closely with that given by clock D. Thus, clocks A, B, and C must have been stopped by the Woodstock vibrations, and clock D about half-a-minute later by those coming from the Rantowles focus. DEPTH OF THE SEISMIC FOCI. Two methods of estimating the depth of the seismic focus have been described in the preceding pages--namely, Mallet's, depending on the angle of emergence, and Falb's, based on the interval between the initial epochs of the sound and shock. To these, Major Dutton adds a third method, in which he relies on the rate at which the intensity of the shock varies with the distance from the epicentre. _Dutton's Method of determining the Depth of the Focus._--If the seismic focus is either a point or a sphere, and the initial impulse equal in all directions, and if the intensity of the shock diminishes inversely as the square of the distance from the focus, then the continuous curve in Fig. 31 will represent the variation of intensity along a line passing through the epicentre E. The form of the curve on these assumptions does not depend in any way on the initial intensity of the impulse; it is governed solely by the depth of the focus. The deeper the focus, the flatter becomes the curve, as we have seen in discussing the Ischian earthquakes (p. 68). In all directions from the epicentre, the intensity at first diminishes slowly; but the rate of change of intensity with the distance soon becomes more rapid, until it is a maximum at the points C, C; after which it again diminishes and dies out very slowly when the distance becomes great. It will be evident from Fig. 18 that the deeper the focus the greater also is the distance EC of the points where the intensity of the shock changes most rapidly. It may be easily shown, indeed, that this distance always bears to the depth of the focus the constant ratio of 1 to sqrt(3), or about 1 to 1.73.[42] Now, if a series of isoseismals could be drawn corresponding to intensities which differ by constant amounts, we should have a series of circles like those surrounding the Woodstock epicentre in Fig. 29, the distance between successive lines at first decreasing gradually until it is a minimum at the dotted circle and afterwards gradually increasing. This dotted circle is obviously that which passes through all points where the intensity of the shock changes most rapidly. Major Dutton calls it the _index-circle_ and, when its radius is known, the depth of the focus is at once obtained by multiplying the radius by 1.73. In 1858, Mallet proposed a method which bears some resemblance to the above,[43] but depending only on the intensity of the longitudinal waves. Major Dutton claims for his method that the effects of the longitudinal and transverse waves are not separated, that it takes account of the "total energy irrespective of direction or kind of vibration." [Illustration: FIG. 31.--Diagram to illustrate Dutton's method of determining depth of seismic focus.]