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The frustum of a globe or sphere is any part thereof cut off by a plane, the solid contents of which may be found by this rule. To three times the square of the semi-diameter of the base, add the square of its height ; then multiplying that sum by the height, and this product multiplied by 5236, gives the solidity of the frustum. A frustum, or portion of any solid, generated by the revolution of any conic section upon its axis, and terminated by any two parallel planes, may be thus compared to a cylinder of the same altitude, and whose base is equal to the middle section of the frustum made by a parallel plane. 1. The difference between such frustum and cylinder is always the same in different parts of the same or of similar solids, when the inclination of the planes to the axis and the altitude of the frustum are given. 2. In the parabolic conoid, this difference vanishes; the frustum being always equal to a cylinder of the same height, upon the section of the conoid that bisects the altitude of the frustum, and is parallel to its bases. 3. In the sphere, the frustum is always less than the cylinder, by one fourth part of a right angled cone of the same height with the frustum; or by one half of a sphere, of a diameter equal to that height: and this difference is always the same in all spheres whatever, when the altitude of the frustum is given. 4. In the cone, the frustum always exceeds the cylinder, by one fourth part of the content of a similar cone, that has the same height with the frustum. As a general theorem : in the frustum of any solid, generated by the revolution of any conic section about its axis: if to the sum of the two cnds be added four times the middle section, then the last sum divided by six will be the mean area, and being drawn into the altitude of the solid will produce the content: That is, A and a being the areas of the ends, M. equal the middle section, then we have

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or oblique, and not only of the solids generated from the conic sections, but also of all pyramids, cones, and in short of any solid, whose parallel sections are similar figures. FUCHSIA, in botany, so called in honour of Leonard Fuchs, a famous German botanist, a genus of the Octandria Monogynia class and order. Natural order of Onagrae, Jussieu. Essential character: calyx one-leafed, coloured, bearing the corolla, very large; petals four, small; berry inferior, four-celled, with many seeds. There are five species. FUCUS, in botany, a genus of the Cryptogamia Algæ. Generic character: male vesicles smooth, hollow, with villose hairs within, interwoven : female, vesicles smooth, filled with jelly, sprinkled with immersed grains, prominent at the tip. Seeds solitary. . This genus comprehends most of those plants which are commonly called sea-weeds: more than seventy species are enumerated ; they may all be used to manure land, or burnt for alkali. Some of the species are eaten, either fresh out of the sea. or boiled tender, with butter, pepper, &c. If the F. saccharinus is washed in spring water, and then hung up in a warm place, a substance like sugar exudes from it. FUEL. Dr. Black divides fuels into five classes; the first comprehends the fluid inflammable bodies; the second, peat or turf; the third, charcoal of wood; the fourth, pit-coal charred; and the fifth, wood, or pit-coal, in a crude state, and capable of yielding a copious and bright flame. The fluid inflammables are considered as distinct from the solid, on this account, that they are capable of burning upon a wick, and become in this way the most manageable sources of heat; though, on account of their price, they are never employed for producing it in great quantities; and are only used when a gentle degree, or a small quantity of heat, is sufficient. The species which belong to this class are alcohol and different oils. The first of these, alcohol, when pure and free of water, is as convenient and manageable a fuel for producing moderate or gentle heats as can be desired. Its flame is perfectly clean, and free from any kind of soot; it can easily be made to burn slower or faster, and to produce less or more heat, by changing the size or number of the wicks upon which it burns; for as long as these are fed with spirit, in a proper manner, they continue to yield flame of precisely the same strength. The cotton, or other materials, of which the wick is composed, is not scorched or consumed in the least, because the spirit with which it is constantly soaked is incapable of becoming hotter than 174° Fahrenheit, which is considerably below the heat of boiling water. It is only the vapour that arises from it which is hotter, and this too only in its outer parts, that are most remote from the wick, and where only the combustion is going on, in consequence of communication and contact with the air. At the same time, as the alcohol is totally volatile, it does not leave any fixed matter, which, by being accumulated on the wick, might render it foul and fill up its pores. The wick, therefore, continues to imbibe the spirit as freely, after some time, as it did at the first. These are the qualities of alcohol as a fuel. But these qualities belong only to a spirit that is very pure. If, on the contrary, it be weak, and contain water, the water, being less volatile, does not evaporate so fast from the wick as the more spirituous part; and the wick becomes, after some time, so much soaked with water, that it does not imbibe the spirit properly. The flame becomes much weaker, or is altogether extinguished. When alcohol is used as a fuel, therefore, it ought to be made as strong, or free from water, as possible. oil, although fluid like spirit of wine, and capable of burning in a similar manner, is not so convenient in many respects. It is disposed to emit soot; and is applying itself to the bottom of the vessel exposed to it, and increasing in thickness, forms, by degrees, a soft and spongy medium, through which heat is not so freely and quickly transmitted. This was observed by Muschenbroeck, in his experiments upon the expansions of metalline rods heated by lamps. It is true we can prevent this entirely by using very small wicks, and increasing the number, if necessary, to produce the heat required. Or we may employ one of those lamps, in which a stream of air is allowed to rise through the middle of the flame, or to pass over its surface with such velocity as to produce a more complete inflammation than ordinary. But we shall be as much embarrassed in another way, for the oils commonly used, being capable of assuming a heat greatly above that of boiling water, scorch and burn the wick, and change its texture, so that it does not imbibe the oil so fast as before. Some have attempted a remedy, by making the wick of incom

