Page:Proceedings of the Royal Society of London Vol 60.djvu/492

Rh is explained in full in the paper. To lighten in some m easure the labour of th e harm onic analysis, certain districts were throw n together to form a d istrict group. Table I contains the num ber of earthquakes in each d istrict or d istrict group, w hich form ed the m aterial for discussion.

Table I. N umber of Description of District. earthquakes. district. 1 397 N em ura. 2— 5 627 E. coast. 6 1432 S.E. corner. 7 3632 Nagoya, &c. 8 245 K ii Channel. . 9—10 335 E. and S. of K yushu. 11 384 W. of K yushu. 12 112 'i 118 V W. coast of M ain 13 Island. 14—15 145 J

Of the tabulated num bers for each d istrict or d istrict group, overlapping m eans of every successive five were taken, and these were divided by th e mean of all. The num bers so obtained represent relative frequencies throughout the lu n ar day, and are given in Table II, which also contains a like series for all the earthquakes taken in combination. The most im portant are the frequencies for districts 6 and 7, and also for all combined. They are shown graphically in the figure (p. 4 6 i).

Each series of num bers was then discussed by harm onic analysis in accordance w ith the Fourier expansion n — qo 1000 + 2 Cn sin n 71 = 1 9

where x is 1000 times the relative frequency at time t, estim ated in hours after the mei'idian passage of the moon, and where the am plitude cn and the phase a.nare to be calculated. The amplitudes and phases for the first four harmonics are given in Table IV.

There is a tendency for the second harmonic am plitude to be greater than the first, while in half the num ber it is the greatest of all. As regards the times of occurrence of the maxima for the different harmonics, there is no regularity except perhaps in the case of the second harmonic. In four (1, 6, 7, 8) the maximum of the second harmonic falls w ithin two hours of the half time between the upper and lower meridian passage of the moon. In the others it falls w ithin two hours of the times of upper and lower m eridian passage.