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Rh advance necessitated a third movement, the construction of a frontier connecting the annexations of 74 and 83. We know the line of this frontier which ran from the Main across the upland Odenwald to the upper waters of the Neckar and was defended by a chain of forts. We do not, however, know its date, save that, if not Domitian’s work, it was carried out soon after his death, and the whole frontier thus constituted was reorganized, probably by Hadrian, with a continuous wooden palisade reaching from Rhine to Danube. The angle between the rivers was now almost full. But there remained further advance and further fortification. Either Hadrian or, more probably, his successor Pius pushed out from the Odenwald and the Danube, and marked out a new frontier roughly parallel to but in advance of these two lines, though sometimes, as on the Taunus, coinciding with the older line. This is the frontier which is now visible and visited by the curious. It consists, as we see it to-day, of two distinct frontier works, one, known as the Pfahlgraben, is an earthen mound and ditch, best seen in the neighbourhood of the Saalburg but once extending from the Rhine southwards into southern Germany. The other, which begins where the earthwork stops, is a wall, though not a very formidable wall, of stone, the Teufelsmauer; it runs roughly east and west parallel to the Danube, which it finally joins at Heinheim near Regensburg. The Pfahlgraben is remarkable for the extraordinary directness of its southern part, which for over 50 m. runs mathematically straight and points almost absolutely true for the Polar star. It is a clear case of an ancient frontier laid out in American fashion. This frontier remained for about 100 years, and no doubt in that long period much was done to it to which we cannot affix precise dates. We cannot even be absolutely certain when the frontier laid out by Pius was equipped with the Pfahlgraben and Teufelsmauer. But we know that the pressure of the barbarians began to be felt seriously in the later part of the 2nd century, and after long struggles the whole or almost the whole district east of Rhine and north of Danube was lost—seemingly all within one short period—about 250.

The best English account will be found in H. F. Pelham’s essay in ''Trans. of the Royal Hist. Soc. vol. 20, reprinted in his Collected'' Papers, pp. 178-211 (Oxford, 1910), where the German authorities are fully cited.

 LIMESTONE, in petrography, a rock consisting essentially of carbonate of lime. The group includes many varieties, some of which are very distinct; but the whole group has certain properties in common, arising from the chemical composition and mineral character of its members. All limestones dissolve readily in cold dilute acids, giving off bubbles of carbonic acid. Citric or acetic acid will effect this change, though the mineral acids are more commonly employed. Limestones, when pure, are soft rocks readily scratched with a knife-blade or the edge of a coin, their hardness being 3; but unless they are earthy or incoherent, like chalk or sinter, they do not disintegrate by pressure with the fingers and cannot be scratched with the finger nail. When free from impurities limestones are white, but they generally contain small quantities of other minerals than calcite which affect their colour. Many limestones are yellowish or creamy, especially those which contain a little iron oxide, iron carbonate or clay. Others are bluish from the presence of iron sulphide, or pyrites or marcasite; or grey and black from admixture with carbonaceous or bituminous substances. Red limestones usually contain haematite; in green limestones there may be glauconite or chlorite. In crystalline limestones or marbles many silicates may occur producing varied colours, e.g. epidote, chlorite, augite (green); vesuvianite and garnet (brown and red); graphite, spinels (black and grey); epidote, chondrodite (yellow). The specific gravity of limestones ranges from 2.6 to 2.8 in typical examples.

When seen in the field, limestones are often recognizable by their method of weathering. If very pure, they may have smooth rounded surfaces, or may be covered with narrow runnels cut out by the rain. In such cases there is very little soil, and plants are found growing only in fissures or crevices where the insoluble impurities of the limestone have been deposited by the rain. The less pure rocks have often eroded or pitted surfaces, showing bands or patches rendered more resistant to the action of the weather by the presence of insoluble materials such as sand, clay or chert. These surfaces are often known from the crust of hydrous oxides of iron produced by the action of the atmosphere on any ferriferous ingredients of the rock; they are sometimes black when the limestone is carbonaceous; a thin layer of gritty sand grains may be left on the surface of limestones which are slightly arenaceous. Most limestones which contain fossils show these most clearly on weathered surfaces, and the appearance of fragments of corals, crinoids and shells on the exposed parts of a rock indicate a strong probability that that rock is a limestone. The interior usually shows the organic structures very imperfectly or not at all.

Another characteristic of pure limestones, where they occur in large masses occupying considerable areas, is the frequency with which they produce bare rocky ground, especially at high elevations, or yield only a thin scanty soil covered with short grass. In mountainous districts limestones are often recognizable by these peculiarities. The chalk downs are celebrated for the close green sward which they furnish. More impure limestones, like those of the Lias and Oolites, contain enough insoluble mineral matter to yield soils of great thickness and value, e.g. the Cornbrash. In limestone regions all waters tend to be hard, on account of the abundant carbonate of lime dissolved by percolating waters, and caves, swallow holes, sinks, pot-holes and underground rivers may occur in abundance. Some elevated tracts of limestone are very barren (e.g. the Causses), because the rain which falls in them sinks at once into the earth and passes underground. To a large extent this is true of the chalk downs, where surface waters are notably scarce, though at considerable depths the rocks hold large supplies of water.

The great majority of limestones are of organic formation, consisting of the debris of the skeletons of animals. Some are foraminiferal, others are crinoidal, shelly or coral limestones according to the nature of the creatures whose remains they contain. Of foraminiferal limestones chalk is probably the best known; it is fine, white and rather soft, and is very largely made up of the shells of globigerina and other foraminifera (see ). Almost equally important are the nummulitic limestones so well developed in Mediterranean countries (Spain, France, the Alps, Greece, Algeria, Egypt, Asia Minor, &c.). The pyramids of Egypt are built mainly of nummulitic limestone. Nummulites are large cone-shaped foraminifera with many chambers arranged in spiral order. In Britain the small globular shells of Saccamina are important constituents of some Carboniferous limestones; but the upper portion of that formation in Russia, eastern Asia and North America is characterized by the occurrence of limestones filled with the spindle-shaped shells of Fusulina, a genus of foraminifera now extinct.

Coral limestones are being formed at the present day over a large extent of the tropical seas; many existing coral reefs must be of great thickness. The same process has been going on actively since a very early period of the earth’s history, for similar rocks are found in great abundance in many geological formations. Some Silurian limestones are rich in corals; in the Devonian there are deposits which have been described as coral reefs (Devonshire, Germany). The Carboniferous limestone, or mountain limestones of England and North America, is sometimes nearly entirely coralline, and the great dolomite masses of the Trias in the eastern Alps are believed by many to be merely altered coral reefs. A special feature of coral limestones is that, although they may be to a considerable extent dolomitized, they are generally very free from silt and mechanical impurities.

Crinoidal limestones, though abundant among the older rocks, are not in course of formation on any great scale at the present time, as crinoids, formerly abundant, are now rare. Many Carboniferous and Silurian limestones consist mainly of the little cylindrical joints of these animals. They are easily recognized by their shape, and by the fact that many of them show a tube along their axes, which is often filled up by carbonate of lime; under the microscope they have a punctate or fenestrate structure and each joint behaves as a simple crystalline plate with uniform optical properties in polarized light. Remains of other echinoderms (starfishes and sea urchins) are often found in plenty in Secondary and Tertiary limestones, but very seldom make up the greater part of the rock. Shelly limestones may consist of mollusca or of brachiopoda, the former being common in limestones of all ages while the latter attained their principal development in the Palaeozoic epoch. The shells are often broken and may have been reduced to shell sand before the rock consolidated. Many rocks of this class are impure and pass