about them than simply the rules, without any demonstrations. That however even such persons should be compelled to learn these rules in their boyhood appears to us a mere waste of time, since they cannot be retained in the memory, and their acquirement may be safely left to the time when they are required for actual use; while on the other hand no boy capable of comprehending the geometry of any even of the most simple questions in mensuration should be set to learn rules and work out examples entirely in the dark. As a schoolbook therefore we can only regard this work of value for the sake of the arithmetical exercises which it contains, -as a compendium of rules in mensuration it seems very complete, and the numerous examples which are given would render it very useful to those who have to deal practically with measurements.

An Elementary Treatise on Conic Sections and Algebraic Geometry. By G. HALE PUCKLE, M.A. Third Edition. Macmillan & Co. THE author of this treatise says in his preface that his chief object has been to write with special reference to those difficulties and misapprehensions that he has found most common to begin

ners; we think that an examination of the work will show that this statement is amply justified; it is a book by a writer who by experience in teaching has learnt how to teach, and is constantly upon his guard against leaving any doubtful point without clearing it up. It is we suppose necessary in accordance with established usage to call such a work a Treatise on Conic Sections; but the plan pursued is not to commence with geometrical definitions, or from geometry simple to pass to geometry treated algebraically, but commencing with algebra to show how certain algebraical formulæ and equations admit of geometrical interpretation. Indeed, it is one of the strong points of the book that the writer constantly points out to the student that he cannot be too careful in considering the meaning, not only of his algebraical results, but also of every algebraical step he takes. The plan of the work is the same as that followed in Salmon's Conic Sections, where the reduction of the general equation of the second degree precedes the discussion of the properties of the curves; by this method, the work may be made quite as systematic as by that usually followed; but it may be questioned whether, on the whole, this arrangement is the best for those who are commencing the study of the subject. It is also a little difficult to avoid the use of known terms relative to the different conics before the curves themselves have been actually defined; for instance, on p. 146, the axis of a parabola is spoken of before the parabola has been defined. After a good preliminary chapter explaining the various systems of co-ordinates, the author in chapters ii. and iii. proceeds to consider the general equation of the first degree, and here he is not content to deduce special forms from the general equation, but also in most instances is careful to verify the results by independent geometrical considerations; the student can hardly work through these chapters without having acquired the habit of always considering carefully the meaning of the algebraic expressions he has to manipulate. The succeeding chapters give some applications of the results obtained, and an introduction to abridged notation and trilinear co-ordinates; the part relating to the last we think might in some points have been improved, for instance, in explaining the meaning of the equation an + bẞ +cy = 0, would it not have been better to show directly that the intercepts on the sides of the fundamental triangle all become infinitely great? In chapter vii. the author has, we think wisely, somewhat broken through the general plan of his work, to investigate separately equations which represent circles. The following chapters on the general equation of the second degree are exceedingly good, the geometry of the curves represented by it being fully made out, first by its reduction to

simpler forms, and afterwards by discussing the original form. The last chapter contains a clear and concise introduction to trilinear equations of the second degree. There is a good collection of examples attached to each chapter, and many problems carefully worked out in the text. It is, on the whole, the best introductory book on the subject with which we are acquainted.

A Treatise on Elementary Statics. By J. H. SMITH, M.A. Macmillan & Co.

We do not find much in this work which seems to call for any very special notice; it may be said to be well arranged for use by a certain class of students—namely, those whose ambition does not soar beyond the attainment of just sufficient knowledge to enable them to pass certain examinations which obstruct their path in life. This may not be thought to be very high praise except by those tutors to whom the task of preparing such students for examinations is entrusted; but the book is really carefully done, and though evidently intended only for weak intellectual appetites, aims at rendering digestion and assimilation as healthful and easy as may be. Mr. Smith is especially careful to give clear and not too abstract definitions, with full illustrations bearing thereon,-we may point out, for example, the remarks he makes on the importance of the distinction between mass and weight. The propositions are given with great conciseness, but we have not been able to find that any are so much condensed as to be made puzzling to a student of ordinary intelligence. Examinees who have the unfortunate habit of leaving out important clauses in a proof, will find it difficult to obtain marks if they attempt to curtail still further demonstrations of propositions as given by Mr. Smith. The collection of examples is well chosen to illustrate the subject, and there appear to be none admitted that would be considered too difficult for the pass examinations for which this text-book is prepared. If Mr. Smith has been careful not to give much to oppress the mind of the learner, he has certainly also been specially careful that what he does give should be sound.