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    "chunk_id": "1911:lemming:5cdf2007913a",
    "title": "LEMMING",
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    "verified_text": "lemming, the native name of a small scandinavian rodent mammal _lemmus norvegicus_ (or _l. lemmus_), belonging to the mouse tribe, or _muridae_, and nearly related, especially in the structure of its cheek-teeth, to the voles. specimens vary considerably in size and colour, but the usual length is about 5 in., and the soft fur yellowish-brown, marked with spots of dark brown and black. it has a short, rounded head, obtuse muzzle, small bead-like eyes, and short rounded ears, nearly concealed by the fur. the tail is very short. the feet are small, each with five claws, those of the fore feet strongest, and fitted for scratching and digging. the usual habitat of lemmings is the high lands or fells of the great central mountain chain of norway and sweden, from the southern branches of the langfjeldene in christiansand _stift_ to the north cape and the varangerfjord. south of the arctic circle they are, under ordinary circumstances, confined to the plateaus covered with dwarf birch and juniper above the conifer-region, though in tromso _amt_ and in finmarken they occur in all suitable localities down to the level of the sea. the nest, under a tussock of grass or a stone, is constructed of short dry straws, and usually lined with hair. the number of young in each nest is generally five, sometimes only three occasionally seven or eight, and at least two broods are produced annually. their food is entirely vegetable, especially grass roots and stalks, shoots of dwarf birch, reindeer lichens and mosses, in search of which they form, in winter, long galleries through the turf or under the snow. they are restless, courageous and pugnacious little animals. when suddenly disturbed, instead of trying to escape they sit upright, with their back against a stone, hissing and showing fight in a determined manner. [illustration: the norwegian lemming (_lemmus norvegicus_).] the circumstance which has given popular interest to the lemming is that certain districts of the cultivated lands of norway and sweden, where in ordinary circumstances they are unknown, are, at uncertain intervals varying from five to twenty or more years, overrun by an army of these little creatures, which steadily and slowly advance, always in the same direction, and regardless of all obstacles, swimming streams and even lakes of several miles in breadth, and committing considerable devastation on their line of march by the quantity of food they consume. in their turn they are pursued and harassed by crowds of beasts and birds of prey, as bears, wolves, foxes, dogs, wild cats, stoats, weasels, eagles, hawks and owls, and never spared by man; even domestic animals, as cattle, goats and reindeer, join in the destruction, stamping them to the ground with their feet, and even eating their bodies. numbers also die from diseases produced apparently from overcrowding. none returns, and the onward march of the survivors never ceases until they reach the sea, into which they plunge, and swimming onwards in the same direction perish in the waves. these sudden appearances of vast bodies of lemmings, and their singular habit of persistently pursuing the same onward course of migration, have given rise to various speculations, from the ancient belief of the norwegian peasants, shared by olaus magnus, that they fall down from the clouds, to the hypothesis that they are acting in obedience to an instinct inherited from ancient times, and still seeking the congenial home in the submerged atlantis, to which their ancestors of the miocene period were wont to resort when driven from their ordinary dwelling-places by crowding or scarcity of food. the principal facts regarding these migrations seem to be as follows. when any combination of circumstances has occasioned an increase of the numbers of the lemmings in their ordinary dwelling-places, impelled by the restless or migratory instinct possessed in a less developed degree by so many of their congeners, a movement takes place at the edge of the elevated plateau, and a migration towards the lower-lying land begins. the whole body moves forward slowly, always advancing in the same general direction in which they originally started, but following more or less the course of the great valleys. they only travel by night; and, staying in congenial places for considerable periods, with unaccustomed abundance of provender, notwithstanding the destructive influences to which they are exposed, they multiply excessively during their journey, having families more numerous and frequent than in their usual homes. the progress may last from one to three years, according to the route taken, and the distance to be traversed until the sea-coast is reached, which in a country so surrounded by water as the scandinavian peninsula must be the ultimate goal of such a journey. this may be either the atlantic or the gulf of bothnia, according as the migration has commenced from the west or the east side of the central elevated plateau. those that finally perish in the sea, committing what appears to be a voluntary suicide, are only acting under the same blind impulse which has led them previously to cross shallower pieces of water with safety. in eastern europe, northern asia and north america the group is represented by the allied _l. obensis_, and in alaska, by _l. nigripes_; while the circumpolar banded lemming, _dicrostonyx torquatus_, which turns white in winter, represents a second genus taking its name from the double claws on one of the toes of the forefeet. for habits of lemmings, see r. collett, _myodes lemmus, its habits and migrations in norway_ (christiania videnskabs-selskabs forhandlinger, 1895). (w. h. f.; r. l.