Chapter XIV: Part 14

LAPIS LAZULI, or azure stone,[1] a mineral substance valued for decorative purposes in consequence of the fine blue colour which it usually presents. It appears to have been the sapphire of ancient writers: thus Theophrastus describes the [Greek: sappheiros] as being spotted with gold-dust, a description quite inappropriate to modern sapphire, but fully applicable to lapis lazuli, for this stone frequently contains disseminated particles of iron-pyrites of gold-like appearance. Pliny, too, refers to the _sapphirus_ as a stone sprinkled with specks of gold; and possibly an allusion to the same character may be found in Job xxviii. 6. The Hebrew _sappir_, denoting a stone in the High Priest's breastplate, was probably lapis lazuli, as acknowledged in the Revised Version of the Bible. With the ancient Egyptians lapis lazuli was a favourite stone for amulets and ornaments such as scarabs; it was also used to a limited extent by the Assyrians and Babylonians for cylinder seals. It has been suggested that the Egyptians obtained it from Persia in exchange for their emeralds. When the lapis lazuli contains pyrites, the brilliant spots in the deep blue matrix invite comparison with the stars in the firmament. The stone seems to have been sometimes called by ancient writers [Greek: kyanos]. It was a favourite material with the Italians of the _Cinquecento_ for vases, small busts and other ornaments. Magnificent examples of the decorative use of lapis lazuli are to be seen in St Petersburg, notably in the columns of St Isaac's cathedral. The beautiful blue colour of lapis lazuli led to its employment, when ground and levigated, as a valuable pigment known as ultramarine (q.v.), a substance now practically displaced by a chemical product (artificial ultramarine).

Lapis lazuli occurs usually in compact masses, with a finely granular structure; and occasionally, but only as a great rarity, it presents the form of the rhombic dodecahedron. Its specific gravity is 2.38 to 2.45, and its hardness about 5.5, so that being comparatively soft it tends, when polished, to lose its lustre rather readily. The colour is generally a fine azure or rich Berlin blue, but some varieties exhibit green, violet and even red tints, or may be altogether colourless. The colour is sometimes improved by heating the stone. Under artificial illumination the dark-blue stones may appear almost black. The mineral is opaque, with only slight translucency at thin edges.

Analyses of lapis lazuli show considerable variation in composition, and this led long ago to doubt as to its homogeneity. This doubt was confirmed by the microscopic studies of L. H. Fischer, F. Zirkel and H. P. J. Vogelsang, who found that sections showed bluish particles in a white matrix; but it was reserved for Professor W. C. Brögger and H. Bäckström, of Christiania, to separate the several constituents and subject them to analysis, thus demonstrating the true constitution of lapis lazuli, and proving that it is a rock rather than a definite mineral species. The essential part of most lapis lazuli is a blue mineral allied to sodalite and crystallized in the cubic system, which Brögger distinguishes as lazurite, but this is intimately associated with a closely related mineral which has long been known as haüyne, or haüynite. The lazurite, sometimes regarded as true lapis lazuli, is a sulphur-bearing sodium and aluminium silicate, having the formula: Na4(NaS3Al) Al2(SiO4)3. As the lazurite and the haüynite seem to occur in molecular intermixture, various kinds of lapis lazuli are formed; and it has been proposed to distinguish some of them as lazurite-lapis and haüyne-lapis, according as one or the other mineral prevails. The lazurite of lapis lazuli is to be carefully distinguished from lazulite, an aluminium-magnesium phosphate, related to turquoise. In addition to the blue cubic minerals in lapis lazuli, the following minerals have also been found: a non-ferriferous diopside, an amphibole called, from the Russian mineralogist, koksharovite, orthoclase, plagioclase, a muscovite-like mica, apatite, titanite, zircon, calcite and pyrite. The calcite seems to form in some cases a great part of the lapis; and the pyrite, which may occur in patches, is often altered to limonite.

Lapis lazuli usually occurs in crystalline limestone, and seems to be a product of contact metamorphism. It is recorded from Persia, Tartary, Tibet and China, but many of the localities are vague and some doubtful. The best known and probably the most important locality is in Badakshan. There it occurs in limestone, in the valley of the river Kokcha, a tributary to the Oxus, south of Firgamu. The mines were visited by Marco Polo in 1271, by J. B. Fraser in 1825, and by Captain John Wood in 1837-1838. The rock is split by aid of fire. Three varieties of the lapis lazuli are recognized by the miners: _nili_ of indigo-blue colour, _asmani_ sky-blue, and _sabzi_ of green tint. Another locality for lapis lazuli is in Siberia near the western extremity of Lake Baikal, where it occurs in limestone at its contact with granite. Fine masses of lapis lazuli occur in the Andes, in the vicinity of Ovalle, Chile. In Europe lapis lazuli is found as a rarity in the peperino of Latium, near Rome, and in the ejected blocks of Monte Somma, Vesuvius. (F. W. R.*)

FOOTNOTE:

[1] The Med. Gr. [Greek: lazourion], Med. Lat. _lazurius_ or
_lazulus_, as the names of this mineral substance, were adaptations
of the Arab. _al-lazward_, Pers. _lajward_, blue colour, lapis
lazuli. The same word appears in Med. Lat. as _azura_, whence O.F.
azur, Eng. "azure," blue, particularly used of that colour in
heraldry (q.v.) and represented conventionally in black and white by
horizontal lines.

