No. 53.

CLASSICAL TRANSLATIONS FOR ENGLISH READERS.

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By FANNY JOHNSON.

Late Headmistress of Bolton High School.

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ERTAIN difficulties in education are due to what may be called machinery. But when Government Bills and private efforts have done their best-and worst-the real crux of the situation remains. And this may be summed up in the one word-curriculum. Every teacher is occupied in the main with what, in old-fashioned phraseology, was called "imparting knowledge," and the instinct is natural to impart such portions of knowledge as the teacher has most at heart, or in which he feels most at home. A man who has spent the better part of his own life in digging for Greek roots finds a fascination in the pursuit that he would fain share with another, while the rarer teacher whose circumstances and inclination have led him into out-door life thinks "nature-study" all important. These secret desires on the part of teachers are, of course, decently veiled under high-sounding expressions, such as "training of the observation," of the " soning powers," of the "imagination" and the like. But when we honestly consider the mental condition of an average boy or girl at the schoolleaving age, whether, among the middle classes, that age be sixteen, or lower down in the social scale, twelve or thirteen, as the case may be, it is clear that what counts is not the arithmetic, or history, or French that the pupil may have acquired, but the attitude of mind towards these or any other subject of instruction that he has imbibed as a result of school training. In other words, the How, rather than the What, is the cardinal matter for educationists. Schoolmasters are distracted by the multiplicity of subjects; they honestly attempt for an all-round curriculum, the more honest and conscientious falling betweennot two-but many stools in their efforts. So that, especially among girls' schools, the crowded time-table frequently leads to a condition of chronic indigestion. There is much to be said in favour of limitation to the three R's, taking them in their wider sense. For the man who can read-intelligently-has the key to all book knowledge, and No. 53, VOL. 5.]

SIXPENCE.

the greater part of knowledge is, after all, contained. in books; while he who can write-in which we ought to include the power of drawing-is able to record his first-hand observations. And the arithmetician, having once learnt to reason about numbers, can apply his logical powers to any other subject that presents itself. Teachers are in too much of a hurry, and the examiners, inspectors, universities, and makers of the educational machines are the most to blame for this.

The curriculum which vexes our souls need not disturb us, if only we frankly acknowledge that Life (of the schoolboy) is short, and education (in its broader sense) is unendlich lang, and therefore the digestibility rather than the quantity of mental food given to the school child is the all-important point. And this brings me to my main thesis, that at school-acquaintance with "the classics,' or indeed with any literature outside our own, may well be gained through the medium of translations. Let me quote from the prospectus of a series of translations, not unfavourably known in their day, "The Valpy Family Classical Library" [the italics are mine]:

So diversified are the objects to which general education is at present (i.e., in 1830) directed, that sufficient time cannot be allowed, in most instances, to lay the foundation of an adequate acquaintance with the most popular authors in the Greek and Latin languages. The facility of reference

to a series of correct and elegant translations must afford pleasure and occasional assistance even to the scholar. To him who, as Dr. Knox observes, although engaged in other pursuits, is still anxious to "retain a tincture of that elegance and liberality of sentiment which the mind acquires by a study of the Classics, and which contributes more to form the true gentleman than all the substituted ornaments of modern affectation," such a collec. tion will, it is confidently hoped, prove acceptable. As the learned languages do not form part of the education of females, the only access which they have to the valuable stores of antiquity is through the medium of correct translation.

The series here referred to was followed at no long interval by the immortal Bohn's libraries, which, including a vast number of translations, began in 1846 and have never ceased, under the auspices of the original publishers, nor (since 1863) of their present guardians, Messrs. Geo. Bell and Sons, to maintain the reputation designed for them by their founder. Unequal in merit as are the translations lurking under the shelter of the

name of Bohn, the scheme of bringing all the literatures of the world within the view of the man, poor in purse and education, who can only read in his own language, is a magnificent one. Its success

can be estimated to some extent by the fact that new volumes are constantly issued, and in most instances compare favourably both for readableness and accuracy with their forerunners. Thus the publishers early recognised the "felt want' which, by all the signs, will become more and more felt, and is, in fact, being more and more recognised.

