d²y / dx² or (3x² - c²) / (c² + x²)³
is zero, which is satisfied when c = x √3
[43] British Association Report, 1858, pp. 101-103.
[44] The above time would have to be increased by one second if the depth of the focus were very small, and diminished by one second if it were as great as 23 miles; the difference in either case being less than the probable error.
[45] The method employed is as follows: Let t0 be the computed time (9h. 51m. 6s.) at the focus, x seconds the error in this estimate, t the reported time at a given place, D its distance from the focus in miles, and y the number of seconds required to travel one mile; then, assuming that y does not vary with the distance, we have x + Dy = t + t0. An equation of this form is obtained from each observation, and the method of least squares is then applied to determine the most probable values of x and y.
[46] This seems to me the more probable course. It is possible, however, that the fault-line may pass from Mount Holly Station to the east of the Woodstock epicentre as shown in Fig. 28, and then to the west of the Rantowles epicentre, the fault changing its direction of hade in the intermediate district.