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 ALGERIA 315 Ex. gr. For order 3 of the cubic we find looted Mathematical Papers. Cambridge, 1898.—Salmon. Lessons Introductory to the Modern Higher Algebra. Dublin, 1885.—E. B. (L2 + 9 sin2 w)a0= 6(a0 - 2ax cos o> + a2), Elliott. Algebra of Quantics. Oxford, 1895.—F. Beioschi. where a0- 2ajCos co + a2 appertains to the linear covariant naax‘, Teoriadei Covarianti. Rome, 1861.—W. Fiedler. Die Elements der neueren Geometric und dcr Algebra der binaren For men. and it is easy to verify that (L2 + sin2w)c*anix = 0. Leipzig, 1862.—A. Clebsch. Theorie der bindren algebraIt is to he remarked that the sources of linear covariants are ischen Formen. Leipzig, 1872. Vorlesungen iiber Geometric. annihilated by L2 + sin2o;. It has been customary for writers to Leipzig, 1875.—Faa de Bruno. Thiorie dcs formes binaries. iegaid the orthogonal and Boolian theories as particular cases of Turin, 1876.—P. Gordan. Vorlesungcn uber Invariantentheorie, that arising from the general linear substitution. The above Bd. i. “ Determinanten,” Leipzig, 1885; Bd. ii. Bindre Formen, sketch will convince the reader that the latter theory is more Leipzig, 1887.—G. Rubini. Teoria delle forme in generate, e properly viewed as a particular case of the former theories. specialmente delle binarie. Leue, 1886.—E. Study. Mcthoden Theorie der terndren Formen. Leipzig, 1889.—Lie. Theorie Investigations, connected with this section, are a desideratum. zur Transformationsgruppen. Leipzig, 1888-90.—Franz Meyer. No references can be given other than those alluded to, incident- der Bericht uber den gegenwdrtigen Stand der Invariantentheorie; ally, m the text. Jahresbericht der Deutschen Mathematiker-Vereinigung, Bd. i. References. Cayley. “Memoirs on Quantics” in the Col- Berlin, 1892. (P< At M

Algeria., in North Africa, the most important of the colonies of France, lies between Tunis on the east and Morocco on the west, and extends from the Mediterranean to the Sahara. Its area is estimated at 98,500,000 acres, or 153,906 square miles. The principal indentations of

the coast are the Gulf of Oran, the Gulf of Arzeu, the Bay of Algiers, the Gulfs of Bougie, Stora, and B6ne. The ports are Nemours, Mers el Kebir, Oran, Arzeu, Mostaganem, Tenes, Cherchelle, Algiers, Dellys, Bougie, Jijelli, Collo, Philippeville, Bone, La Calle. Algeria is

reality of seventeen distinct ranges, among which it is sufficient to mention the Tlemcen range (5500 feet), the Waransenis (6000 feet), the Titeri range (4900 feet), the Jerjera or Grand Kabyle range (7100 feet), with the peak of Lalla Kedija, and the Babor range (6000 feet). The streams of the Tell are the Tafna (105 miles), the Macta, formed by the Sig and the Habra; the Cheliff (415 miles), the Isser (130 miles), the Sahel (125 miles), the Kebir (140 miles), the Seybouse (145 miles), and the Mejerda, which flows through Tunis to the sea. None of these rivers is navigable. The temperature of the Tell is moderated by the sea-breeze, but the sirocco wind sometimes brings scorching heat. The climate is very healthy, except in the extreme coast region. The high plateaus form a plain of an average height of from 2500 to 3000 feet, dominated by the ridges of the second or Saharan chain of the Atlas, of which the chief points are the Ksour (6000 feet), the Amour and the Aures (7200 feet). At the foot and to the north of this chain, towards the middle of the plateaus, is a depression containing saline lakes or chotts, of which the best known are the Chergui and the Hodna. The rivers are unimportant ; the temperature is variable, passing from one extreme to the other, and rain seldom falls. The Saharan region consists of wide sandy or rocky plains without noteworthy features. The water in general remains under the surface; the temperature is very high by day; rain falls scarcely in one year out of three. Life exists only round the oases or cultivated places. Geologically, the Atlas of the Tell consists of crystalline rocks, schists, and lias. The Tertiary formation hardly ever appears except in its eastern portion. On the other hand, the Little or Saharan Atlas is essentially of Cretaceous and Jurassic formation, like the rocks of the desert itself. Population. —The population consists of Kabyles or Berbers, Arabs, Moors, Jews, Turks, Coulouglis, Negroes, Mozabides, and

n.v.o&oj.R.H

French Territory French Protectorate Map showing the Political Position of Algeria.

Native. . . . French and naturalized Other Europeans.

2,850,886 269,502 190,014

3,847,448 334,713 211,535

4,393,696 naturally divided into three parts — the Tell, or coast Total 3,310,402 region, with a breadth varying from 75 to 160 miles, the high plateaus; and the Sahara region. The Tell Europeans of various nationality. The Berber population is is traversed by the first chain of the Atlas, consisting m estimated at 75 per cent, and the Arab at 15 per cent, ot the