LAPITHAE, a mythical race, whose home was in Thessaly in the valley of the Peneus. The genealogies make them a kindred race with the Centaurs, their king Peirithoüs being the son, and the Centaurs the grandchildren (or sons) of Ixion. The best-known legends with which they are connected are those of Ixion (q.v.) and the battle with the Centaurs (q.v.). A well-known Lapith was Caeneus, said to have been originally a girl named Caenis, the favourite of Poseidon, who changed her into a man and made her invulnerable (Ovid, _Metam._ xii. 146 ff). In the Centaur battle, having been crushed by rocks and trunks of trees, he was changed into a bird; or he disappeared into the depths of the earth unharmed. According to some, the Lapithae are representatives of the giants of fable, or spirits of the storm; according to others, they are a semi-legendary; semi-historical race, like the Myrmidons and other Thessalian tribes. The Greek sculptors of the school of Pheidias conceived of the battle of the Lapithae and Centaurs as a struggle between mankind and mischievous monsters, and symbolical of the great conflict between the Greeks and Persians. Sidney Colvin (_Journ. Hellen. Stud._ i. 64) explains it as a contest of the physical powers of nature, and the mythical expression of the terrible effects of swollen waters.

LA PLACE (Lat. _Placaeus_), JOSUÉ DE (1606?-1665), French Protestant divine, was born in Brittany. He studied and afterwards taught philosophy at Saumur. In 1625 he became pastor of the Reformed Church at Nantes, and in 1632 was appointed professor of theology at Saumur, where he had as his colleagues, appointed at the same time, Moses Amyraut and Louis Cappell. In 1640 he published a work, _Theses theologicae de statu hominis lapsi ante gratiam_, which was looked upon with some suspicion as containing liberal ideas about the doctrine of original sin. The view that the original sin of Adam was not imputed to his descendants was condemned at the synod of Charenton (1645), without special reference being made to La Place, whose position perhaps was not quite clear. As a matter of fact La Place distinguished between a direct and indirect imputation, and after his death his views, as well as those of Amyraut, were rejected in the _Formula consensus of_ 1675. He died on the 17th of August 1665.

La Place's defence was published with the title _Disputationes
academicae_ (3 vols., 1649-1651; and again in 1665); his work _De
imputatione primi peccati Adami_ in 1655. A collected edition of his
works appeared at Franeker in 1699, and at Aubencit in 1702.

LAPLACE, PIERRE SIMON, MARQUIS DE (1749-1827), French mathematician and astronomer, was born at Beaumont-en-Auge in Normandy, on the 28th of March 1749. His father was a small farmer, and he owed his education to the interest excited by his lively parts in some persons of position. His first distinctions are said to have been gained in theological controversy, but at an early age he became mathematical teacher in the military school of Beaumont, the classes of which he had attended as an extern. He was not more than eighteen when, armed with letters of recommendation, he approached J. B. d'Alembert, then at the height of his fame, in the hope of finding a career in Paris. The letters remained unnoticed, but Laplace was not crushed by the rebuff. He wrote to the great geometer a letter on the principles of mechanics, which evoked an immediate and enthusiastic response. "You," said d'Alembert to him, "needed no introduction; you have recommended yourself; my support is your due." He accordingly obtained for him an appointment as professor of mathematics in the École Militaire of Paris, and continued zealously to forward his interests.

Laplace had not yet completed his twenty-fourth year when he entered upon the course of discovery which earned him the title of "the Newton of France." Having in his first published paper[1] shown his mastery of analysis, he proceeded to apply its resources to the great outstanding problems in celestial mechanics. Of these the most conspicuous was offered by the opposite inequalities of Jupiter and Saturn, which the emulous efforts of L. Euler and J. L. Lagrange had failed to bring within the bounds of theory. The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of Newton. In a paper read before the Academy of Sciences, on the 10th of February 1773 (_Mém. présentés par divers savans_, tom, vii., 1776), Laplace announced his celebrated conclusion of the invariability of planetary mean motions, carrying the proof as far as the cubes of the eccentricities and inclinations. This was the first and most important step in the establishment of the stability of the solar system. It was followed by a series of profound investigations, in which Lagrange and Laplace alternately surpassed and supplemented each other in assigning limits of variation to the several elements of the planetary orbits. The analytical tournament closed with the communication to the Academy by Laplace, in 1787, of an entire group of remarkable discoveries. It would be difficult, in the whole range of scientific literature, to point to a memoir of equal brilliancy with that published (divided into three parts) in the volumes of the Academy for 1784, 1785 and 1786. The long-sought cause of the "great inequality" of Jupiter and Saturn was found in the near approach to commensurability of their mean motions; it was demonstrated in two elegant theorems, independently of any except the most general considerations as to mass, that the mutual action of the planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the Jovian system were expressed in the so-called "laws of Laplace." He completed the theory of these bodies in a treatise published among the Paris _Memoirs_ for 1788 and 1789; and the striking superiority of the tables computed by J. B. J. Delambre from the data there supplied marked the profit derived from the investigation by practical astronomy. The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (_Memoirs_, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit. The last apparent anomaly, and the last threat of instability, thus disappeared from the solar system.

With these brilliant performances the first period of Laplace's scientific career may be said to have closed. If he ceased to make striking discoveries in celestial mechanics, it was rather their subject-matter than his powers that failed. The general working of the great machine was now laid bare, and it needed a further advance of knowledge to bring a fresh set of problems within reach of investigation. The time had come when the results obtained in the development and application of the law of gravitation by three generations of illustrious mathematicians might be presented from a single point of view. To this task the second period of Laplace's activity was devoted. As a monument of mathematical genius applied to the celestial revolutions, the _Mécanique céleste_ ranks second only to the _Principia_ of Newton.

