On Lunar Periodicities in Earthquake Frequency. 459 



is explained in full in the paper. To lighten in some measure the 

 labour of the harmonic analysis, certain districts were thrown 

 together to form a district group. Table I contains the number of 

 earthquakes in each district or district group, which formed the 

 material for discussion. 



Table I. 



Number of Description of 



District. earthquakes. district. 



1 397 ISTemura. 



25 627 E. coast. 



6 1432 S.E. corner. 



7 3632 Nagoya, &c. 



8 245 Kii Channel. 

 910 335 E. and S. of Kyushn. 



11 384 W. of Kyushu." 



12 112 i" 



W. coast of Main 



13 U8 ( Tl A 



14-15 145 J 



Of the tabulated numbers for each district or district group, over- 

 lapping means of every successive five were taken, and these were 

 divided by the mean of all. The numbers so obtained represent 

 relative frequencies throughout the lunar day, and are given in 

 Table II, which also contains a like series for all the earthquakes 

 taken in combination. 



The most important are the frequencies for districts 6 and 7, and 

 also for all combined. They are shown graphically in the figure 

 (p. 461). 



Each series of numbers was then discussed by harmonic analysis in 

 accordance with the Fourier expansion 



x = 1000 -f c sin ( --- |- a, 

 = 1 \ 25 



where x is 1000 times the relative frequency at time t, estimated 

 in hours after the meridian passage of the moon, and where the 

 amplitude c and the phase a n are to be calculated. The amplitudes 

 and phases for the first four harmonics are given in Table IY. 



There is a tendency for the second harmonic amplitude to be 

 greater than the first, while in half the number 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 within two hours of the half time between the 

 upper and lower meridian passage of the moon. In the others it falls 

 within two hours of the times of upper and lower meridian passage. 



2 M 2 