Such names as Messrs. Macmillan and Messrs. Bell, among publishers, and among scholars such reputations as those of Messrs. Kennedy, Long, Calverley (translators respectively of Demosthenes, Plutarch, Theocritus, published by Messrs. Bell), or Messrs. Leaf, Church and Brodribb (translators of Homer and Tacitus, published by Messrs. Macmillan), &c., carry with them their own guarantee. Messrs. Methuen have also a shorter series of classical translations, including Lucian, "Six Dialogues," translated by S. T. Irwin, and Tacitus," Agricola and Germania," translated by R. B. Townshend; both works well calculated to appeal in their English form to the ordinary reader. And Messrs. Nutt, whose unfailing efforts in the direction of pure scholarship are well known, have recently issued a translation of Aeschylus, “Prometheus Bound," by E. R. Bevan, whose preface is not only an interesting modern counterpart to the puff preliminary of the Valpy series, quoted above, but also expresses better than any words of my own, the views I am upholding in this paper [the italics are mine].

In

To hand down translations may seem too poor a mark for the ambition of the age. And yet the Book which has been the most powerful force in English literature is a translation. the case of the Greek poets, how much of our intellectual heritage comes from them, even though all the while a strange tongue has had to be mastered in order to know them, no one needs to be reminded. Such mastery was possible to the few, and literature was mainly the concern of the few. But this is so less and less, and if democracy is destined to lay hold of literature, as of everything else, that generation will have made no mean contribution which delivers to the people a standard rendering of the great works upon which our own literature has been nourished

. . If our age is to bring forth a translation of the Greek poets of permanent and universal authority, it would probably have to be by the co-operation of many minds, in which the idiosyncrasies of each would find correction. With so much ability at large, directed to the production of excellent verse and genuine poetry, which yet represents no new force in literature, would it be impossible to consecrate some of it on such a work as I have named ?

The democratising of learning is indeed a kind of democracy with which all generous spirits have constantly sympathised. And now that the tone of the best public opinion is set towards the production of an educated community, as against the earlier ideal of the educated select ones, so much Greek" as may become a gentleman" must be put within the reach of all. That being so, it is evident that translation is the only way. I seem to

remember the time when, among one's pastors and masters, the peep into a "crib" was held an offence worthy of awful punishment. Nowadays, I believe, the student is encouraged in the intelligent use of translations while wrestling with the difficulties of a foreign tongue. But the vast majority will never, perhaps, reach even this preliminary wrestle. Why, then, should the treasures of the past be debarred from them, or offered in such attenuated forms as Kingsley's "Heroes," or the "Tanglewood Tales?" The worst translation of Homer that was ever made brings one more in touch with the spirit of the elder world than all the "Tales from Homer" that were ever devised. We must get as near as we can to the sources. In literary matters, this corresponds to the investigation of origins in science. Though Homer may speak to us in muffled tones through the voices of Messrs. Lang, Leaf and Myers, it must be recollected that the revelations of the gods are always partial, and the Word, which was from the beginning, is still only half understood. What I have said would apply to some extent to modern and living languages, but it is peculiarly fitting that we should approach the ancients, at first, robed in a modern dress. We cannot recite Hamlet so that Shakespeare would follow what we were saying, and still less can we speak as Herodotus and Tacitus pronounced their respective dialects. After all, matter is more than form, and thought is better than speech. We can get at the minds of the ancients as well, or better, when we are not carefully puzzling out their sentences phrase by phrase. It is rarer than would perhaps be admitted for even a scholar to read a Greek or Latin classic without any sense of effort, as he would read an English or French novel.

spective dialects.

Even for those who hereafter may be destined to soak themselves fully in the originals, I believe the best way would be to begin with translations. One hears not infrequently of the schoolboy for whom the name of Caesar carries a life-long sting, because he has first made Caesar's acquaintance in scraps and paragraphs, slowly puzzled out, of Caesar De Bello Gallico, Book I. If Caesar, and Xenophon, and Herodotus, all the ancient writers of straightforward narrative, in fact, were first presented to youthful minds in the guise of an attractive English reading book, illustrated by pictures, &c., and read in school as part of the ordinary course in history and literature, how different the effect would be! Pleasanter, no doubt, says the pedagogue, but what about the discipline of the mind? Well, as I began by saying, the mind of the average schoolboy remains to the end of his schooldays pretty much undisciplined anyhow. Let him read, read, the best you can get him to read, translated Homer, or abbreviated Scott, the whole of the Iliad in English, rather than half a book of it in Greek. Let him learn to adore Alexander through Messrs. Stuart and Long (translators of Plutarch's "Lives," in Bohn library) rather than detest Hannibal through Livy. Greek, in the original, might be banished from all