The declared aim of the author[2] was to offer a complete solution of
the great mechanical problem presented by the solar system, and to
bring theory to coincide so closely with observation that empirical
equations should no longer find a place in astronomical tables. His
success in both respects fell little short of his lofty ideal. The
first part of the work (2 vols. 4to, Paris, 1799) contains methods for
calculating the movements of translation and rotation of the heavenly
bodies, for determining their figures, and resolving tidal problems;
the second, especially dedicated to the improvement of tables,
exhibits in the third and fourth volumes (1802 and 1805) the
application of these formulae; while a fifth volume, published in
three instalments, 1823-1825, comprises the results of Laplace's
latest researches, together with a valuable history of progress in
each separate branch of his subject. In the delicate task of
apportioning his own large share of merit, he certainly does not err
on the side of modesty; but it would perhaps be as difficult to
produce an instance of injustice, as of generosity in his estimate of
others. Far more serious blame attaches to his all but total
suppression in the body of the work--and the fault pervades the whole
of his writings--of the names of his predecessors and contemporaries.
Theorems and formulae are appropriated wholesale without
acknowledgment, and a production which may be described as the
organized result of a century of patient toil presents itself to the
world as the offspring of a single brain. The _Mécanique céleste_ is,
even to those most conversant with analytical methods, by no means
easy reading. J. B. Biot, who assisted in the correction of its proof
sheets, remarked that it would have extended, had the demonstrations
been fully developed, to eight or ten instead of five volumes; and he
saw at times the author himself obliged to devote an hour's labour to
recovering the dropped links in the chain of reasoning covered by the
recurring formula. "Il est aisé à voir."[3]

The _Exposition du système du monde_ (Paris, 1796) has been styled by Arago "the _Mécanique céleste_ disembarrassed of its analytical paraphernalia." Conclusions are not merely stated in it, but the methods pursued for their attainment are indicated. It has the strength of an analytical treatise, the charm of a popular dissertation. The style is lucid and masterly, and the summary of astronomical history with which it terminates has been reckoned one of the masterpieces of the language. To this linguistic excellence the writer owed the place accorded to him in 1816 in the Academy, of which institution he became president in the following year. The famous "nebular hypothesis" of Laplace made its appearance in the _Système du monde_. Although relegated to a note (vii.), and propounded "Avec la défiance que doit inspirer tout ce qui n'est point un résultat de l'observation ou du calcul," it is plain, from the complacency with which he recurred to it[4] at a later date, that he regarded the speculation with considerable interest. That it formed the starting-point, and largely prescribed the course of thought on the subject of planetary origin is due to the simplicity of its assumptions, and the clearness of the mechanical principles involved, rather than to any cogent evidence of its truth. It is curious that Laplace, while bestowing more attention than they deserved on the crude conjectures of Buffon, seems to have been unaware that he had been, to some extent, anticipated by Kant, who had put forward in 1755, in his _Allgemeine Naturgeschichte_, a true though defective nebular cosmogony.

The career of Laplace was one of scarcely interrupted prosperity. Admitted to the Academy of Sciences as an associate in 1773, he became a member in 1785, having, about a year previously, succeeded E. Bezout as examiner to the royal artillery. During an access of revolutionary suspicion, he was removed from the commission of weights and measures; but the slight was quickly effaced by new honours. He was one of the first members, and became president of the Bureau of Longitudes, took a prominent place at the Institute (founded in 1796), professed analysis at the École Normale, and aided in the organization of the decimal system. The publication of the _Mécanique céleste_ gained him world-wide celebrity, and his name appeared on the lists of the principal scientific associations of Europe, including the Royal Society. But scientific distinctions by no means satisfied his ambition. He aspired to the rôle of a politician, and has left a memorable example of genius degraded to servility for the sake of a riband and a title. The ardour of his republican principles gave place, after the 18th Brumaire, to devotion towards the first consul, a sentiment promptly rewarded with the post of minister of the interior. His incapacity for affairs was, however, so flagrant that it became necessary to supersede him at the end of six weeks, when Lucien Bonaparte became his successor. "He brought into the administration," said Napoleon, "the spirit of the infinitesimals." His failure was consoled by elevation to the senate, of which body he became chancellor in September 1803. He was at the same time named grand officer of the Legion of Honour, and obtained in 1813 the same rank in the new order of Reunion. The title of count he had acquired on the creation of the empire. Nevertheless he cheerfully gave his voice in 1814 for the dethronement of his patron, and his "suppleness" merited a seat in the chamber of peers, and, in 1817, the dignity of a marquisate. The memory of these tergiversations is perpetuated in his writings. The first edition of the _Système du monde_ was inscribed to the Council of Five Hundred; to the third volume of the _Mécanique céleste_ (1802) was prefixed the declaration that, of all the truths contained in the work, that most precious to the author was the expression of his gratitude and devotion towards the "pacificator of Europe"; upon which noteworthy protestation the suppression in the editions of the _Théorie des probabilités_ subsequent to the restoration, of the original dedication to the emperor formed a fitting commentary.

During the later years of his life, Laplace lived much at Arcueil, where he had a country-place adjoining that of his friend C. L. Berthollet. With his co-operation the Société d'Arcueil was formed, and he occasionally contributed to its _Memoirs_. In this peaceful retirement he pursued his studies with unabated ardour, and received with uniform courtesy distinguished visitors from all parts of the world. Here, too, he died, attended by his physician, Dr Majendie, and his mathematical coadjutor, Alexis Bouvard, on the 5th of March 1827. His last words were: "Ce que nous connaissons est peu de chose, ce que nous ignorons est immense."

