= 1. To draw a right line C T, a tangent to a given circle, (fig. 12.) BCA, in a` given point, C. Let C S be perpendicular to the diameter, A B, and put A B a, BS = x, and S C y. Then, by the property of the circle, y2 (= CS')=BS XAS (= x × a − x) = ax➡ x2; whereof the fluxion being taken, in order to determine the ratio of and y, we get 2 y ya x − 2x ; consequently = 2y a- 2x by y, gives yx y za- -X = the sub-tan gent, S T. Whence O, being supposed the centre, we have O S (=a-x): CS (=y) :: CS (=y): ST; which is also found to be the case from other principles. 2. To draw a tangent to any given point, C, (fig. 13.) of the conical parabola, AC G. If the latus rectum of the curve be denoted by a, the ordinate M C, by y, and its corresponding absciss, A M, by x; then the known equation, expressing the relation of x and y, being a x = y2, we have, in this case, the fluxion a i 2yy; whence 2y; and consequently 2 y' a y 2 ax a a 2x = M F. Therefore the sub-tangent is just the double of its corresponding absciss, A M. And so for finding the tangents of other species of curves. TANNING, the art of manufacturing leather from raw hides and skins. Before we detail the process, it may be proper to observe, that raw hides and skins being composed of minute fibres, intersecting each other in every direction, the general operation of tanning consists chiefly in expanding the pores, and dissolving a sort of greasy substance contained in them; and then, by means of the astringency and gummy resinous properties of oak bark, to fill and reunite them, so as to give firmness and durability to the whole texture. But this theory has been controverted by some chemists, who suppose that the animal jelly contained in the skin is not dissolved, but unites during the process with the astringent principle of the bark, and forms a combination insoluble in water. The process of tanning varies considerably, not only in different countries, but even in different parts of the same country. The following is the method most approved and practised in London and its vicinity. The leather consists VOL. XII. chiefly of three sorts, known by the name of butts or backs, hides, and skins. Butts are generally made from the stoutest and heaviest ox-hides, and are managed as follows. After the horns are taken off, the hides are laid smooth in heaps, for one or two days in the summer, and for five or six in the winter.They are then hung on poles, in a close room, called a smoke-house, in which is kept a smouldering fire of wet tan: this occasions a small degree of putrefaction, by which means the hair is easily got off, by spreading the hide on a sort of woodcrooked knife. The hair being taken off, en horse or beam, and scraping it with a the hide is thrown into a pit or pool of which being done, the hide is again water to cleanse it from the dirt, &c. grease, loose flesh, extraneous filth, &c. spread on the wooden beam, and the carefully scrubbed out or taken off; the liquor, called ooze or wooze, prepared hides are then put into a pit of strong in pits called letches or taps, kept for the purpose, by infusing ground bark in water: this is termed colouring; after which they are removed into another pit called a scowering, which consists of water strongly impregnated with vitriolic acid, or with a vegetable acid prepared from rye or barley. This operation (which is called raising), by distending the pores of the hides, occasions them more readily to imbibe the ooze, the effect of which is to astringe and condense the fibres, and give firmness to the leather. The hides are then taken out of the scowering, and spread smooth in a pit, commonly filled with water, called a binder, with a quantity of ground bark strewed between each. After lying a month or six weeks, they are taken up; and the decayed bark and liquor being drawn out of the pit, it is filled again with strong ooze, when they are put in as before, with bark between each hide. They now lie two or three months, at the expiration of which the same operation is repeated; they then remain four or five months, when they again undergo the same process; and after being three months in the last pit, are completely tanned, unless the hides are so remarkably stout as to want an additional pit or layer. The whole process requires from eleven to eighteen months, and sometimes two years, according to the substance of the hide, and discretion of the tanner. When taken out of the pit to be dried, they are hung on poles; and after being compress F ed by a steel pin, and beat out smooth by wooden hammers called beetles, the operation is complete; and when thoroughly dry, they are fit for sale. Butts are chiefly used for the soles of stout shoes. The leather which goes under the denomination of hides is generally made from cowhides, or the lighter