laid from 9 the same way, will reach to 12, the fourth proportional required.4. To find a mean proportional between any two given numbers. Suppose 8 and 32: extend the compasses from 8, in the left hand part of the line, to 32 in the right; then, bisecting this distance, its half will reach from 8 forward, or from 32 backward, to 16, the mean proportional sought. -5. To extract the square root of a number. Suppose 25: bisect the distance between 1 on the scale and the point representing 25; then half of this distance, set off from 1, will give the point representing the root 5. In the same manner, the cube root, or that of any higher power, may be found by dividing the distance on the line, between 1 and the given number, into as many equal parts as the index of the power expresses; then one of those parts, set from 1, will find the point representing the root required.

GUNTER'S QUADRANT is a quadrant made of wood, brass, or some other substance; being a kind of stereographic projection on the plane of the equinoctial, the eye being supposed in one of the poles; so that the tropic, ecliptic and horizon form the arches of circles; but the hour circles are other curves, drawn by means of several altitudes of the sun for some particular latitude every year. This instrument is used to find the hour of the day, the sun's azimuth, &c., and other common problems of the sphere or globe; as also to take the altitude of an object in degrees. GUNTER'S SCALE, usually called, by seamen, the gunter, is a large plain scale, having various lines upon it, of great use in working the cases or questions in navigation. This scale is usually two feet long, and about an inch and a half broad, with various lines upon it, both natural and logarithmic, relating to trigonometry, navigation, &c. On the one side are the natural lines, and on the other the artificial or logarithmic ones. The former side is first divided into inches and tenths, and numbered from 1 to 24 inches, running the whole length, near one edge. One half of the length of this side consists of two plane diagonal scales, for taking off dimensions for three places of figures. On the other half of this side, are contained various lines relating to trigonometry, as performed by natural numbers, and marked thus, viz., Rhumb, the rhumbs or points of the compass; Chord, the line of chords; Sine, the line of sines; Tang., the tangents; S. T., the semi-tangents: and at the other end of this half, are, Leag., leagues or equal parts; Rhumb, another line of rhumbs;

M. L., miles of longitude; Chor., another line of chords. Also, in the middle of this foot are L. and P., two other lines of equal parts: and all these lines on this side of the scale serve for drawing or laying down the figures to the cases in trigonometry and navigation. On the other side of the scale are the following artificial or logarithmic lines, which serve for working or resolving those cases, viz., S. R., the sine rhumbs; T. R., the tangent rhumbs; Numb.,line of numbers; Sine, sines; V.S., the versed sines; Tang., the tangents; Meri., meridional parts; E. P., equal parts.

GUNWALE, or GUNNEL, OF A SHIP, is that piece of timber which reaches, on either side of the ship, from the half-deck to the fore-castle, being the uppermost bend, which finishes the upper works of the hull in that part, and wherein they put the stanchions which support the waisttrees. This is called the gunwale, whether there be guns in the ship or not.-The lower part of any port, where any ordnance is, is also tormed the gunwale. GURNARD (trigla, Lin.). Τριγλα, which the Romans called mullus, does not belong to this genus, though it was included in it by Artedi. These fish, which are marine, all afford excellent food. They have a scaly body, of a uniform shape, compressed laterally, and attenuated towards the tail. The head is broader than the body, and slopes towards the snout, where it is armed with spines; the upper jaw is divided, and extends beyond the lower. The eyes are near the top of the head, large and prominent, particularly the upper margin of the orbits. The dorsal fins are unequal, the first short, high and aculeate; the second long, sloping and radiate. The ventral and pectoral are uncommonly large, and from their base hang three loose and slender appendages. Many of the species utter a peculiar noise when taken; many of the species are provided with pectoral fins, sufficiently large to enable them to spring out of the water. One of the species has been denominated the lyre fish, on account of its bifurcated rostrum, which bears a faint resemblance to that instrument.

