The signs of the 2nd, 3rd, and 4th lines are formed from those of the 1st by the addition of lower dots. The signs of the 1st line when preceded by the prefix for numbers stand for the nine numbers and the cipher. The stereotype plates from which books are printed are produced in precisely the same manner, only that instead of paper thin sheets of tin are used, on which the dots are elevated, and the manufacture of these same plates opens out a new field of remunerative employment for the blind, who at this work can earn from ten shillings to one pound per week, while the want of educational and other books, which has been so long felt, can be soon overcome by merely setting plenty of blind stereotypers to work. Already the association has thus enormously enlarged the range of literature available for the blind. It has published at a low rate many standard works which have been hitherto literally sealed books to the sightless. high-class education is to them. For only in the field of intellectual occupation have they any chance of competing fairly with their seeing brethren. It is on this account that the blind, when properly educated, succeed better as tuners, teachers of music, and organists, than in the mere manual labour of basket and brush-making, etc. There is no reason why a person without eyes should not be just as good an author, poet, or musician—either as instrumentalist, vocalist, or composer -as if he were endowed with the great gift of sight, be he once properly educated. But there are a hundred reasons why he can never compete with the seeing in mechanical labour, not to mention the superiority of the cultivating and elevating influences of Besides the Scriptures and many hymns, these the intellectual means of bread-winning. Such work, works include selections from the poems of Macaulay, therefore, as it has been shown the British and Gray, Tennyson, Milton, Longfellow, Coleridge, as Foreign Blind Association is engaged in, surely dewell as the entire plays of "Macbeth" and "Ham- serves large recognition, and though hitherto any let," to say nothing of a mass of rudimentary educa- deficit in the accounts has been met by the liberality tional matter that was before beyond the reach of of the honorary secretary, it is evident that if the the blind. Geography, in the shape of improved work for the future is to be permanent, the expenses elevated maps, etc., cunning devices for teaching should be more nearly met by the annual subscriparithmetic, and last, not least, every appliance for tions to the institution and by the sales of the the application of the Braille system to musical nota-books. ARITHMETICAL SQUARES. Arithmetical Problem which we published arrangement may not be arrived at until after hours from which we make a selection. I. In the "Leisure Hour," 1878 (p. 591), is given Herr Meyer's arrangement of the numbers 1-64 in a square, having the same total (260) in each of the horizontal and vertical lines and the diagonals. This is compared with two similar squares which do not yield the like product in the diagonals; but as they give the Knight's Tour, which Herr Meyer's does not, they must still be considered as unrivalled. Herr Meyer's performance comes solely within the province of arithmetic, having no reference to the moves of the chess-piece in question. In this paper I lay before the reader my solution of a regular series of such problems. From what I have observed in working them out, I believe that any sequence commencing with 1 and ending with a square number can be so arranged in the form of a square as to give the like total in each of the horizontal and vertical lines and diagonals. This total is always the product of the square root of the last number by half the sum of the first and last numbers. 25 √ 25 × 25+ 1 2 = 5 x 13 = 65 6; and the which in the case of 1-25 gives 24 numbers forming the diagonal will be 1, 7, 13, 19, 25. By this arrangement, where the last number of the sequence is odd, the central number of the sequence will also be the central number of the square (as in figs. 3, 5, 7). To impart an air of finish, the other diagonal should also be composed of numbers in arithmetical progression; in odd sequences it will have the same central number as the first diagonal. This will admit in some cases-probably in all-of the second diagonal being a sequence. Having formed the diagonals, the next step is to make the verticals right. This presents no difficulty; the puzzling and tedious operation One line may is to get the horizontals equal. be considerably in excess of the requisite total, another much under; and the numbers must be shifted, as required, up and down in their own verticals to adjust the balance. If this cannot be done with the verticals as first arranged, they must be altered prior to trying the horizontals again. The proper then reversing the two diagonals. A square of 256 terms is divided into *This is produced by writing the numbers in their regular order, and 16 squares of 16 terms each, then 1 to 16 is arranged into the first square, 17 to 32 into the next, and so on till the 16th is completed; and these squares similarly arranged will complete the large square. Of the foregoing squares, figs. 2, 3, 4, 6 are built on the plan described. All except No. 1 (which cannot be so treated) and No. 8 have the same diagonal composed of numbers in arithmetical progression, proceeding from 1 to the last number in the sequence; and in all but No. 1 the first and last numbers of the sequence are also the first and last numbers respectively of the square. In every case all the pairs of numbers equidistant from the centre of the diagonals are equal to the sum of the first and last numbers in the sequence. In conclusion, I am not aware of the existence of any similar solution of this set of problems; but enough is here shown to prove that all sequences from 1 to a square number can be so arranged. But it is quite another question, and to me a matter of some doubt, whether the sequence 1-64 can be made to give the Knight's Tour in addition to the equal horizontals, verticals, and diagonals. Darieties. W. H. W. POCOHONTAS.