Expressions occur in Laplace's private letters inconsistent with the atheistical opinions he is commonly believed to have held. His character, notwithstanding the egotism by which it was disfigured, had an amiable and engaging side. Young men of science found in him an active benefactor. His relations with these "adopted children of his thought" possessed a singular charm of affectionate simplicity; their intellectual progress and material interests were objects of equal solicitude to him, and he demanded in return only diligence in the pursuit of knowledge. Biot relates that, when he himself was beginning his career, Laplace introduced him at the Institute for the purpose of explaining his supposed discovery of equations of mixed differences, and afterwards showed him, under a strict pledge of secrecy, the papers, then yellow with age, in which he had long before obtained the same results. This instance of abnegation is the more worthy of record that it formed a marked exception to Laplace's usual course. Between him and A. M. Legendre there was a feeling of "more than coldness," owing to his appropriation, with scant acknowledgment, of the fruits of the other's labours; and Dr Thomas Young counted himself, rightly or wrongly, amongst the number of those similarly aggrieved by him. With Lagrange, on the other hand, he always remained on the best of terms. Laplace left a son, Charles Emile Pierre Joseph Laplace (1789-1874), who succeeded to his title, and rose to the rank of general in the artillery.

It might be said that Laplace was a great mathematician by the original structure of his mind, and became a great discoverer through the sentiment which animated it. The regulated enthusiasm with which he regarded the system of nature was with him from first to last. It can be traced in his earliest essay, and it dictated the ravings of his final illness. By it his extraordinary analytical powers became strictly subordinated to physical investigations. To this lofty quality of intellect he added a rare sagacity in perceiving analogies, and in detecting the new truths that lay concealed in his formulae, and a tenacity of mental grip, by which problems, once seized, were held fast, year after year, until they yielded up their solutions. In every branch of physical astronomy, accordingly, deep traces of his work are visible. "He would have completed the science of the skies," Baron Fourier remarked, "had the science been capable of completion."

It may be added that he first examined the conditions of stability of
the system formed by Saturn's rings, pointed out the necessity for
their rotation, and fixed for it a period (10^h 33^m) virtually
identical with that established by the observations of Herschel; that
he detected the existence in the solar system of an invariable plane
such that the sum of the products of the planetary masses by the
projections upon it of the areas described by their radii vectores in
a given time is a maximum; and made notable advances in the theory of
astronomical refraction (_Méc. cél._ tom. iv. p. 258), besides
constructing satisfactory formulae for the barometrical determination
of heights (_Méc. cél._ tom. iv. p. 324). His removal of the
considerable discrepancy between the actual and Newtonian velocities
of sound,[5] by taking into account the increase of elasticity due to
the heat of compression, would alone have sufficed to illustrate a
lesser name. Molecular physics also attracted his notice, and he
announced in 1824 his purpose of treating the subject in a separate
work. With A. Lavoisier he made an important series of experiments on
specific heat (1782-1784), in the course of which the "ice
calorimeter" was invented; and they contributed jointly to the
_Memoirs_ of the Academy (1781) a paper on the development of
electricity by evaporation. Laplace was, moreover, the first to offer
a complete analysis of capillary action based upon a definite
hypothesis--that of forces "sensible only at insensible distances";
and he made strenuous but unsuccessful efforts to explain the
phenomena of light on an identical principle. It was a favourite idea
of his that chemical affinity and capillary attraction would
eventually be included under the same law, and it was perhaps because
of its recalcitrance to this cherished generalization that the
undulatory theory of light was distasteful to him.

The investigation of the figure of equilibrium of a rotating fluid
mass engaged the persistent attention of Laplace. His first memoir was
communicated to the Academy in 1773, when he was only twenty-four, his
last in 1817, when he was sixty-eight. The results of his many papers
on this subject--characterized by him as "un des points les plus
intéressans du système du monde"--are embodied in the _Mécanique
céleste_, and furnish one of the most remarkable proofs of his
analytical genius. C. Maclaurin, Legendre and d'Alembert had furnished
partial solutions of the problem, confining their attention to the
possible figures which would satisfy the conditions of equilibrium.
Laplace treated the subject from the point of view of the gradual
aggregation and cooling of a mass of matter, and demonstrated that the
form which such a mass would ultimately assume must be an ellipsoid of
revolution whose equator was determined by the primitive plane of
maximum areas.

The related subject of the attraction of spheroids was also signally
promoted by him. Legendre, in 1783, extended Maclaurin's theorem
concerning ellipsoids of revolution to the case of any spheroid of
revolution where the attracted point, instead of being limited to the
axis or equator, occupied any position in space; and Laplace, in his
treatise _Théorie du mouvement et de la figure elliptique des
planètes_ (published in 1784), effected a still further generalization
by proving, what had been suspected by Legendre, that the theorem was
equally true for any confocal ellipsoids. Finally, in a celebrated
memoir, _Théorie des attractions des sphéroides et de la figure des
planètes_, published in 1785 among the Paris _Memoirs_ for the year
1782, although written after the treatise of 1784, Laplace treated
exhaustively the general problem of the attraction of any spheroid
upon a particle situated outside or upon its surface.

These researches derive additional importance from having introduced
two powerful engines of analysis for the treatment of physical
problems, Laplace's coefficients and the potential function. By his
discovery that the attracting force in any direction of a mass upon a
particle could be obtained by the direct process of differentiating a
single function, Laplace laid the foundations of the mathematical
sciences of heat, electricity and magnetism. The expressions
designated by Dr Whewell, Laplace's coefficients (see SPHERICAL
HARMONICS) were definitely introduced in the memoir of 1785 on
attractions above referred to. In the figure of the earth, the theory
of attractions, and the sciences of electricity and magnetism this
powerful calculus occupies a prominent place. C. F. Gauss in
particular employed it in the calculation of the magnetic potential of
the earth, and it received new light from Clerk Maxwell's
interpretation of harmonics with reference to poles on the sphere.