ox-hides, which are thus managed After the horns are taken off, and the hides washed, they are put into a pit of water saturated with lime, where they remain a few days, when they are taken out, and the hair scraped off on a wooden beam, as before described; they are then washed in a pit or pool of water, and the loose flesh, &c. being taken off, they are removed into a pit of weak ooze, where they are taken up and put down, (which is technically termed handling,) two or three times a day for the first week: every second or third day they are shifted into a pit of fresh ooze, somewhat stronger than the former; till, at the end of a month or six weeks, they are put into a strong ooze, in which they are handled once or twice a week with fresh bark for two or three months. They are then removed into another pit, called a layer, in which they are laid smooth, with bark ground very fine, strewed between each hide. After remaining here two or three months, they are generally taken up, when the ooze is drawn out, and the hides put in again with fresh ooze and fresh bark; where, after lying two or three months more, they are completely tanned, except a few very stout hides, which may require an extra layer: they are then taken out, hung on poles, and being hammered and smoothed by a steel pin, are, when dry, fit for sale. These hides are called crop hides; they are from ten to eighteen months in tanning, and are used for the soles of shoes. Skins is the general term for the skins of calves, seals, hogs, dogs, &c. These, after being washed in water, are put into lime-pits, as before mentioned, where they are taken up and put down every third or fourth day, for a fortnight or three weeks, in order to dilate the pores and dissolve the gelatinous parts of the skin. The hair is then scraped off, and the flesh and excrescences being removed, they are put into a pit of water impregnated with pigeon dung, (called a grainer or mastring,) forming a strong alkaline ley, which in a week or ten days soaking out the lime, grease, and saponaceous matter, (during which period they are several times scraped over with a crooked knife to work out the dirt and filth,) softens the skins, and prepares them for the reception of the ooze. They are then put into a pit of weak ooze, in the same manner as the hides, and being frequently handled, are by degrees removed into a stronger and still stronger liquor, for a month or six weeks, when they are put into a very strong ooze, with fresh bark, ground very fine; and at the end of two or three months, according to the substance, are sufficiently tanned; when they are taken out, hung on poles, dried, and fit for sale. These skins are afterwards dressed and blacked by the currier; and are used for the upper-leathers of shoes, boots, &c. The lighter sort of hides, called dressing hides, as well as horse-hides, are managed nearly in the same manner as skins, and are used for coach-work, harness-work, &c. Having given some account of the process, as commonly used in this country, we proceed to one recommended by M. Seguin in France, who is supposed to have done much towards simplifying and rendering perfect the art. In order to give currency to the knowledge which he had obtained by a long course of experiments and actual practice in the business, he exhibited without reserve all that he had discovered, and at the same time actually executed his processes on the large scale, furnishing gratuitously skins and tan, in order that others who were witnesses to his plans might repeat for themselves, and at their leisure, the experiments they had seen him go through. We shall give an outline of his plan and reasoning on this important subject. Skins swell up, and become soft, by moisture, which renders them permeable to water. Hence they are easily destroyed by the putrid process which ensues, and they become dry and brittle when the moisture is evaporated. Accident, no doubt, occasioned the discovery of the means of preventing these inconveniences by the use of certain vegetable substances, particularly the bark of oak. It was seen that skins prepared with these substances acquired new properties; that, without losing their flexibility, they became less permeable to water, more firm, more compact, and in some measure incapable of putrefaction. These observations gave birth to the art of the tanner. This art, no doubt of high antiquity, because founded on one of the earliest wants of man in society, comprehends a succession of processes, which was executed by habit and imitation, without a knowledge of the essential objects. The preparation of skins accordingly required several years, and frequently, in spite of the care, expense, and slowness of the operation, the tanning was incomplete; the skin formed a soft and porous leather, which was soon