the schools in England, but yet the Greek spirit and all that is best in the Greek ideal flourish. For children nourished on such adequate translations as Mr. Bevan generously forecasts for them would long but the more for a draught from the fountain head. A pious grocer's assistant whom I knew, for love of his English New Testament, spent the evenings of a hardworking life in learning to read it in the Greek; so these school pupils, I fancy, would sometimes continue their education by conning the Greek and Latin grammar in their maturer years in order to get nearer to the heart of those delightful raconteurs, Homer, Virgil, Xenophon, Tacitus, and the rest. The best efforts of every teacher are spent in providing solace for his pupils in later life. It is indeed a commonplace and trite reflection, uttered in one form or another on every school speech-day, that the things of beauty we learn at school are joys for ever. The habit of learning a language is soon acquired; it really does not matter which language you begin with. Grown persons have been known to learn even Hebrew and Russian; many grown women have learnt Greek or Latin having had no previous acquaintance with these languages in their childhood.

For school use, the work in its translated form must look as little like a translation as possible. There should be no reference to the original language in the notes.

Such words as "lictor," "parasang," "peltast," &c., should be explained in note or glossary, as though they were unusual English, not foreign words. Some of us were brought up in the belief, or at any rate under the impression, that Isaiah was divinely inspired to utter the words, "Comfort ye, comfort ye, my people," exactly as they stand in the English Bible, and neither our religious sense, nor our literary taste, nor even our knowledge of Jewish or universal history, has suffered from having been led to abandon that half-truth only in later life. Of course, the teachers should "know better." They should, and must, be as learned as can possibly be managed. But a teacher who has first approached his Homer, his Sophocles, and his Virgil as charming story-tellers will be able the better to commend these authors to his pupils as the "best of good fellows." There are certain foreign authors, not to speak of the Hebrews, whom we think it no shame to know only in borrowed plumes. We do not blush to confess that "Don Quixote," or to take later examples, the works of Tolstoi, or Ibsen, are unknown to us in their original tongues. Fewer still can read the "Arabian Nights' Tales" as they were spoken at the first. I only plead to extend this principle a little further, and to provide school children from the first, not with snippets, or arrangements, or derangements from the classics, but to give them at least whole episodes, or carefully connected portions, in a form as attractive as possible, i.e., in pleasant readable English, printed in an easily handled book, and not overloaded with extraneous learning. Something of this sort has already been tried in French and German, and I believe, in American schools. One great English

headmaster, at least, was much for "Hellenising without Greek." And to the rabid Hellenists we would say, that this method is bound in the long run to prevail in the majority of schools, if any tincture of that elegance and liberality of mind which is inseparably bound up with a study of the two classical languages is to be maintained.

THE GEOMETRICAL TREATMENT OF ANGLES AND PARALLELS.

E

By H. B. WOODALL.

St. Asaph County School, Flintshire.

UCLID'S difficulty in treating parallels is due. to his failure to define angle, the essential nature of which seems to have eluded his grasp. His statement about parallels is a negation, and not a definition, while his "inclination of one line to another" is merely an ingenious makeshift for a definition. Every geometer since the days of Proclus has been aware of the difficulty, but, until quite modern times, none saw that it arose out of the notion that angle is a function of line, or of line and surface. Thus, Borelli (1608-1679), treating of the difficulty in his "Euclides restitutus," says that angle is neither line nor surface, but he nevertheless regards it as a function of these magnitudes, and uses the analogy that the proportion of two magnitudes is a quantity different from either of them.

The doctrine that kinematical notions should not be admitted into pure geometry is, no doubt, largely responsible for the practice of keeping beginners as long as possible in ignorance of the modern definition of angle. If we look for this definition in our text-books we find it relegated to footnotes, and teachers who are not content to leave it embedded there like a fossil are regarded as innovators by the upholders of the said doctrine. If it were a fact that, in every case, geometry is concerned only with the statical result of motion, it would by no means be an argument in favour of this doctrine; for, if the motion is necessary for the production of the result, it may well be that the conception of the motion is necessary, or at least helpful, to the conception of the result. Even when we speak of a line "meeting" another, or of being "produced," or of one figure being " applied" to another, kinematical notions are in the mind, and it is practically impossible to treat geometry without the constantly recurring use of words which imply motion of some kind or other. Borelli defines a circle as formed by the revolution of a finite straight line in a plane about one extremity, which is fixed, until the moving line reaches its original position. The same kinematical notion used differently gives us the modern definition of angle. Indeed, we may almost say that the difference between the ancient and the modern view of angle is the difference between associating it with line and associating it with circle.