bustible materials, as asbestos, or wire; but still, as the oil does not totally eva. porate, but leaves a small quantity of gross fixed carbonaceous matter, this, constantly accumulating, clogs the wick to such a degree, that the oil cannot ascend, the flames become weaker, and, in some cases, are entirely extinguished. There is, however, a difference among the different oils in this respect; some being more totally volatile than others. But the best are troublesome in this way, and the only remedy is, to change the wicks often, though we can hardly do this and be sure of keeping always an equal flame. The second kind of fuel mentioned, peat, is so spongy, that, compared with the more solid fuels, it is unfit to be employed for producing very strong heats. It is too bulky for this; we cannot put into a furnace, at a time, a quantity that corresponds with the quick consumption that must necessarily go on when the heat is violent. There is, no doubt, a great difference in this respect among different kinds of this fuel ; but this is the general character of it. However, when we desire to produce and keep up, by means of cheap fuel, an extremely mild gentle heat, we can hardly use any thing better than peat. But it is best to have it previously charred, that is scorched, or burnt to black coal. The advantages gained by charring have been already explained. When prepared for use in that manner, it is capable of being made to burn more slowly and gently, or will bear, without being extinguished altogether, a greater diminution of the quantity of air with which it is supplied, than any other of the solid fuels. Dr. Boerhaave found it extremely convenient and manageable in his Furnus Studiosorum. The next fuel in order is the charcoal of wood. This is prepared by piling up billets of wood into a pyramidal heap, with several spiracles, or flues, formed through the pile. Chips and brushwood are put into those below, and the whole is so constructed, that, when kindled, it kindles almost over the whole pile in a very short time. It would burst out into a blaze, and be quickly consumed to ashes, were it not covered all over with earth or clay, beaten close, leaving openings at all the spiracles. These o: fully watched; and whenever the white watery smoke is observed to be succeeded by thin blue and transparent smoke, the hole is immediately stopped; this

being the indication of all the watery vapour being gone, and the burning of the true coaly matter commencing. Thus is a pretty strong red heat raised through the whole mass, and all the volatile matters are dissipated by it, and nothing now remains but the charcoal. The holes being all stopped in succession, as this change of the smoke is observed, the fire goes out for want of air. The pile is now allowed to cool. This requires many days; for, charcoal being a very bad conductor of heat, the pile long remains red hot in the centre, and, if opened in this state, would instantly burn with fury. Small quantities may be procured at any time, by burning wood in close vessels. Little pieces may be very finely prepared, at any time, by plunging the wood in lead melted and red hot. This is the chief fuel used by the chemists abroad, and has many good properties. It kindles quickly, emits few watery or other vapours while burning, and when consumed leaves few ashes, and those very light. They are, therefore, easily blown away, so that the fire continues open, or pervious to the current of air which must pass through it to keep it burning. This sort of fuel, too, is capable of producing as intense a heat as can be obtained by any; but in those violent heats it is quickly consumed, and needs to be frequently supplied. Fossil coals charred, called cinders, or coaks, have, in many respects, the same roperties as charcoal of wood; as kinding more readily in furnaces than when they are not charred, and not emitting watery, or other gross smoke, while they burn. This sort of charcoal is even greatly superior to the other in some properties. It is a much stronger fuel, or contains the combustible matter in greater quantity, or in a more condensed state. It is, therefore, consumed much more slowly on all occasions, and particularly when employed for producing intense melting heats. The only inconveniences that attend it are, that, as it consumes, it leaves much more ashes than the other, and these much heavier too, which are, therefore, liable to collect in such quantity as to obstruct the free passage of air through the fire; and further, that when the heat is very intense, these ashes are disposed to melt or vitrify into a tenacious drossy substance, which clogs the grate, the sides of the furnace, and the vessels. This last inconvenience is only troublesomc,