destroyed by moisture. These defects essentially sprung from ignorance of the true principles of this operation, because no discovery had been made respecting the action of the tan upon the skin, and circumstances or conditions which might accelerate or retard the process. To arrive at this knowledge in an accurate manner, it is necessary to consider, first, the nature and properties of tan; and, secondly, the structure and composition of the skin. We shall not enter into the detail of such precautions as are requisite in the choice of oak-bark, the time and manner of separating it from the tree, preserving it, or pulverizing it. It will be sufficient for our object to remark, that water poured into a vessel upon tan acquires, after some hours infusion, at the common temperature of the atmosphere, a brown colour, an astringent taste, and becomes charged with the most soluble substances contained in the tan; that by drawing off the water, and adding a similar quantity to the tan repeatedly, the whole of the soluble parts may be successively extracted, the water ceases to acquire colour, and there remains in the tub a mere fibrous matter or parenchymatous texture, insoluble in water, and no longer adapted to promote the operation of tanning. This residue is therefore always rejected in the manufactories as useless. It is only used by gardeners for their hot-beds, but might probably be advantageously applied in the fabrication of coarse paper. On It is therefore in the water of infusion, or the lixiviations of tan, that we must seek for the soluble substances which alone are effiacious in tanning. examination of the water of the last filtration, it is found to be not only clearer, less impregnated, and less acrid than the water of the first lixiviation, but likewise that it possesses all the properties of the gallic acid. It reddens the infusion of turnsol, acts upon metallic solutions, and more particularly it precipitates a black fecula from sulphate of iron, &c. And it is also found, that a piece of fresh skin, divested of its fat and sanguine humours, and macerated in this liquor, instead of becoming compact, is softened and swells up. The liquor of the first lixiviation exhi bits a very different character. It is more coloured and astringent; it not only exhibits the properties of the gallic acid, by the alterations it causes in the blue colours of vegetables, and the black precipitate it forms with the sulphate of iron, but it likewise possesses the remarkable quality of forming, with animal gelatine, or glue, a yellowish abundant precipitate, insoluble in water, not putrescible, which becomes hard and brittle by drying; and if a piece of skin, properly prepared, be immersed in this fluid, it becomes gradually more compact, and is converted into leather. There exist, therefore, in the same fluid, two very different substances: the one, which precipitates a black matter from iron, is the gallic acid or principle; the other, which precipitates animal gelatine or glue, is called the tanning prin ciple, on account of its efficacy in the preparation of leather. point, it was proved, by a number of exTo leave no doubt on this important periments easy to be repeated, 1. That the liquor of the last lixiviation, though coloured, and of an astringent taste, affords no precipitate with glue; a fact, which seems to show that the gallic acid contained in the bark is less soluble than the tanning principle. In fact, as has already been remarked, when water is successively poured on the tan, an infusion is at last obtained, which no longer precipiof iron very well. 2. The liquor of the tates glue, though it precipitates sulphate first lixiviation, after having been saturated with glue or animal gelatine, and forming an abundant precipitate with that substance, is entirely deprived of the tanning principle. It no longer differs from the liquor of the last filtrations, and contains merely a portion of the gallic acid. Hence the addition of sulphate of iron affords a new precipitate with this liquor. 3. As the tanning principle has a strong attraction to the animal gelatine, with which it always forms an insoluble precipitate, this property affords a very convenient re-agent to ascertain its presence immediately in any fluid, and to determine with precision its quantity. Accordingly, the infusion of tan poured into milk, whey, serum, broth, &c. forms, with these liquors, a precipitate more or less abundant, according to the quantity of gelatine they contain. This peculiar property of the tanning principle affords an application, which may become of great importance in the art of treating diseases, to determine the nature of urine, and to ascertain some of its changes. In the healthy subject, all whose functions are duly exercised, the urine does not contain gelatine, nor afford a precipitate with the infusion of tan: on the contrary, in all the gastric affections, the urine is more or less charged with gelatine; and forms, with the infusion of tan, a precipitate more or less abundant. The same observation is applicable to acute and chronical diseases, in which the assimilating or digestive forces are troubled, deranged, or perverted. 