book. Why lecture when the whole subject is explained in print far better than the lecturer can explain it? The professor would be better occupied in keeping text-books up to date. A good library can do much which a university fancies that it alone can do. Universities remind Mr. Wells of "an absent-minded waterseller bearing his precious jars and crying his wares knee-deep, and going deeper into a rising stream." Naturally he makes much of books. Nature-study, counting the petals of flowers, is a poor thing for town boys. A town boy must observe all he sees about him in the streets and shop windows. No doubt Nature-study may be made a craze. Let us take Mr. Wells' remarks as meant for those who are crazed on the subject.

I have been able barely to touch on the many suggestions in the book. Certainly it repays reading. A schoolmaster will find much good advice in it, accompanied with the mustard of gibe and jeer with which he is familiar.

ΤΗ

A NEW LATIN GRAMMAR.1

HIS book, taken as a whole, is admirable. We are so used in this country to see schoolbooks compiled by persons who have no authority that it is a pleasant change to read a grammar compiled by two well-known scholars; in particular, the co-operation of a philologist is to be commended. The phonetics and morphology of this book are especially well done; the classification of the syntax is clear and practically helpful, although in that part too little prominence is given to the historical side. The basis of classification is logical, and grammar is not logical; logic helps the learner, but the student needs that it should be supplemented by a careful historical treatment. The reader will see in a moment what we mean by examining the classification of the uses of the moods (p. 240). It is useful to have meanings like natural likelihood and ideal certainty given to the subjunctive; but the student wishes to know how one shades into the other, and from what source, or sources, they came; for which purposes another table is necessary. What need is there, by the way, to coin an ugly term like volitive subjunctive for the subjunctive of will? or to use actuality instead of fact, which the authors are constrained to put in as an explanation? Other most praiseworthy points in the book are the spelling, the marking of concealed quantity, the insistence that language is a thing spoken, not a thing written, and the importance given to agreement by sense, not form, which is a category by itself.

We add a few criticisms, which perhaps the authors may take into account in future editions.

1 "A Latin Grammar." By W. G. Hale, Professor of Latin, and C. D. Buck, Professor of Comparative Philology, in the University of Chicago. xi. +388 pp. (Ginn.) 4s. 6d.

The vowel sound in they is a diphthong, and ought not to be given as equivalent to Latinè (p. 3). The statement that "a syllable is also long, even where the vowel is short, provided it ends in a consonant" (p. 143), is misleading as it stands, even with its following explanation; the words might be taken to imply that dat is a long syllable. We do not see what is gained by calling the fourth principal part "nom. sing. neut. of the pf. part. pass." (p. 77), instead of the supine. Admirandus and similar forms have not exactly the meaning of a future participle passive (106), although they approach it sometimes; at other times they approach the present (as in volvenda dies). How can nescio-quis be said to have "iambic shortening" (151, note1)? Both this and the iambic shortening are due to accentual influences, but nescio is a cretic. The genitive after accuso, &c., is due to ellipse, and needs explanation (182). The "poeti cal and later prose uses of the infinitive" (322) are all older prose and colloquial uses; many mistakes, as a supposed Greek influence, have arisen from neglecting this fact. So, too, the use of the adverbial accusative id, &c. (205) is colloquial, and found in Cicero's Letters. In the remarks on style, whilst the treatment of emphasis and position is good, the implication that Latin does not "complete the thought" in each successive phrase is untrue; the thought is always complete in a word-group, the construction is incomplete. In the lengthening of -que by Virgil the Greek influence must be taken into account (352); unlike syntax, the Latin quantitative metre is wholly Greek in origin. In the syntax reasons might often be given with advantage, as the ablative with opus and usus is easily associated with the instrumental (226).

THE STUDY OF NATURE.'

By LORD AVEbury.

THE establishment of such a school as this appears to imply that Nature is worth studying. It would indeed almost have seemed as if this was a self-evident proposition. We live in a wonderful and beautiful world, full of interest, and one which it is most important to understand, and dangerous, if not fatal, to misunderstand. Yet until lately our elementary schools were practically confined to reading, writing, and arithmetic; our grammar schools mainly, as the very name denotes, to grammar; while our great public schools even now omit the study of Nature altogether, or devote to it only an hour or two in the week, snatched from the insatiable demands of Latin and Greek. The result is, in many cases, the most curious ignorance of common things.

