divided by 2 is equal to 5. Proportion; or that the figures between which they are placed bear the same proportion to each other; thus, 46: 8:12, which denotes that in the same proportion as 4 is to 6, so is 8 to 12; four being twothirds of the amount of six, and eight being two-thirds of the amount of twelve. √3 or 3* denotes the square root of SIR,-Having seen in your 149th number, page 135, a letter from Philo Twist'em, stating it to be his opinion, "that a series of papers, explaining, in a plain and familiar style, the science of figures," would g be acceptable to a numerous class of your readers, I take leave to offer you the following, as the first of a series, which I shall continue at my leisure. I shall commence with vul gar fractions; but should any of your young readers require information on some of the earlier rules, I shall be most happy to communicate it to them. I am, &c. 1 and 2 make 3. Characters Explained. +means plus or addition, or that the figures between which it is placed are to be added together, thus 1+5 make 6. Minus or subtraction; or that the figure which is placed after it is to be subtracted from that which is placed before it, thus 6-4 leaves 2. Multiplication; or that the figures between which it is placed are to be multiplied, together, thus 3×3 make 9. Division; or that the figure which is placed before it is to be divided by that which is placed after it; thus 10+2 leaves 5. Equality; or that the figures which precede are of the same numerical value, or amount to the same sum as the figure placed after it; thus, in the last example, 10+2=5, meaning that 10. 5 or number 3. denotes that the number 7 is to be squared. denotes that the number 8 is to be cubed. Vulgar Fractions. A FRACTION is a part of a whole number, or if a whole be divided into any number of parts, those parts are called fractional parts or fractions. A fraction is expressed by two numbers separated by a line, the lower of which denotes the number of parts into which the whole has been divided, and the upper, the number of those parts which a person, for ex ample, may have. Thus, means that you are to divide one whole into three equal parts, and take two of the parts so divided. The upper figure is called the numerator, and the lower the denominator. We shall treat of four kinds of fractions, proper, improper, compound, and mixed, 1st. A fraction is termed proper when the upper number or numerator is less than the lower number or denominator, thus, are proper fractions, because each of them is less than a whole number; for if you, were to divide any thing into Sequal parts, and take but four of those parts, there would be four parts left,, 2nd. An improper fraction is that in which the numerator is equal to, or of greater value than the denominator; thus,,, are improper fractions. 2 4 3 5 3rd. A compound fraction is the fractional part of a fraction, and is known by the word "of;" thus, Messrs. Richardson and Hirst, of Leeds, have obtained a patent for this invention, which consists in covering parts of the surfaces of woollen fabrics with a certain composition that will resist the chemical action of the coloured liquor, into which the fabric is to be immersed in the process of dyeing in order that when the cloth so covered is withdrawn from the dyeing vat, and the composition is removed from its surface, those parts which have been thus guarded, may have retained their original colour, and not have been in any degree affected by the dyeing liquor. The composition is to be made by mixing about five stone of wheaten flour, with about four gallons of water; making a smooth paste, about the consistency of treacle. (It is not to be boiled, we presume, as the specification is silent upon that subject.) After this mixture has stood for three or four days, the yolks and whites of forty raw eggs are to be added, and the whole stirred well together. The composition is then ready for use; and is to be laid upon the fabric by means of a brush when large portions of the surface are to be protected, or by printing blocks when small parts of the surface are to be preserved from the ground colour in the form of a pattern. A small quantity of powdered glass or shells, or fine sand, is then to be sifted over the composition, for the purpose of assisting to set and bind it firmly this, however, may be dispensed with, if the composition is thick, and can be dried soon. The fabric being thus prepared, is then ready to be immersed in the dyeing vat, and treated as usual. When the dyeing process has been performed, the fabric is to be with 207 drawn from the vat, and the composition being scraped off, or otherwise removed, presents those parts which were covered perfectly free from the colour of which the other portions of the surface of the fabric have been dyed. The For the purpose of further illustration, the patentee describes the lady's shawl in several colours. process of dyeing and figuring a Suppose one side of the shawl is to be dyed of a plain blue, all over its surface, and the other side is to have a rose-coloured ground, with a white border, to be afterwards printed with a chintz or other pattern. shawl being stretched upon a square frame, that side which is to be blue, and that part of the other side intended for the border, is to be covered with the composition as a guard, leaving only that part exposed which is designed to be dyed a rose colour; the frame with the shawl, is then immersed in the dyeing vat, and remains there until it has imbibed its tint. The shawl being now withdrawn from the dye, that side which is intended to be blue, is to be cleared from the composition, and the other side covered completely. It is then immersed in the blue dye, and after that operation has been performed, the whole of the composition is to be removed, and the shawl will appear blue entirely on one side, and rosecoloured, with a white border, on the other; which being afterwards printed in the ordinary way, with a chintz or other suitable pattern, finishes the colouring of the shawl. Newton's Journal, OXALIC ACID. THIS acid was discovered by Scheele, and first described by Bergman. It is obtained by heating a solution of sugar in nitric acid. It crystallizes in small four-sided prisms, terminated by dihedral summits. These crystals are composed of 77 parts acid, and 23 water. When exposed to heat, it sublimes, but at the same time is partly decomposed. 