however, when the heat required is very intense. In ordinary heat the ashes do not melt, and though they are more copious and heavy than those of charcoal of wood, they seldom choke up the fire considerably, unless the bars of the grate be too close together. This fuel, therefore, is preferable, in most cases, to the charcoal of wood, on account of its burning much longer, or giving much more heat before it is consumed. The heat produced by equal quantities, by weight, of pit-coal, woodcharcoal, and wood itself, are nearly in proportion of 5, 4, and 3. The reason why both these kinds of charcoal are preferred, on most occasions, in experimental chemistry, to the crude wood, or fossil coal, from which they are produced, is, that the crude fuels are deprived, by charring, of a considerable quantity of water, and some other volatile principles, which are evaporated during the process of charring, in the form of sooty smoke or flame. These volatile parts, while they remain in the fuel, make it unfit (or less fit) for many purposes in chemistry. For, besides obstructing the vents with sooty matter, they require much heat to evaporate them; and therefore, the heat of the furnace, in which they are burnt, is much diminished and wasted by every addition of fresh fuel, until the fresh fuel is completely inflamed, and restores the heat to its former strength. But these great and sudden variations of the heat of a furnace are quite inconvenient in most chemical processes. In the greater number of chemical operations, therefore, it is much more convenient to use charred fuel, than the same fuel in its natural state. There are, at the same time, some kinds of fossil coal, which are exceptions to what has now been delivered in general. We meet with some of them that leave a smaller proportion of ashes than others, and the ashes of some are not so liable to melt in violent heats. There is one species too, such as the Kilkenny coal of Ireland, and which occurs likewise in some parts of this country, that does not contain any sensible quantity of water, or other such volatile principles. But this may be called a sort of native charcoal. It has the appearance of ordinary coal, but, when thrown into the fire, does not emit smoke or soot. It merely becomes red, gives a subtile blue flame, and consumes like charcoal ; only it lasts surprisingly long, or continues to gives heat for a very long time before it is totally consumed. But it cannot be made to burn so as to produce a gentle heat. If not in considerable quantity, and violently heated, it is soon extinguished. - - - In using this kind of fuel, it is proper to be on our guard against the dangerous nature of the burnt air which arises from charcoal of all kinds. Charcoal burns without visible smoke. The air arising from it appears to the eye as pure and as clear as common air. Hence it is much used abroad by those who are studious of neatness and cleanliness in their apartments. But this very circumstance should make us more watchful against its effects, which may prove dangerous, in the highest degree, before we are aware of it. The air arising from common crude fuel is no doubt as bad, but the smoke renders it disagreeable before it becomes dangerous. The first sensation is a slight sense of weakness: the limbs seem to require a little attention, to prevent falling. A slight giddiness, accompanied by a distinct feeling of a flush, or glow in the face and neck. Soon after, the person becomes drowsy, would sit down, but commonly falls on the floor, insensible of all about him, and breathes strong, snoring as in an apoplexy. If the person is alarmed in time, and escapes into the open air, he is commonly seized with a violent headach, which gradually abates. But when the effect is completed, as above described, death very soon ensues, unless relief be obtained. There is usually a foaming at the mouth, a great flush or suffusion over the face and neck, and every indication of an oppression of the brain, by this accumulation of blood. The most successful treatment is, to take off a quantity of blood immediately, and throw cold water on the head repeatedly. A strong stimulus, such as hartshorn, applied to the soles of the feet, has also a very good effect. The fifth and last kind of fuel is wood, or fossil coals, in their crude state, which it is proper to distinguish from the charcoals of the same substances. The difference consists in their giving a copious and bright flame, when plenty of air is admitted to them, in consequence of which they must be considered as fuels very different from charcoal, and adapted to different purposes. See FLAME. Flaming fuel cannot be managed like the charcoals. If little air be admitted, it gives no flame, but sooty vapour, and a diminution of heat. And if much air

be admitted, to make those vapours break out into flame, the heat is too violent. These flaming fuels, however, have their particular uses, for which the others are far less proper. For it is a fact, that flame, when produced in great quantity, and made to burn violently, by mixing it with a proper quantity of fresh air, by driving it on the subject, and throwing it into whirls and eddies, which mix the air with every part of the hot vapour, gives a most intense heat. This proceeds from the vaporous nature of flame, and the perfect miscibility of it with the air As the immediate contact and action of air is necessary to the burning of every combustible body; so the air, when properly applied, acts with far greater advantage on flame, than on the solid and fixed inflammable bodies : for when air is applied to these last, it can only act on their surface, or the particles of them that are outermost: whereas, flame being a vapour or elastic fluid, the air, by proper contrivances, can be intimately mixed with it, and made to act on every part of it, exter. nal and internal, at the same time. This great power of flame, which is the consequence of this, does not appear when we try small quantities of it, and allow it to burn quietly, because the air is not intimately mixed with it, but acts only on the outside, and the quantity of burning matter in the surface of a small flame is too small to produce much effect. But when flame is produced in large quantity, and is properly mixed and agitated with air, its power to heat bodies is immensely increased. It is therefore peculiarly proper for heating large quantities of matter to a violent degree, especially if the contact of solid fuel with such matter is inconvenient. Flaming fuel is used for this reason in many operations performed on large quantities of metal, or metallic minerals, in the making of glass, and in the baking or burning of all kinds of earthen ware. The potter's kiln is a cylindrical cavity, filled from the bottom to the top with columns of wares, the only interstices are those that are left between the columns; and the flame, when produced in sufficient quantity, proves a torrent of liquid fire, constantly flowing up through the whole of the interstices, and heats the whole pile in an equal manner. Flaming fuel is also proper in many works or manufactories, in which much fuel is consumed, as in breweries, distil. leries, and the like. In such works, it is evidently worth while to contrive the