Most children are inspired by the divine gift of curiosity, sometimes inconveniently so. They ask more questions than the wisest man can answer, and want to know the why and the wherefore of everything. Their minds are bright, eager, and thirsting for knowledge. We send them to school, their intellect is dulled, and their interest is crushed out; they may have learnt

From an address delivered at the opening of the Cambridge and County School for Boys, October 24th, 1903.

much, but they have too often lost what is far more important, the wish to learn.

No doubt both Cambridge and Oxford have admirable science schools. A man can study there with many advantages, and under excellent teachers. But the prizes and fellowships are still given mainly to classics and mathematics. Moreover, natural science is not yet regarded as a necessary part of education. A degree in Science is not given without evidence of some study of classics, but a literary degree, the regular M.A. for instance, may be obtained without the slightest knowledge of even the most elementary science, yet the most profound classical scholar, if he knows nothing of science, is but a halfeducated man after all.

Educational authorities often seem to consider that the elements of science are in themselves useless. This view appears to depend on a mistaken analogy with language. It is no use to know a little of a number of languages, however well taught, unless indeed one is going into the countries where they are spoken. But it is important to know the rudiments of all sciences, and it is in reality impossible to go far in any one without knowing something of several others. So far as children are concerned, it is a mistake to think of astronomy and physics, geology and biology, as so many separate subjects. For the child, nature is one subject, and the first thing is to lay a broad foundation. We should teach our children something of everything, and then, as far as possible, everything of something. Specialisation should not begin before seventeen, or at

any rate sixteen.

Everyone would admit that it is a poor thing to be a great ichthyologist or botanist unless a man has some general knowledge of the world he lives in, and the same applies to a mathematician or a classical scholar. Before a child is carried far in any one subject, it should be explained to him that our earth is one of several planets revolving round the sun; that the sun is a star; that the solar system is one of many millions occupying the infinite depths of space; he should be taught the general distribution of land and sea, the continents and oceans, the position of England, and of his own parish; the elements of physics, including the use and construction of the thermometer and barometer; the elements of chemistry, geology and biology. Pari passu with these should be taken arithmetic, some knowledge of language, drawing, which is almost, if not quite, as important as writing, and perhaps music. When a child has thus acquired some general conception of the world in which we live, it will be time to begin specialising and concentrating his attention on a few subjects.

I submit, then, that some study of Nature is an essential part of a complete education; that just as any higher education without mathematics and classics would be incomplete, so without some knowledge of the world we live in, it is also one. sided and unsatisfactory-a half education only.

In the study of natural history, again, we should proceed from the general to the particular. Commence with the characteristics in which animals and plants agree, their general structure, and the necessities of existence. Animals, again, agree together on some points, as regards which they differ from plants.

A general idea should then be given of the principal divisions of the animal and vegetable kingdoms. In many respects, though animals are perhaps more interesting, plants present greater facilities for study. They are easier to find, to handle, and to examine. Specimens of the principal divisions can be more readily obtained and studied; the structure also can be more pleasantly demonstrated. Almost all children are born with a love of natural history and of collecting.

Far be it from me to underrate the pleasure and interest of collecting. Indeed collections are in many branches of nature

knowledge almost a necessary preliminary to study. For a collection is a means to an end, not an end in itself. It is like a library, necessary for study, but useless unless studied—unless the books are read. Moreover, we have all access to the great National Museum. Still, private collections are in many ways useful, but not of course unless they are used. Moreover, if I confine my remarks to natural history, plants lose half their interest when they are gathered, animals when they are killed. In the streets and toyshops many ingenious puzzles are sold in which children, and even grown-up people, seem to find great interest and amusement. What are they to the puzzles and problems which Nature offers us without charging even a penny? These are innumerable.

Take geography and biology alone :

Why are there mountains in Wales and the Lake district?
What determined the course of the Thames?

Why are the Cotswolds steep on the north-west and with a gentle slope on the south-east?

What are the relations between the North and South Downs? How did the Thames cut the Goring Gap and the Medway that through the Chalk ridge?

