Seebach now says that _if we have given the position of_ M _or epicentrum of the shock_, and draw through it rectangular axes like M _m_{3}_ and M T_{3}, and lay down on M _m_{3}_ in miles the distances from M of the various stations which have been shaken, and in equal divisions for minutes lay down on M T_{3} the differences of time at which M, _m_{1}_, _m_{2}_, &c. were shaken, then M_{1} T_{1}, M_{2} T_{2}, &c. are the co-ordinates of points on an hyperbola. The degree of exactness with which this hyperbola is in any given case constructed is a check upon the accuracy of the time observations and the position of the _epicentrum_. The apex of the hyperbola is the _epicentrum_. The intersection of the asymptote with the ordinate axis is the time point of the first shock, which, because the scale for time and for space were taken as equal, gives the absolute position of the _centrum_. This intersection is shown by dotted lines. Knowing the position of the _centrum_, we can directly read from our diagram how far the disturbance has been propagated in a given time. CHAPTER XI. THE DEPTH OF AN EARTHQUAKE CENTRUM. The depth of an earthquake centrum—Greatest possible depth of an earthquake—Form of the focal cavity. _Depth of centrum._—The first calculations of the depth at which an earthquake originated were those made by Mallet for the Neapolitan earthquake of 1857. These were made on the assumption that the earth wave radiated in straight lines from the origin, and, therefore, at points at different distances from the _epicentrum_ it had different angles of emergence. These angles of emergence were chiefly calculated from the inclination of fissures produced in certain buildings, which were assumed to be at right angles to the direction of the normal motion. If we have determined the _epicentrum_ of an earthquake and the muzoseismal circle, and make either the assumption that the angle of emergence in this circle has been 45° or 54° 44′ 9″ (see page 54), it is evidently an easy matter by geometrical construction to determine the depth of the _centrum_. Höfer followed this method when investigating the earthquake of Belluno. Other methods of calculation which have been employed are based on time observations, as, for instance, the method of Seebach, the method of co-ordinates, the method of hyperboloids or spheres (see pages 200–212). By means of a number of lines parallel to twenty-six angles of emergence, drawn in towards the seismic vertical, Mallet found that twenty-three of these intersected at a depth of 7⅛ geographical miles. The maximum depth was 8⅛ geographical miles, and the minimum depth 2¾ geographical miles. The mean depth was taken at a depth of 5¾ geographical miles where, within a range of 12,000 feet, eighteen of the wave paths intersected the seismic vertical.