208 NOTICES TO CORRESPONdents. These crystals have a very acid taste, and redden vegetable blues. They dissolve in their own weight of boiling water, and in twice their weight of cold water. They dissolve, also, readily in alcohol. When exposed to dry air, they effloresce; but in moist air they are not altered. Neither oxygen, nor the simple combustibles or incombustibles act on this acid. It oxidizes some of the metals; but most of them are not affected by it. It combines with the salifiable bases, and forms a class of salts, called oxalates. Muriatic and acetic acids dissolve it; sulphuric acid decomposes it, by the assistance of heat. Nitric acid converts it into water and carbonic acid. When combined with a base and distilled, it is decomposed, and converted into water, carbonic acid, carbonic oxide, carburetted hydrogen, and charcoal. It is composed, according to the experiments of Dr. Thompson, of 64 oxygen hydrogen 4 SUBSTANCES PRESERVED FROM When a mixture of one part of oil and two parts of resin is forced, by the application of a high temperature, to penetrate porous substances, as building stones, plaster, &c. it renders them perfectly impermeable to moisture. Merino Worarai 1687.1 Island of Mowee. Highest Peak 1669 1 NOTICES TO CORRESPONDENTS. T. C. E. in our next. The numbers published by Messrs. Hunt and Clark, do not belong to our series of the Mechanics' Magazine, and, consequently, will not be noticed in the Index of the Sixth Volume. Communications have been received from "A Civil Engineer,"-A. D.G. G.-A Constant Subscriber,-A Mechanic, and J. Hall, the whole of which shall meet with due attention. COMPOUND OF VARIOUS METALS. M. DITTMER has shown in the Hanoverian Magazine, that the following mixture, compounded by the privy counsellor, Doctor Hermstadt, may be substituted for gold, not only with respect to colour, but also to specific gravity, density, and ductility:-16 loth (less than 8 French ounces) of virgin platina, 7 loth of copper, and 1 loth of zinc, equally pure: place these metals together in a crucible, cover them with powdered charcoal, and melt them completely Printed by D. Sidney, Northumberland Street, into a single mass. Communications (post paid) to be addressed to the Editor, at the Publishers', KNIGHT and LACEY, 55, Paternoster Row, London. Strand. Mechanics' Magazine, MUSEUM, REGISTER, JOURNAL, AND GAZETTE. No. 154.] SATURDAY, AUGUST 5, 1826. [Price 3d. "Though the arts which minister to luxury and refinement have attained a higher eminence in other countries, yet, in every department of intellect which is really useful, Britain has no rival among nations, and has, in fact, opened and explored more new regions of thought, in every direction, than all the rest of the world since the restoration of learning." 210 IMPROVED MÖDE OF CASTING CYLINDERS.' cess of casting, the patentee states that he is enabled also to give a casehardened surface to the articles if required. For this purpose, it is proposed to employ both exhaustion and condensation of air in the process, and therefore he combines such apparatus as will enable him to effect those objects in a convenient way. But as the great variety of articles to be cast, must necessarily require differently formed apparatus, and as it is impossible to describe every form that circumstances may render eligible, he merely exhibits, in the drawing which accompanies his specification, one construction of apparatus, (by way of elucidation) which he proposes to employ for casting cylinders or rollers. The figure represents a section of the mould in which the article is to be cast, with the other parts of the apparatus suspended by means of chains to an ordinary crane, in which is also shewn a section of the pan or chest that holds the melted metal, with an air pump and air vessel connected, both to the mould and to the metal chest, by means of tubes with union joints. The mould in this instance consists of a hollow cylinder of iron, a, a, a, a, with flanges at the ends, the interior being bored, or otherwise truly formed to the figure of the intended cylinder or roller about to be cast; b, b, is an outer case or jacket surrounding the mould, and leaving a space between for the passage of cold water, which is intended to be conducted through this passage at the time of casting, by means of a pipe leading from a cistern, or otherwise, and a cock at bottom, in order to cool the mould; c, c, and d, d, are caps to be attached to the ends of the mould, in which is formed the hollows or recesses for casting the gudgeons and ends of the roller; these caps and the jacket are all united to the cylindrical mould by means of screws passing through the flanges. In the upper part of the cap, c, a small channel is made with a conical valve, and a short piece of pipe, e, is attached at the mouth of the orifice with a stop cock, through which channel and pipe the mould is to be exhausted. At the lower end The mould thus put together is to be suspended by chains from the crane, and then the pipe, g, which is attached by a cock joint to the air pump, h, is to be connected to the short pipe, e, by means of the union joint. The joints of the mould being now properly luted and rendered air tight, the air pump is put to work, and the interior of the mould exhausted, in which state it is ready for casting, or it may have been previously exhausted by the ordinary application of an air pump. The pan or metal chest may be of any convenient form; that shewn in the figure at i, i, is preferred, and it must be of such capacity as will contain a sufficient quantity of melted metal to produce the article about to be cast. This pan is to be inserted in another pan or vessel, k, k; and the space between the two to be filled with pulverized charcoal or other materials that are imperfect conductors of heat. The pan with the melted metal is to be brought from the furnace, and placed in such a situation under the mould, that the mould may be lowered down to it, and the pipe, f, immersed in the melted metal, the conical form of the flange at the bottom of the cap, d, fitting into the rim, e, e, on the top of the metal chest; and in order to make the joint more close, a springing hoop, m, of wrought iron, and of a wedge form, is placed round within the rim in contact, and forming an air tight joint with the upper edge of the rim, which giving way at bottom, to the pressure of the mould, secures the joint air tight. Through the lower flange of the cap, d, there is a small aperture, with a short piece of pipe, n, attached to it, through |