Part 2

DESAIX DE VEYGOUX (d[.e]-s[=a] d[.e] v[=a]-g[:o]), Louis Charles Antoine, a distinguished French general, born in 1768 at St. Hilaire d'Ayat, in Auvergne, died 1800. He was of noble family, and entered the army as a sub-lieutenant. He distinguished himself greatly in 1794 under Pichegru, and two years later with the army of the Rhine under Moreau. In 1797 he accompanied Bonaparte to Egypt, and was very successful in reducing Upper Egypt. After the Treaty of El Arish he followed Bonaparte to Italy, took command of the corps of reserve, and, arriving on the field of Marengo at a critical moment, decided the victory by a brilliant charge, 14th June, 1800. He himself fell, mortally wounded by a musket bullet.

DESAULT (d[.e]-s[:o]), Pierre Joseph, one of the most celebrated surgeons of France, was born in 1744, and died in 1795. After some experience in the military hospital at B['e]fort, he went to Paris in 1764, studied under Petit, and two years afterwards became a lecturer on his own account. His reputation soon increased, and he became principal surgeon in the Hospital de la Charit['e], and in 1788 was put at the head of the great H[^o]tel Dieu in Paris. Here he founded a surgical school, in which many of the most eminent surgeons of Europe were educated. A digest of his surgical works was published by Bichat in 1798 (_Oeuvres chirurgicales de Desault_).

DES'CANT, in music, an addition of a part or parts to a subject or melody, a branch of musical composition which preceded the more modern counterpoint and harmony, coming into existence at the end of the eleventh or beginning of the twelfth century.

DESCARTES (d[=a]-k[:a]rt), Ren['e], a great French philosopher and mathematician, with whom the modern or new philosophy is often considered as commencing. He was born 31st March, 1596, at La Haye, in Touraine, died 11th Feb., 1650. Educated at the Jesuit College of La Fl[`e]che, where he showed great talent, he entered the military profession and served in Holland and in Bavaria. In 1621 he left the army, and after a variety of travels finally settled in Holland, and devoted himself to philosophical inquiries. Descartes, seeing the errors and inconsistencies in which other philosophers had involved themselves, determined to build up a system anew for himself, divesting himself first of all of the beliefs he had acquired by education or otherwise, and resolving to accept as true only what could stand the test of reason. Proceeding in this way, he found (_Meditationes de Prima Philosophia_) that there was one thing that he could not doubt or divest himself of the belief of, and that was the existence of himself as a thinking being, and this ultimate certainty he expressed in the celebrated phrase "_Cogito, ergo sum_" (I think, therefore I am). Here, then, he believed he had found the test of truth. Starting from this point Descartes found the same kind of certainty in such propositions as these: that the thinking being or soul differs from the body (whose existence consists in space and extension) by its simplicity and immateriality and by the freedom that pertains to it; that every perception of the soul is not distinct; that it is so far an imperfect finite being; that this imperfection of its own leads it to the idea of an absolutely perfect being; and from this last idea he deduces all further knowledge of truth. Descartes has been rightly called the father of modern philosophy, for in him the modern spirit came into existence. In an age of unrest and ferment his work was that of a great systematizer. He also contributed greatly to the advancement of mathematics and physics, the method of co-ordinates, which has revolutionized geometry, and is of fundamental importance in modern mathematical physics, being due to him. His system of the universe attracted great attention in his time. One of his fundamental doctrines was that the universe is full of matter, there being no such thing as empty space. On this basis he developed the hypothesis of celestial _vortices_, immense currents of ethereal matter, by which he accounted for the motion of the planets (_Principia Philosophiae_, 1644). His works effected a great revolution in the principles and methods of philosophy. In 1647 the French court granted him a pension of 3000 livres, and two years later, on the invitation of Christina of Sweden, he went to Stockholm, where he died.--BIBLIOGRAPHY: Sir J. P. Mahaffy, _Descartes_; A. Fouill['e]e, _Descartes_; E. Boutroux, _L'Imagination et les math['e]matiques selon Descartes_; N. Smith, _Studies in Cartesian Philosophy_; E. S. Haldane, _Descartes: his Life and Times_.

