No. 1. Green Dye.-Shoemakers' Implement. 7 with vains; dyed with madder, and then ||ments, used in making boots, which are kept washed with spirit of vitriol, a veiny green firm upon it by a stirrup or endless strap. wood; with a strong bath of logwood, and then washed with virdigris, black. Elm, dyed with gamboge or saffron, imitates lignumvita. When the wood is properly colored, and thoroughly dry, it should be polished with Dutch rushes. Green Dye. The following is the process of making the beautiful Schweinfurt dye : One part of verdigris is to be dissolved in a sufficient quantity of good vinegar, by heat, in a copper kettle. When it is dissolved, add to the same a solution of one part of white arsenic in water. A dusky green precipitate generally ensues, which must be re-dissolved by the addition of more vinegar. This mixture is now to be boiled, when a graduated precipitate will be produced, of the most beautiful green color, which after being separated from the liquid, (either by filtration or by decanting after the color has subsided) is to be well washed and dried, when it is ready for use either as a dye or pigment. If the liquor, after this process, should be found to contain more copper, more of the solution of arsenic may be added, but if it contains instead an excess of arsenic, then more of the solution of copper may be added, completing the process as before mentioned; and if the liquid should contain an excess of the acetic acid, it may be advantageously employed in the solution of more verdigris. "This hollow block is joined into another piece (which connects it with the stand) so as to admit of a vertical motion; and it is retained at any angle in this motion, by a circular catch, with notches formed in its side to fasten it on an iron catch projecting from the lower piece. This lower piece is shaped into a small cylinder beneath, which entering into a hole formed for it in the top of the pillar of the stand, permits the hollow block to be moved round about, without stirring the stand; so that by the combination of these two motions, it may be placed in any position. "Behind the hollow block and on a level with it, a horizontal piece or board is supported by a small pillar, rising from one of the feet of the stand, and secured firm by a brace to the stand itself. This board supports the tools and implements wanted, ready at hand for the workman's use. "The design of this invention is to obviate the necessity of using that very unwholesome posture in which shoemakers are accustomed to work; which compresses the lungs and bowels in such a manner, as to occasion consumption, inflammation of the bowels, and a variety of other frightful complaints. "The efficacy of the alteration of posture, permitted by this instrument, which enables the workman to stand at his work, is very well proved in the case of the inventor of it, who has produced a medical certificate, that he was for many years so afflicted with bowel complaints and piles, that he was under the necessity of leaving off his trade entirely, if he could not contrive to work standing; and that since he has made use of this implement his complaints are entirely removed, and he is so improved in flesh and countenance that he "looks not like the same man ;" and for some years he had no occasion for medicine. He has made many hundred pairs of shoes on this stand, and recommends its general use as the "quickest way of closing all the thread work." The color prepared by the preceding process is of a bluish green; but as a deeper and more yellowish green is frequently required, this is obtained by dissolving a pound of common potash in water, to which add ten pounds of the green colour prepared by the former process, and warm the mixture over a gentle fire, when the desired tint will be acquired. If allowed to boil long, the color will approximate in hue to Scheele's green, nevertheless, as it is in all the tints, of greater brilliancy and beauty. The alkaThe editors of the "Retrospect of Disline fluid that remains may be advantage-coveries" make the following, among other ously employed in making Scheele's green. Implement to enable shoemakers to work in a standing posture. From the Transactions of the Society of Arts, &c. observations on this invention. "This implement might be made still more simple by leaving out the part used to give the hollow block a circular motion, which does not appear necessary, from the facility Fifteen guineas were given to Mr. Thomas which the workman has, when standing at Holden, of Fettleworth, Sussex, by the So- it, to place himself instantly at any side of the eiety of Arts, for contriving this implement. work he pleases; and it seems therefore it "It resembles a stand, such as is used for would be full as little, or rather less trouble reading desks: at its top is a small block to him to let the instrument remain unmoved, of wood, excavated so as to form a proper and turn himself round instead of it, as to bed for the last, and the moulds or instru-stand still while he turned it about, Essays on Mathematics. "A wooden vice of a proper height, fixed || to a stake, and secured even by a wedge, if a screw should be deemed expensive, would also hold a last in any position required for the workman. "These circumstances are mentioned, because the invention is highly valuable, and whatever can tend to render it cheaper, or enable the workman to procure other instruments for this purpose, which chance might render more easy to acquire, or his fancy make more agreeable, must be of use. "It would be a matter of great humanity to persuade other orders of workmen, as well as shoemakers, to work in postures less injurious to their health than those they are in the habit of using, some of which use them without any apparent reason; for instance tailors, who could full as well perform their work standing or sitting before a table which supported it, as by coiling themselves up into a form equally preposterous and useless, and still