furnaces so, that heat may be obtained from the volatile parts of the fuel, as well as from the fixed; for when this is done, less fuel serves the purpose than would otherwise be necessary. But this is little attended to, or ill understood, in many of those manufactories. It is not uncommon to see vast clouds of black smoke and vapour coming out of their vents. This happens in consequence of their throwing too large a quantity of crude fuel into the furnace at once. The heat is not sufficient to inflame it quickly, and the consequence is a great loss of heat. See Labon Atoy. FUGUE, in music, signifies a composition, in which one part leads off some determined succession of notes called the subject, which, after being answered in the fifth and eighth by the other parts, is interspersed through the movement, and distributed amid all the parts in a desultory manner, at the pleasure of the composer. There are three distinct descriptions of fugues: the simple, which contains but one subject; the double, that which consists of two subjects; and the counter fugue, is that in which the subjects move in a direction contrary to each other. FUIRENA, in botany, so named in memory of George Fuiren, a genus of the Triandria Monogynia class and order. Natural order of Calamarize. Cyperoi. deae, Jussieu. Essential character: ament imbricate, with awned scales; calyx none ; corolla with three-petal shaped obcordate glumes, ending in a tendril. There is but one species, viz. F. paniculata, a lofty grass. Native of Surinam and Jamaica. FULCRUM, in mechanics, the prop or support, by which a lever is sustained. See MechANics. FULGORA, in natural history, lanternfly, a genus of insects of the order Hemiptera. Head hollow, inflated, extended forward; antennae short, seated beneath the eyes, consisting of two joints, the outer one larger and globular; snout elongated, inflected, four-jointed; legs formed for walking. There are about 25 species, most of which inhabit hot climates. Mr. Donovan has described the F. Europaea; the body of which is green; wings hyaline, reticulate ; front conic. This is a small insect, and destitute of the shining quality, by which foreign species are distinguished. But the F. lanternaria, or Peruvian lantern-fly, is one of the most curious of insects; it is three inches long, and the breadth between the tips of the WOL, V,

expanded wings is about five or six in. ches. This beautiful insect is a native of Surinam and other parts of South America, and during the night it diffuses so strong a phosphoric splendour from its head, which is nearly as large as the rest of the body, that it may be employed for the purpose of a candle or torch. Some have asserted that these insects were a source of much alarm to the Spaniards when newly arrived in South America. Observing one night a number of lights passing to and fro with much rapidity in the forest, they betook themselves precipitately to their ships, fearing an immediate attack from the natives, and were much chagrined, when they discovered the source of their alarm to be the light of this insect. FULICA, the gallinule and the coot, in natural history, a genus of birds of the order Grallae. Generic character: bill strong, thick, and sloping to the point; upper mandible arched over the lower at the edge, and reaching far up the forehead : nostrils nearly oval; front bald; toes four, long, and furnished with broad scalloped membranes. There are twenty-five species. F. atra-coot, is distinguished from the gallinule by pinnated feet. It inhabits Europe, Asia, and America, and is about the size of a small fowl. It feeds on small fish and water insects, is common in some parts of this country at all seasons, but in the breeding season is seen almost always in pairs, about the borders of ponds and lakes well fringed with rushes, of which it mats itself a large nest, said to be often observed floating on the water. These birds are devoured when young by the buzzards, which infest their haunts, and prevent them from that great multiplication which might be otherwise expected. Rallus crex, or the crake galliaule, is found in various parts of Europe, and is particularly abundant in Ireland, where it is supposed by Latham to winter. Wherever quails are, the crake is to be met with. It runs fast, but flies with great awkwardness, with its legs hanging down. Its food is grain and insects. On its arrival in England, where it is migratory, it is poor and emaciated, but fattens afterwards with great rapidity, and is esteemed excellent for the table. Its full weight is about eight ounces. F. porphyrio, or the purple water-hen, occurs in almost all the warmer latitudes of the globe. It is of the size of a fowl; in Sicily it is kept merely for its beauty. h

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