Fig. 30.—Planes of oscillation of stopped pendulum clocks at Charleston.[ToList]
Again, since the earlier part of the shock is almost uniformly described as the stronger, it follows that the Woodstock focus was the first in action. A curious fact recorded by Major Dutton supports this inference. In Charleston, four clocks were stopped by the shock, the errors of which at the time were certainly less than eight or nine seconds. The planes in which their pendulums oscillated are shown by the lines lettered A, B, C, and D in Fig. 30, the broken lines W and R representing respectively the directions from Charleston of the Woodstock and Rantowles epicentres. Clock A stopped at 9h. 51m. 0s., B at 9h. 51m. 15s., C at 9h. 51m. 16s., and D (which had been reset to the second earlier in the day) at 9h. 51m. 48s. Now, if the plane of oscillation coincided nearly with the direction of the shock, the only effect would be a temporary change in the period of oscillation; but if it was at right angles to the direction of the shock, the clock might be stopped by the point of the pendulum catching behind the graduated arc in front of which it oscillated. The planes of the first three clocks, it will be seen, were approximately at right angles to the direction of the Woodstock epicentre, and B and C were indeed stopped in the manner just described; while the plane of shock D was nearly perpendicular to the direction of the Rantowles epicentre. As the pendulums of B and C might make a few staggering oscillations before their final arrest, Major Dutton assigns 9h. 51m. 12s. as the epoch of the first maximum at Charleston; and, as the interval between the two maxima was about 34 seconds, this would give about 9h. 51m. 46s. for the epoch of the second maximum—a time which agrees very 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 √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."