Laplace nowhere displayed the massiveness of his genius more
conspicuously than in the theory of probabilities. The science which
B. Pascal and P. de Fermat had initiated he brought very nearly to
perfection; but the demonstrations are so involved, and the omissions
in the chain of reasoning so frequent, that the _Théorie analytique_
(1812) is to the best mathematicians a work requiring most arduous
study. The theory of probabilities, which Laplace described as common
sense expressed in mathematical language, engaged his attention from
its importance in physics and astronomy; and he applied his theory,
not only to the ordinary problems of chances, but also to the inquiry
into the causes of phenomena, vital statistics and future events.

The device known as the method of least squares, for reducing numerous
equations of condition to the number of unknown quantities to be
determined, had been adopted as a practically convenient rule by Gauss
and Legendre; but Laplace first treated it as a problem in
probabilities, and proved by an intricate and difficult course of
reasoning that it was also the most advantageous, the mean of the
probabilities of error in the determination of the elements being
thereby reduced to a minimum.

Laplace published in 1779 the method of generating functions, the
foundation of his theory of probabilities, and the first part of his
_Théorie analytique_ is devoted to the exposition of its principles,
which in their simplest form consist in treating the successive values
of any function as the coefficients in the expansion of another
function with reference to a different variable. The latter is
therefore called the generating function of the former. A _direct_ and
an _inverse_ calculus is thus created, the object of the former being
to determine the coefficients from the generating function, of the
latter to discover the generating function from the coefficients. The
one is a problem of interpolation, the other a step towards the
solution of an equation in finite differences. The method, however, is
now obsolete owing to the more extended facilities afforded by the
calculus of operations.

The first formal proof of Lagrange's theorem for the development in a
series of an implicit function was furnished by Laplace, who gave to
it an extended generality. He also showed that every equation of an
even degree must have at least one real quadratic factor, reduced the
solution of linear differential equations to definite integrals, and
furnished an elegant method by which the linear partial differential
equation of the second order might be solved. He was also the first to
consider the difficult problems involved in equations of mixed
differences, and to prove that an equation in finite differences of
the first degree and the second order might always be converted into a
continued fraction.

In 1842, the works of Laplace being nearly out of print, his widow was
about to sell a farm to procure funds for a new impression, when the
government of Louis Philippe took the matter in hand. A grant of
40,000 francs having been obtained from the chamber, a national
edition was issued in seven 4to vols., bearing the title _Oeuvres de
Laplace_ (1843-1847). The _Mécanique céleste_ with its four
supplements occupies the first 5 vols., the 6th contains the _Système
du monde_, and the 7th the _Th. des probabilités_, to which the more
popular _Essai philosophique_ forms an introduction. Of the four
supplements added by the author (1816-1825) he tells us that the
problems in the last were contributed by his son. An enumeration of
Laplace's memoirs and papers (about one hundred in number) is rendered
superfluous by their embodiment in his principal works. The _Th. des
prob._ was first published in 1812, the _Essai_ in 1814; and both
works as well as the _Système du monde_ went through repeated
editions. An English version of the _Essai_ appeared in New York in
1902. Laplace's first separate work, _Théorie du mouvement et de la
figure elliptique des planètes_ (1784), was published at the expense
of President Bochard de Saron. The _Précis de l'histoire de
l'astronomie_ (1821), formed the fifth book of the 5th edition of the
_Système du monde_. An English translation, with copious elucidatory
notes, of the first 4 vols. of the _Mécanique céleste_, by N.
Bowditch, was published at Boston, U.S. (1829-1839), in 4 vols. 4to.;
a compendium of certain portions of the same work by Mrs Somerville
appeared in 1831, and a German version of the first 2 vols. by
Burckhardt at Berlin in 1801. English translations of the _Système du
monde_ by J. Pond and H. H. Harte were published, the first in 1809,
the second in 1830. An edition entitled _Les Oeuvres complètes de
Laplace_ (1878), &c., which is to include all his memoirs as well as
his separate works, is in course of publication under the auspices of
the Academy of Sciences. The thirteenth 4to volume was issued in 1904.
Some of Laplace's results in the theory of probabilities are
simplified in S. F. Lacroix's _Traité élémentaire du calcul des
probabilités_ and De Morgan's _Essay_, published in Lardner's _Cabinet
Cyclopaedia_. For the history of the subject see _A History of the
Mathematical Theory of Probability_, by Isaac Todhunter (1865).
Laplace's treatise on specific heat was published in German in 1892 as
No. 40 of W. Ostwald's _Klassiker der exacten Wissenschaften_.

AUTHORITIES.--Baron Fourier's _Éloge, Mémoires de l'institut_, x.
lxxxi. (1831); _Revue encyclopédique_, xliii. (1829); S. D. Poisson's
Funeral Oration (_Conn. des Temps_, 1830, p. 19); F. X. von Zach,
_Allg. geographische Ephemeriden_, iv. 70 (1799); F. Arago, _Annuaire
du Bureau des Long_. 1844, p. 271, translated among Arago's
Biographies of Distinguished Men (1857); J. S. Bailly, _Hist. de
l'astr. moderne_, t. iii.; R. Grant, _Hist. of Phys. Astr._ p. 50,
&c.; A. Berry, _Short Hist. of Astr._ p. 306; Max Marie, _Hist. des
sciences_ t. x. pp. 69-98; R. Wolf, _Geschichte der Astronomie_; J.
Mädler, _Gesch. der Himmelskunde_, i. 17; W. Whewell, _Hist. of the
Inductive Sciences_, ii. _passim_; J. C. Poggendorff, _Biog-lit.
Handwörterbuch._ (A. M. C.)