What is the age of the English Channel?

Why are so many of our Midland meadows thrown into ridges and furrows!

Why is Scotland intersected by lines at right angles?
Why are some Scotch lochs so deep?

Why have beeches triangular seeds and sycamores spherical seeds?

Why are beech leaves oval and pointed, and sycamore leaves palmate?

Why are beech leaves entire and oak leaves cut into rounded bays?

Why has the Spanish chestnut long, sword-shaped leaves? Why have some willows broad leaves, and others narrow leaves?

Why do some flowers sleep by day and others by night?
Why do flowers sleep at all?

Why have roses five petals and veronicas four, and why are so many flowers tubular?

Why are white and light-yellow flowers so generally sweet

scented?

Why are tigers striped, leopards spotted, lions brown, sheep grey, and so many caterpillars green?

Why are some caterpillars so brightly coloured?

Why are fish dark above and pale below?

Why do soles have both eyes on one side?

Why are gulls' eggs more or less pointed and owls' eggs round?

It would be easy to ask any number of such questions; some of them easy to answer, others less so.

Many people keep pets, but how few study them? Descartes regarded all animals as unconscious automata; Huxley thought the matter doubtful; my own experiments and observations have led me to the conclusion that they have glimmerings of reason, but the subject is still obscure. I have often been told that dogs are as intelligent as human beings, but when I have asked whether any dogs yet realised that 2 and 2 make 4, the answer is doubtful. The whole question of the consciousness and intelligence of animals requires careful study.

Take, again, the life-history of animals. There is scarcely one which is fully known to us. Really, I might say not one, for some of the most interesting discoveries of recent years have been made in respect to the commonest animals, such as ants, bees, and eels.

Coming now to plants. Any one who has given a thought to the subject will admit how many problems are opened up by flowers. But leaves and seeds are almost equally interesting.

There is a reason for everything in this world, and there must be some cause for the different forms of leaves. In Ruskin's vivid words, "they take all kinds of strange shapes, as if to invite us to examine them. Star-shaped, heart-shaped, spear-shaped, arrowshaped, fretted, fringed, cleft, furrowed, serrated, sinuated, in whorls, in tufts, in spires, in wreaths, endlessly expressive, deceptive, fantastic, never the same from foot-stalk to blossom, they seem perpetually to tempt our watchfulness and take delight in outstepping our wonder."

Some of these indeed have been explained, but for the differences in the leaves of ferns, for instance, of seaweeds, and many others, no satisfactory suggestion, so far as I know, has yet been offered.

Look, again, at fruits and seeds, what beauty both of form and colour, and what infinite variety! Even in nearly allied species, in our common wild geraniums, veronicas, forget-me-nots, &c., no two species have seeds which are identical in size, form, or texture of surface. In fact, the problems which every field and wood, every common and hedgerow, every pond and stream, offer us are endless and most interesting.

But the scientific and intellectual interests are only a part of the charm of Nature.

The aesthetic advantages are inestimable. How much our life owes to the beauty of flowers!

"Flowers," says Ruskin, "seem intended for the solace of ordinary humanity. Children love them; quiet, tender, contented, ordinary people love them as they grow; luxurious and disorderly people rejoice in them gathered. They are the cottager's treasure, and in the crowded town mark, as with a little broken fragment of rainbow, the windows of the workers in whose heart rests the covenant of peace." But in the crowded streets, or even in the formal garden, flowers always seem, to me at least, as if they were pining for the freedom of the woods and fields, where they can live and grow as they list.

The open air is not a cure for the body only, but for the mind also. I wish there was more open-airiness in our educational system!

Science appeals to some types of mind as no other subject does.

A great deal of nonsense is, it seems to me, talked about the necessity of knowing things "thoroughly." In the first place, no one knows anything thoroughly. To confine the attention of children to two or three subjects is to narrow their minds, to cramp their intellect, to kill their interest, and in most cases make them detest the very thing you wish them to love.

Would you teach a child all you could about Europe, and omit Africa, Asia, and America, to say nothing of Australasia ? Would that be teaching geography? Would you teach him one century, and omit the rest? Would that be history?

