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ence is capable of expression in algebraic forms. Algebraic functions are, in their simplest forms, the sum or difference, the product or quotient, the power or root, the exponent or logarithm, and the trigonometric or circular functions. To these we may add others, but all might by ingenuity be reduced to sum or difference. Very important uses are made of derived functions, functions which are definite functions of other functions. The principal derived function is the differential coefficient, which expresses the rate at which the original function changes for any change in the quantity of which it is a function. FUNDY, BAY OF, an arm of the Atlantic ocean, between the British provinces of New Brunswick and Nova Scotia, about 180 m. long, and from 30 to 50 m. wide. From its mouth, between the S. W. extremity of Nova Scotia and the easternmost point of Maine, its coasts trend N. E. until near its upper extremity it branches into 2 inlets; the N., called Chignecto bay, is about 30 m. long and 8 m. broad; the S. bears the name of Minas channel, and opens into Minas basin in Nova Scotia. At St. John, N. B., situated at the mouth of the river St. John, on the N. coast, the bay is 36 m. wide, and it continues of nearly uniform width from that point to its branching. It is deep, but difficult of navigation. It is remarkable for its extraordinary tides, which rush up from the sea with such rapidity as sometimes to overtake swine feeding on shell fish on the shores, and which rise in Minas basin 40 feet, and in Chignecto channel 60 feet. The bay contains Grand Menan and Long islands, and receives the rivers St. John and St. Croix.

attempted to introduce into the university the study of the higher mathematics, the law of nations, the modern languages, music, and drawing. During the revolutionary tumults the possessions of his father were confiscated by the royalist party. Funes had acquired a thorough historical knowledge of his country, which he put to use by writing the Essayo de la historia civil del Paraguay, Buenos Ayres, y Tucuman (3 vols. small 4to., Buenos Ayres, 1816 et seq.), which contains an excellent epitome of the annals of a vast territory, of which but little was yet known in Europe.

FÜNFKIRCHEN (five churches; in Hungarian Pécs, which, in the language of the surrounding Slavic tribes, means five), a town of Hungary, capital of the county of Baranya, 105 m. S. S. W. from Buda; pop. 18,500. It is surrounded by rich vineyards, in the vicinity of mineral springs, and is one of the pleasantest towns of Hungary. It contains an old Gothic cathedral, built on the site of a Roman castle, 2 monasteries, a public library, several schools and hospitals, and a theatre. The population consists chiefly of Magyars, but the Slavic and German inhabitants are also numerous. The town has considerable commercial industry, its trade being chiefly in coal, alum, vitriol, wine, grain, tobacco, rape seed, wool, and other products of the neighboring country. Fünfkirchen is supposed to be the Colonia Serbinum of the Romans. In the time of Hungarian independence it was larger and much more important than now. History mentions that 2,000 of its students marched out to the battle field of Mohács, where the Hungarians were defeated by the Turks under Solyman, Aug. 29, 1526. This sultan passed some time at Fünfkirchen, during the siege of the fortress of Szigeth, and was so delighted with the place that he called it a paradise on earth. It remained in the hands of the Mussulmans from 1543 till 1686. During the late Hungarian revolution it was mostly in the hands of the Austrians.

FÜNEN (Dan. Fyen), an island of Denmark, having on the N. the Cattegat, W. the Little Belt, and S. and E. the Great Belt and the Binnenmeer; pop. 176,000. It is the largest of the Danish isles after Seeland, is about 185 m. in circumference, and forms with Langeland a circle of the kingdom. The coast is not very elevated, but is in general rugged and steep, and much indented by bays and arms of the sea. The interior to- FUNGI, an extensive family of cryptogamic ward the W. is somewhat hilly; in every other plants, generally known under the names of direction it is composed of large and fruitful mushrooms, toadstools, rusts, smuts, bunt, and plains, which are well cultivated, and produce mildews. They are, with rare exceptions, paabundant crops of corn, the greater part of rasitic plants, growing upon and drawing their which is exported. The largest stream in the nourishment (or at least a part of it) from the island is the Odense-aue, which has a course of substance of the object they infest. They occur 36 m. from S. to N., and discharges into the in all parts of the globe, finding their maximum Odensefiord, about 9 m. long, and from 1 to in the moist temperate zones; abounding in a nearly 5 m. wide. The largest lake is the Ar- climate like that of Sweden, which has proreskov; it is about 9 m. in circuit, and abounds duced more species upon a given area than in fish. Fünen is divided into two bailiwicks- any other known locality, except perhaps the Odense, which contains the capital of the same southern United States. They are found whername, and Svendborg. It has annexed to it nu- ever there is decaying vegetation, upon which merous small islands. they feed; and in some instances they prey upon living tissues, which they destroy by their attacks. Nothing of vegetable origin is free from their ravages when exposed to influences favorable to their growth. They are found also on animal dejections, on insects, whose death they cause, on the human skin, and even on bare stones, on iron which was in a forge a few