FOOTNOTES:

[1] "Recherches sur le calcul intégral," _Mélanges de la Soc. Roy. de
Turin_ (1766-1769).

[2] "Plan de l'Ouvrage," _Oeuvres_, tom. i. p 1.

[3] Journal des savants (1850).

[4] _Méc. cél._, tom. v. p. 346.

[5] _Annales de chimie et de physique_ (1816), tom. iii. p. 238.

LAPLAND, or LAPPLAND, a name used to indicate the region of northern Europe inhabited by the Lapps, though not applied to any administrative district. It covers in Norway the division (amter) of Finmarken and the higher inland parts of Tromsö and Nordland; in Russian territory the western part of the government of Archangel as far as the White Sea and the northern part of the Finnish district of Uleåborg; and in Sweden the inland and northern parts of the old province of Norrland, roughly coincident with the districts (_län_) of Norbotten and Vesterbotten, and divided into five divisions--Torne Lappmark, Lule Lappmark, Pite Lappmark, Lycksele Lappmark and Åsele Lappmark. The Norwegian portion is thus insignificant; of the Russian only a little lies south of the Arctic circle, and the whole is less accessible and more sparsely populated than the Swedish, the southern boundary of which may be taken arbitrarily at about 64° N., though scattered families of Lapps occur much farther south, even in the Hardanger Fjeld in Norway.

The Scandinavian portion of Lapland presents the usual characteristics of the mountain plateau of that peninsula--on the west side the bold headlands and fjords, deeply-grooved valleys and glaciers of Norway, on the east the long mountain lakes and great lake-fed rivers of Sweden. Russian Lapland is broadly similar to the lower-lying parts of Swedish Lapland, but the great lakes are more generally distributed, and the valleys are less direct. The country is low and gently undulating, broken by detached hills and ridges not exceeding in elevation 2500 ft. In the uplands of Swedish Lapland, and to some extent in Russian Lapland, the lakes afford the principal means of communication; it is almost impossible to cross the forests from valley to valley without a native guide. In Sweden the few farms of the Swedes who inhabit the region are on the lake shores, and the traveller must be rowed from one to another in the typical boats of the district, pointed at bow and stern, unusually low amidships, and propelled by short sculls or paddles. Sailing is hardly ever practised, and squalls on the lakes are often dangerous to the rowing-boats. On a few of the lakes wood-fired steam-launches are used in connexion with the timber trade, which is considerable, as practically the whole region is forested. Between the lakes all journeying is made on foot. The heads of the Swedish valleys are connected with the Norwegian fjords by passes generally traversed only by tracks; though from the head of the Ume a driving road crosses to Mo on Ranen Fjord. Each principal valley has a considerable village at or near the tail of the lake-chain, up to which a road runs along the valley. The village consists of wooden cottages with an inn (_gästgifvaregård_), a church, and frequently a collection of huts without windows, closed in summer, but inhabited by the Lapps when they come down from the mountains to the winter fairs. Sometimes there is another church and small settlement in the upper valley, to which, once or twice in a summer, the Lapps come from great distances to attend service. To these, too, they sometimes bring their dead for burial, bearing them if necessary on a journey of many days. Though Lapland gives little scope for husbandry, a bad summer being commonly followed by a winter famine, it is richly furnished with much that is serviceable to man. There are copper-mines at the mountain of Sulitelma, and the iron deposits in Norrland are among the most extensive in the world. Their working is facilitated by the railway from Stockholm to Gellivara, Kirunavara and Narvik on the Norwegian coast, which also connects them with the port of Luleå on the Gulf of Bothnia. The supply of timber (pine, fir, spruce and birch) is unlimited. Though fruit-trees will not bear there is an abundance of edible berries; the rivers and lakes abound with trout, perch, pike and other fish, and in the lower waters with salmon; and the cod, herring, halibut and Greenland shark in the northern seas attract numerous Norwegian and Russian fishermen.

The climate is thoroughly Arctic. In the northern parts unbroken daylight in summer and darkness in winter last from two to three months each; and through the greater part of the country the sun does not rise at mid-winter or set at midsummer. In December and January in the far north there is little more daylight than a cold glimmer of dawn; by February, however, there are some hours of daylight; in March the heat of the sun is beginning to modify the cold, and now and in April the birds of passage begin to appear. In April the snow is melting from the branches; spring comes in May; spring flowers are in blossom, and grain is sown. At the end of this month or in June the ice is breaking up on the lakes, woods rush into leaf, and the unbroken daylight of the northern summer soon sets in. July is quite warm; the great rivers come down full from the melting snows in the mountains. August is a rainy month, the time of harvest; night-frosts may begin already about the middle of the month. All preparations for winter are made during September and October, and full winter has set in by November.