To teach one branch of science and ignore the rest is not teaching science, and lastly to teach one or two subjects only, however well, is not education. If you think I am drawing too gloomy a picture, let me give you the opinion of a great authority on education, the late Bishop of London, Dr. Creighton. In his "Thoughts on Education he says, speaking of the new Birmingham Exhibition :

"In your own regulations for matriculation I em glad to see that science is included. But I am rather sorry to see that the expression is a science, the prescribed sciences being mechanics, chemistry, and physiography. Suppose, then, that chemistry is taken. A man may get a degree without knowing the difference between a planet and a star, or why the moon goes through phases. At this early stage of education should not science be treated as one subject, and a general knowledge of the rudiments be required?"

that I am not able to believe that we have made any real educational progress during that time. I am not even sure whether we have not gone back."

And again :

"The more subjects people can study at the same time, the better they will get on with every one of them."

Of course we cannot expect from everyone knowledge of scientific details, but everyone might have some idea of the principles, and some general conceptions of the interest and vastness of the problems involved. Yet there is no single animal, or plant, which would not well repay—I do not merely say the study of an hour, but even the devotion of a lifetime.

Kingsley used to speak with enthusiasm of the heaths and moors round his home, "where I have so long enjoyed the wonders of nature; never, I can honestly say, alone; because when man was not with me, I had companions in every bee, and flower and pebble; and never idle, because I could not pass a swamp, or a tuft of heather, without finding in it a fairy tale of which I could but decipher here and there a line or two, and yet found them more interesting than all the books, save one, which were ever written upon earth."

The love of Nature, again, helps us greatly to keep ourselves free from those mean and petty cares which interfere so much with calm and peace of mind. It turns "every ordinary walk into a morning or evening sacrifice" and brightens life until it becomes almost like a fairy tale.

May we not hope also that some of the students here will add to the stores of human knowledge?

The late Lord Derby used to say that, considering the marvellous discoveries of the last hundred years, we could not expect so much in the future. To me it seems, on the contrary, that we may reasonably expect even more, and for three reasons. In the first place, our instruments and apparatus are so much more elaborate and ingenious. In the second place, the students are more numerous. Even now the harvest is plenteous, and the labourers are few, but yet they are more than they were. Thirdly, as the circle of human knowledge widens, the opportunities for research become more numerous! Every discovery opens the way to others-suggests new ideas and fresh researches. We seem to be on the threshold of great discoveries.

There is no single substance in Nature the properties of which are fully known to us. There is no animal or plant which would not well repay, I do not say merely the attention of an hour, but even the devotion of a lifetime. I often grieve to think how much happiness our fellow-countrymen lose from their ignorance of science. Some knowledge of the world we live in would add immensely to the interest of life. Man, we know, is born to sorrow and suffering, but he is not born to be dull, and no one with any knowledge of science ever could be. If anyone is ever dull it is his own fault. Every wood, every field, every garden, every stream, every pond, is full of interest for those who have eyes to see. No one would sit and drink in a public-house if he knew how delightful it was to sit and think in a field; no one would seek excitement in gambling and betting if he knew how much more interesting science is; science never ruined anyone, but is a sort of fairy godmother ready to shower on us all manner of good gifts if we will only let her. In mediaval fairy-tales the nature spirits occasionally fell in love with some peculiarly attractive mortals, and endowed their favourites with splendid presents. But Nature will do all this, and more, for anyone who loves her.

If anyone, says Seneca, "gave you a few acres, you would say that you had received a benefit; can you deny that the

1 Mandell Creighton, "Thoughts on Education," p. 21.

2 Mandell Creighton, "Thoughts on Education," p. 4.

boundless extent of the earth is a benefit? If a house were given you, bright with marble, its roof beautifully painted with colours and gilding, you would call it no small benefit. God has built for you a mansion that fears no fire or ruin covered with a roof which glitters in one fashion by day, and in another by night. Whence comes the breath which you draw? the light by which you perform the actions of your life? the blood by which your life is maintained? the meat by which your hunger is appeased? . . . The true God has planted not a few oxen, but all the herds on their pastures through the world, and furnished foods to all the flocks; He has ordained the alternation of summer and winter He has invented so many arts and varieties of voice, so many notes to make music. . We have implanted in us the seeds of all ages, of all arts; and God our Master brings forth our intellects from obscurity."