GUSTAVUS I, king of Sweden, known under the name of Gustavus Vasa, born in 1490, was a son of duke Erich Vasa, of Grypsholm, and a descendant of the old royal family. He was one of those great men, whom Nature so seldom produces, who appear to have been endowed by her with every quality becoming a sovereign. His handsome person and noble countenance prepossessed all in his

favor. His artless eloquence was irresistible; his conceptions were bold, but his indomitable spirit brought them to a happy issue. He was intrepid, and yet prudent, full of courtesy in a rude age, and as virtuous as the leader of a party can be. When the tyrant Christian II of Denmark sought to make himself master of the throne of Sweden, Gustavus resolved to save his country from oppression; but the execution of his plans was interrupted, as Christian seized his person, and kept him prisoner in Copenhagen as a hostage, with six other distinguished Swedes. When, at last, in 1519, he heard of the success of Christian, who had nearly completed the subjection of Sweden, he resolved, while yet in prison, that he would deliver his country. He fled in the dress of a peasant, and went more than 50 miles the first day, through an unknown country. In Flensborg, he met with some cattle drivers from Jutland. To conceal himself more securely, he took service with them, and arrived happily at Lübeck. Here he was indeed recognised, but he was taken under the protection of the senate, who even promised to support him in his plans, which he no longer concealed. He then embarked, and landed at Calmar. The garrison, to whom he made himself known, refused to take the part of a fugitive. Proscribed by Christian, pursued by the soldiers of the tyrant, rejected both by friends and relations, he turned his steps towards Dalecarlia, to seek assistance from the inhabitants of this province. Having escaped with difficulty the dangers which surrounded him, he was well received by a priest, who aided him with his influence, money and counsel. After he had prepared the minds of the people, he took the opportunity of a festival, at which the peasants of the canton assembled, and appeared in the midst of them. His noble and confident air, his misfortunes, and the general hatred against Christian, who had marked the very beginning of his reign by a cruel massacre at Stockholm,-all lent an irresistible power to his words. The people rushed to arms; the castle of the governor was stormed; and, imboldened by this success, the Dalecarlians flocked together under the banners of the conqueror. From this moment, Gustavus entered upon a career of victory. At the head of a selfraised army, he advanced rapidly, and completed the expulsion of the enemy. In 1521, the estates gave him the title of administrator. In 1523, they proclaimed him king. Upon receiving this honor,

he appeared to yield with regret to the wishes of the nation; but he deferred the ceremony of the coronation. that he might not be obliged to swear to uphold the Catholic religion and the rights of the clergy. He felt that the good of the kingdom required an amelioration of the affairs of the church; and he felt, too, that this could only be effected by a total reform. His chancellor, Larz Anderson, advised him to avail himself of the Lutheran doctrines to attain his object. Gustavus was pleased with this bold plan, and executed it more by the superiority of his policy than of his power. While he secretly favored the progress of the Lutheran religion, he divided the vacant ecclesiastical dignities among his favorites; and, under pretence of lightening the burdens of the people, he laid upon the clergy the charge of supporting his army. Soon after, he dared to do still more: in 1527, he requested and obtained from the estates the abolition of the privileges of the bishops. In the mean while, the doctrines of Luther were rapidly spreading. Gustavus anticipated all seditious movements, or suppressed them. He held the malecontents under restraint; he flattered the ambitious; he gained the weak; and, at last, openly embraced the faith which the greater part of his subjects already professed. In 1530, a national council adopted the confession of Augsburg for their creed. Gustavus, after having, as he said, thus conquered his kingdom a second time, had nothing more to do but to secure it to his children. The estates granted this request also, and, in 1542, abdicated their right of election, and established hereditary succession. Although Sweden was a very limited monarchy, Gustavus exercised an almost unlimited power; but this was allowed him, as he only used it for the benefit of his country, and he never violated the forms of the constitution. He perfected the legislation; formed the character of the nation; softened manners; encouraged industry and learning, and extended commerce. After a glorious reign of 37 years, he died in 1560, at the age of 70. (See Von Archenholz's Geschichte Gustavs Wasa (History of Gustavus Vasa), published at Tübingen, 1801, 2 vols.)

