[15] If _a_ be the amplitude of a simple harmonic vibration, _T_ its complete period, _v_ its maximum velocity, and _f_ its maximum acceleration, we have v=2*pi*a/T and f=4*pi^2*a/T^2 [16] _Earthquakes and other Earth Movements_, pp. 81-82. [17] Obtained from the formula: T=2*pi*a/v=2*pi*x*(1/3)/12 [18] If we take the maximum velocity to be 12 feet per second, and the period to be one second, the amplitude would be about 11-1/2 inches. [19] Vol. ii., p. 299. The punctuation of the original is not followed in the above extract. [20] _British Association Report_, 1851, pp. 272-320. CHAPTER III. THE ISCHIAN EARTHQUAKES OF MARCH 4TH, 1881, AND JULY 28TH, 1883. Separated from Italy by a distance of not more than six miles, Ischia and the intermediate island of Procida strictly form part of the Phlegræan Fields, the well-known volcanic district to the north of Naples. Ischia, the larger of the two islands, is six miles long from east to west, and five miles from north to south, and contains an area of twenty-six square miles. In 1881, the total population was 22,170, that of Casamicciola, the largest town, being 3,963. VOLCANIC HISTORY OF ISCHIA. The central feature of Ischia is the great crater of Epomeo (_a_, Fig. 14). On the south side, and partly also on the east, the crater-wall has been broken down and removed; the portion remaining is about 1-1/2 mile in diameter from east to west, and reaches a height of 2,600 feet above the sea-level. All the upper part of the mountain is composed of a pumiceous tufa, rich in sanidine and of a characteristic greenish colour. At two points, to the west near Forio and to the north between Lacco and Casamicciola, this tufa is seen reaching down to the sea; but, in all other parts, it is covered by streams of trachitic lava, by more recent tufas, or by a deposit of marly appearance, which is regarded by Fuchs as resulting from the decomposition of the Epomean tufa. There are two distinct periods in the geological history of Ischia. The first, a submarine period, probably began with the dawn of the quaternary epoch, for all the marine fossils of the island belong to existing species. About this time, Epomeo seems to have originated in eruptions occurring in a sea at least 1,700 feet in depth--eruptions that preceded the formation of Monte Somma and were either contemporaneous or alternating with those that gave rise to the oldest trachitic tufas of the Phlegræan Fields. The destruction of the south wall may have occurred much later through some great eruptive paroxysm, but more probably, as Professor Mercalli suggests, through early marine erosion and subsequent subaerial denudation. To the submarine period must also be assigned the formation of the trachitic masses which compose Monti Trippiti, Vetta, and Garofoli (_b_, _c_, _d_, Fig. 14), on the east side of Epomeo; and, in part only, those of Monte Campagnano and Monte Vezza (_f_, _g_).