Those who love Nature can never be dull. They may have other temptations, but at least they will run no risk of being beguiled by ennui, idleness, or want of occupation, "to buy the merry madness of an hour with the long penitence of aftertime."

Lastly, in the troubles and sorrows of life science does much to soothe, comfort, and console. If we contemplate the immeasurable lapse of time indicated by geology, the almost infinitely small and quite infinitely complex and beautiful structures rendered visible by the microscope, or the depths of space revealed by the telescope, we cannot but be carried out of ourselves.

A man, said Seneca, "can hardly lift up his eyes towards the heavens without wonder and veneration to see so many millions of radiant lights, and to observe their courses and revolutions." The stars, moreover, if we study them, will not only guide us over the wide waters of the ocean, but, what is even more important, light us through the dark hours which all must expect. The study of Nature, indeed, is not only most important from a practical and material point of view, and not only most interesting, but will also do much to lift us above the petty troubles and help us to bear the greater sorrows of life.

THE REFORM OF MATHEMATICAL TEACHING IN THE UNITED STATES.1

A SPECIAL committee was appointed in September, 1902, by the American Mathematical Society to report upon the requirements in mathematics at College entrance examinations. This committee worked in co-operation with committees already appointed by the Society for the Promotion of Engineering Education and by the National Education

Association.

The committee appointed by the Mathematical Society included Prof. H. W. Tyler, of the Massachusetts Institute of Technology (Chairman), Profs. T. S. Fiske, Columbia University, W. F. Osgood, Harvard University, J. W. A. Young, University of Chicago, Alexander Ziwet, University of Michigan. The committee duly considered previous recommendations which had been made by various authorities, carefully inquired into existing conditions in American schools and colleges, and sought and obtained advice from teachers in secondary schools and from other members of the Mathematical Society. It is not implied that all the subjects enumerated in the following report should be required by any one college, or be taught in any one school.

1 Report of a Committee of the American Mathematical Society on Definitions of College Entrance Requirements in Mathematics. Abridged from the New York Educational Review, October, 1903.

REPORT.

The committee understands its duties in the following sense: First: To specify those mathematical subjects which are generally recognised as appropriate requirements for admission to colleges and scientific schools.

Second: To specify details under these subjects in such a manner as to represent the standards of the best secondary school instruction-the word "best" being interpreted in a qualitative rather than a quantitative sense.

Third: The committee understands also that the consideration of pedagogic questions is not primarily among its duties. It has therefore made no attempt to deal with methods of secondary school education in mathematics, or the order of taking up the subjects and their correlation with each other and with other sciences. The order in which the subjects and the topics under them are presented below does not necessarily imply preference of the committee as to the order of teaching either the subjects or the topics. It is the opinion of the committee that these are the subjects and the topics which, according to the best present usage, should be offered for admission to colleges and scientific schools.

The recommendations are not to be interpreted as exhaustive. They represent rather the extent to which, in the opinion of the committee, definite specification should be undertaken by it; it is expected that further details will be determined in accordance with the judgment of the particular college, school, or teacher.

The subjects proposed are based on present usage and standards. In case of divergence between standard text-books and what seemed a more scientific presentation of the subject in question, the committee has endeavoured to make a choice which should not depart so far from current usage as to involve hardship to schools or teachers. The committee is of opinion that no formulation should be considered as having more than temporary validity. No advantages attendant upon uniformity could counterbalance any tendency of the recommendations to retard progress of secondary education in mathematics. It is therefore suggested that if the recommendations are approved, they be revised at intervals, perhaps of ten years.

Subjects. (1) Elementary Algebra. (2) Plane Geometry. (3) Solid Geometry. (4) Trigonometry. (5) Advanced Algebra. 1. Elementary Algebra.-The four fundamental operations for rational algebraic expressions.

Factoring, determination of highest common factor and lowest common multiple by factoring.

Fractions; including complex fractions, ratio and proportion. Linear equations, both numerical and literal, containing one or more unknown quantities.

Problems depending on linear equations.

Radicals, including the extraction of the square root of polynomials and of numbers.

Exponents, including the fractional and negative.
Quadratic equations, both numerical and literal.