By defining angle as "amount of turning" we

have a definition independent of other geometrical definitions, and one which greatly simplifies the proofs of many fundamental theorems. A spinning top is making a continuously increasing angle. The natural unit of angle is one complete turn. If, therefore, the top has made a hundred turns, a hundred is the measure of the angle it has made. When we have defined a right angle as a quarter of a turn, the statement that all right angles are equal becomes the statement that a quarter of a turn is equal to a quarter of a turn, and is, therefore, axiomatic beyond dispute.

Of

It may be advisable, after careful revision, to retain some of the conventional phrases associated with the line-and-space notion of angle, but many of them must be condemned as misleading. the former, "angle between two lines" is the most important. Let a line turning in a plane be pivoted at any point in itself, and let its initial position be marked by a fixed line in the plane, then, reckoning from this initial position the amount of turning made by the pivoted line, moving always the same way round, is called the angle between the fixed line and the pivoted line. Or, alternately, we may say that the angle between two given crossing lines is the amount of turning that the first-named of them must make in order to lie along the other. "Interior" and "exterior," as applied to the angles between adjacent sides of a rectilineal figure, are useful conventions which we shall notice presently; but "interior" and "exterior," as applied to the angles between two non-intersecting lines and a transversal, are to be classed with "alternate " and "vertically opposite" as erroneous terms, inconsistent with clearness of thinking.

The consideration that, if one line crosses another, there are two ways in which one of them may turn so as to lie along the other, introduces the definitions of positive and negative ways of turning. To avoid ambiguity we observe the convention that the first position of conformity shall determine the angle, and then the definition of supplementary angles and a formal statement of Euclid's thirteenth proposition naturally follow; but the theorem is clearly axiomatic. Next, let us draw any triangle, and name its corners A, B, C, in negative order-the order in which they would be passed by a line turning negatively about a pivot inside the triangle. Let a straight edge, whose ends are distinguishable, lie along A B. Let it be pivoted at B, and turn positively, until it lies along BC. Then, let it be pivoted at C, and turn positively, until it lies along C A. Lastly, let it be pivoted at A, and turn positively, until it lies along A B once more. Two things are evident. First, that the straight edge moves across the area of the triangle in each motion. This gives us the definition of "interior" angle, while "exterior" angle is that made by the straight edge in turning from the direction of one side to the direction of another without moving across the area of the triangle. Second, that the straight edge has, by turning through the three interior angles of the triangle, made half a turn. That is to say, the sum of the

interior angles of any triangle is half a turn, or 180 degrees, if we define a degree as the 360th part of a turn. The important fundamental propositions 13 and 32 of Euclid's first book are thus established immediately from the definition of angle. Taken together, they give us the fact that the exterior angle whose pivot is any corner of a triangle is equal to the sum of the interior angles whose pivots are the other corners. Propositions 16 and 17 follow as immediate corollaries, although the former may be deduced directly from the definition of angle, and the second case of proposition 26 is brought under the first case, for, if two angles of a triangle are known, so is the third angle. The placing of the above and other important proposi tions on an independent basis is one of the distinct advantages of this method of treating angles. The Euclidean plan of making all succeeding theorems depend on the first, and grow out of it, in the fashion of a genealogical tree, is unnecessary to a scientific treatment of geometry, and can be regarded only as an ingenious device, often laboured, often producing an unnatural sequence, and founding many simple and almost axiomatic theorems on involved and otherwise useless lemmae.

If a line pivoted at a point in itself is turned through any positive angle, and then through an equal negative angle, it will obviously conform with its original position. If, however, we choose one point in the moving line as pivot for the posi tive angle, and another point in it as pivot for the equal negative angle, the line will then be parallel to its original position. Two co-planar lines are thus defined to be parallel when one of them can by equal amounts of positive and negative turning be brought to lie along the other. The definition, unlike Euclid's statement, is positive. In place of Euclid's 29th proposition we have the immediate and important deduction that the positive angle between a transversal and one of two parallels is equal to the positive angle between that transversal and the other parallel. For, let a and b be the parallels, and t the transversal; then, from the definition, the positive angle between a and is equal to the negative angle between t and b, but this latter is the same scalar magnitude as the positive angle between b and t. We may observe that this definition of parallels is not equivalent to Euclid's 27th proposition, which refers to the transversal; but that if in place of this proposition we put the statement that parallel lines, if produced, do not meet, we shall have a theorem capable of a reductio ad absurdum proof; for, if they do meet, then a positive angle of less than half a turn alone suffices to bring about conformity. Revisers of Euclid have frequently proposed to interchange his definition of parallels and his 27th proposition, and the complication of the latter due to its dependence upon the transversal has been the chief objection to so doing.

