V A R V A R 69 situated on the Nartuby, the principal tributary of the Argens. Other streams are, in the north the Verdon, a tributary of the Durance, in the west the Huvaune and Arc, in the south the Gapeau, and in the east the Siagne. flie coast-line, which is one of the most beautiful and picturesquely varied in France, runs from west to east between the Gulf of La Ciotat and Cape Comarat, then from south-west to north-east between the Gulfs of St Tropez and La Napoule. The shore is dotted from west to east with the sand-covered remains of the Phocsean city of Tauroentuin ; the little ports of Bandol and St Nazaire ; the peninsula of Cape Sicie, 1180 feet high, with its projection Cape Cepet (see TOULON) ; the roads of Toulon ; the roads of Giens, the site of the Gallo-Roman town of 1 omponiana ; the peninsula of Giens, formerly an island attached to the mainland by two long spits of sand, between which lies the lagoon of Les Pesquiers with its "salines"; the great anchorage of Hyeres, shut off from the Mediterranean on the south by the hilly and wooded islands of Porquerolles, Port-Cros, and Le Levant ; the bold promontories of the Maures Mountains, dividing the coast into lovely bays ; Cape Comarat (430 feet), with a lighthouse; the deep Gulf of St Tropez, with perhaps the best anchorage in all Provence ; the Gulf of Frejus, where owing to the accumulated alluvial deposits of the Argens the site of the Roman port of Forum Julii is now occu pied by the inland town of St Raphael ; the porphyry headlands of the Esterel Range, with the roads of Agay between them ; and Cape Roux (1486 feet). The climate is remarkably fine and mild on the coast, where there is complete shelter from the north wind, but is more severe in the mountains. Hyeres and St Raphael are favourite invalid resorts. The average temperature is 58 Fahr. at Toulon, 59 at Hyeres. The annual rainfall is 19 inches at Toulon and 24 in the valley of the Argens. Of the total area of 1,489,488 acres 379,021 are arable, 529,660 muler wood, 185,333 under vineyards, 14,857 are meadows and orchards, 49,606 pasture, and 142,466 uncultivated. The live stock includes 8460 horses (many of Arab blood), 13,230 mules, 5420 asses. 3015 cattle, 105,840 sheep (wool-clip in 1879, 234 tons 4 cwts., valued at 10,000), 19,900 pigs, and 14,815 goats. There were 14,380 beehives (42 tons 10 cwts. of honey and 28 tons 7 cwts. of wax in 1879). In 1884 366 tons 15 cwts. of silk cocoons were produced. The crops in 1884 were 1,485,000 bushels of wheat, 13,200 of meslin, 11,000 of rye, 30,250 of barley, 7150 of maize, 2640 of millet, 125,400 of oats, 4,840,000 of potatoes, 2512 tons of beetroot, and 103,000 tons of different kinds of fodder. The vines, reduced by 60 per cent, since 1875 by the phylloxera, yielded in 1884 over 7,000,000 gallons of wine (average of previous 10 years over 29,000,000 gallons.). In 1879 olives occupied 77,777 acres and yielded 1,384,856 bushels ; four-fifths of the crop was pressed for oil and yielded 5256 tons. Mulberries, strawberries, pears, peaches, plums, figs, almonds, oranges, pomegranates, lemons, jujubes, guavas, and Japanese medlars are grown ; and the laurel, palm tree, date tree, eucalyptus, cactus, and sugar cane flourish. An export trade is carried on in flowers, and also in trullles, capers, and onions. The forests are planted with white and evergreen oaks, cork trees, maritime pines, and chestnuts. In the dense, and almost virgin, forest of St Baume are beeches, maples, limes, oaks, elms, yews, and pines, and the flora of the district is botanically most interesting. Var possesses mines of iron, lead, aluminium, and coal (2846 tons of coal, 2075 tons of lignite in 1885). From 300 to 400 workmen are employed in the production of salt and chemicals. Hyeres (population 13,170 in 1886) produces annually from 20,000 to 25,000 tons of salt. Marble, plaster, stone, chalk, clay, sandstone, and sand for glass are quarried or dug. There are 200 manufactories of pottery, earthen ware, and tiles. Toulon (57,635), La Seyne (12,186), St Tropez (3622), and Bandol, where ships are built, are the chief industrial centres. There are silk, woollen (250 spindles, 6 looms), and cotton (350 spindles, 9 looms) mills, hat, cloth, and cork manufactories (1000 workmen), tan-yards, paper-mills (670 tons in 1879), print ing establishments, tinned food manufactories, soap-works (172 tons), breweries, glass-works, oil-mills in all 173 establishments. There are tunny, anchovy, and sardine fisheries. The department has 140 miles of railway, 