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of the world. The name of felwort given to G. Amarella, | increase the general nutrition, without exerting any direct but occasionally applied to the whole genus, is stated by Dr Prior to be given in allusion to these properties-fel meaning gall, and wort a plant. In the same way the Chinese call the G. asclepiaderi, and the Japanese the G. Buergeri, "dragon's gall plants," in common with several other very bitter plants whose roots they use in medicine. G. campestris is sometimes in Sweden and other northern countries a substitue for hops.

By far the most important of the species used in medicine is the G. lutea, a large handsome plant 3 or 4 feet high, growing in open grassy places on the Alps, Apennines, and Pyrenees, as well as on some of the mountainous ranges of France and Germany, extending as far east as Bosnia and the Danubian principalities. It has large oval stronglyribbed leaves and dense whorls of conspicuous yellow flowers. Its use in medicine is of very ancient date. Pliny and Dioscorides mention that the plant was noticed by Gentius, a king of the Illyrians, living 180-167 B.C., from whom the name Gentiana is supposed to be derived. During the Middle Ages it was much employed in the cure of disease, and as an ingredient in counter-poisons. In 1552 Tragus mentions the use of the root as a means of dilating wounds.

The root, which is the part used in medicine, is tough and flexible, scarcely branched, and of a brownish colour and spongy texture. It has a pure bitter taste and faint distinctive odour. On account of its porous nature it has been used in modern surgery, as in the time of Tragus, as a substitute for sponge tents. The root has been several times analysed with varying results, but Kromayer in 1862 first obtained the bitter principle in a state of purity. This substance, to which the bitterness of the root is due, he called gentiopicrin (C20H30012). It is a neutral glucoside, crystallizing in colourless needles, and is contained in the fresh root in the proportion of about 6th per cent., but has not been obtained in a crystalline state from the dried root. It is soluble in water and spirit of wine, but it does not dissolve in ether. It is easily decomposed, dilute mineral acids splitting it up into glucose and gentiogenin, the latter being an amorphous yellowish-brown neutral substance. It is not precipitated by tannin or subacetate of lead. A solution of caustic potash or soda forms with gentiopicrin a yellow solution, and the tincture of the root to which either of these alkalies has been added loses its bitterness in a few days. Gentian root also contains gentianic acid (C14H1005), which is inert and tasteless. It forms pale yellow silky crystals, very slightly soluble in water or ether, but soluble in hot strong alcohol and in aqueous alkaline solutions. This substance, which is also called gentianin, gentisin, and gentisic acid, has been shown by Ville to partake of the nature of tannin, giving the reactions of that substance with ferric chloride, gelatin, and albumen. On this account he proposes to change the name to gentiano-tannic acid.

The root also contains 12 to 15 per cent. of an uncrystallizable sugar, of which fact advantage has long been taken in Switzerland and Bavaria, for the production of a bitter cordial spirit called Enzianbranntwein. The use of this spirit, especially in Switzerland, has sometimes been followed by poisonous symptoms, which have been doubtfully attributed to inherent narcotic properties possessed by some species of gentian, the roots of which may have been indiscriminately collected with it; but it is quite possible that it may be due to the contamination of the root with that of Veratrum album, a poisonous plant growing at the same altitude, and having leaves extremely similar in appearance and size to those of G. lutea. Gentian is considered by therapeutists to be one of the most efficient of the simple bitter tonics, that is, of that class of substances which act upon the stomach so as to invigorate digestion and thereby

influence upon any other portion of the body than the alimentary canal. It is used in dyspepsia, chlorosis, anæmia, and various other diseases, in which the tone of the stomach and alimentary canal is deficient, and is sometimes added to purgative medicines to increase and improve their action. In veterinary medicine it is also used as a tonic, and enters into a well-known compound called diapente as a chief ingredient.