DESCENT', in law, is the transmission of the right and title to lands to the heir, on the decease of the proprietor, by the mere operation of law. The rule determining to whom an estate belongs, on the decease of the proprietor, is that of consanguinity, or relationship by blood, though with some exceptions, as in the case of the portion, or the use of a portion, of a man's property given by the laws of Britain to his widow. The rules of descent, designating what relations shall inherit, and their respective shares, will be determined by the genius and policy of the Government and institutions. Hence the practice of entailments in the feudal system. And wherever the Government is founded in family privileges, or very intimately connected with them, as is the case in all Governments where the hereditarily aristocratical part of the community has a great preponderance, the sustaining of families will very probably be a characteristic feature in the code of laws. Thus, in Britain, all the lands of the father, unless otherwise directed by will, go to the eldest son. (In England, however, this privilege may shortly be abolished, or the succession to real estate assimilated to the succession to personal estate.) In the United States of America this distinction in favour of the eldest son has been abolished, and the laws there are founded upon the principle of equal distribution both of real and personal estate among heirs of the nearest surviving degree. Kindred in blood are divided into three general classes, viz. 1, descendants; 2, ancestors; 3, collateral relatives, that is, those who have descended from the same common ancestor. The civil law computes the degrees by counting the generations up to the common ancestor, as father, grandfather, great-grandfather; or mother, grandmother, great-grandmother; and from him or her down to the collateral relative, as brother, cousin, &c., making the degree of relationship the sum of these two series of generations. Every person has two sets of ancestors, the paternal and maternal, and therefore two sets of collateral relatives. There is also a distinction of collateral kindred, into those of the whole blood and those of the half blood.--Cf. Pollock and Maitland, _History of English Law_.

DESCHANEL, Paul Eug[`e]ne Louis, French statesman and tenth President of the French Republic, born at Brussels on 13th Feb., 1856, where his father was in exile for opposition to Napoleon III. Educated at the Coll[`e]ge Sainte Barbe and the Lyc['e]e Condorcet, Paris, he was private secretary first to De Marc[`e]re, the Home Secretary, in 1876, and then to the Premier, Jules Simon, in 1877. Sub-prefect at Dreux, Brest, and Meaux, he was elected to the Chamber of Deputies in Oct., 1885, for Nogent le Rotrou. In the Chamber of Deputies he soon displayed his power of eloquence, and eventually became the leader of the Progressive Republicans and exponent of the separation of Church and State. His authority, which he owed not only to his eloquence but also to his great tact and correct and dignified conduct during debates, gradually increased in the Chamber of Deputies, and even his political enemies admired his courage and his superiority of intellect. He was consequently elected Vice-President of the Chamber in 1896 and in 1897, and succeeded Henri Brisson as President of the Chamber in 1898, retaining his office till 1902, when M. L['e]on Bourgeois became President of the Chamber. Re-elected President of the Chamber in 1912, and withdrawing his candidature to the presidency of the Republic in favour of Poincar['e] in 1913, Deschanel retained his post until 1920, when he was elected President of the Republic by 734 votes. In the meantime, however, his health had given way, and on 23rd May, 1920, he fell out of a moving train, an accident resulting in a prolonged illness. A prompt recovery was at first expected, but this hope soon proved vain. Unable to attend to the duties of his office, he resigned on 16th Sept., and was succeeded by Alexandre Millerand. He was elected to the Acad['e]mie Francaise on 18th May, 1899, and his works include: _La Question du Tonkin_ (1883), _La Politique Francaise en Oc['e]anie_ (1884), _Orateurs et Hommes d'['E]tat_ (1888), _Figures des Femmes_ (1889), _Figures Litt['e]raires_ (1889), _La Question Sociale_ (1898), _Quatre ans de Pr['e]sidence_ (1902), _Politique Int['e]rieure et ['e]trang[`e]re_ (1906), _Paroles Francaises_ (1911), _La France Victorieuse_ (1919), and _Gambetta_ (1920).

DESEADA (de-se-[:a]'d[.a]), or D['E]SIRADE, one of the Leeward Islands, belonging to the French, in the Caribbean Sea, about 10 miles long and hardly 5 miles broad. The soil is in some places black and good, in others sandy and unproductive. Pop. about 1500.