4. The gallic acid, or, if other terms be preferred, the principle which precipitates the sulphate of iron, is often found alone, or at least without being accompanied by the tanning principle. Thus, quinquina, crude or torrefied coffee, the roots of the strawberry-plant, scrofularia, milfoil, arnica, the flowers of Roman chamomile, and all the multitude of plants vaguely comprised under the title of astringents, contain the gallic acid only. All these form with the sulphate of iron a precipitate, more or less colour. ed and abundant; but none of them produce the slightest change in the solution of animal glue. On the contrary, the tanning principle has never been found alone, but always united or combined with the gallic principle. It was long supposed to exist exclusively in the oak, the nut-gall, and sumac, the only substances used at the tan-works; but it is found more or less abundantly in the siliquastrum, the rose-tree, the larix, several species of pines, the acacias, the lotus, the squill, the roots of bistort, of rhubarb, of parella, and several other plants. We have also found this principle in the products of distillation of different vegetable substances, where it was in some measure formed during the operation. From these different considerations, founded on experiment, the following general principles may be deduced: 1. Every substance, of which the infusion is capable of precipitating animal jelly, possesses the tanning property. 2. Every substance which possesses the tanning property, likewise precipitates the sulphate of iron black. 3. Every substance, which precipitates the sulphate of iron, but not the solution of glue, does not possess the tanning property. Upon M. Seguin's principle, a patent was some years since taken out by Mr. W. Desmond, who obtains the tanning principle by digesting oak-bark, or other As proper material, in cold water, in an apparatus nearly similar to that used in the saltpetre works. That is to say, the water which has remained upon the powdered bark for a certain time, in one vessel, is drawn off by a cock, and poured upon fresh tan. This is again to be drawn off and poured upon other fresh tan; and in this way the process is to be continued to the fifth vessel. The liquor is then highly coloured, and marks, as Mr. Desmond says, from six to eight degrees on the hydrometer for salts. He calls this the tanning lixivium. The criterion to distinguish its presence is, that it precipitates glue from its aqueous solution, and is also useful to examine how far other vegetable substances, as well as oak-bark, may be suitable to the purpose of tanning. The strong tanning liquor is to be kept by itself. It is found, by trials with the glue, that the tanning principle of the first digester which receives the clear water is, of course, first exhausted; but the same tan will still give a certain portion of the astringent principle, or gallic lixivium, to water. The presence of this principle is ascertained by its striking a black colour when added to a small quantity of the solution of vitriol of iron, or green copperas. soon as the water from the digester ceases to exhibit this sign, the tan is exhausted, and must be replaced with new. The gallic lixivium is reserved for the purpose of taking the hair off from hides. Strong hides, after washing, cleaning, and fleshing, in the usual way, are to be immersed for two or three days in a mixture of gallic lixivium, and a thousandth part, by measure, of dense vitrolic acid. By this means the hair is detached from the hides, so that it may be scraped off with a round knife. When swelling or raising is required, the hides are to be immersed for ten or twelve hours in another vat, filled with water, and one five hundredth part of the same vitriolic acid. The hides being then repeatedly washed and dressed, are ready for tanning; for which purpose they are to be immersed for some hours in a weak tanning lixivium, of only one or two degrees; to obtain which, the latter portions of the infusions are set apart, or else some of that which has been partly exhausted by use in tanning. The hides are then to be put into a stronger lixivium, where, in a few days, they will be brought to the same degree of saturation with the liquor in which they are immersed. The strength of the liquor will by this means be considerably diminished, and must therefore be renewed. When the hides are by this means completely saturated, that