See Sowerby, English Botany, 3d edit., vol. vi. p. 74-81; Hemsley, Handbook of Hardy Trees, Shrubs, and Herbaceous Plants, p. 303; Journal of Botany, 1864, p. 65; 1872, p. 166; 1878, p. 265; Pharmacographia, p. 389; Pharmaceutical Journal (1), vol. xii. p. 371; (3) vol. iii. p. 42; (3) vol. vi. p. 90; (3) vol. viii. p. 182; Wood and Bache, United States Dispensatory, 14th edit., p. 438; Porter Smith, Chinese Materia Medica, p. 102. (E. M. H.)

His

GENTILESCHI, ARTEMISIA and ORAZIO DE', painters. ORAZIO (1565-1646) is generally named Orazio Lomi de' Gentileschi; it appears that De' Gentileschi was his correct surname, Lomi being the surname which his mother had borne during her first marriage. He was born at Pisa, and studied under his half-brother Aurelio Lomi, whom in course of time he surpassed. He afterwards went to Rome, and was associated with the landscape-painter Agostino Tasi, executing the figures for the landscape backgrounds of this artist in the Palazzo Rospigliosi, and it is said in the great hall of the Quirinal Palace, although by some authorities the figures in the last-named building are ascribed to Laufranchi. His best works are Saints Cecilia and Valerian, in the Palazzo Borghese, Rome; David after the death of Goliath, in the Palazzo Doria, Genoa; and some works in the royal palace, Turin, noticeable for vivid and uncommon colouring. At an advanced age Gentileschi went to England at the invitation of Charles I., and he was em ployed in the palace at Greenwich. Vandyck included him in his portraits of a hundred illustrious men. works generally are strong in shadow and positive in colour. He died in England in 1646. ARTEMISIA (1590-1642), Orazio's daughter, studied first under Guido, acquired much renown for portrait-painting, and considerably excelled her father's fame. She was a beautiful and elegant woman; her likeness, limued by her own hand, is to be seen in Hampton Court. Her most celebrated composition is Judith and Holofernes, in the Pitti palace; certainly a work of singular energy, and giving ample proof of executive faculty, but repulsive and unwomanly in its physical horror. She accompanied her father to England, but did not remain there long; the best picture which she produced for Charles I. was David with the head of Goliath. Artemisia refused an offer of marriage from Agostino Tasi, and bestowed her hand on Pier Antonio Schiattesi, continuing however to use her own surname. She settled in Naples, whither slie returned after her English sojourn; she lived there in no little splendour, and there she died in 1642. She had a daughter and perhaps other children.

GENTILI, ALBERICO (1552-1608), may fairly be called the founder of the science of international law. He was the second son of Matteo Gentili, a physician of noble family and scientific eminence, and was born 14th January 1552 at Sanginesio, a small town of the march of Ancona which looks down from the slopes of the Apennines upon the distant Adriatic. After taking the degree of doctor of law at the university of Perugia, and holding a judicial office at Ascoli, he returned to his native city, and was entrusted with the task of recasting its statutes, but, sharing the Protestant opinions of his father, shared also his flight to Carniola, where Matteo was appointed physician to the duchy. The Inquisition condemned the fugitives as contumacious, and they soon received orders to quit the dominions of Austria. Alberico set out for England, travelling by way of Tübingen and Heidelberg, and every