DESER'TION. In the military sense this implies the act of an officer or soldier who, either with the intention of not returning at all or of returning when by reason of his absence it has become impossible for him to perform a given duty, absents himself from His Majesty's service. The essence of the offence is intention, and this must be proved to the satisfaction of the court martial by which the offender is tried. The distance travelled is no criterion, and a man arrested while leaving the barracks in disguise may be tried for attempted desertion. In this connection it should be noted that an attempt to desert, or an attempt to procure another person to desert, is also an offence, and is punishable under Section 12 of the Army Act equally with the completed act. As far back as the middle of the fifteenth century the crime of desertion by a soldier was made a felony triable by the ordinary law of the land, and with certain interludes death remained the maximum penalty for desertion for some 200 years. The present existing Army Act recognizes two degrees of desertion, i.e. that committed on active service or when under orders for

## active service, and that committed under other circumstances. Under the

former heading the maximum punishment is death; under the latter, imprisonment or penal servitude, according to the number of times the offence has been committed. A soldier convicted of desertion forfeits the whole of his service prior to conviction.

DESERTION, in law, the term applied to the act by which a man abandons his wife or a wife her husband. Such desertion without due cause is, in England, ground for a judicial separation. Property a wife may have acquired since desertion is protected against her husband, and he may be forced to provide for her maintenance. By Scottish law, where either the husband or wife has deserted and remained separate without due cause for four years, divorce may be obtained.

DESHOULI[`E]RES (d[=a]-s[:o]l-y[=a]r), Antoinette du Ligier de Lagarde, a French woman of much literary reputation in the seventeenth century, born 1638, died 1694. She was the centre of attraction in the best circles of the period, and was elected a member of several learned societies. She wrote in the _Mercure Galant_ under the name of Amaryllis, and Boileau has described her in his tenth _Satire_. Among her works are odes, eclogues, idyls, and a tragedy (_Genseric_).

DESICCATION, a process of dispelling moisture by the use of air, heat, or chemical agents such as chloride of calcium, quicklime, oil of vitriol, and fused carbonate of potash.--_Desiccation cracks_, in geology, are the fissures caused in clayey beds by the sun's heat, and seen in various rock strata.

DESIGN, thought, arrangement, or grouping, imagination or invention in works of art. A design is a composition or invention, pictorial, architectural, or decorative. It may be simply an imperfect sketch, as a record of a first thought; or it may be a fully matured work, as a cartoon in preparation for fresco painting, or a drawing to illustrate a book.

DESMIDIA'CEAE, or DESMIDIE'AE, a family of microscopic, fresh-water Green Algae, group Conjugatae. They are green gelatinous plants composed of variously formed cells having a bilateral symmetry, which are either free, or in linear series, or collected into bundles or into star-like groups, and embedded in a common gelatinous coat. Desmidiaceae differ from Diatomaceae in their green colour and absence of silica.

DESMO'DIUM, a large genus of leguminous plants, sub-ord. Papilionaceae, natives of tropical and sub-tropical countries. _D. gyrans_ is the telegraph plant, so called from the curious movements performed by the two small lateral leaflets of each leaf, which, at high temperatures, wave up and down like the arms of a semaphore.

DES MOINES (d[.e] moin), a city of the United States, capital of the state of Iowa and of Polk County, on the Des Moines River, about 350 miles west of Chicago. Among its chief buildings are the new State house, the State arsenal, university, and opera-houses. There are coal-mines in the vicinity, and the manufactures and other industries are varied and rapidly increasing. Pop. 104,052 (1917).

DES MOINES, the largest river in the state of Iowa, rises in the S.W. of Minnesota, and flows in a south-easterly direction till it falls into the Mississippi about 4 miles below Keokuk, after a course of 300 miles.

DESMONCUS, a genus of tropical American climbing palms, scrambling by means of stout hooks which are modified leaflets.

DESMOULINS (d[=a]-m[:o]-lan), Beno[^i]t Camille, born in 1760, was conspicuous during the first period of the French Revolution. He was amongst the most notable of the pamphleteers and orators who urged the multitude forward in the path of revolution. He, along with others, prepared the plan for the taking of the Bastille (July, 1789), was one of the founders of the club of Cordeliers, and the promoter of the assembly in the Champ de Mars. In 1789 he began his career as a journalist by the issue of a weekly publication (_Les R['e]volutions de France et de Brabant_). In 1793 he gave his vote for the death of the king. Having become closely connected with Danton and the party of opposition to Robespierre, and inveighing against the reign of blood and terror, he was arrested on the order of the latter on 30th March, 1794, tried on the 2nd April, and executed on the 5th. He met his fate in an agony of despair.--Cf. F. A. Aulard, _Les Orateurs de la L['e]gislative et de la Convention_.