Simple cases of equations with one or more unknown quantities, that can be solved by the methods of linear or quadratic equations.

Problems depending on quadratic equations.

The binomial theorem for positive integral exponents. The formulae for the nth term and the sum of the terms of arithmetic and geometric progressions, with applications.

It is assumed that pupils will be required throughout the course to solve numerous problems which involve putting questions into equations. Some of these problems should be chosen from mensuration, from physics, and from commercial life. The use of graphical methods and illustrations, particularly in connection with the solution of equations, is also expected.

2. Plane Geometry.-The usual theorems and constructions of good text-books, including the general properties of plane rectilinear figures; the circle and the measurement of angles; similar polygons; areas; regular polygons and the measurement of the circle.

The solution of numerous original exercises, including loci problems.

Applications to the mensuration of lines and plane surfaces. 3. Solid Geometry.-The usual theorems and constructions of good text-books, including the relations of planes and lines in space; the properties and measurement of prisms, pyramids, cylinders, and cones; the sphere and the spherical triangle. The solution of numerous original exercises, including loci problems.

Applications to the mensuration of surfaces and solids.

4. Trigonometry.-Definitions and relations of the six trigonometric functions as ratios; circular measurement of angles.

Proofs of principal formulae, in particular for the sine, cosine, and tangent of the sum and the difference of two angles, of the double angle and the half angle, the product expressions for the sum or the difference of two sines or of two cosines, &c.; the transformation of trigonometric expressions by means of these formulae.

Solution of trigonometric equations of a simple character. Theory and use of logarithms (without the introduction of work involving infinite series).

The solution of right and oblique triangles, and practical applications, including the solution of right spherical triangles. 5. Advanced Algebra.-Permutations and combinations, limited to simple cases.

Complex numbers, with graphical representation of sums and differences.

Determinants, chiefly of the second, third, and fourth orders, including the use of minors and the solution of linear equations.

Numerical equations of higher degree, and so much of the theory of equations, with graphical methods, as is necessary for their treatment, including Descartes' rule of signs and Horner's method, but not Sturm's functions or multiple roots.

By this arrangement the inner asbestos coating becomes red-hot, so that, in addition to the direct heat from the burner, the vessel is heated by radiation from the heated asbestos lining.

The furnace is made in two sizes and is supplied with special burners, which are superior in heating power to the ordinary Bunsen burner.

In comparing the efficiency of this furnace with other methods of heating we observed the length of time required to convert completely one gram of crushed marble into quicklime. With gas pressure equal to 2 inches of water, the following results were obtained :-

THE ESSEX COUNTY TECHNICAL LABORATORIES, CHELMSFORD.

ON October 30th Lord Onslow, President of the Board of Agriculture, opened the new County Technical Laboratories at Chelmsford. During the past ten years the teaching of agriculture, horticulture, and dairying, and the sciences forming the foundation of these industries, has been carried on in an old grammar-school which was temporarily fitted up for the purpose. Valuable experience has thus been obtained, and the arrangement and equipment of these new buildings should merit the attention of those who are connected with technical education in rural districts.

The work of the laboratories is divided into three sections, viz. :-(1) the chemical and agricultural, (2) the biological and horticultural, and (3) the dairying. The new buildings are so arranged that, while the students of each section can attend classes in the others and can use the same common rooms, each department is separate and distinct and under the control of a different responsible head, so that a personal oversight of the students can be better secured and discipline easily maintained.

At Chelmsford the practical study of science in the laboratory forms the basis on which instruction in agriculture and horticulture rests. The principal feature, therefore, of the biological and horticultural department, to deal with this first, is the two large biological laboratories. Each of these accommodates twenty students at a time; they are lighted on each side by windows, under which are lockers for the students' microscopes, and they are provided with ten working-tables, so arranged that all the students face the blackboard and demonstration table. Opening out of the laboratories are bacteriological and seedtesting rooms, while adjoining are the lecturer's private room and class-room, a museum lighted from above so as to secure a maximum of wall space for the cabinets, and a store and dark room. The school garden is within three-quarters of a mile. It is three acres in extent, and is partly laid out in botanical plots and partly in borders for practical instruction in fruit,