_The Lapps._--The Lapps (Swed. _Lappar_; Russian _Lopari_; Norw. _Finner_) call their country _Sabme_ or _Same_, and themselves _Samelats_--names almost identical with those employed by the Finns for their country and race, and probably connected with a root signifying "dark." Lapp is almost certainly a nickname imposed by foreigners, although some of the Lapps apply it contemptuously to those of their countrymen whom they think to be less civilized than themselves.[1]

In Sweden and Finland the Lapps are usually divided into fisher, mountain and forest Lapps. In Sweden the first class includes many impoverished mountain Lapps. As described by Laestadius (1827-1832), their condition was very miserable; but since his time matters have improved. The principal colony has its summer quarters on the Stora-Lule Lake, possesses good boats and nets, and, besides catching and drying fish, makes money by the shooting of wild fowl and the gathering of eggs. When he has acquired a little means it is not unusual for the fisher to settle down and reclaim a bit of land. The mountain and forest Lapps are the true representatives of the race. In the wandering life of the mountain Lapp his autumn residence, on the borders of the forest district, may be considered as the central point; it is there that he erects his _njalla_, a small wooden storehouse raised high above the ground by one or more piles. About the beginning of November he begins to wander south or east into the forest land, and in the winter he may visit, not only such places as Jokkmokk and Arjepluog, but even Gefle, Upsala or Stockholm. About the beginning of May he is back at his njalla, but as soon as the weather grows warm he pushes up to the mountains, and there throughout the summer pastures his herds and prepares his store of cheese. By autumn or October he is busy at his njalla killing the surplus reindeer bulls and curing meat for the winter. From the mountain Lapp the forest (or, as he used to be called, the spruce-fir) Lapp is mainly distinguished by the narrower limits within which he pursues his nomadic life. He never wanders outside of a certain district, in which he possesses hereditary rights, and maintains a series of camping-grounds which he visits in regular rotation. In May or April he lets his reindeer loose, to wander as they please; but immediately after midsummer, when the mosquitoes become troublesome, he goes to collect them. Catching a single deer and belling it, he drives it through the wood; the other deer, whose instinct leads them to gather into herds for mutual protection against the mosquitoes, are attracted by the sound. Should the summer be very cool and the mosquitoes few, the Lapp finds it next to impossible to bring the creatures together. About the end of August they are again let loose, but they are once more collected in October, the forest Lapp during winter pursuing the same course of life as the mountain Lapp.

In Norway there are three classes--the sea Lapps, the river Lapps and the mountain Lapps, the first two settled, the third nomadic. The mountain Lapps have a rather ruder and harder life than the same class in Sweden. About Christmas those of Kautokeino and Karasjok are usually settled in the neighbourhood of the churches; in summer they visit the coast, and in autumn they return inland. Previous to 1852, when they were forbidden by imperial decree, they were wont in winter to move south across the Russian frontiers. It is seldom possible for them to remain more than three or four days in one spot. Flesh is their favourite, in winter almost their only food, though they also use reindeer milk, cheese and rye or barley cakes. The sea Lapps are in some respects hardly to be distinguished from the other coast dwellers of Finmark. Their food consists mainly of cooked fish. The river Lapps, many of whom, however, are descendants of Finns proper, breed cattle, attempt a little tillage and entrust their reindeer to the care of mountain Lapps.

In Finland there are comparatively few Laplanders, and the great bulk of them belong to the fisher class. Many are settled in the neighbourhood of the Enare Lake. In the spring they go down to the Norwegian coast and take part in the sea fisheries, returning to the lake about midsummer. Formerly they found the capture of wild reindeer a profitable occupation, using for this purpose a palisaded avenue gradually narrowing towards a pitfall.

The Russian Lapps are also for the most part fishers, as is natural in a district with such an extent of coast and such a number of lakes, not to mention the advantage which the fisher has over the reindeer keeper in connexion with the many fasts of the Greek Church. They maintain a half nomadic life, very few having become settlers in the Russian villages. It is usual to distinguish them according to the district of the coast which they frequent, as Murman (Murmanski) and Terian (Terski) Lapps. A separate tribe, the Filmans, i.e. Finnmans, wander about the Pazyets, Motov and Pechenga tundras, and retain the peculiar dialect and the Lutheran creed which they owe to a former connexion with Sweden. They were formerly known as the "twice and thrice tributary" Lapps, because they paid to two or even three states--Russia, Denmark and Sweden.

The Lapps within the historical period have considerably recruited themselves from neighbouring races. Shortness of stature[2] is their most obvious characteristic, though in regard to this much exaggeration has prevailed. Düben found an average of 4.9 ft. for males and a little less for females; Mantegazza, who made a number of anthropological observations in Norway in 1879, gives 5 ft. and 4.75 ft., respectively (_Archivio per l'antrop._, 1880). Individuals much above or much below the average are rare. The body is usually of fair proportions, but the legs are rather short, and in many cases somewhat bandy. Dark, swarthy, yellow, copper-coloured are all adjectives employed to describe their complexion--the truth being that their habits of life do not conduce either to the preservation or display of the natural colour of their skin, and that some of them are really fair, and others, perhaps the majority, really dark. The colour of the hair ranges from blonde and reddish to a bluish or greyish black; the eyes are black, hazel, blue or grey. The shape of the skull is the most striking peculiarity of the Lapp. He is the most brachycephalous type of man in Europe, perhaps in the world.[3] According to Virchow, the women in width of face are more Mongolian in type than the men, but neither in men nor women does the opening of the eye show any true obliquity. In children the eye is large, open and round. The nose is always low and broad, more markedly retroussé among the females than the males. Wrinkled and puckered by exposure to the weather, the faces even of the younger Lapps assume an appearance of old age. The muscular system is usually well developed, but there is deficiency of fatty tissue, which affects the features (particularly by giving relative prominence to the eyes) and the general character of the skin. The thinness of the skin, indeed, can but rarely be paralleled among other Europeans. Among the Lapps, as among other lower races, the index is shorter than the ring finger.

The Lapps are a quiet, inoffensive people. Crimes of violence are almost unknown, and the only common breach of law is the killing of tame reindeer belonging to other owners. In Russia, however, they have a bad reputation for lying and general untrustworthiness, and drunkenness is well-nigh a universal vice. In Scandinavia laws have been directed against the importation of intoxicating liquors into the Lapp country since 1723.