DESNA, a river in the Ukraine, which rises in the government of, and about 50 miles east of the town of Smolensk, flows through the governments of Orel and Tshernigov till it joins the Dnieper near Kiev. It is 500 miles in length and navigable nearly throughout.

DE SOTO, Hernando, a Spanish explorer and discoverer of the Mississippi, born about 1496, died in 1542. He accompanied expeditions to the New World under Davila and Pizarro, and played a distinguished part in the conquest of Peru. In 1536 he led an expedition to Florida, whence after many difficulties he penetrated to the Mississippi, where he was attacked with fever and died.--The name De Soto has been given to a county in the N.W. of Mississippi, and to several places in the United States.

DES'POT (Gr. _despot[=e]s_), originally a master, a lord; at a later period it became an honorary title which the Greek emperors gave to their sons and sons-in-law when governors of provinces. At present _despot_ means an absolute ruler, and in a narrower sense a tyrannous one.

DESSALINES (d[=a]-s[.a]-l[=e]n), Jean Jacques, Emperor of Hayti, born in Africa about 1760. He was a slave in 1791, when the insurrection of the blacks occurred in that island, but was set free along with the other slaves in St. Domingo in 1794. His talents for war, his courage, and unscrupulous conduct raised him to command in the insurrections of the coloured people, and after the deportation of Toussaint-L'Ouverture, and the subsequent evacuation of the island by the French, Dessalines was appointed Governor-General for life with absolute power; and the year following (1804) was declared Emperor with the title of Jacques I. But his rule was savage and oppressive, and both the troops and the people, sick of his atrocities, entered into a conspiracy against him, and on 17th Oct., 1806, he was slain by one of his soldiers.

DESSAU (des'ou), a town in Germany, capital of the former Duchy of Anhalt, in a beautiful valley on the left bank of the Mulde, mostly well built, with fine squares and many handsome buildings. The manufactures consist of woollens, woollen yarn, carpets, machinery, and tobacco. The former ducal palace has a picture-gallery and interesting relics and antiquities. Pop. 56,606.

DE STENDHAL. See _Beyle, Marie-Henri_.

DESTER'RO, now FLORIANOPOLIS, a seaport of Brazil, capital of the state of Santa-Catharina. The harbour, next to Rio de Janeiro, is the best in Brazil. Pop. 9000.

DESTRUCTORS, REFUSE, the apparatus or plant used in the cremation of house and factory refuse. Formerly refuse from large towns and populous areas was either disposed of for manurial purposes or spread over waste land, where its presence speedily became a nuisance. The consequent danger to the public health, coupled with the increasing difficulty and cost of its disposal, led to attempts being made to deal with it by more sanitary methods. The first attempts to cremate it in a closed furnace on a large scale, made in London in 1870, were not successful, primarily owing to the unscientific design of the furnace. In 1877, however, there was built in Manchester the forerunner of the modern destructor, to the designs of the late Mr. Alfred Fryer. This consisted of two simple cells, the primary feature of the design being 'the charging of the refuse into the back of the furnace, and drawing out the resulting clinker from the front'. With certain modifications, this design is in general use at the present time. The basic principles underlying their scientific design may be summed up in the following points: (_a_) Charging at regular intervals, the refuse being dumped into a hopper, and fed into the back of the furnace as a charge, means being taken to prevent undue escape of gases. The moisture having evaporated, the material may then be raked forward onto the fire-bars, where combustion takes place. (_b_) To avoid nuisance, the resulting gases must be inodorous, which requires a temperature of about 2000degF. This is obtained by passing the products of combustion over the hottest portion of the fire, prior to their passage into the main flue. (_c_) Removal of the fine dust and particles in suspension in the flue gases by means of spiral chambers at the base of chimney. (_d_) Provision of forced draught. A well-designed plant should show little, if any, suspended matter in the gases on emission from the chimney. Formerly no use was made of the heat generated, but modern installations now invariably have steam-raising plant incorporated in the design. This power is commonly used to generate electricity. Some portion may be utilized in crushing and screening the clinker, which is frequently used in making slab-paving, or ground fine and used as a substitute for sand in mortar. The following data may be found of service: (_a_) 60 per cent of the average refuse is combustible. (_b_) The calorific value may be taken as being one-seventh that of good steam-coal. (_c_) 100 electrical units may be obtained from each ton of refuse consumed. (_d_) With forced draught, as much as 100 lb. of refuse has been burnt per square foot of grate area per hour. (_e_) 250 tons of refuse per annum per 1000 of population may be estimated for.--BIBLIOGRAPHY: W. H. Maxwell, _Removal and Disposal of Town Refuse_; Kempe, _Engineer's Year Book_.