FUNERAL RITES. See BURIAL. FUNES, GREGORIO, an Argentine historian, born in Cordova, S. A., died in the same city in 1820. The son of a wealthy proprietor, he was educated in the university which had been founded in Cordova by the Jesuits, entered holy orders, became dean in the cathedral church, and

hours before, on lead, and on chemical solutions. The disease in silkworms is caused by a mould (botrytis bassiana). The flies found adhering to our windows in autumn, fixed by the proboscis, are destroyed by a mould (sporendonema musca), which produces the little white rings between the abdominal segments and discharges its seed upon the glass around like a little cloud. The celebrated caterpillar fungus of New Zealand (cordyceps Robertsii), which infests the caterpillar of hepialus virescens, is a remarkable instance. Our American caterpillars are destroyed by another species (C. militaris). Onygena equina grows on the hoofs and horns of animals. Some of the microscopic species cause cutaneous disorders in the human system, and others have been found in the brains of birds. (See EPIPHYTES.) But these latter are exceptional cases. They principally affect decaying vegetation. Their vegetating fibres are of such extreme minuteness that they penetrate the hardest woods, and are thus powerful agents in their decay. Their delicate, evanescent, fragile mycelium fastens upon the fallen giants of the forest and hurries their slow decomposition. They attack the housekeeper's bread, cheese, vinegar, paste, yeast, preserves, and mustard, the farmer's corn and potatoes, the vintager's grapes, the gardener's berries, and the joiner's timber; while a host of forms prey upon the living tissues of plants, scarce any of which are free from their depredations, and many of which are assailed by a dozen different species at once. -Notwithstanding the long time which has been given to the study of fungi, there is no class of organized structures so little known. Their microscopic character, their abnormal growths, their polymorphic forms, have baffled the researches of the closest observers. Even at the present day, with all the light of modern science, the improved means of research, and the multiplied observations of a host of zealous students, a large proportion of the microscopic forms are but imperfectly understood. A century's study has left the subject an undeveloped and disputed field. It is only within a comparatively short time that an approach has been made to a clear insight into their laws of growth and reproduction. There are those, even now, who deem them to be of spontaneous or chemical origin, an opinion which their sudden appearance in vast numbers after a long rest, and their occurrence in closed cavities, have tended to establish. But this idea has been clearly disproved. That they are perfect plants, growing from and reproducing bodies analogous to seeds, is too firmly established to be questioned. When we ascertain that a single plant produces millions of these reproductive bodies, so small that they float on the air scarcely influenced by the force of gravity, that they may remain an indefinite period inert, and be called into sudden vitality by atmospheric changes favorable to their germination, their sudden appearance can be readily understood. They have been traced through their metamorphoses. The infinitesi