GUSTAVUS II, Adolphus, the greatest monarch of Sweden, was a son of Charles IX (who ascended the Swedish throne upon the deposition of Sigismund), and a grandson of Gustavus Vasa. born at Stockholm, in 1594, and received a most careful education. At the age of

He was

12, he entered the army, and, at 16, directed all affairs, appeared in the state council and at the head of the army, obeyed as a soldier, negotiated as a minister, and commanded as a king. In 1611, after the death of Charles IX, the estates gave the throne to the young prince, at the age of 18, and, without regard to the law, declared him of age; for they saw that only the most energetic measures could save the kingdom from subjection, and that a regency would infallibly cause its ruin. The penetrating eye of Gustavus saw in Axel Oxenstiern, the youngest of the counsellors of state, the great statesman, whose advice he might follow in the most dangerous situations. He united him to himself by the bands of the most intimate friendship. Denmark, Poland and Russia were at war with Sweden. Gustavus, unable to cope at once with three such powerful adversaries, engaged, at the peace of Knared, in 1613, to pay Denmark 1,000,000 dollars, but received back all that had been conquered from Sweden. After a successful campaign, in which, according to his own confession, his military talent was formed by James de la Gardie, Russia was entirely shut out from the Baltic by the peace of Stolbowa, in 1617. But Poland, although no more successful against him, would only consent to a truce for six years, which he accepted, partly because it was in itself advantageous, partly because it afforded him opportunity to undertake something decisive against Austria, whose head, the emperor Ferdinand II, was striving, by all means, to increase his power, and was likewise an irreconcilable enemy of the Protestants. The intention of the emperor to make himself master of the Baltic, and to prepare an attack upon Sweden, did not admit of a doubt. But a still more powerful inducement to oppose the progress of his arms, Gustavus Adolphus found in the war between the Catholics and the Protestants, which endangered at once the freedom of Germany and the whole Protestant church. Gustavus, who was truly devoted to the Lutheran doctrines, determined to deliver both. After explaining to the estates of the kingdom, in a powerful speech, the resolution he had taken, he presented to them, with tears in his eyes, his daughter Christina, as his heiress, with the presentiment that he should never again see his country, and intrusted the regency to a chosen council, excluding his wife, whom, how ever, he tenderly loved. He then invaded Germany in 1630, and landed, with 13,000

men, on the coasts of Pomerania. What difficulties opposed him on the part of those very princes for whose sake he had come; how his wisdom, generosity and perseverance triumphed over inconstancy, mistrust and weakness; what deeds of heroism he performed at the head of his army, and how he fell, an unconquered and unsullied general, at the battle of Lützen, November 6, 1632, may be seen in the article Thirty Years' War. The circumstances immediately attending his death have long been related in various and contradictory ways; but we now know, from the letter of an officer who was wounded at his side, that he was killed on the spot, by an Austrian ball. The king's buff coat was carried to Vienna, where it is still kept; but Bernhard von Weimar carried the body to Weissenfels to give it to the queen. There the heart was buried, and remained in the land for which it had bled.

GUSTAVUS III, king of Sweden, born in 1746, was the eldest son of Adolphus Frederic, duke of Holstein-Gottorp, who was chosen to succeed to the Swedish throne in 1743, and of Ulrica Louisa, sister of Frederic II of Prussia. Count Tessin, to whose care the prince was intrusted from his fifth year, endeavored to form his mind and character with a constant view to his future destination, and was especially anxious to restrain the ambition of the youth, and to inspire him with respect for the constitution of Sweden. His successor, count Scheffer, pursued the same course; but the ambition of the young prince was not eradicated. His docility of disposition, affability of manners, and gentleness, concealed an ardent thirst for power and action. Manly exercises, science and the arts, the pleasures of society, and displays of splendor, united with taste, appeared to be his favorite occupations. Sweden was then distracted by factions, especially those of the caps and hats, by which names the partisans of Russia and France were distinguished. Both parties, however, were united in their efforts to weaken the royal power as much as possible. The father of Gustavus, a wise and benevolent prince, had found his situation quite perplexing. Gustavus himself encountered, with great boldness and art, the difficulties which met him on his accession to the throne, after his father's death, February 12, 1771. He established the order of Vasa, to gain over some enterprising officers of the army, and a party was formed, principally consisting of young