DESTUTT DE TRACY, Antoine Louis Claude, French philosophical writer, born in 1754 of a family of Scottish extraction, died in 1836. As a philosopher he belonged to the Sensationalist school, and considered all our knowledge to be derived originally from sensation. He has been called the logician and metaphysician of the school of Condillac. Among his chief works are: _Id['e]ologie_ (1801), _Logique_ (1805), and _Trait['e] de la Volont['e] _(1815).

DETER'MINANT, a mathematical expression which appears in the solution of a system of equations of the first degree.

The solution of the equations

a_1x + b_1y = c_1, a_2x + b_2y = c_2,

is given by

x(a_1b_2 - a_2b_1) = c_1b_2 - c_2b_1, y(a_1b_2 - a_2b_1) = a_1c_2 - a_2c_1.

Here x and y have the same coefficient a_1b_2 - a_2b_1. This is called a determinant of the second order, and is written

|a_1, b_1| |a_2, b_2|.

We may now write

|a_1, b_1| |c_1, b_1| x| | = | | |a_2, b_2| |c_2, b_2|.

Similarly with three equations,

a_1x + b_1y + c_1z = d_1, a_2x + b_2y + c_2z = d_2, a_3x + b_3y + c_3z = d_3,

we find

x{a_1(b_2c_3 - b_3c_2) + a_2(b_3c_1 - b_1c_3) + a_3(b_1c_2 - b_2c_1)} = d_1(b_2c_3 - b_3c_2) + d_2(b_3c_1 - b_1c_3) + d_3(b_1c_2 - b_2c_1)

The coefficient of x, and the right-hand member, are here determinants of the third order, and the result is written

|a_1, b_1, c_1| |d_1, b_1, c_1| x|a_2, b_2, c_2| = |d_2, b_2, c_2| |a_3, b_3, c_3| |d_3, b_3, c_3|.

When the coefficient of x is expanded fully, it consists of six terms, half of them positive and half negative, each term being the product of three letters, one from each row and one from each column. Thus in every term, such as the leading term a_1b_2c_3, the three letters a, b, c, and the three suffixes 1, 2, 3, all occur once and once only. With regard to the signs, we note that if the letters a, b, c are always kept in this order, an interchange of two suffixes changes the sign. Thus, e.g. we may start from + a_1b_2c_3, interchange the suffixes 2 and 3, and thus find - a_1b_3c_2. Again, if in the latter term - a_1b_3c_2 we interchange the suffixes 1 and 3, we find + a_3b_1c_2. It is easy to verify that after any number of interchanges of this kind a particular term will always come up with the same sign.

Thus the interchange of two rows (and similarly of two columns) changes the sign of the determinant. It follows that if two rows (or two columns) are identical, the determinant is zero. It is now easy to define functions of n^2 letters, arranged in a square array of n rows and n columns, with similar properties to those observed above in the case of determinants of the third order. Determinants are very extensively used in higher algebra, co-ordinate geometry, and other branches of mathematics. See also _Elimination_.--BIBLIOGRAPHY: C. Smith, _Algebra_; T. Muir, _Theory of Determinants_.

DETERMINANTS, in biology, the name applied by Weismann to hypothetical

## particles contained in the nuclei of germ-cells, which determine the

existence and nature of the various parts of the body of the embryo. The theory of determinants is part of an elaborate attempt to explain the facts of heredity on a mechanical basis. Although it may serve as a working hypothesis, it is regarded with disfavour by many experts, and may be regarded as an elaboration of the 'provisional theory of pangenesis' advanced by Darwin.