*) lemniscate (from gr. [greek: lemniskos], ribbon), a quartic curve invented by jacques bernoulli (_acta eruditorum_, 1694) and afterwards investigated by giulio carlo fagnano, who gave its principal properties and applied it to effect the division of a quadrant into 2.2^m, 3.2^m and 5.2^m equal parts. following archimedes, fagnano desired the curve to be engraved on his tombstone. the complete analytical treatment was first given by leonhard euler. the lemniscate of bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points. it is therefore a particular form of cassini's oval (see oval). its cartesian equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x2 + y2)2 = 2a2(x2 - y2) and the polar equation is r2 = 2a2 cos 2[theta]. the curve (fig. 1) consists of two loops symmetrically placed about the coordinate axes. the pedal equation is r3 = a2p, which shows that it is the first positive pedal of a rectangular hyperbola with regard to the centre. it is also the inverse of the same curve for the same point. it is the envelope of circles described on the central radii of an ellipse as diameters. the area of the complete curve is 2a2, and the length of any arc may be expressed in the form [int](1 - x^4)^(-1⁄2)dx, an elliptic integral sometimes termed the _lemniscatic integral_. [illustration: fig. 1.] [illustration: fig. 2.] [illustration: fig. 3.] [illustration: fig. 4.] [illustration: fig. 5.] the name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis. such curves are given by the equation x2 - y2 = ax^4 + bx2y2 + cy^4. if a be greater than b the curve resembles fig. 2 and is sometimes termed the _fishtail-lemniscate_; if a be less than b, the curve resembles fig. 3. the same name is also given to the first positive pedal of any central conic. when the conic is a rectangular hyperbola, the curve is the lemniscate of bernoulli previously described. the _elliptic lemniscate_ has for its equation (x2 + y2)2 = a2x2 + b2y2 or r2 = a2 cos2[theta] + b2 sin2[theta] (a > b). the centre is a conjugate point (or acnode) and the curve resembles fig. 4. the _hyperbolic lemniscate_ has for its equation (x2 + y2)2 = a2x2 - b2y2 or r2 = a2 cos2[theta] - b2 sin2[theta]. in this case the centre is a crunode and the curve resembles fig. 5. these curves are instances of unicursal bicircular quartics. lemnos (mod. _limnos_), an island in the northern part of the aegean sea. the italian form of the name, stalimene, i.e. [greek: es ten lemnon], is not used in the island itself, but is commonly employed in geographical works. the island, which belongs to turkey, is of considerable size: pliny says that the coast-line measured 1121⁄2 roman miles, and the area has been estimated at 150 sq. m. great part is mountainous, but some very fertile valleys exist, to cultivate which 2000 yoke of oxen are employed. the hill-sides afford pasture for 20,000 sheep. no forests exist on the island; all wood is brought from the coast of rumelia or from thasos. a few mulberry and fruit trees grow, but no olives. the population is estimated by some as high as 27,000, of whom 2000 are turks and the rest greeks, but other authorities doubt whether it reaches more than half this number. the chief towns are kastro on the western coast, with a population of 4000 greeks and 800 turks, and mudros on the southern coast. kastro possesses an excellent harbour, and is the seat of all the trade carried on with the island. greek, english and dutch consuls or consular agents were formerly stationed there; but the whole trade is now in greek hands. the archbishops of lemnos and ai strati, a small neighbouring island with 2000 inhabitants, resides in kastro. in ancient times the island was sacred to hephaestus, who as the legend tells fell on lemnos when his father zeus hurled him headlong out of olympus. this tale, as well as the name aethaleia, sometimes applied to it, points to its volcanic character. it is said that fire occasionally blazed forth from mosychlos, one of its mountains; and pausanias (viii. 33) relates that a small island called chryse, off the lemnian coast, was swallowed up by the sea. all volcanic action is now extinct. the most famous product of lemnos is the medicinal earth, which is still used by the natives. at one time it was popular over western europe under the name _terra sigillata_. this name, like the gr. [greek: lemnia sphragis], is derived from the stamp impressed on each piece of the earth; in ancient times the stamp was the head of artemis. the turks now believe that a vase of this earth destroys the effect of any poison drunk from it--a belief which the ancients attached rather to the earth from cape kolias in attica. galen went to see the digging up of this earth (see kuhn, _medic. gr. opera_, xii. 172 sq.); on one day in each year a priestess performed the due ceremonies, and a waggon-load of earth was dug out. at the present time the day selected is the 6th of august, the feast of christ the saviour. both the turkish _hodja_ and the greek priest are present to perform the necessary ceremonies; the whole process takes place before daybreak. the earth is sold by apothecaries in stamped cubical blocks. the hill from which the earth is dug is a dry mound, void of vegetation, beside the village of kotschinos, and about two hours from the site of hephaestia. the earth was considered in ancient times a cure for old festering wounds, and for the bite of poisonous snakes. the name lemnos is said by hecataeus (ap. steph. byz.) to have been a title of cybele among the thracians, and the earliest inhabitants are said to have been a thracian tribe, called by the greeks sinties, i.e. \"the robbers.\" according to a famous legend the women were all deserted by their husbands, and in revenge murdered every man on the island. from this barbarous act, the expression lemnian deeds, [greek: lemnia erga], became proverbial. the argonauts landing soon after found only women in the island, ruled over by hypsipyle, daughter of the old king thoas. from the argonauts and the lemnian women were descended the race called minyae, whose king euneus, son of jason and hypsipyle, sent wine and provisions to the greeks at troy. the minyae were expelled by a pelasgian tribe who came from attica. the historical element underlying these traditions is probably that the original thracian people were gradually brought into communication with the greeks as navigation began to unite the scattered islands of the aegean (see jason); the thracian inhabitants were barbarians in comparison with the greek mariners. the worship of cybele was characteristic of thrace, whither it spread from asia minor at a very early period, and it deserves notice that hypsipyle and myrina (the name of one of the chief towns) are amazon names, which are always connected with asiatic cybele-worship. coming down to a better authenticated period, we find that lemnos was conquered by otanes, one of the generals of darius hystaspis; but was soon reconquered by miltiades, the tyrant of the thracian chersonese. miltiades afterwards returned to athens, and lemnos continued an athenian possession till the macedonian empire absorbed it. on the vicissitudes of its history in the 3rd century b.c. see kohler in _mittheil. inst. athen._ i. 261. the romans declared it free in 197",
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