Who that can feel Presumes to steel Himself to say, I don't believe in Him? Enfolds, upholds He not Does not the heaven o'erarch us yonder? Do not my eyes look into yours, And weave themselves, in mystery eternal, Fill your heart full of that, it is so great; Then name it what you will, Name 't Bliss, Heart, Love, God! Feeling is everything; Name is but sound and smoke, MARGARET. That's all right fair and good, and even The priest almost said that, only he spoke With other words, that differed just a bit. FAUST. They say it everywhere; say it, From this point the tragedy of Margaret speeds on to its dreadful close. For a moment Faust, in the presence of Nature, alone amid forest and cavern, had seen whither he was hurrying them both, the abyss that yawned at their feet; but the demon, with his lure of pleasure, had them too closely in his grasp to escape. The mocking girls at the fountain tell the sad story; and we see its effect in the awful agony of soul sobbing through the young creature's prayer to the Virgin Mother, and her vain attempt to pray in the cathedral, with the taunting fiend at her elbow. Meanwhile, the Demon of Selfishness bears Faust away, to forget his remorse in that carnival of sensuality and seeking on the Brocken, the wiches' revel. Goethe laughs with Zelter over the German commentary which hunts down the historical foundation of the scene, as if the prose fact were important, though he admits using it as the foundation of his "poetical fable." Let us see, then, what they are doing in these witches' orgies. Faust, in the lovely wood-path, would linger and enjoy the beauty of the spring night. Mephistopheles urges him to hasten to the summit. He asks an ignis fatuus, a light of error, as the Germans call it, to light the path upward. Through what swarms of animal creatures they thread their way! The mountain is alive with a seething mass of deformed animal humanity, all struggling to get to the top. It is the night of the witches. The lurid light, like the gleam of ruddy gold in the firelight, glimmers through the abyss, glows in clouds of mist through a vaporous veil, threads the valley with a hundred veins, here confined sparkles like golden sand. "And see, in their whole height rise o'er us, Enkindled, all the mountain walls." Here, says Mephistopheles, is a midway elevation, where we can see, with astonishment, "How Mammon in the mountain glows." Need we go far afield to find the meaning of the poet's fable? On that midway elevation of what is called an "easy competence," as we come from the country into the mad whirl of struggling humanity in a great city, we realize vividly the rush for wealth, the constant struggle to get to the top. Look out, again with Goethe's eyes, on the orgies that preceded the French Revolution. "Call me Sir Baron," remarks Mephistopheles to The Witch. "I ar am a cavalier like other cavaliers." As we see all this, shall we be quite at a loss for the poet's meaning? Mephistopheles, looking on the scene, exclaims to Faust, that Soul of Man: "Las not Sir Mammon grandly lighted His palac or this festival!" "Our country people," says Goethe to Eckermann, continuing a remark about the last day seeming to be near, which we find repeated in this scene as Faust and Mephistopheles approach the horrible revelry," our country people have certainly kept up their strength, and will, I hope, long be able to secure us from total decay and destruction. The rural population are to be regarded as a magazine, from which the forces of declining manhood are always recruited and refreshed. But just go into our great towns, and you will feel quite differently. Just take a turn beside a second Diable Boiteux or a physician of large practice, and he will whisper to you tales which will horrify you at the misery, and astonish you at the vice, with which human nature is visited, and from which society suffers." Here, then, in Mephistopheles we find our "second diable boiteux," by whose side we take a turn through the great city; and, after reading this paragraph, we may enjoy with Goethe his quiet laugh with Zelter over the labors of the commentators who have "taken such pains to convert poetry back into prose." They have rendered a service, however, in searching out the originals who sat for the different portraits; for here, as everywhere, Goethe always draws, even his most fanciful figures, from a living model. We may, perhaps, in connection with this recall Goethe's remark to Schiller, on "the peculiar character of the public in a great city. It lives in an incessant tumult of getting and spending; and what we call the higher mood can neither be produced there nor communicated;" and his observation to Eckermann, that he "anticipates special pleasure from Delacroix's scenes on the Brocken. You will see here the extensive experience of life for which a great city like Paris has given him such opportunities." With the disgust which comes to Faust, dancing with his fair, nude partner, as her animal nature shows itself to him, the image of his purer love returns; and in the next scene, again face to face with Nature, he sees his action in its true light, curses Mephistopheles, and bids him bear him to where Gretchen is imprisoned. In that most pathetic scene of all literature which ends the First Part, we learn from the distracted utterances of poor Gretchen, raving amid the straw on the prison floor, the secret of her tragic end. 66 "The world," says Goethe, "is to me like a great factory, where, amid the whirring looms and wheels, we all work out the purposes of the Master Workman." To Gretchen, with the great gift of love, the great responsibility of another life has been given. She too, at work in this whirring loom of time, has been made the guardian of a part of that fabric, the Garment of Life, by which we recognize the Deity. "If we work with the Master," Goethe