more injurious than that used by shoemakers, as it compresses and deranges the vital parts still more, while at the same time it cripples their limbs. But such is the force of custom, that sickness, pain, and ridicule are endured rather than change a useless posture, which nothing but the total absence of chairs and tables can excuse, and which can now serve no purpose but to prove the antiquity of the profession to have preceded the invention of furniture. But as this is a point no one will dispute, it is to be hoped that some of them will have sense enough to lay it aside; and that some masters may be induced to provide tables at which men may work either standing or sitting as they choose; who would find their account in this piece of humanity, both in having the work less interrupted by a change of hands, in keeping it more clean, and probably also in other particulars. Much might be added also here, with propriety, as to the humanity of having workshops of all kinds, where many men work together, better ventilated and larger, to improve the health of the workmen, but that it is feared the observations on this subject will be thought already too much extended." Essays on Mathematics.-No. 1. Glasgow. The word mathematics originally signified discipline or learning, (science;) but it is now appropriated to that science which teaches the comparison and mensuration of magnitude. It has also been termed the science of quantity, and in this view, the objects to which it may be applied are equally merous and various as the objects of our VOL. I. senses; for whatever is the object of our senses, is capable of being considered, either with respect to its number, its extension, or its quantity. Mathematics is divided into pure and mixed. PURE MATHEMATICS considers magnitudes generally, simply, and abstractedly, without any relation to matter or sensible objects. Under this class are comprehended, 1, ARITHMETIC, or the art of numerical computation; 2, GEOMETRY, which teaches us to mea sure extension; 3, ANALYSIS, or the comparison and calculation of magnitudes in general; 4, MIXED GEOMETRY, or the combination of geometry with analysis. MIXED MATHEMATICS borrow from physics that is natural philosophy, one or more incontestible experiments, and then, by a demonstrative chain of reasoning, they deduce. from established principles, conclusions as certain as those of pure mathematics.Under this division are comprehended, 1, MECHANICS, the science which treats of the effect of moving powers, or forces, and the laws of motion; 2, HYDRODYNAMICS, which explains the motion of fluids, and the laws of their action; 3, ASTRONOMY, which considers the revolutions and various phenomena of the sun, moon, and other heavenly bodies; 4, OPTICS, the science of vision, including the properties of light and colors; 5, ACOUSTICS, the theory of sounds. Mathematics have also been divided into speculative and practical; a division which applies both to the pure and mixed. SPECULATIVE MATHEMATICS inquires after knowledge which it is proposed to attain, and simply contemplates the truth or falsehood of what is asserted. PRACTICAL MATHEMATICS is the application of the speculative, and shows how to perform something useful or advantageous to mankind. It is not possible to fix the origin of mathematics with precision, though we are able to affirm that it goes back to the remotest ages. Josephus asserts that they were studied before the flood; that the sons of Seth were observers of the heavens; that they built two pillars, the one of brick, the other of stone, to commemorate their discoveries, and that Abraham taught these sciences to the Egyptians, who, however, there is reason to suppose, were acquainted with the science previous to the period of the Patriarch's sojournment among them. The most certain and best established opinion is, that the mathematics began to acquire a certain so No.1. Essays on Mathematics 9 lidity almost at the same period among the || east, the museum and library of Alexandria Chaldeans and Egyptians, the two most an- were destroyed. cient people known in history. The magi, or priests of Egypt, directed by the laws of their institution to study and collect the secrets of nature, were become the depositaries and dispensers of all human knowledge; but they have been blamed with involving their discoveries in mystery. It is said that Thales traveled into Egypt about 600 years before Christ, and brought the mathematical sciences into Greece; and, whether this be true or not, it is only from this time that we have any certain accounts of them. However, though the chain of mathematical discovery was broken by this fatal catastrophe, a few links remained, which this nation of destroyers, softened by the charms of peace, strove to collect and unite afresh. In less than a century we find the Arabs cultivating astronomy, and their taste for a particular science gradually extended to all the branches of knowledge. For the space of seven hundred years, the mathematics flourished in the extensive dominions of the caliphs; by the Moors they were carried into Spain, and spread over the rest With the mathematics of the ancients we of Europe. And the Arabs rendered essen, are acquainted only through the writings tial service by their translations of the works of the Greeks, and we do not possess the of the ancient Greeks, with some of which necessary documents to estimate the instruc- we are acquainted, only through the me tion which these derived from their inter-dium of the Arabic version. course with the more eastern nations. We The conquests of the Turks brought back know, however, that as soon as the mathe-ignorance and barbarism, on the delightful matics took root in Greece, their progress countries which the Arabs inhabited; and was rapid, and the Grecians became, in some measure, the preceptors of all nations. The elementary books collected and arranged by Euclid, have been translated into all languages, and have continued for more