where meeting with the reception to which his already high reputation entitled him. He arrived at Oxford in the autumn of 1580, with a commendatory letter from the earl of Leicester, at that time chancellor of the university, and was shortly afterwards qualified to teach by being admitted to the same degree which he had taken at Perugia. His lectures on Roman law soon became famous, and the dialogues, disputations, and commentaries, which he published henceforth in rapid succession, established his position as an accomplished civilian, of the older and severer type, and secured his appointment in 1587 to the regius professorship of civil law. It was, however, rather by an application of the old learning to the new questions suggested by the modern relations of states that his labours have produced their most lasting result. In 1584 he was consulted by Government as to the proper course to be pursued with Mendoza, the Spanish ambassador, who had been detected in plotting against Elizabeth. He chose the topic to which his attention had thus been directed as a subject for a disputation when Leicester and Sir Philip Sidney visited the schools at Oxford in the same year; and this was six months later expanded into a book, the De legationibus libri tres. In 1588 Alberico selected the law of war as the subject of the law disputations at the annual " Act" which took place in July; and in the autumn published in London the De Jure Belli commentatio prima. A second and a third Commentatio followed, and the whole matter, with large additions and improvements, appeared at Hanau, in 1598, as the De Jure Belli libri tres. It was doubtless in consequence of the reputation gained by these works that Gentili became henceforth more and more engaged in forensic practice, and resided chiefly in London, leaving his Oxford work to be partly discharged by a deputy. In 1600 he was admitted to be a member of Gray's Inn, and in 1605 was appointed standing counsel to the king of Spain. He died 19th June 1608, and was buried, by the side of Dr Matteo Gentili, who had followed his son to England, in the churchyard of St Helen's, Bishopsgate. By his wife, Hester de Peigni, he left two sons and a daughter. His notes of the cases in which he was engaged for the Spaniards were posthumously published in 1613 at Hanau, as Hispanicæ advocationis libri duo. This was in accordance with his last wishes; but his direction that the remainder of his MSS. should be burnt was not complied with, since fifteen volumes of them found their way, at the beginning of this century, from Amsterdam to the Bodleian library.

The true history of Gentili and of his principal writings has only been ascertained quite recently, in consequence of a revived appreciation of the services which he rendered to international law. The movement to do him honour, which originated four or five years sinoe, has in spreading through Europe encountered two curious cross-currents of opinion,-one the ultra-Catholic, which three centuries ago ordered his name to be erased from all public documents and placed his works in the Index; another the narrowly-Dutch, which is, it seems, needlessly careful of the supremacy of Grotius, Preceding writers had dealt with various international questions, but they dealt with them singly, and with a servile submission to the decisions of the church. It was left to Gentili to grasp as a whole the relations of states one to another, to distinguish international questions from questions with which they are more or less intimately connected, and to attempt their solution by principles entirely independent of the authority of Rome. He uses, without yielding to them implicit deference, the reasonings of the civil and even the canon law, but he proclaims as his real guide the Jus Naturæ, the highest common sense of mankind, by which historical precedents are to be criticized, and, if necessary, set aside

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His faults are not few. His style is prolix, obscure, and to the modern reader pedantic enough; but a comparisou of his greatest work with what had been written upon tho same subject by, for instance, Belli, or Soto, or even Ayala, will show that he greatly improved upon his predecessors, not only by the fulness with which he has worked out points of detail, but also by clearly separating the law of war from martial law, and by placing the subject once for all upon a non-theological basis. If, on the other hand, the same work be compared with De Jure Belli et Pacis of Grotius, it is at once evident that the later writer is indebted to the earlier, not only for a large portion of his illustrative erudition, but also for all that is commendable in the method and arrangement of the treatise. The following is probably a complete list of the writings of Gentili, with the places and dates of their first publication:-De Juris interpretibus dialogi sex, Lond., 1582; Lectionum et epist. quæ ad jus civile pertinent libri tres, Lond., 1583-4: De divers. temp. appellationibus, Hanau, 1584; De Legationibus libri tres, Lond., 1585; Legal. comitiorum Oxon. actio, Lond., 1585-6; De nascendi tempore disputatio, Witteb., 1586; Disputationum decas prima, Loud., 1587; Conditionum liber singularis, Lond., 1587; De Jure Belli comm. prima, Lond., 1588; secunda, ib., 1588-9; tertia, 1589; De injustitia bellica Romanorum, Oxon., 1590; Do. Armis Romanis, &c., Hanau, 1599; De ludis scenicis epist. dua, Middleburg, 1599; De actoribus et de abusu mendacii, Hanau, 1599; Lectiones Virgilianæ, Hanau, 1600; De nuptiis libri septem, 1601; Ad 1 Maccab, et de linguarum mistura, Lond., 1604; In til. si quis principi, et ad leg. Jul, maiest., Hanau, 1604; In tit. de Malef. et Math., et de Prof. et Med., Hanau, 1604; De latin. vet. Bibl., Hanau, 1604; De libro Pyano, Oxon., 1604; Laudes Acad, Perus. et Oxon., Hanau, 1605; De unione Angliæ et Scotia, Lond., 1605; Disputationes tres, de libris jur. can., de libris jur. civ., de latinitate vet. vers., Hanau, 1605; Regales disput. tres, de pot. regis absoluta, de unione regnorum, de vi civium, Lond., 1605; Hispanicæ ad vocationis libri duo, Hanau, 1613; In tit. de verb, signif., Hanau, 1614; De legatis in teet., Amsterd., 1661. An edition of the Opera Omnia, commenced at Naples in 1770, was cut short by the death of the publisher, Gravier, after the second volume, Of his numerous unpublished writings, Gentili complained that four volumes were lost "pessimo pontificiorum facinore," meaning probably that they were left behind in his flight to Carniola.