164 of national roads, and 2448 of other roads. About half the population of 288,577 (1881) were agricul tural, 46,691 manufacturing, and 30,228 marine. In 1886 the total population of the department numbered 283,689. "Var is divided into 3 arrondissements (Draguignan, the chef-lieu, with 8562 in habitants in 1886 ; Brignoles, with 4393 inhabitants ; and TOULON (q.v. ), 28 cantons, and 145 communes ; it forms the diocese of Frejus, and belongs to the jurisdiction of the Aix court of appeal and to the district of the Marseilles army corps. VARASD (Germ. Warasdin"), a royal free city of Hungary, in the county of Varasd, in Croatia, lies about 40 miles north -north-east of Zagrab (Agram), on the river Drave. It was once used as a stronghold, but now only the castle remains fortified. Varasd possesses several churches of interest, a fine new county hall, two gym nasia, and a real school. It has also tobacco and liqueur factories, and enjoys a brisk trade in wood and fruits, especially plums. The inhabitants numbered 13,701 in 1880. VARENIUS, BERNHARDUS, or BERXHARD VAREN (1622- 1670), geographer, was born at Hitzacker on the Elbe, in the Liineburg district of Hanover. His early years were spent at Uelzen, where his father was court preacher to the duke of Brunswick. Varenius studied at the gym nasium of Hanover and at Konigsberg and Leyden uni versities, where he devoted himself to medicine, taking his degree in 1649. He then settled at Amsterdam, in tending to practise medicine. But the recent discoveries of Tasman, Schouten, and other Dutch navigators, and his friendship for Blauw and other geographers, roused in Varenius an interest in geography, and it was in this study that the principal achievements of his life were gained. He died in 1670. In 1649 he published, through Elzevir, his Dcscriptio Eegni Japonife, an excellent compilation, which may still be read with profit. In this was included a translation into Latin of Schouten s account of Siam and chapters on the religions of various peoples. Next year appeared the work by which he is best known, his Gcogmphia Generalis, in which he endeavoured to lay down the general principles of the subject on a wide scientific basis, accord ing to the knowledge of his day. The work is divided into (1) absolute geography, (2) relative geography, and (3) comparative geography. The first investigates mathematical facts relating to the earth as a whole, its figure, dimensions, motions, their measure ment, &c. The second part considers the earth as affected by the sun and stars, climates, seasons, the difference of apparent time at different places, variations in the length of the day, &c. The third part treats briefly of the actual divisions of the surface of the earth, their relative positions, globe and map construction, longitude, navigation, &c. Though the subject as treated by Yarenius is crude and ill-defined, still, with the materials at his command, he dealt with it on the whole in a really philosophic and scientific spirit ; and it long held its position as the best treatise on scientific geography in existence. The work went through many editions. Sir Isaac Newton introduced several important improvements into the Cambridge edition of 1672 ; in 1712 Dr Jurin issued an edition with a valuable appendix ; in 1733 the whole work was translated into English by Dugdale ; and in 1736 Dugdale s second edition was revised by Shaw. In 1755 a French translation of Shaw s edition appeared in Paris. There was also an Italian edition printed at Naples in 1716. See a paper on Varenius by II. Blink in Tijilschf. van hvt Nederl. Aardrijks. Genootschnp, ser. ii. pt. iii., 1SS7. VARIABLE, COMPLEX. 1. The solution of a quad ratic equation involves the extraction of the square root of a quantity which may be negative. In that case the solution is of the form a + / - b 2 , which may be written a + b/~l, or a + ib, putting, with Gauss, for brevity, N / - 1 = i. Analysis was, therefore, at a very early stage compelled to contemplate the possibility that symbols of magnitude may represent combinations of dissimilar con stituents ; but it is only within the 19th century, mainly owing to the initiative of Cauchy and of Gauss, that the whole domain of analysis has been explored from this point of view. A quantity, a + ?7>, consisting of a real part containing a units and an imaginary part containing b units, was called by Gauss a complex number, and the conception of it includes those of each kind, the real and
the purely imaginary as they are found from it by making