mally small spore has been watched in its growth into a perfect plant; and one such observation, unquestionably made, is positive proof of their being perfect plants, having a development following certain laws; and we need not resort to the unsatisfactory theory of spontaneous or accidental origin, if indeed we are able to conceive of any vast assemblage of organized structures permanently reproductive, and identical through centuries, being the result of chance chemical action.-Fungi are of purely cellular growth. They form no woody fibre like flowering plants, nor do they form chlorophyl in their tissues. They consist of mere aggregations of homogeneous cells. Though many become corky, woody, and horny in the course of their. growth, they have no other identity with true wood than of density and weight, possessing none of the complex structure of flowering plants. They exhibit a wonderful variety of external forms; but the composition of them all is the same, an aggregation of simple cells. Their earliest vegetation is a prolongation of the membranes of their spores, a name given to their reproductive seminal dust, which, though performing the office of seeds, differs from true seeds in being mere individual cells. From these arises a delicate, minute, webby growth, called the mycelium, which is the true vegetation of the plant, and which gives rise to the reproductive bodies at once, or builds up a receptacle which contains them. It is this mycelium which penetrates and destroys the object on which it is parasitic. It is made up of radiating and intertwining fibres formed of rows of cells placed end to end. These are in many instances so minute that they easily traverse the tissues of living plants and the pores of solid wood. From this mycelium grow the spores, which in their simplest form consist of the terminal cell or cells, which drop off to form new plants. They are of the extremest minuteness, appearing to the eye like a mere cloud of impalpable powder. As we rise in the scale, special branches and processes are formed to bear the spores, either singly or in groups. Still more complex forms build up a special organ called the peridium, within which the spores arise contained in little sacs termed asci. The large fleshy growths which we meet with in the woods or on trees are processes belonging properly to the reproduction and not the vegetation of the plant. They are very disproportionately large compared with the mycelium, and consist of a main stem called a stipe and an expanded top called a pileus, on which these spores are borne in various ways, on gills, ribs, prickles, spores, &c. The mycelium is sometimes reduced to a mere trace of evanescent, floccose growth; while the reproductive body becomes a fleshy mass, several pounds in weight. But the spores are always minute, being sometimes only of an inch in diameter.-Fungi occupy an intermediate position between algae and lichens, into which orders they gradually merge at different points. Indeed, so

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nice is the distinction at times, that some systematists have reduced lichens to a sub-order of fungi, They differ from lichens in deriving their sustenance from the object on which they grow (though this has exceptions), in not producing a foliaceous thallus, and in not forming green chlorophyl; from algae, in being aërial, not aquatic, and in deriving their nourishment from their matrix and not from the surrounding medium. Such, at least, are the main points of difference. Those species of fungi which are found in fluids, such as the yeast and vinegar plants, are now proved to be merely submerged mycelia of certain moulds (penicillium), which do not attain their perfect stage until they reach the air. The propagation which takes place in fluids is due to a power the mycelium possesses of retaining its vitality under a variety of circumstances, of suffering division and enduring extremes of temperature. Beside this, it has a propagating power analogous to that of budding. In some aerial forms it goes on reproducing itself in peculiar ways, and rarely reaching the normal or perfect ascigerous fructification. For this reason many species have been thought to be distinct plants when they are merely arrested stages of growth of one single species. Some aerial forms never reach a further growth than a compact, dense mass of mycelium. Oak trees sometimes contain a solid mass of a leathery texture (xylostroma giganteum), which never advances beyond that stage. The genera sclerotium and rhizomorpha, with their so called species, are mere compact bodies of mycelium, which have in some instances been artificially forced to develop themselves, and have produced plants of a widely different structure. The ergots of grain are objects of this kind. Tulasne and others have watched their development into species of cordyceps. These forms remain constantly arrested; but very many of those which under favorable circumstances reach perfection remain similarly checked, and confuse the student with their multiple forms. This has caused the naming of hosts of species which are merely forms of others. There is no branch of science whose synonymy is more burdensome. It is almost a hopeless task to attempt to identify the species of authors by description alone, the plant itself being necessary for comparison. Long and continued observations are required to determine and connect the many forms which a single fungus may assume in the course of its existence. Few objects in nature exhibit more gorgeous colors. The larger, fleshy forms present an endless variety of graduated tints. Some of the boleti exhibit on being broken a remarkable change of color, the white or yellowish hue of the interior changing instantly to a vivid blue. This is supposed by Prof. Robinson to be due to a molecular and not to a chemical change. Their texture is as variable as their color. Some are almost fluid, others fleshy, papery, leathery, corky, or hard and horny. Their size is equally various, from