Authorities.-Several tracts by the Abate Benigni in Colucci, Antichità Picene, 1790; a Dissertation by W. Reiger annexed to the Program of the Groningen Gymnasium for 1867; an Inaugural Lecture delivered in 1874 by T. E. Holland, and the preface to a new edition of the Jus Belli, 1877, by the same; works by Valdarnini and Foglietti, 1875; Speranza and De Giorgi, 1876; Fiorini (a translation of the Jus Belli, with essay), 1877; A. Saffi, 1878. See also E. Comba, in the Rivista Christiana. 1876-7; and Sir T. Twiss, in the Law Review, 1878. (T. E. H.)

GENTILLY, a town of France, in the department of the Seine, is situated on the Bièvre, a short distance south of the fortifications of Paris. Its manufactures include, biscuits, soap, vinegar, mustard, wax candles, buttons, leather, and pottery wares. It possesses a church of the 13th century, a lunatic asylum, a convent, a monastery, and several The population in 1876 was charitable institutions. 10,378.

GENTZ, FRIEDRICH VON (1764-1832), born at Breslau, May 2, 1764, aptly and accurately described by his dis tinguished friend Varnhagen von Ense as a writer-statesman (Schriftsteller Staatsmann). He was more than a His position was peculiar, publicist or political writer. and his career without a parellel. It is believed that no other instance can be adduced of a man exercising the same amount of influence in the conduct of public affairs, without rank or fortune, without high office, without being a member of a popular or legislative assembly, without in fact any ostenible means or instrumentality besides his pen, Born in the middle class in an aristocratic country, he lived on a footing of social equality with princes and ministers, the trusted partaker of their counsels and the chosen exponent of their policy.

His father held an employment in the Prussian civil service; his mother was an Ancillon distantly related to the states. man of that name. On his father's promotion to the mint

career.

directorship at Berlin and consequent removal to the capital, I leave. Berlin with Adam Müller, never to see it again.' he was sent to a gymnasium there, and in due course com- It does not appear that he ever saw his wife again either; pleted his education at the university of Frankfort-on-the- and his intimacies with other women, mostly of the highest Oder. He is said to have shown neither liking nor aptitude rank, are puzzling from their multiplicity. He professes for intellectual pursuits till after his attendance on the himself unable to explain the precise history of his settlelectures of Kant at Königsberg, in his twentieth or twenty-ment in Vienna. All he remembers is that he was received first year, when, suddenly lighted up as by inspiration, with signs of jealousy and distrust, and that the emperor, he set to work in right earnest, mastered the Greek and to whom he was presented by Count Colloredo, showed no Latin languages, acquired as perfect a knowledge of French desire to secure his services. Many years were to elapso as could well be attained by one who was not a Frenchman, before the formation of the connexion with Metternich, and a sufficient familiarity with English to enable him the most prominent feature and crowning point of his to translate from it with clearness and fluency. He also managed to gain an intimate acquaintance with English commerce and finance, which he afterwards turned to good account. The extent of his acquirements was rendered more remarkable by his confirmed habits of dissipation; for from the commencement to the conclusion of his career he was remarkable for the manner in which, in the midst of the gravest occupations, he indulged his fondness for female society and a ruinous passion for play. In 1786 he was appointed private secretary to the royal general directory, and was soon afterwards promoted to the rank of Kriegsrath (war-councillor). Like Mackintosh, he was fascinated by the French Revolution at its dawn, and, like Mackintosh, was converted to a sounder estimate of its then pending results by Burke. He broke ground in literature in 1794, by a translation of the celebrated Essay on the French Revolution, followed in 1794 and 1795 by translations from Mallet du Pan and Mouuier. In 1795 he founded and edited a monthly journal which soon came to an untimely end. In November 1797 he published a pamphlet under the title of a Sendscreiben or Missive addressed to Frederick William III. of Prussia on his accession, pointing out the duties of the new sovereign and especially recommending the complete freedom of the press. In the course of the next three years he contributed to the Historisches Journal a series of crticles "On the Origin and Character of the War against the French Revolution," with express reference to Great Britain. These led to his visiting England, where he formed intimate relations with Mackintosh, Lord Grenville, Pitt, and other eminent men, which proved lasting, flattering, and remunerative. The first entries in his published diary, beginning April 14, 1800, and continued (with breaks) to the end of 1828, run thus:

