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GEOMETRY extensive accumulations of vegetable-matter were made in the western third of the United States. These were subsequently converted into coal, mostly soft. The coal of the western part of the United States mostly belongs to the late stages of the Cretaceous period.

The Cenozoic era or era of modern life followed the Mesozoic. Mammals, the earliest remains of which are found in the rocks of the Triassic system, abounded during the Cenozoic era, while the huge reptiles which had been especially characteristic of the Mesozoic era had disappeared. Reptiles still existed as now, but they were of relatively small types, and their numbers appear to have been relatively few. As the Cenozoic era progressed, the forms of life approached more and more closely to those of the present time, and by the end of the Pliocene the life was nearly the same as that which now exists. The Pleistocene period was a remarkable one, on account of the great climatic changes which occurred at this time. The result of these climatic changes brought on a glacial climate, and an ice-sheet or series of ice-sheets covered something like 4,000,000 square miles in the northern part of North America. A large ice-sheet was developed, probably contemporaneously, on the continent of Europe, affecting especially its northwestern part. The history of the Glacial period has been worked out in sufficient detail, so that it is known that there was a series of ice-sheets and not a single one. That is, there were several glacial epochs, with intervening epochs when the ice largely or completely disappeared and the climate became genial. Most of the lakes, waterfalls, etc. of the northeastern part of the United States and of the region to the north owe their existence to the glaciation of the area where they occur. The ice reached its most southerly limit in Illinois, where it descended to about 37° 30′.

The duration of the earth's history is a matter which has received much attention, but no conclusions have been reached which can be relied upon, beyond the very general one that the history of the earth has been exceedingly long. Various conjectures as to the number of years occupied in bringing the earth to its present condition have been made. They range from twenty-five million or so to several hundred million. Geologists in general would not be surprised if it could be demonstrated that the history of the earth since Archean time has occupied 50,000,000 to 100,000,000 years. The Proterozoic era was perhaps as long as all subsequent time. The Paleozoic era was perhaps three to six times as long as the Mesozoic, and the Mesozoic was perhaps three or four times as long as the Cenozoic.

The climatic changes which the earth has undergone have been great, but their causes are not well-understood. There is little basis for the belief, formerly widespread, that the climate has on the whole been growing cooler. Cold periods seem to have alternated with warmer ones. Glaciation was extensive at the close of the Paleozoic and, again, late in the Cenozoic, and there is some indication of cold periods at other times. On the other hand the lands of high latitudes enjoyed genial climates during some parts of the earth's history, even as late as the mid-Tertiary time.

Volcanic activity seems to have been greater at some periods than at others, but on the whole to have been about as great, so far as now known, in the early as in the late stages of the earth's history. See Dana's Manual of Geology; Scott's Introduction to Geology; Le Conte's Elements of Geology; Geikie's Text-Book of Geology.

 Geom′etry in its origin was the science of measuring the surface of the earth (Greek gē, the earth, and metron, measure). With the ancient Egyptians, for instance, it took the form of mensuration, because of the need of a yearly survey of the lands that were left bare and muddy after each annual overflow of the Nile. Geometry now is the science of form; although, indeed, the exact geometrical forms are seldom found in nature. Perhaps one should begin to teach geometry as the Egyptians learned it, through making simple geometrical measurements and surveys in the play-ground, of baseball diamonds, hopscotch courts, a lawn tennis court and so on. For, according to the strictly logical form of Euclid's teaching, it is seldom that a child perceives the need of geometry or begins with an interest in it. For this reason, top, geometrical properties should be taught in the first place largely by paper-folding and cutting, by the use of models, such as the kindergarten gifts, and by the graphical representation of facts that have to do with the other interests and studies of children. The classic work upon Geometry is still the Elements of Euclid, who wrote about 285 B. C. in the great days of Alexandria. But geometers of the 19th century declined to be bound by the Elements. There arose a new geometry, which began perhaps with Carnot. It certainly is necessary for the teacher of geometry to abandon the logical order of Euclid for a more practical and interesting and, in short, more psychological method.  Geoph′ilous Plants are those plants with special subterranean structures which enable them to pass through unfavorable seasons. For example, during a period of drought or cold the aerial parts of such plants disappear, but with the return of favorable conditions the underground parts