mere specks to masses some feet in girth. Their rapid growth is astonishing. Puff-balls sometimes grow 6 inches in diameter in a night. Masses of paper pulp thrown out hot from a vat have been found within 24 hours filled and swollen with a species of agaricus. Schweinitz records the growth of a species of athalium found on a piece of iron which was heated the night before in a forge. Some of the ephemeral coprini grow up in a night and melt away in the morning sun. Other species, like the polypori, grow very slowly and add a new layer every year, covering that of the previous season. Their expansive force in growing is very great. Notwithstanding their soft, yielding texture, agarics are able to raise heavy stones under which they spring up; and Bulliard tells of a phallus which burst a glass vessel in which it had beer. confined. They are meteoric in occurrence, depending upon peculiar states of the atmosphere. They generally appear in the greatest abundance in moist autumn weather, though some are found wherever there is moisture. Some depend so much on peculiar states of the atmosphere, perhaps electrical, that they appear suddenly and then disappear for a while. The pustular forms, however, which abound on the dead bark of trees, shrubs, old stumps, and fallen twigs, are more durable from their more solid structure. Some species of agaricus possess a remarkable luminosity, and certain rhizomorpha growing in mines shed a phosphorescent light of extreme brilliancy. Fungi differ from flowering plants in their chemical influence upon the air. They absorb oxygen and exhale carbonic acid, performing the same office in this respect as animals, which they most resemble in chemical composition, in being highly azotized. The odors they emit in decay are more like putrescent animal than vegetable matter. The fleshy sorts generally possess a peculiar earthy odor, but some species of phallus and clathrus emit a most intolerably offensive stench, which will render a close apartment untenantable. Others, on the contrary, are very agreeable to the smell, and some in drying acquire a fine aroma. They are quite as variable to the taste. The prevailing flavor is rather negative and peculiar to the order; but they are also bitter, acrid, biting, astringent, oily, and nauseous, as well as savory and agreeable. Most of them lose these qualities in drying. -Fungi have been used as an article of food for untold centuries. The writings of the ancients make frequent mention of them as among their most esteemed viands. They are extensively eaten in Europe by all classes, and many works have been written laudatory of their virtues, with copious directions for dressing them in a great variety of ways. Notwithstanding the virulent poisonous qualities of some, others are eagerly sought for, and in some places it is said that the people have burned down woods to get certain species of fungi whose growth followed the combustion. But in America they have been regarded as noisome and disgust

ing by the great mass of the people; they have been usually despised as the unsightly evidences of decay, rather than eagerly collected as delicious food, which many of them are. Badham states that the return of taxed mushrooms in Rome during a period of 10 years gave a yearly average of between 60,000 and 80,000 lbs. weight, beside the untold quantity consumed which did not fall under government notice. He estimates that in that city alone the annual consumption would reach a value of $20,000. They form an extensive article of food for the poor all over Europe, and some species are sought for at high prices by the rich. The species commonly cultivated, the mushroom proper, is the agaricus campestris, which grows wild in old fields and pastures, but is propagated by planting its spawn, which is the mycelium of the plant, in hot-beds. Although this is the most widely used, many other species are equally excellent. The truffle (tuber cibarium) grows beneath the ground, and is eaten with avidity by different animals. Dogs are trained to scent it out by those who collect truffles for market. Their reputation as aphrodisiacs is thought to be unfounded, having its origin in the old doctrine of resemblances. Polyporus tuberaster grows from the celebrated fungus stone pietra funghia, which is a mass of earth traversed by the mycelium of the plant; the latter is watered from time to time and produces successive crops. The heads of poplar trees are watered in autumn, and they then bear the agaricus caudicinus, greatly esteemed. Blocks of the hazel tree are singed over straw and watered, and they produce in abundance the polyporus corylinus. Among other species eaten, the principal are agaricus prunulus, orcella, procerus, and exquisitus, lactarius deliciosus, cantharellus cibarius, boletus edulis, marasmius oreades, hydnum repandum, fistulina hepatica, morchella esculenta, and helvella crispa. These are all fleshy fungi. Many other species known to be at times poisonous are eaten in different countries in different ways. They are dried, pickled, salted, and cooked in an endless variety of fashions. Some of the most virulent poisons are found among fungi, and many fatal accidents have arisen from the eating of poisonous species, yet fungi which are known to be ordinarily injurious are eaten with impunity by some. Rye meal containing large quantities of ergot produces a terribly disgusting and fatal gangrenous disease; while the ergots themselves are eaten largely in the north of Europe by children, under the name of St. John's bread, without any such result. Pickling and salting renders many innocuous. Agaricus muscarius is one of the most injurious; yet it is used as a means of intoxication by the Kamtchatkadales. One or two of them are sufficient to produce a slight intoxication, which is peculiar in its character. It stimulates the muscular powers, and greatly excites the nervous system, leading the partakers into the most ridiculous extravagances. The only fungus used at the