"On the 14th of April, an agreeable surprise. The Jew elder, Hirsch, brought me 50 thalers for drawing up I know not what representation (Vorstellung). May 28.-Received through Baron Krüdener a watch set with (small) brilliants, a present from the emperor of Russia. June 1.-Received through Garlicke a letter from Lord Grenville, together with a donation of £500, the first of

its kind."

The last entry for this year, 1800, is :-" At the end of the year great pecuniary embarrassment. Received £100 from Garlicke and negotiated with Carysfort:"

The diary for 1801 begins :-" February.-Very remarkable that on the one side Lord Carysfort charged me with the translation into French of the English Notes against Prussia, and shortly afterwards Count Haugwitz with the translation into German of the Prussian Notes against England."

Frequently recurring entries of this kind illustrate his position through life. He was to all intents and purposes a mercenary of the pen, but he was so openly and avowedly, and he was never so much as suspected by those who knew him best of writing contrary to his own convictions at the time. This is why he never. lost the esteem or confidence of his employers;-of Prince Metternich, for example, who, when he was officially attached to the Austrian Government, was kept regularly informed of the sources from which the greater part of his income was derived. Embarrassments of all sorts, ties and temptations from which he was irresistibly impelled to tear himself, led to his change of country; and an entry for May 1802 runs :— "On the 15th I take leave of my wife, and at three in the morning of the 20th

Before entering into any kind of engagements with the Austrian Government he applied to the king of Prussia for a formal discharge, which was granted with an assurance that his Majesty, "in reference to his merits as a writer, coincided in the general approbation which he had so honourably acquired." A decisive proof of the confidence placed in him was his being invited by Count Haugwitz to the Prussian headquarters shortly before the battle of Jena, and commissioned to draw up the Prussian manifesto and the king's letter to Napoleon. It was in noticing this letter that Napoleon spoke of the known and avowed writer as "a wretched scribe named Gentz, one of those men without honour who sell themselves for money." In the course of 1806, he published War between Spain and England, and Fragments upon the Balance of Power in Europe, on receiving which (at Bombay) Mackintosh wrote:-" I assent to all you say, sympathize with all you feel, and admire equally your reason and your eloquence throughout your masterly fragment." The bond of union between him and Metter. nich was formed in 1840. This was one reason, joined to his general reputation, for his being named first secretary to the congress of Vienna in 1814, where, besides his regular duties, he seems to have made himself useful to several of the plenipotentiaries, as he notes in his, diary that he received 22,000 florins in the name of Louis XVIII. from Talleyrand, and £600 from Lord Castlereagh, accompanied by "les plus folles promesses." He acted in the same capacity at the congress or conference of Paris in 1815, of Aix in 1818, Karlsbad and Vienna in 1819, Troppau and Laybach in 1820 and 1821, and Verona in 1822. The following entry in his diary for December 14, 1819, has exposed him to much obloquy as the interested advocate of reactionary doctrines:-"About eleven, at Prince Metternich's: attended the last and most important sitting of the commission to settle the 13th article of the Bundes-Akt, and had my share in one of the greatest and worthiest results of the transactions of our time. A day more important than, that of Leipsic." The 13th article provides that in all states of the Bund the constitutional government shall be by estates instead of by a representative body in a single chamber: "in allen Bundestaaten wird eine landständische Verfassung stattfinden." Remembering what ensued in France from the absorption of the other estates in the Tiers État, it would have been strange if Gentz had not supported this 13th article. He was far from a consistent politician, but he was always a sound Conservative at heart; and his reputation rests on his foreign policy, especially on the courage, eloquence, and efficiency with which he made head against the Napoleonic system till it was struck down.