says, our holiday will come, and our reward. If we strive to seize the web or destroy it, we shall destroy ourselves." Gretchen, neglecting the loom, has, for her own convenience, stretched out her hand to get rid of the responsibility imposed upon her, and the awful wheels of God come over and crush her. But notice, as the night ends, in the gray streak of dawn she recognizes the divine justice, and, refusing to escape the penalty, becomes, in her exalted reunion with the Divine Purpose, the influence that still shall lead her lover upward and on. In the Second Part we see, reviewing the larger field, the life of the race; what this influence, this manifestation of the Ewig-weibliche, the Woman-Soul, has there done for us. But all this must be reserved for another occasion. William P. Andrews. MODERN TEACHING OF ARITHMETIC. IN his book On the Education of an Orator, Quintilian gives an excellent series of reasons why the pleader should be taught mathematics. His doctrine is that geometry, as he calls it, is, in its two branches of "numbers" and "forms," important for an orator on practical grounds, for example in cases concerning real estate or accounts; and he vividly pictures the embarrassment which the speaker will show if he is awkward at the problems of arithmetic which necessarily come into his oration. Quintilian does not stop here: he admits as a well-known principle that geometry is an admirable training for the reasoning powers; and the experience of later ages has fully confirmed this view. It will be remembered that the Greeks and Romans had no algebra, and very troublesome systems of arithmetical notation. For both reasons their arithmetic furnishes an admirable mental training of the kind which is still much in favor with old-fashioned teachers, -a training now based upon the use of artificial obstacles. If any one who knows Greek or Latin will take the pains to read the seventh and following books of Euclid, especially the voluminous tenth, he will find ordinary arithmetic treated under difficulties of a kind quite analogous to those which have been artificially produced in our "higher arithmetics." Indeed, it must seem strange to any one who holds certain theories of mathematical teaching to discover that these books have for centuries been neglected in the schools, and replaced by vastly easier methods. For an English Euclid containing them we must look in editions published a century or more ago; and if mere difficulty supplies an excellent basis for mathematical training (as some people seem to think), this neglect of so much of the immortal author's work appears disrespectful. Archimedes was the discoverer of an approximation to the quadrature of the circle; the latest editions of this great writer's books show very clearly how much he was hampered by the Greek method of calculation, and how much more he could have done had algebra and the Arabic notation been then invented. We now employ the infinitesimal calculus to gain with great ease the results which he obtained with enormous labor. No one at present thinks of using his method in instruction, although its difficulties are so considerable. After the Middle Ages the Arabic notation was introduced into Europe; and at the revival of learning great mathematicians restored the science and art of numbers to its old place in the schools, and began the scientific investigation of nature with the study of astronomy. These philosophers made it possible for the mariner to find his latitude at sea, and occasionally to guess at his longitude; the ocean was no longer absolutely unknown, and the discovery of America was possible. Such writers taught arithmetic more as a matter of rules than of reasoning. Very possibly the rules were supplemented, in some cases, by the abstract theories of Euclid; but on the whole the rules prevailed in the schools, and the numerical part of mathematics was a practical subject, taught for the sake of mechanical facility. In England and her colonies this method was long retained, owing in part to the extremely artificial character of the denominations employed in money, weights, and measures, and the steady conservatism of the English people. Even now children in England gain much "mental training" (of the kind due to needless diffi Our conservative instructors held on to the debased currency in English denominations used in this country much longer and more strenuously than was at all necessary; and I have no doubt that they delayed the final introduction of federal money more than a few years. The worst consequence of the old ways the teaching by rule rather than by reasoning has not entirely disappeared. The ordinary books give, it is true, a short course of reasoning preparatory to each rule; but the rules are many, and the reasoning is often so lightly indicated that many teachers lay no great stress upon it, and the children work by the mechanical process. So, at least, it appears when the methods are tested at a later stage of education. The ideas of the celebrated Pestalozzi were translated into practice by his numerous disciples in all civilized counIn arithmetic Warren Colburn was the most practical and successful American writer of this century. He emphasized the idea brought forward by Quintilian, that mathematics is especially valuable as means of mental training; and it may be questioned whether, at first, some teachers did not pay too strict attention to this side of the matter. But it soon became the usual practice to combine the two methods: to employ Colburn's First Lessons as a textbook for mental arithmetic, and some larger one for written. The consequence in many cases has been the retention of mechanical methods in written arithmetic, which has been sometimes kept quite separate from mental. Since Colburn's time graded schools have been established far and wide in this