The definition of angle taken along with Borelli's definition of circle gives the principle of the usual. method of measuring angles less than one turn. Let a line AB, of constant length, be pivoted at A and revolve positively. Then, when AB has made one

turn, B has traced the circumference of a circle. Therefore, when AB has made any given fraction of a turn, B has traced the same fraction of the circumference. Hence, by determining the latter fraction, we shall determine the angle in terms of the natural unit of angle. The practical outcome of this is, firstly, the method of copying the limits of an angle, and, secondly, the circular protractor. Lastly, we have a simple and readily proved method of finding the bisector of an angle. Let A and Z be the ends of the arc determined by the angle whose pivot is the centre of the circle. In the arc take points B and Y, so that AB = ZY; then the mid-point of arc AZ is in arc BY. In the arc BY take points C and X, so that AC ZX, then midpoint of arc AZ is in arc CX. As the process is continued the points thus found approach one another till in the limit they coincide in the midpoint of the arc AZ. If M is this mid-point, then it is clear that the angle between the radius drawn to A and the radius drawn to M is equal to the angle between the radius drawn to M and the radius drawn to Z. In practice, it is easy to find the mid-point in the second, or, at most, the third step of the process, and accuracy is as nearly attainable as by any other method with the instruments used. The principle of this method of finding the mid-point of a line is obvious at once; but its chief merit in our present point of view is that the bisection of the angle is provable immediately from the fundamental relationship between angle and circle. It is worthy of passing notice that those who wish to prove Euc. i. 5 by bisecting the "vertical" angle, and using i. 4, may do so without the logical somersault which comes about by making the proof of the bisection of an angle depend indirectly upon that very proposition.

graduated in 1° C. may be recommended. The reading of the temperature is most important, and it takes some time and patience on the part of the teacher before the students understand that the virtue of weighing to the nearest milligram will not compensate. for the vice of estimating the temperature merely to the nearest degree.

With regard to the important subject of calorimeters, certain definite requirements are evolved from long experience. In the first place, it is essential that the calorimeter should be made of "spun" metal, copper or aluminium for preference. If the vessel is slightly thickened round the upper edge it is practically unbreakable and will last for years. Soldered calorimeters should not be tolerated in any good laboratory; the specific heat of the metal is an unknown quantity, and, moreover, such calorimeters have a habit of developing an exasperating leak while the experiment is in progress. A convenient size of vessel for ordinary use is 3 inches height x 13 inches diameter; these will cost Is. each, and may be obtained from Messrs. J. J. Griffin & Co., Sardinia Street, London, W.C., or from Mr. F. Jackson, Cross Street, Manchester. Other makers stock them in slightly different sizes.

APPARATUS FOR EXPERIMENTS IN CALORIMETRY.

By E. S. A. ROBSON, M.Sc. Lecturer in Physics Royal Salford Technical Institute.

TH

HE experiments and apparatus to be described in this article are intended for students in secondary schools, and the apparatus is intended for use by the boys and girls themselves. For the purpose of weighing, chemical balances reading from 250 grams to 1 centigram (price £110s. of any good maker) will be required; while, for heavier weights, a flat-pan kilogram balance (price £1 5s.) is necessary.

In most calorimetric experiments the temperature will require estimating to C., and a preliminary test in noting time and temperature readings when heating a tank of water may be performed by the student. Chemical thermometers 0°-100° C., etched on the stem, with enamelled back and marked in single degrees, may be purchased for 2s. each from any apparatus maker. For more accurate work a o°-35° C. thermometer

FIG. 1.-Simple calorimeter and enclosure.

1

The calorimeters must be placed in an enclosure, for which a double-walled cylindrical tin-vessel may be recommended, the inner portion 3 inches height x 24 inches diameter being soldered to the outer portion, which is 4 inches height x 4 inches diameter. The inner vessel is lined with -inch sheet asbestos which acts as a non-conducting material, and the space between the inner and outer vessel may be filled with cold water or left empty. The calorimeter, enclosure, and lid (Fig. 1) will cost 2s. 6d. each (Jackson). The substance, the specific heat of which is to be determined, will have to be heated in a steam heater, and after trying most of the usual forms of apparatus, I can recommend the following simple combined. boiler and heater (Fig. 2). It consists of two drawn-brass tubes 7 inches height x 24 inches diameter brazed inside a cylindrical copper vessel 9 inches height x 5 inches diameter which contains the water. The apparatus is fitted at the top with an outlet for the steam and is heated by placing it on a tripod. The price is 15s. (Mr. G. Cussons,

Price 2s. per sheet 40 inches x 40 inches. United Asbestos Company, Billiter Street, London, E. C.