present day in medicine is the ergot of rye, sometimes employed in cases of protracted labor. Several others have been used in times past like the cordyceps Sinensis, a sphærioid species parasitic on a caterpillar; but these are now thought to be of no value. The lycoperdons or puff-balls have been used as styptics. Some polypori make admirable razor strops when sliced with a sharp knife. Polyporus fomentarius and igniarius have for many years furnished the punk which is used as tinder; the corky portion being pounded till its compact mass of soft, silky fibres becomes loosened and flexible. Agaricus muscarius is used as fly poison.-Some fungi are among the greatest pests of the agriculturist. The rusts, smuts, and bunt of grain are all fungi of the genera uredo, ustilago, and puccinia. Their mycelium penetrates the tissues of the plants, destroys their vitality, and bursting through their cuticles, covers them with myriads of their orange, brown, yellow, or black spores. They probably induce decay by a chemical influence which they exert on the juices of the infested plant, as well as by their mechanical interference with its organism. It has been a question how their spores are carried into the tissues, where their earliest growth is entirely separated from the outer atmosphere. But when we remember their extreme minuteness, we can understand that they may be drawn up with the fluids which enter the roots, or receive them directly into their tissues through the infinity of breathing pores with which the surfaces of the plants they infest are perforated. The mildews of the grape and other fruits are myceloid growths, which in certain stages have been thought to be perfect plants (oidium), from their possessing a power of reproduction. Certain cells take on a vesicular growth filled with a mass of minute bodies which were thought to be the true fruit. But the later observations of Léveillé, Tulasne, and others, have shown that these are arrested stages of growth of an entirely different ascigerous genus, erysiphe. These produce their fruit in minute black pustules, from the base of which peculiar radiating processes arise, sometimes of great beauty. The mildews grow on the surface of fruits, and injure them more by choking up their pores and mechanically confining them with their dense, felty growth, than by abstracting their juices. The potato rot is accompanied by a rapid growth of the mycelium of botrytis infestans, which penetrates the leaves, stems, and tubers, inducing rapid decay. It appears on the surface in the form of a minute white mould. Many other plants are similarly affected. Boleti are sometimes traversed by a minute mould, sepedonium chrysospermum, which gives a golden yellow hue to the flesh. Dry rot in timber is caused by the penetrating mycelium of merulius lacrymans and polyporus destructor. The black excrescent growth on plum trees is occasioned by the sphæria morbosa, which covers the warts its mycelium has made with its minute black, compacted perithecia. The fairy rings which, in olden times, were