-It seems that measures are being taken for the purpose of raising a monument to the memory of this historical and heroic Indian lady. She died at Gravesend, as certified by the following entry in the register :-" 1616, May 21, Rebecca Wrolfe, wyffe of Thomas Wrolfe, gent., a Virginia lady borne, was buried in the chancel." Up to the present time there is not even a tablet by the grave. A good deal of the romance of the story evaporates when Mrs. Rolfe is substituted for the Princess Pocohontas! It is like the "Maid of Athens," known in later life as Mrs. Black! However, the story is truly a romantic one, and has been immortalised in prose and verse, on canvas and in marble. When the Prince of Wales was visiting, now many years ago, the studio of a famous American sculptor at Rome, a statue of the Indian damsel was the chief object of interest. "Who was Pocohontas?" asked more than one of those present. The Prince of Wales at once told them, and we have some idea that the early knowledge of the romantic story was derived from the "Leisure Hour," in which the history, with illustrations by Sir John Gilbert, had appeared; and which we know was well read in the Royal household, under the guidance of the noble and good father of the Prince of Wales. MR. BRASSEY, M. P., ON TRADES UNIONS.-In a recent lecture at Hastings, Mr. Brassey said that trades unions might secure an earlier advance of wages in prosperous times, and delay a reduction in adverse times; but if they tried to exact terms which rendered it impossible that the trade in which they were employed could be carried on at a profit, its speedy cessation was inevitable. The latest reports of the most powerful trade unions clearly show how little could be effected by their instrumentality to arrest the downward movement in wages when trade is depressed. Trade unions, he went on to say, did wrong, not only in objecting to piecework, but in giving no positive and direct encouragement to diligence and superior intelligence amongst their members. He considered that no corporate body, under any plea, was entitled to deprive the individual workman of his freedom. BAD HANDWRITING.-It is a very grand thing to edit a magazine, but when you have to write a leading article on six out of every seven days in the week, you do not feel very much inclined to pore half the night through over more or less illegible contributions sent to you by unknown ladies and gentlemen. I used to make about fifty deadly enemies per mensem in the "Temple Bar" time, owing to my inability to read crabbed manuscripts; and even now, when I have nothing whatever to do with any kind of editing, the unknown ladies and gentlemen persist in sending me bolsters of "copy," accompanied by polite requests that I will read them, and tell the writers what I think of their productions. I candidly own that I do not think any. thing of them, for I never, by any chance, look at them. If I did I should not be able to pay the butcher, nor could I pass the butterman without blushing. If people could only be made to understand that a journalist has to work for his living, and that time to him literally means bread.-G. A. Sala, in the "Illustrated News." He was a man of the world, and viewed events and their colourings from a standpoint altogether different from her own. He had assured her that he knew no actual harm of Edward, that the result of the inquiries made for her satisfaction was that her brother was not worse than other young men. "You must allow him a little rope, Miss Moreton," Cecil had said, without considering that in a place where the business of life is chiefly pleasure, and in which society does not always either give or exact a brevet of respectability, so lax a principle is fraught with peculiar danger. "Not worse than others!" how little consolation can accrue from being weighed against a multitude, the Divine, not the social balance, being the one that must eventually decide our individual value. "Not worse!" repeated Mona, as she stood mechanically watching a few stragglers on the Promenade, from which the hot April sun had chased the greater number of visitors who, on cooler mornings, frequented it. "Not worse than others!' that is no commendation for my father's son. Oh, Edward, have you forgotten him?" She was expecting her pupil's drawing-master, and hearing footsteps, turned round. It was not he, but Captain Orde, in company with Miss Lestocq, who immediately joined her. They were talking of the closing season, the friends gone or going, and of Cecil's approaching