tilian forms of immense dimensions, and having curious resemblances to birds, are met with; while the birds themselves, which then first appeared, had remarkable reptilian affinities. The earliest evidences of mammals appear in the trias; throughout the mesozoic they were insignificant in size, and chiefly marsupial. In the eocene and miocene divisions of the tertiary we find the greatest development of mammalian forms. The deposits of these strata to the west of the Mississippi have within the last few years afforded a great number of remarkable species of mammals, which have been described by Leidy, Marsh, and Cope. The flora of the tertiary period is not less remarkable than its fauna. The geographical and climatic conditions of the northern hemisphere were then widely different from those of the present day. Not only over Europe, but in North America, and northward as far as Greenland and Spitzbergen, a mild and equable climate prevailed, and the abundant plant remains preserved in the tertiary beds of those arctic regions show a luxuriant vegetation like that of the warmer parts of the temperate zone of to-day. This condition of things had been of long continuance; for in western America great beds of coal or lignite are found both in the cretaceous and the eocene strata. It was continued far into the pliocene; but as this went on, a cold climate like that which now characterizes the northern hemisphere prevailed, and gave rise to the glacial phenomena which have been described under the head of Diluvium. This change of climate is one of the most perplexing problems of geology. That a different distribution of land and water and of the oceanic currents may have contributed in some degree to this former climatic condition of the arctic regions is probable. Astronomical conditions connected with changes in the eccentricity of the earth's orbit have also been suggested as a cause; and finally it has been supposed that a somewhat different chemical composition of the earth's atmosphere prevailing up to that time may have coöperated with geographical conditions to maintain the peculiarly mild climate which, so far as we can judge, prevailed throughout the arctic regions in palæozoic times, and perhaps without interruption nearly to the close of the tertiary.—The distribution of metallic ores and other economic materials in the various geological series is a point of much interest, and demands a brief notice in this place, although the subject is discussed more in detail under Mineral Veins, and in the articles on the different metals. Metallic ores are met with both in beds interstratified with the rocky layers and in veins cutting these. The eozoic rocks are remarkable for their great deposits of crystalline iron ores, of which those of the Laurentian on Lake Champlain and those of the Huronian on Lake Superior are remarkable examples, as are also those of Missouri. Similar deposits occur in the eozoic rocks of Scandinavia and Russia. It is in these rocks also that titanic and chromic iron and emery occur; and to them belong graphite and beds of iron pyrites and copper pyrites, often associated with gold and with silver. Oxide of tin also appears to be characteristic of these crystalline rocks. These various ores are found not only in contemporaneous layers, but also in veins and beds cutting the crystalline strata. But the metallic ores are not confined to these more ancient rocks, for beds of oxide and carbonate of iron are met with at various horizons from the Cambrian up to recent times, while under the heads of Copper and Gold the distribution of those metals and their ores is described. Besides these contemporaneous deposits, veins or lodes carrying the ores of various metals are found cutting rocks of all ages, and are probably even now in process of formation.—The question of eruptive or exotic rocks has already been briefly alluded to, but from its intimate connection with volcanic phenomena, from which it cannot well be separated, it is proposed to consider the whole subject in the article Volcano, in which connection the various theories with regard to the nature of the earth's interior, the sources of subterranean heat and of ancient and modern eruptive rocks, as well as of the gaseous products of volcanic eruptions, will be discussed. (See also Granite.) Under the head of Mountain will be considered some of the most important questions of geological dynamics, namely, those relating to the elevation of continents, the phenomena of denudation, and the origin of mountains. The chemical history of the globe, or what may be called chemical geology, will be discussed under the titles Rocks and Water.
GEOMETRY (Gr. γεωμετρία, from γῆ, the earth, and μετρεῖν, to measure), the science of relations in space. As its name indicates, it originally denoted the measurement of land, and was equivalent to what is known in modern times as surveying. As at present understood, surveying is but a subordinate application of the science, and although geometry retains its ancient name, it has by the labors of many successive generations grown to be a vast and comprehensive system, forming the basis of many of the most important arts and sciences. It has been defined as “the science which treats of forms in space;” and if we give a sufficiently extended meaning to the word “form,” the definition is perhaps as good as any other. It regards material objects only in so far as they occupy space. With their other physical qualities, their color, weight, hardness, &c., geometry has nothing to do. Assuming that a billiard ball and the sun are each a perfect sphere, then the only geometrical difference between them is the difference in size. Neither has geometry anything to do with the nature of space abstractly considered. It assumes the notion of space as it is assumed by all men in practical life, and leaves to philosophy