thought to be the scenes of midnight fairy revels, are produced by the growth of different species of agaricus. As they exhaust the soil by one year's growth, their mycelium pushes into the richer portion around; and thus they extend the circle of their growth, furnishing by their decay a manure for the next year's grass, which is darker and denser in consequence. This is one of the many instances where exact observation has reduced the fanciful ideas of superstition and poetry to the less romantic but more satisfactory basis of natural causes.-Fungi have been classified in various ways by different mycologists. By the early writers they were arranged according to their external appearances; but as more exact means of observation multiplied, their microscopic structure became better known, and a nearer approach was made to a classification in consonance with their true affinities. From Cæsalpinus in 1583 to Nees von Esenbeck in 1817, the progress of knowledge was comparatively small for a period of nearly 250 years. But in 1821 appeared the Systema Mycologicum of Elias Fries, a work of the most learned and profound character, evincing a comprehensiveness and thoroughness far surpassing all that had preceded it. It is even now the great work to which all students refer, though since that time a host of observers have been exploring this obscure field, and collecting a vast array of facts concerning the laws which govern these minute organisms. Minds of the first class are engaged at present in the elucidation of their structures-Montagne, Léveillé, Tulasne, Berkeley, Desmazières, and many others. The latest system given to the world is that in the Rev. Mr. Berkeley's "Introduction to Cryptogamic Botany," which is essentially similar to that of Fries. The two principal divisions are: sporidiiferi, spores contained in special sacs called asci; and sporiferi, spores naked, not enclosed. These are again subdivided into 6 principal orders, all formed on the mode in which the spores are borne, viz.: 1. Ascomycetes (Berk.), spores produced in little sacs (asci), and formed out of the protoplasm they contain. This order comprises a vast number of the black, pustular growths, abundant on dead wood, bark, twigs, leaves, &c. They are generally formed of a mass of carbonized cells arranged in the form of hollow spheres or cups called perithecia. Within these grow the asci containing the spores, which escape either from a pore in the perithecium or by its breaking up irregularly. The basal cells bearing the asci are collectively termed the hymenium. Among these are the mildews (erysiphe) and the black mildews (capnodium), and the whole great tribe of sphæria. The truffles (tuber) also belong here. They are subterraneous, fleshy forms, whose substance is intersected by veins which are inward folds of the hymenium, covered by the expanding growth of the fleshy receptacle. The morels (morchella) and the helvelle are carnose, bulky forms, which have their asci on the outer surface of a variously folded, wrinkled, and pitted

hymenium. The cyttaria is akin to these, of a sub-gelatinous consistence. These are all made up of compacted cells, forming horny, carbonized, or heavy, fleshy masses. 2. Physomycetes (Berk.), spores growing in bladder-shaped cells on the end of delicate, individual, scattered fibres, composed of cells applied to each other in a linear series. A small group comprising the true moulds (mucor). 3. Hyphomycetes (Fr.), spores naked, simple, or aggregated on the ends of fertile threads. These differ from the last in the naked growth of the spores. Here belongs the great host of minute moulds which cover almost every substance exposed to dampness with their floccose fibres. Nothing organic is free from their attacks. Their colors are sometimes extremely beautiful. To this order belong the mould of the potato rot (botrytis infestans), and many which induce decay in fruit (oidium), the bread and cheese moulds (penicillium, aspergillus), the rigid black moulds (cladosporium, helminthosporium), and the yeast and vinegar plants, which are submerged mycelia of penicillium. 4. Coniomycetes (Fr.), spores naked on the ends of filaments or vesicles; hymenium sometimes obsolete, sometimes contained in a perithecium. This order differs from the last in having scarcely any filamentous growth, and in having the spores produced in the utmost profusion, greatly disproportionate to the rest of the plant. It comprises an infinity of minute pustular forms, which infest the tissues of every variety of plant, many presenting to the eye but a mere speck on their surface. Here belong the whole family of rusts, smuts, and bunt (puccinea, uredo, ustilago, tilletia, acidium, &c.), which creep through the tissues of living plants, and finally burst forth on the exterior and fructify in dense, dusty masses, which cover their whole surfaces. Different species affect different organs, some being on stems and leaves, others on flowers and fruit. They are the scourge of the farmer, whose fields they devastate. The savin trees (juniperus) are attacked by a peculiar genus (podisoma), which bursts from their bark and swells under the influence of moisture to a gelatinous mass. It also occasions the globular excrescent growth called cedar apples, from orifices in which it protrudes in long orangecolored spurs, formed by the spores, tipping the aggregated mass of filaments. The black, irregular scars on apples are caused by the spilocæa fructigena. An extensive group of this order comprises those minute pustular forms which, resembling the true ascigerous fungi in many respects, differ in producing their spores on the ends of the filaments instead of being contained in asci. There is great obscurity overhanging this whole group. They exhibit themselves in so many anomalous forms that it is almost impossible to establish limits to genera which may be clearly understood. Writers on the subject record great numbers of genera, but hardly any two agree upon their characters, and the whole subject is burdened with an inhar

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