than 2000 years to be exclusively taught in every mathematical school-a certain proof of their excellence. The conics of Apollonius hold an equal rank in what has been called the higher geometry. Many other mathematicians labored in the same field, but the most exalted rank in this legion of honor has been assigned, both by reason and fable, to the sublime genius of Archimedes. In the accurate sciences, which require cool attention, silence, and profound meditation, the Romans never surpassed mediocrity. Useless as the means of attaining the first offices of the state, they were the occupation of a few obscure individuals, remote from the agitation of public affairs. The Roman mathematicians were little more than translators or commentators of Archimedes, Apollonius, &c. extinguished the lamp of science which had long glimmered with fading lustre in the dissolute and desolated provinces of the eastern empire. At the taking of Constantinople by Mohammed II. a persecution arose against artisans and men of learning, by which many of them were destroyed; but some escaped, and carried with them the remains of the mathematical sciences into Italy, France, Germany, and England, countries in which a taste for literature had already begun to take root. From this period, all the branches of the mathematics made rapid progress. The improvements of the moderns have put us in possession of an infinite number of problems, inaccessible to the ancient geometricians. The ancients have given us nearly the whole of what has been termed pure or speculative geometry, few additions have been made to the fundamentals of the science-most of the modern works on plane geometry, or the conic sections, are compilations from theirs; but the moderns have improved arithmetic. On the death of Theodosius, and the di- The ancients knew little, if any thing of alvision of the empire, the western part was gebra, and we claim the sublime invention long ravaged, and at length subjugated by of fluxions as our own. We have applied barbarians, and soon sunk into profound the mathematics to the improvement of pracignorance; while the eastern schools were tical arts and sciences, as mechanics, prowholly employed in theological disputes.jectiles, gunnery, astronomy, and optics, far The accurate sciences had taken refuge in the Alexandrian museum, (almost the only refuge they had left them,) which was founded by Ptolemy Philadelphus, about 320| But let it not be supposed that the moderus years before Christ. Here the mathematics have surpassed the ancients in genius. It flourished near ten centuries. But of this is probable that the discoveries which they asylum they were deprived about the middle made, required, in the infancy of science, of the seventh century, when the Arabs, con- intellectual exertions as great as any modern ducted by the successors of Mohammed, improvement. The most important improvespread carnage and devastation through the||ments in science have always been preceded more extensively than they; and they were ignorant of the combination of analysis and geometry which we employ. 10 Invention of the Mariner's Compass. by gradual advances. The discovery which astonishes when it is announced, can often be traced through many previous steps which all contribute to bring it to light; and the wonder that it should not have been sooner made, is often greater than the surprise which it occasions. We are possessed of instruments, which are equally just, which arrive, by a shorter process, at the end proposed; but we are inferior to the ancients in pure geometry. If Archimedes were to return to this earth, with all the wonderful attainments he possessed, he would be obliged to subject himself to a long course of study before he could place himself on a level with Newton; yet Newton lamented that he had too much neglected the strict geometrical reasonings of the Syracusan sage. Invention of the Mariner's Compass. The invention of this precious instrument has hitherto been awarded to Favio Gioia, a Neapolitan, in 1302, or 1303. But this statement has rested on no satisfactory evidence; and, when it was discovered that the Chinese and Arabian authors had spoken of the magnet's polarity before the fourteenth century, it began to be suspected that the Neapolitan was merely the introducer of the compass into Europe. To settle the question, in January, 1834, Baron Humboldt wrote to M. Klaproth to ascertain the epochs.-1st. When the Chinese discovered the polarity of the magnet; and 2d. When they began to apply it to the purposes of navigation. M. Klaproth has replied in a work, published in Paris towards the close of the year, in which the most remarkable proof of the Chinese claims to this invention, is in the history of the magnetic chariots, whose origin is lost in the obscurity of the mythological ages. The accompanying representation of one of these chariots is taken from the 33d volume of Japanese Encyclopædia." The figure in front of the chariot was made of some light material; it was fixed upon a pivot, and its finger invariably pointed to the south, which, as we have already said, was the kibleh, or sacred point of the Chinese, to which they always turn when performing their devotions. It is intimated rather obscurely, that these magnetic chariots were first invented for a religions purpose, namely, to enable the devout to discover their kibleh when the sun and stars were obscured by clouds-a purpose to which the compass is frequently applied in the present day by Mohammedan nations; but there are very full descriptions of the use made of these chariots in directing the march of armies, nd guiding ambassadors. M. Klaproth has! VOL. I. "The wooden figure placed on the magnetic car resembled a genius wearing a dress made of feathers; whatever was the position of the car, the hand of the genius always pointed to the south. When the emperor went in state, one of these cars headed the procession, and served to indicate the cardinal points." In the