GEOLOGY 286 GEOMETRY ERAS AND SERIES. 9. Quaternary or Post Tertiary: (3) Recent, (2) Champlain, (1) Glacial, 8. Tertiary Era: (4) Pliocene, (3) Miocene, (2) Oligocene, (1) Eocene. 7. Ci'etaceous Era: (4) Laramie, (3) Colorado, (2) Dakota, (1) Lower. 6. Jura-Trias: (b) Jurassic; (3) Pur- beck, (2) Oolite, (1) Lias, (a) Triassic: (4) Rhffitic, (3) Upper, (2) Middle, (1) Lower. 5. Carboniferous Era: (3) Permian, (2) Carboniferous, (1) Sub-carbonifer- ous. 4. Devonian Era: (5) Catskill and Chemung, (4) Portage, (3) Hamilton, (2) Corniferous, (1) Oriskany. 3. Upper Silurian: (3) Lower Helder- berg, (2) Onondaga, (1) Niagara. 2. Lower Silurian: (3) Trenton, (2) Chazy, (1) Calciferous. 1. Cambrian. Eozoic (dawn of life) , Azoic (lifeless). SUB-DIVISIONS. 9. Quaternary: Pleistocene; 8. Terti- ary: English Crag, Upper Molasse, Ru- pelian and Tongrian of Belgium; 7. Cretaceous: Upper Chalk, Lower Chalk, Chalk Marl, Gault, Neocomian, Lower Greensand; 6. Jura-Trias: Wealden, Pur- beck, Portland, Kimmeridge, Oxford Oolites, Lower or Bath Oolite, Lower Lias, Marlstone, Upper Lias, Kossen beds, Dachstein beds; Alpine Trias, in part; Keuper, Muschelkalk, Bunter- Sandstein; 5. Carboniferous: Magnesian Limestone, Lower Red Sandstone, or Rothliegendes, Upper Coal Measures, Lower Coal Measures, Millstone Grit, Lower Carboniferous, Mountain Lime- stone; 4. Devonian: Old Red Sandstone — Catskill Red Sandstone, Chemung, Por- tage, Genesee Slate, Hamilton beds, Mar- cellus Shale, Upper Helderberg, Scho- harie, Grit, Oriskany Sandstone; 3. Upper Silurian: Lower Helderberg, On- ondaga Salt Group, Salina beds, Water Lime, Niagara Group, Wenlock Group, Clinton Group, Medina Sandstone (Upper Llandovery) ; 2. Lower Silurian: Hudson River beds, Cincinnati Group, Lower Llandovery, Utica Shales, Tren- ton Limestone, Caradoc and Bala Lime- stone, Black Shales, Armorican Grit, Gothlandian Calcareous Sandrock, Mag- nesian Limestone, Lower, Middle and Upper Cambrian; 1. Archaean: Lauren- tian, Huronian. Other Rocks. — For these, see Igneous Rocks. Fossils. — For these, see Fossil: Pa- leontology. Applied Geology. — Geology applied to industrial or other practical purposes; as, for instance, to mininfr, drainage, railway tunneling, etc. GEOMETRIC SQUARE, an instru- ment for measuring distances and heights, and useful for its portability as well as for the facility, by the common rule of three, of solving most of the prob- lems arising from its use. It is made of brass or wood, 12 or 18 inches square, and the quadrant is graduate in each direction. The two sides opposite to the axial point of the alidade are graduated to 100 equal parts, with major divisions of 10 of said parts. The 100 point finishes at the angle obliquely opposite the center from which the arc is struck. One side represents the horizon, and the alidade with two sides is equal in length to the diagonal of the square. The ali- dade has divisions equal to those on the sides of the square. GEOMETRY (Greek geometria =the measurement of land; gee, for geios=he- longing to the earth, and metria=mesLS- urement) , properly the measurement of the earth or of land, but now used exclu- sively of the abstract science to which practical land measurement gave or may have given birth. It is the science of space, whether linear, superficial, or solid. History. — Who first invented or cul- tivated geometry is uncertain. The Hindus have a geometry apparently of indigenous growth. Some knowledge of geometry was apparently possessed by the builders of the Egyptian pyra- mids. Diodorus and others attribute the invention or discovery of geometry to Egypt, which is doubtful. The Greeks surpassed all ancient nations in their at- tainments in the science. Euclid founded a school of mathematics at Alexandria some time in the reign of Ptolemy Lagus, B. e. 323 to 284. His "Elements" are still in use in many schools and colleges. See Mathematics, Nature of the Science. — Geometry, like mathematics, is built up on rigorous demonstration. To prevent the possibility of error in reasoning it is needful to com- mence with definitions of the terms em- ployed. Then follow in Euclid's "Ele- ments" postulates or concessions de- manded as to what is possible to be done ; then axioms, simple mathematical state- ments worthy of being believed. A popu- lar belief is that the whole science of geometry rests on the axioms; it is really, however, based on the definitions; thus the whole third book of Euclid follows naturally from the definition of a circle. Analytical Geometry. — The analytical investigation of the relations and prop- erties of geometrical magnitudes. It is divided into determinate and indeter- minate geometry, according as the num-
