[Footnote 128: Chas. Davisson: On the Annual and Semi-annual Seismic Periods; Roy. Soc. of London, Philosophical Transactions, Vol. 184, 1893, 1107 _ff._] [Footnote 129: C. G. Knott: The Physics of Earthquake Phenomena, Oxford, 1908.] [Footnote 130: In Table 8 the first column indicates the region; the second, the dates; and the third, the number of shocks. The fourth column gives the month in which the annual maximum occurs when the crude figures are smoothed by the use of overlapping six-monthly means. In other words, the average for each successive six months has been placed in the middle of the period. Thus the average of January to June, inclusive, is placed between March and April, that for February to July between April and May, and so on. This method eliminates the minor fluctuations and also all periodicities having a duration of less than a year. If there were no annual periodicity the smoothing would result in practically the same figure for each month. The column marked "Amplitude" gives the range from the highest month to the lowest divided by the number of earthquakes and then corrected according to Schuster's method which is well known to mathematicians, but which is so confusing to the layman that it will not be described. Next, in the column marked "Expected Amplitude," we have the amplitude that would be expected if a series of numbers corresponding to the earthquake numbers and having a similar range were arranged in accidental order throughout the year. This also is calculated by Schuster's method in which the expected amplitude is equal to the square root of "pi" divided by the number of shocks. When the actual amplitude is four or more times the expected amplitude, the probability that there is a real periodicity in the observed phenomena becomes so great that we may regard it as practically certain. If there is no periodicity the two are equal. The last column gives the number of times by which the actual exceeds the expected amplitude, and thus is a measure of the probability that earthquakes vary systematically in a period of a year.] [Footnote 131: N. F. Drake: Destructive Earthquakes in China; Bull. Seism. Soc. Am., Vol. 2, 1912, pp. 40-91, 124-133.]