Superficially at least the great bulk of the Lapps have been Christianized--those of the Scandinavian countries being Protestants, those of Russia members of the Greek Church. Although the first attempt to convert the Lapps to Christianity seems to have been made in the 11th century, the worship of heathen idols was carried on openly in Swedish Lappmark as late as 1687, and secretly in Norway down to the first quarter of the 18th century, while the practices of heathen rites survived into the 19th century, if indeed they are extinct even yet. Lapp graves, prepared in the heathen manner, have been discovered in upper Namdal (Norway), belonging to the years 1820 and 1826. In education the Scandinavian Lapps are far ahead of their Russian brethren, to whom reading and writing are arts as unfamiliar as they were to their pagan ancestors. The general manner of life is patriarchal. The father of the family has complete authority over all its affairs; and on his death this authority passes to the eldest son. Parents are free to disinherit their children; and, if a son separates from the family without his father's permission, he receives no share of the property except a gun and his wife's dowry.[4]

The Lapps are of necessity conservative in most of their habits, many of which can hardly have altered since the first taming of the reindeer. But the strong current of mercantile enterprise has carried a few important products of southern civilization into their huts. The lines in which James Thomson describes their simple life--

The reindeer form their riches: these their tents,
Their robes, their beds, and all their homely wealth
Supply; their wholesome fare and cheerful cups--

are still applicable in the main to the mountain Lapps; but even they have learned to use coffee as an ordinary beverage and to wear stout Norwegian cloth (_vadmal_).

Language.

Linguistically the Lapps belong to the Finno-Ugrian group (q.v.); the
similarity of their speech to Finnish is evident though the phonetics
are different and more complicated. It is broken up into very distinct
and even mutually unintelligible dialects, the origin of several of
which is, however, easily found in the political and social
dismemberment of the people. Düben distinguishes four leading
dialects; but a much greater number are recognizable. In Russian
Lapland alone there are three, due to the influence of Norwegian,
Karelian and Russian (Lönnrot, _Acta Soc. Sci. Fennicae_, vol. iv.).
"The Lapps," says Castren, "have had the misfortune to come into close
contact with foreign races while their language was yet in its
tenderest infancy, and consequently it has not only adopted an endless
number of foreign words, but in many grammatical aspects fashioned
itself after foreign models." That it began at a very early period to
enrich itself with Scandinavian words is shown by the use it still
makes of forms belonging to a linguistic stage older even than that of
Icelandic. Düben has subjected the vocabulary to a very interesting
analysis for the purpose of discovering what stage of culture the
people had reached before their contact with the Norse. Agricultural
terms, the names of the metals and the word for smith are all of
Scandinavian origin, and the words for "taming" and "milk" would
suggest that the southern strangers taught the Lapps how to turn the
reindeer to full account. The important place, however, which this
creature must always have held in their estimation is evident from the
existence of more than three hundred native words in connexion with
reindeer.

The Lapp tongue was long ago reduced to writing by the missionaries;
but very little has been printed in it except school-books and
religious works. A number of popular tales and songs, indeed, have
been taken down from the lips of the people. The songs are similar to
those of the Finns, and a process of mutual borrowing seems to have
gone on. In one of the saga-like pieces--Pishan-Peshan's son--there
seems to be a mention of the Baikal Lake, and possibly also of the
Altai Mountains. The story of Njavvisena, daughter of the Sun, is full
of quaint folk-lore about the taming of the reindeer. Giants, as well
as a blind or one-eyed monster, are frequently introduced, and the
Aesopic fable is not without its representatives. Many of the Lapps
are able to speak one or even two of the neighbouring tongues.

Witchcraft.

The reputation of the Laplanders for skill in magic and divination is
of very early date, and in Finland is not yet extinct. When Erik
Blood-axe, son of Harold Haarfager, visited Bjarmaland in 922, he
found Gunhild, daughter of Asur Tote, living among the Lapps, to whom
she had been sent by her father for the purpose of being trained in
witchcraft; and Ivan the Terrible of Russia sent for magicians from
Lapland to explain the cause of the appearance of a comet. One of the
powers with which they were formerly credited was that of raising
winds. "They tye three knottes," says old Richard Eden, "on a strynge
hangyng at a whyp. When they lose one of these they rayse tollerable
wynds. When they lose an other the wynde is more vehement; but by
losing the thyrd they rayse playne tempestes as in old tyme they were
accustomed to rayse thunder and lyghtnyng" (_Hist. of Trauayle_,
1577). Though we are familiar in English with allusions to "Lapland
witches," it appears that the art, according to native custom, was in
the hands of the men. During his divination the wizard fell into a
state of trance or ecstasy, his soul being held to run at large to
pursue its inquiries. Great use was made of a curious divining-drum,
oval in shape and made of wood, 1 to 4 ft. in length. Over the upper
surface was stretched a white-dressed reindeer skin, and at the
corners (so to speak) hung a variety of charms--tufts of wool, bones,
teeth, claws, &c. The area was divided into several spaces, often into
three, one for the celestial gods, one for the terrestrial and one for
man. A variety of figures and conventional signs were drawn in the
several compartments: the sun, for instance, is frequently represented
by a square and a stroke from each corner, Thor by two hammers placed
crosswise; and in the more modern specimens symbols for Christ, the
Virgin, and the Holy Ghost are introduced. An _arpa_ or divining-rod
was laid on a definite spot, the drum beaten by a hammer, and
conclusions drawn from the position taken up by the arpa. Any Lapp who
had attained to manhood could in ordinary circumstances consult the
drum for himself, but in matters of unusual moment the professional
wizard (_naid_, _noide_ or _noaide_) had to be called in.