He

The most remarkable phase of Gentz's declining years was his passion, in his sixty-seventh year, for Fanny Elssler, the celebrated danseuse, which forms the subject of some very remarkable letters to his attached friend Rahel (the wife of Varnhagen von Ense) in 1830 and 1831. died June 9, 1832. There is no complete edition of his works. The late Baron von Prokesch was engaged in preparing one when the Austrian Government interfered, and the design was perforce abandoned

(A.. H.)

GE

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GEODESY

EODESY (y, the earth, 8aiw, to divide) is the science of surveying extended to large tracts of country, having in view not only the production of a system of maps of very great accuracy, but the determination of the curvature of the surface of the earth, and eventually of the figure and dimensions of the earth. This last, indeed, may be the sole object in view, as was the case in the operations conducted in Peru and in Lapland by the celebrated French astronomers Bouguer, La Condamine, Maupertuis, Clairaut, and others; and the measurement of the meridian arc of France by Mechain and Delambre had for its end the determination of the true length of the "metre" which was to be the legal standard of length of France.

The basis of every extensive survey is an accurate triangulation, and the operations of geodesy consist in the measurement, by theodolites, of the angles of the triangles; the measurement of one or more sides of these triangles on the ground; the determination by astronomical observations of the azimuth of the whole network of triangles; the determination of the actual position of the same on the surface of the earth by observations, first for latitude at some of the stations, and secondly for longitude.

To determine by actual measurement on the ground the length of a side of one of the triangles, wherefrom to infer the lengths of all the other sides in the triangulation, is not the least difficult operation of a trigonometrical survey. When the problem is stated thus-To determine the number of times that a certain standard or unit of length is contained between two finely marked points on the surface of the earth at a distance of some miles asunder, so that the error of the result may be pronounced to lie between certain very narrow limits, then the question demands very serious consideration. The representation of the unit of length by means of the distance between two fine lines on the surface of a bar of metal at a certain temperature is never itself free from uncertainty and probable error, owing to the difficulty of knowing at any moment the precise temperature of the bar; and the transference of this unit, or a multiple of it, to a measuring bar, will be affected not only with errors of observation, but with errors arising from uncertainty of temperature of both bars. If the measuring bar be not self-compensating for temperature, its expansion must be determined by very careful experiments. The thermometers required for this purpose must be very carefully studied, and their errors of division and index error determined.

The base apparatus of Bessel and that of Colby have been described in FIGURE OF THE EARTH (vol. vii. p. 598). The average probable error of a single measurement of a base line by the Colby apparatus is, according to the very elaborate investigations of Colonel Walker, C.B., R.E., the Surveyor-General of India, ± 1.5μ (μ meaning "one millionth"). W. Struve gives 08μ as the probable error of a base line measured with his apparatus, being the mean of the probable errors of seven bases measured by him in Russia; but this estimate is probably too small. Struve's apparatus is simple: there are four wrought iron bars, each two toises (rather more than 13 feet) long; one end of each bar is terminated in a small steel cylinder presenting a slightly convex surface for contact, the other end carries a contact lever rigidly connected with the bar. The shorter arm of the lever terminates below in a polished hemisphere, the upper and longer arm traversing a vertical divided arc. In measuring, the plane end of one bar is brought into contact with the short arm of the contact lever (pushed forward by a weak spring) of the next bar. Each bor has

two thermometers, and a level for determining the inclination of the bar in measuring. The manner of transferring the end of a bar to the ground is simply this: under the end of the bar a stake is driven very firmly into the ground, carrying on its upper surface a disk, capable of movement in the direction of the measured line by means of slow-motion screws. A fine mark on this disk is brought vertically under the end of the bar by means of a theodolite which is planted at a distance of 25 feet from the stake in a direction perpendicular to the base. Struve investigates for each base the probable errors of the measurement arising from each of these seven causes:alignment, inclination, comparisons with standards, readings of index, personal errors, uncertainties of temperature, and the probable errors of adopted rates of expansion.