departure, when the drawing-master entered and Mona took a chair near the table where Fanny had already prepared her sketches. Helen placed herself at the other end of the room and Captain Orde did the same. The room was too small for secrets, even if they had any, but neither just now appeared to wish to converse. Helen was serious and Captain Orde silent. He was watching Mona, whose face, reflected in the glass opposite, hung over a piece of tapestry-work, unconscious that the expression of every flitting thought was visible to those behind her, and that one of the two was really sorry for the carking care, the long dark lashes resting on the cheek only slightly veiled. "I will not tell her what I saw yesterday," thought Captain Orde, recalling the face of Edward Moreton as he had seen it flushed with eagerness and exultation over the green cloth at Monaco; "only a youthful indiscretion, perhaps, but she may take it too much to heart. Nevertheless, I will give him a word of warning before I go." "You are grave, Cecil," said Helen, breaking in upon his apparent abstraction. "And you are not gay." "How can I be?" retorted Helen. Cecil's dark eyes turned quickly upon her. There was a querulousness in her voice, a faint echo of something akin to sorrow, which made him look at her attentively. The whirl of gaiety was relaxing, but Nice was bursting into verdant beauty, and much enjoyment for those who could extract it from natural sources still remained. Helen, however, found no pleasure in the country-no admiration for its sapphire sky, no joy in its myrtle-scented woods, where the fragrant thyme thrust its roots among the rocks, and the restless lizard played in the sunshine under the stones. Such scenes brought her no interest, or rather associated themselves with others awaiting her in a tame village, where the summer horizon was always hazy and the winters brown and cheerless. "I am tired of everything," she remarked, fretfully-" almost of life." "Of this life, this butterfly existence," said Captain Orde, correcting her phraseology. "Unlike me, you have a better one in prospect. In a short time you and Warren will have made up your differences, and on my return home, some six months hence, I shall find the present promessi sposi cooing like gentle doves in their quiet aviary at Hillesden. When you burn the yule log at Christmas I shall be there. You know you must marry him," said Captain Orde, dropping his half-jesting tone, and suddenly speaking with decision. Helen bent her head, and a pinker shade passed into her cheeks. She knew that must be her fate. With all the attractions given by her unusual beauty, all the homage that had been paid to it, she was left with no alternative but that or the chances of another year. The season was virtually over. Society was settling upon its lees; those members of it whom courtesy designates the haut ton had left or were leaving. Count Marinski was gone, ending his acquaintance with Helen by a flourish of compliments, repeated with his hand where he supposed his heart was placed, and now Cecil Orde was going, intending to be away or wandering for an indefinite period. All these things were against her notions of happiness, but they could not be altered. Playing absently with a bunch of sweet Parma violets which Cecil had brought her, she plunged into the old subject of Hillesden dulness, asking afresh questions that had been frequently answered. "If we could but live at the Abbey," she said, harping upon the often considered grievance. That might have consoled her for having to spend her days in the country. A fine residence, or the highsounding name of one, would have done something towards reconciling her, but a dull, uninteresting parsonage presented but a dreary picture. A thought suddenly occurred which she immediately translated into language. Carelessly as we do many things, trifling in themselves, yet fraught with unknown weal or woe, in idle curiosity rather than with design, she asked, "If Warren had died in that glacier, who would have inherited his property?" "My unworthy self," answered Cecil, speaking gaily, and then suddenly flushed to a swarthy hue as his eyes met Helen's, earnest, eager, and yearning. They told a tale that quickly sent the blood back cold to his heart. Staggered, confounded, his mind almost turned from its balance by the one glance he encountered, he pressed his hand to his brow, covering his face as if to shut from view something that would not bear inspection. "Cecil! oh, Cecil! I did not mean it," said a weeping voice. On removing his hand his face was deadly pale, and Helen, more touchingly beautiful in her new character of penitent, was gazing on him through a mist of tears. Neither of them perceived the ghastly countenance reflected in the mirror opposite, nor even surmised that the hideous unspoken regret had been witnessed by a third party. Their conversation, carried on in English, had in no way disturbed the drawing lesson, and Mona heard without heeding the murmur of their voices until the name of Warren Sinclair caught her ear. By some rapid impulse she lifted her eyes just as Cecil replied and caught the mute answer of Helen's, remaining with her own fixed upon the glass, dilating with an expression of terror and horror blended together, while her cheek blanched and her heart turned |