were sent to gain over the troops stationed in the other parts of the kingdom. Some influential individuals, among whom were the counts Hermanson and Scheffer, had also joined the royal party. A new plan was devised, and the parts so distributed, that the king's brothers were to begin the revolution in the country, while the king himself should commence operations in the capital. Agreeably to this plan, the commandant of Christianstadt, captain Hellickius, one of the truest and boldest adherents of the king, August 12, 1772, caused the city gates to be shut, and all the entrances to be guarded, and published a manifesto against the states general. Prince Charles then appeared before Christianstadt, and commenced a pretended siege, wherein no one was in jured. The king, in the mean time, played his part so perfectly, as to dissipate the suspicions of the secret committee of the states. The committee ordered patrols of the citizens in the capital, which the king always attended, and, by his insinuating address, gained over to his cause the principal part of the soldiery and many of the officers. While he was thus preparing for the decisive moment, he appeared serene and composed; and, on the evening preceding the accomplishment of the project, he held a splendid court, which he enlivened by his affability and gayety. On the following day, August 19, 1772, after taking a ride, the king went to the council of the estates, at the castle, where, for the first time, he entered into a warm dispute with some of the counsellors. He then went to the arsenal, on horseback, where he exercised the guard. In the mean time, the officers, upon whom he thought he could depend, assembled, in consequence of a secret order to that effect, and accompanied him to the castle, where, at that time, they were changing guard, so that those who were retiring, and those who were mounting guard, met. With the entrance of the king into the castle, the revolution began. The king then collected the officers about him, in the guard room, unfolded to them his plan, and demanded their support. Most of them were young men, and were immediately gained over by the thought of delivering their country. Three older officers, who refused, had their swords taken from them by the king. The rest swore fidelity to his cause. The king's address to the soldiers was received with loud acclamations. He then set a guard over the entrances to the

to remain quiet, after which he returned to the arsenal, amidst the acclamations of the people, and secured the adherence of the regiments of artillery. A public proclamation exhorted the inhabitants of Stockholm to remain tranquil, and to obey no orders but those of the king. Cannon were planted, guards distributed, and several persons arrested, by way of precaution. Thus was the decisive blow struck without bloodshed, and the king returned to the castle, where he received the congratulations of foreign ambassadors, whom he had invited to his table. On the following day, the magistrates of the city took the oath of allegiance in the great market-place, amid the acclamations of the people. But it was necessary for the estates also to approve of the revolution, and to accept the new constitution, by which the royal power was enlarged, not so much at the expense of the estates as of the council. The next day, they were summoned to meet at the castle, where they found themselves without any attendants. The court of the castle was guarded by soldiers, cannon were planted before the hall of assembly, and a cannoneer stationed at each piece with a lighted match. The king appeared with a numerous retinue of officers and unusual pomp, depicted, in a forcible manner, the situation of the kingdom and the necessity of a reform, declared the moderation of his views, and caused the new constitution to be read, which was immediately approved and confirmed by subscription and oath. Almost all the public officers retained their stations; those persons who had been arrested were set at liberty, and the revolution was completed. The king now exerted himself to promote the prosperity of his country. În 1783, he went through Germany to Italy, to use the baths of Pisa, and returned to Sweden the following year through France. During his absence, a famine had destroyed thousands of his subjects; the peopłe murmured; the nobility rose against the king's despotic policy, and the estates of the kingdom, in 1786, rejected almost all his propositions, and compelled him to make great sacrifices. A war having broke out between Russia and the Porte, in 1787, Gustavus, in compliance with former treaties, determined to attack the empress of Russia, who had promoted the dissensions of Sweden. War was declared in 1788; but, when the king attempted to commence operations by an attack on Friedrichsham, he was deserted