Mukaiyama is a rhyolitic volcano located at the southern part of Nii jima(Figs. 1 and 2). The volcano was formed by a single continuous eruption which began in shallow water in A. D. 886. The eruption changed from submarine in the early stage to subaerial in the later stage. The volcanic history is divided into three stages on the basis of the difference in the mode of eruption. The sequence of activities from explosive eruptions in the first stage to effusive eruptions in the third stage can be attributed to the change in the degree of contact of rising magma with sea water as the volcanic body grew.
In the first stage, a low-lying (less than 100 m above sea-level) and flat-topped hill was formed by repeated base-surge eruptions. Since a considerable part of the original hill has been eroded away by wave, the bedded accumulation of the base-surge deposits (Mukai yama base-surge deposits) is very-well exposed along the sea cliff around the volcano (Photo. 1).
Mukaiyama base-surge deposits are characterized by various sedimentary structures such as “antidune structure” (asymmetrical dune-like structure with steep stoss-side laminations and gentle lee-side laminations) and other primary structures (Fig. 4). The deposits are divided into two major groups: the lower coarse-grained Mukaiyama-1 and the upper fine grained Mukaiyama-2, on the basis of the difference in grain size and sedimentary struc tures. The Mukaiyama-1 is composed of plane beds, lenticular beds, pinching and swell ing beds, and large-sized antidune structures. The Mukaiyama-2 is, on the other hand, characterized by abundant cross-beddings and small-sized antidune structures (Photo. 3). Some of the antidune structures in the Mukaiyama-1 have wave length up to several tens of meters, whereas the majority of the antidune structures in the Mukaiyama-2 have wave length of several meters (Fig. 6). The wave length of these antidune structures in both Mukaiyama-1 and -2 tends to decrease with distance from source, presumably, because of decay in flow energy of base surges.
In the second stage, the eruptions remained explosive. In this stage, however, no base surge occurred probably as a result that the volcanic body itself (base-surge hill) hindered to some degree, the contact of magma with sea water. The .second stage activity resulted in the formation of Omine pyroclastic cone with a relative height of about 200 m and basal diameter of about 2 km, on the first stage base-surge hill. The original slope of Omine pyroclastic cone is well preserved in the north and south. Eastern slope has, in contrast, disappeared due to wave erosion, and western slope is also lacking(Figs. 1 and 2).
In the third stage, the grown volcanic edifice served possibly as an effective interceptor against invasion of sea water into the crater. Thus, the eruptions were no more explosive, but viscous lava effused and formed Mukaiyama lava domes. The dome lava (biotite rhyolite) occupies the crater bottom of Omine pyroclastic cone in the east, and rests on the pyroclastic materials in the west, which were probably deposited contemporaneously with Omine cone (Fig.2). Though the present areas covered with the lava is about 1.5 km2, the original lava must have extended further west, for the western end of it is a perpendicular sea cliff. The surface feature of lava is fairly rugged (Fig. 8). The relative heights from furrow bottoms to ridges are up to several tens of meters.

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The average number _??_ελ of streams of order A entering a stream of order ic from the sides provides two parameters: ε₁=_??_ and K=(_??_)
A model of drainage networks is built on the assumption that each parameter is constant in a network. The model is a cyclic system because it not only satisfies the condition that each cycle is entirely similar to the previous and following cycles but also includes structurally Hortoniann networks as a special case (K=O). The law of allometric growth of drainage networks is. formulated by using E1 and K on the assumption that a basin can be devided into infinitesimally small basins and interbasin areas according to the above mentioned cycle. The order m (t) of a subnetwork at time t is expressed by the following equation.
_??_
where l is the lowest order of streams on topographic maps or aerial photos of a given scale, δ is constant,
_??_
and Q=_??_
The above equation holds exactly for networks of infinitely large value of (m(t)-l) and to a fairly good approximation for networks of comparatively large value of it. Setting ε₁=1 and K=2 in the equation leads to the equation which expresses allometric growth of a random graph model (the average or the most probable state of subnetworks in infinite topologically random channel networks). The model corresponds to drainage networks in a stationary state and includes the random graph model as a special case.

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Europe and North America have the longest history of modern nationalism. Boundaries and political activities of European nation-states have left their impress upon European cultural regions. To treat these aspects of the cultural regions as a part of a regional geography of Europe, a method which combines the method of political geography with that of social geography may be suitable. As a few examples of such a method, approaches used in Schöller's “Die rhelnisch-westfälische Grenze zwischen Ruhr and Ebbegebirge”, in Huttenlocher's “Die ehemalige Territorien des Deutschen Reichs in ihrer kulturlandschaftlichen Bedeutung” and in Cohen and Rosenthal's “A geograpical model for political systems analysis” are examined. As a part of materials for such a regional geography, documents and statistics published and accumlated by the offices of European Communities will be useful.

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