The apparatus used in the United States Coast Survey consists of two measuring bars, each 6 metres in length, supported on two massive tripod stands placed at one quarter length from each end, and provided, as in Colby's apparatus, with the necessary mechanism for longitudinal, transverse, and vertical adjustment. Each measuring rod is a compensating combination of an iron aud a brass bar, supported parallel to one another and firmly connected at one end, the medium of connexion between the free ends being a lever of compensation so adjusted as to indicate a constant length independent of temperature or changes of temperature. The bars are protected from external influences by double tubes of tinned sheet iron, within which they are movable on rollers by a screw movement which allows of contacts being made within Too of an inch. The abutting piece acts upon the contact lever which is attached to the fixed end of the compound bar, and carries a very sensitive level, the horizontal position of which defines the length of the bar. It is impossible here to give a full description of this complicated apparatus, and we must refer for details to the account given in full in the United States Coast Survey Report for 1854. This apparatus is doubtless a very perfect one, and the manipulation of it must offer great facilities, for it appears to be possible, under favourable circumstances, to measure a mile in one day, 1.06 mile having been measured on one occasion in eight and a half hours. In order to test to the utmost the apparatus, the base at Atlanta, Georgia, was measured twice in winter and once in summer 1872-73, at temperatures 51°, 45°, 90° F.; the difference of the first and second measurements was +0:30 in., of the second and third +0.34 in., the actual length and computed probable error expressed in metres being 9338 476300166. It is to be noted that in the account of a base recently measured in the United States Lake Survey, some doubt is expressed as to the perfection of the particular apparatus of this de scription there used, on account of a liability to permanent changes of length.

The last base line measured in India with Colby's compensation apparatus had a length of 8912 feet only, and in consequence of some doubts which had arisen as to the accuracy of this compensation apparatus, the measurement was repeated four times, the operations being conducted in such a manner as to indicate as far as possible the actual magnitudes of the probable errors to which such measures are liable. The direction of the line (which is at Cape Comorin) is north and south, and in two of the measurements the brass component was to the west, in the other two it was to the east. The differences between the indi vidual measurements and the mean of the four are +0017, 0049, 0015, + 0045 in feet. The measure

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ments occupied from seven to ten days each,-the average rate of such work in India being about a mile in five days. The method of M. Porro, adopted in Spain, and by the French in Algiers, is essentially different from those just described. The measuring rod, for there is only one, is a thermometric combination of two bars, one of platinum and one of brass, in length 4 metres, furnished with three levels and four thermometers. Suppose A, B, C three micrometer microscopes very firmly supported at intervals of 4 metres with their axes vertical, and aligned in the plane of the base line by means of a transit instrument, their micrometer screws being in the line of measurement. The measuring bar is brought under say A and B, and those micrometers read; the bar is then shifted and brought under B and C. By repetition of this process, the reading of a micrometer indicating the end of each position of the bar, the measurement is made. The probable error of the central base of Madridejos, which has a length of 14664.500 metres, is estimated at 0.17μ. This is the longest base line in Spain; there are seven others, six of which are under 2500 metres in length; of these one is in Majorca, another in Minorca, aud a third in Iviça. The last base just measured in the province of Barcelona has a length of 2483-5381 metres according to the first measurement, and 2483-5383 according to the second. The total number of base lines measured in Europe up to the present time is about eighty, fifteen of which do not exceed in length 2500 metres, or about a mile and a half, and two-one in France, the other in Bavaria-exceed 19,000 metres. The question has been frequently discussed whether or not the advantage of a long base is sufficiently great to warrant the expenditure of time that it requires, or whether as much precision is not obtainable in the end by careful triangulation from a short base. But the answer cannot be given generally; it must depend on the circumstances of each particular case.