history of the second Tchoa dynasty, which lasted from A. D. 319 to A. D. 351, we read, "The Chang-Fang (president of the board of works) ordered Kiai Fei, who was distinguished by his great skill in constructing every kind of instrument, to build a number of magnetic chariots, which were sent as presents to the principal grandees of the empire." There are several accounts of the manner in which the magnetic figures were constructed; as our readers have probably anticipated, a magnetized bar passed through the arm of the figure; and the only variety of ingenuity displayed by the architects was in balancing the figure upon its pivot. The antiquity of these magnetic chariots is established incontrovertibly; the step from them to the compass is so very easy, that we may safely assert that the one must have led immediately to the other. No. 1. Inventions, Discoveries in the Arts, Hints, &c. Inventions, Discoveries in the INTERESTING TO BLACKSMITHS.-Permit me to describe a machine which I have just seen, and which for utility and simplicity, is truly admirable. The article I allude to is a substitute for a smith's bellows, and is far more powerful than the kind in common use. -It is constructed by way of fanners, and stands immediately behind the forge. The box of this implement is only eighteen inches in diameter, and the fans which fill the box are only five inches broad, and are fastened upon a horizontal shaft of three quarters inch iron. On the end of the shaft is a pully two inches diameter, and right above which is large pully twenty inches diameter, with a crank in the centre, which the man at the fire drives with one hand, while he guides the iron in the fire with the other. a Around the large pully and down to the small one, is a leather belt, by which this machine is driven, and with such ease that a child may drive it. The blast is so constant and so efficient that the driver prefers it for heavy work to the best bellows, which cost him 67. while he has the blast-bellows for about 20s.; and he adds that for a few more shillings, he could have it driven by wind. Although bellows on the same plan has been used and driven by steam and by water at our large iron works, yet the merit of constructing one to work with the hand, belongs to Mr. William Bowie, blacksmith, Lower Bridge street, Stirling, where the machine may be seen in operation. What adds much to the value of this contrivance is, its being easily purchased, that it requires little room, and is in many respects superior to the kind in common use. STONE CUTTING MACHINE.-A new stone cutting machine, invented by Mr. Pitts, of Maine, and called Pitts' Stone Cutter, is said to answer admirably in reducing to shape the blocks of granite from the quarries in that region. It has three hammers which are made to pass over the stone. First, one which roughs it over as it is called, knocking off the inequalities, and making the surface approximate to something like a level; next, a hammer or chisel of a different kind passes over, which cuts down all the inequalities and makes the surface flat and more smooth; next comes the dressing hammer-this gives the finishing touch, and leaves the surface as even and smooth as the most expert workman could make it with the hand. MACHINE FOR PLANEING ROCK.-The new machine in Great Britain for planeing rough masses of rock, as if they were pieces of 11 timber, by the help of steam, is exhibited i London. It is complex, but perfect in its construction, and works beautifully. The following is a description: "The moving part of the model does not exceed 1 cwt. but of the machine itself, which is in use at the quarries near Arbreath, the moving part weighs two tons, and may be compared to a beds of stone, with as much ease, apparently, vast hand plane, 21 feet in length, traversing as the tool in the grasp of the hands of a carpenter. During the last summer there were at Leysmill's quarries six of these machines at work, which planed upwards of 170,000 the machines were propelled by one steam feet of pavement; and the whole number of engine of six horse power, which besides worked two inclined planes, upon one of which the stones are dragged from the quarry to the machine. Where stone is plenty, and not exceedingly valuable, the invention must be of great advantage to the proprietors of quarries. WOOD SCREWs.-It is well known that the points of wood-screws, are generally terminated by the thin shell of the worms; now this, especially in hard wood, frequently turns or yields, so as, in fact, instead of merely penetrating the wood, and leaving a thin screw-like passage for the worm of the screw, that blunted end bores a groove as wide as its own increased thickness, and thus considerably affects the firmness of the screw in the wood. Now, instead of this, Mr. Ford files the points of his wood-screws into a conical form, thus entirely removing that hurtful thin shell of the worm, and he also prepares another of the same sized screws, so as to serve the office of a tap, to open the hole in a screw-like manner; and he thus greatly facilitates the entrance of the screw itself into the hole afterwards. This he effects, by filing away the threads flat on four sides, into a square form, and with sharp angular edges to them; and also flattens or spreads the conical screw heard broad, so as to serve to turn the tap so formed, more conveniently than if it had been left of its original conical shape. In using wood-screws end ways of the grain of the wood, and par ticularly when the screws are to be frequently put in and taken out again, Mr. Ford finds this practice eminently useful; and that now we have published it, we have do doubt that it will be frequently adopted in practice. Tech. Rep. MACHINE OF A NEW PRINCIPLE FOR RAISING COAL, WATER, &c.-The construction of this power is very simple, and its steady operation is quite assured. Its chief agent is a pair of wheels, or, if necessary, a series, moving with their diameters in the direction |