country. Their principles have taken up the German method of dividing numbers into so-called “circles," 1 to 10, 10 to 20, 20 to 100, and so forth; at first without definite uniform boundaries. The circles were, in fact, bounded differently for the various operations. Thus the English New Code of 1888 gives as the work of the First Standard: "Notation and numeration up to 1000. Simple addition and subtraction of numbers of not more than three figures. In addition not more than five lines to be given. The multiplication table to 6 times 12." A distinction is thus made between addition and multiplication. Similar programmes have been made in this country for many cities; but the latest tendency is to the general adoption of Grube's method. This is a method in which separate numbers, 1, 2, 3, 4, and so on, as far as 100, are taken up one by one and analyzed. The pupil learns the qualities by his small experience, first of the number 1, then of the number 2, both by itself and as compared with the preceding number. Then follows 3, which is already more complex; its slight complexity is illustrated in every possible way by objects, and it is thoroughly mastered so far as the child's mind can deal with it. The separate numbers are mental "objects," as one may technically express it; the mental objects are definitely presented before the mind by the comparatively small degree of abstraction required to separate the idea of 3 from the idea of 3 fingers, 3 cents, 3 pencils, or other small but familiar things. The underlying theory is that otherwise the child is required to perform so great a degree of abstraction that the thought becomes mechanical; and the method is brought forward as a contribution from experience to the psychology of the growing mind. It is very clear to those who have thought about it that this method of dealing with individual numbers in their orderly succession, one by one, is more natural than the older way of taking for granted, after a few trifling exercises, that the young pupil lack of variety. It seems to have been printed almost as it was written, the occasional hiatuses suggesting no obscure and conjectural private history, but rather serving to point to the meaning between the lines, while the initials are the most transparent veil to the personalities alluded to on every page. Naturally, Mrs. Kemble's return to Philadelphia, in 1874, stirred memories and associations of an experience which, in a life like hers, actually formed but a single chapter, and which during the busy years of her full after career as an actress and a reader must have seemed unreal, but now was brought up at every turn. Her relationship with those closest had, however, little of the intimate habit which usually accompanies ties of blood; thus her constant allusions to her family take a delicate and piquant turn, and her admiring appreciation is tinged with a hundred pretty changeable lights of sentiment and also of criticism. She arranges her life at York Farm as completely as an Englishwoman may who perpetually reminds herself of American limitations. We may follow every detail of the quiet routine at York Farm, and each member of the household, from the central figure down to the setter dog and the canary bird, becomes individualized to us. Many vivid touches set forth the region round about, the burst of spring, the intense heats of summer, the wonderful transfiguration of autumn, the white and glittering splendors of winter, which seems to have expended its worst rigors in the years Mrs. Kemble lived at York Farm. The sloping fields undulate to the woods of Champlost, where lives her friend "M.," who is described over and over again, with a touch made exquisite by tender and admiring af fection. Even the by-path leading to Champlost soon gains charm for the reader, along a lane, across a park where fine oaks grow, with a gush of violets at the foot of the great trees, while the meadows on either side are blue-white with the starry blossoms of the euphrasia. A quick sense for nature's refreshment and renovation to heart and soul is shown in every allusion to out-of-door life. To transfer to this country not only the habits of English life, but also of English thought and the prejudices of a lifetime, was of course to make Mrs. Kemble an inexorable critic of everything American. We are accustomed to judicious strictures upon our manners, habits, and tendencies, in fact, we frequently court them by asking foreigners, and particularly English people, for their candid opinion of us; yet we do not get over a certain expectation of being pronounced faultless, and our withers are wrung when exceptions are taken to our public institutions and our national idiosyncrasies. There is no display of rosepink optimism in Mrs. Kemble's criticisms, but it should be remembered that when she sets out to interpret our domestic habits and our public politics, she is answering the questions of a correspondent curious to know the worst of a country she believes little good of; indeed, is surprised should be inhabited by well-to-do people able to denationalize themselves by living in Europe. That Mrs. Kemble, in spite of her fault-finding with America in certain minor details, was in sympathy with us at the time of the crisis of our history may be seen by this extract from a letter to Mr. Malkin in September, 1861: "The state of the country is very sad, and I fear will long continue to grieve and mortify its well-wishers; but of the ultimate success of the North I have not a shadow of a doubt. I hope to God that neither England nor any other power from the other side of the water will meddle in the matter, but above all not England; and thus, after some bad and good fighting, and an unlimited amount of brag and bluster on both sides, the South, in spite of a much better state of preparation, of better soldiers, |