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It is necessary that the altitude above the level of the sea of every part of a base line be ascertained by spirit levelling, in order that the measured length may be reduced to what it would have been had the measurement been made on the surface of the sea, produced in imagination. Thus if be the length of a measuring bar, h its height at any given position in the measurement, the radius of the earth, then the length radially projected on to the level of the sea is l 1. In the Salisbury Plain base line the reduction to the level of the sea is 0.6294 feet. In working away from a base line ab, stations c, d, e, f are carefully selected so as to obtain from well-shaped triangles gradually increasing sides. Before, however, finally leaving the base line it is usual to verify it by triangulation thus: during the measurement two or more points, as p, q (fig. 1), are marked in the base in positions such that the lengths of the different segments of the line are known; then, taking suitable external stations, as h, k, the angles of the triangles bhp, phq, hqk, kqa are measured. From these angles can be computed the ratios of the segments, which must agree, if all operations are correctly performed, with the ratios resulting from the measures. Leaving the base line, the sides increase up

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to ten, thirty, or fifty miles, occasionally, but seldom, reaching a hundred miles. The triangulation points may either

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be natural objects presenting themselves in suitable positions, such as church towers; or they may be objects specially constructed in stone or wood on mountain tops or other prominent ground. In every case it is necessary that the precise centre of the station be marked by some permanent mark. In India no expense is spared in making permanent the principal trigonometrical stations-costly towers in masonry being erected. It is essential that every trigonometrical station shall present a fine object for observation from surrounding stations.

Horizontal Angles.

In placing the theodolite over a station to be observed from, the first point to be attended to is that it shall rest upon a perfectly solid foundation. The method of obtaining this desideratum must depend entirely on the nature of the ground; the instrument must if possible be supported on rock, or if that be impossible a solid foundation must be obtained by digging. When the theodolite is required to be raised above the surface of the ground in order to command particular points, it is necessary to build two scaffolds,-the outer one to carry the observatory, the inner one to carry the instrument,—and these two edifices must have no point of contact. Many cases of high scaffolding have occurred on the English Ordnance Survey, as for instance at Thaxted Church, where the tower, 80 feet high, is surmounted by a spire of 90 feet. The scaffold for the observatory was carried from the base to the top of the spire; that for the instrument was raised from a point of the spire 140 feet above the ground, having its bearing upon timbers passing through the spire at that height. Thus the instrument; at a height of 178 feet above the ground, was insulated, and not affected by the action of the wind on the observatory.

At every station it is necessary to examine and correct the adjustments of the theodolite, which are these:-the line of collimation of the telescope must be perpendicular to its axis of rotation; this axis perpendicular to the vertical axis of the instrument; and the latter perpendicular to the plane of the horizon. The micrometer microscopes must also measure correct quantities on the divided circle or circles. The method of observing is this. Let A, B, C.... be the stations to be observed taken in order of azimuth ; the telescope is first directed to A and the cross-hairs of the telescope made to bisect the object presented by A, then the microscopes or verniers of the horizontal circle (also of the vertical circle if necessary) are read and recorded. The telescope is then turned to B, which is observed in the same manner; then C and the other stations. Coming round by continuous motion to A, it is again observed, and the agreement of this second reading with the first is some test of the stability of the instrument. In taking this round of angles- -or arc," as it is called on the Ordnance Surveyit is desirable that the interval of time between the first and second observations of A should be as small as may be consistent with due care. Before taking the next arc the horizontal circle is moved through 20° or 30°; thus a dif ferent set of divisions of the circle is used in each arc, which tends to eliminate the errors of division.

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It is very desirable that all arcs at a station should contain one point in common, to which all angular measurements are thus referred,-the observations on each arc commencing and ending with this point, which is on the Ordnance Survey called the "referring object." It is usual for this purpose to select, from among the points which have to be observed, that one which affords the best object for precise observation. For mountain tops a. "referring object" is constructed of two rectangular plates of metal in the same vertical plane, their edges parallel and placed at such a distance apart that the light of the sky seen through

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