is to say, perfectly tanned, they are to be removed, and slowly dried in the shade. Calf-skins, goat-skins, and the like, are to be steeped in lime-water, after the usual fleshing and washing. These are to remain in the lime-water, which contains more lime than it can dissolve, and requires to be stirred several times a day. After two or three days, the skins are to be removed, and perfectly cleared of their lime by washing and pressing in water. The tanning process is then to be accomplished in the same manner as for the strong hides; but the lixivium must be considerably weaker. Mr. Desmond remarks that lime is used instead of the gallic lixivium, for such hides as are required to have a close grain; because the acid mixed with that lixivium always swells the skins more or less: but that it cannot, with the same convenience, be used with thick skins, on account of the considerable labour required to clear them of the lime; any part of which, if left, would render them harsh, and liable to crack. He recommends, likewise, as the best method to bring the whole surface of the the hides in contact with the lixivium, that they should be suspended vertically in the fluid, by means of transverse rods or bars, at such a distance as not to touch each other. By this practice, much of the labour of turning and handling may be saved. Mr. Desmond concludes his specification by observing, that in some eases it will be expedient to mix fresh tan with the lixivium; and that various modifications of strength, and other circumstances, will present themselves to the operator. He affirms that, in addition to the great saving of time and labour in this method, the leather, being more completely tanned, will weigh heavier, wear better, and be less susceptible of moisture, than leather tanned in the usual way; that cords, ropes, and cables, made of hemp, or speartery, impregnated with the tanning principle, will support much greater weights with out breaking, be less liable to be worn out by friction, and will run more smoothly on pullies; insomuch that, in his opinion, it will render the use of tar in many cases, particularly in the rigging of ships, unnecessary; and, lastly, that it may be substituted for the preservation of animal food instead of salt. The intelligent manufacturer will readily perceive, that this new method is grounded on two par ticular circumstances, besides a more scientific management of the general process than has been usual. The first consists in the method of determining the presence and quantity of the tanning principle by the hydrometer, and the precipitation of glue; the second in applying this principle, in a concentrated state, more early in point of time than has, perhaps, been hitherto done. Our tanners, after the common previous processes, and unhairing by acids, by lime, or by piling the hides, that they may heat and begin to putrefy, apply the solution of tan, which they call ooze, in a great number of pits in the tan-yard. They begin with the weakest solution which has been used, and is of a lighter colour than the other; and they pass the hides, according to their judgment and experience, into oozes which are stronger and stronger; until at last, in certain cases, the hides come to be buried, for a certain time, in a solid mass of tan, or oak-bark. The oak-bark itself, in the pits, is not the only source from which the water extracts the tanning principle, but seems, likewise, in some measure, during the last stages of the process, to operate mechanically, by keeping the surfaces of the hides from touching each other. lic fossil, of an iron-black colour on the TANTALITE, in mineralogy, a metalexternal surface, but internally between imbedded, in masses of the size of a hazel It occurs bluish-grey and iron-black. nut, which have a tendency to the octahedral form. Externally it is smooth and glimmering; internally it is shining, and its lustre metallic. Specific gravity is 7.95. Its constituent parts are, tantalium, iron, and manganese. It is found imbedded in quartz, in Sweden; its name is derived from the new metal denominated TANTALIUM, which see. TANTALIUM, a metal discovered by M. Ekeberg, in the mineral just mentioned; and in another named Ytrotantalite. From each he extracted by means of the fixed alkalies a white powder, which he ascertained to be the oxide of a peculiar metal; to this he gave the name of tantalium. When this oxide is powerfully heated with charcoal, it yields a button moderately hard, which, externally, a metallic lustre, but internally it is black, and without any degree of brilliancy. The acids will reduce it again to an oxide, but they will not dissolve it. It melts before the blow-pipe with borax, or phosphate of soda, but gives no colour to either of them. Its specific gravity is about 6.5. has |