1893.] Annual and Semi-annual Seismic Periods. 83 



mean corresponding to the end of January. Six-monthly means are 

 calculated in this way for the end of each month; each mean is 

 divided by the average of all twelve, and the difference between each 

 quotient and unity is multiplied by the augmenting factor 1*589, in 

 order to obtain the correct value of the ratio a\ : a . The curve 

 obtained by plotting these reduced means thus gives special pro- 

 minence to the annual period, by eliminating the semi-annual period 

 and all those which are fractions of six months, and by diminishing 

 the amplitudes of all other periods with respect to that of the annual 

 period. 



In investigating the semi-annual period, the numbers corresponding 

 to the first halves of January and July are added together, and so 

 on ; the rest of the method being the same as for the annual period. 

 The result gives special prominence to the semi-annual period by 

 eliminating the annual period, and by eliminating or Diminishing the 

 amplitudes of all periods less than six months. 



Seismic Periodicity in relation to Intensity. This discussion is 

 founded on : (1) lists compiled from Mallet's great catalogue, first, 

 of shocks which were so slight as to be just perceptible, and, secondly, 

 of those which were strong enough to damage buildings ; (2) Pro- 

 fessor Milne's classification of the Japanese earthquakes of 1885 to 

 1889 according to the areas disturbed by them ; and (3) different 

 catalogues relating to the same district, it being obvious that two 

 such catalogues for the same time can only differ by the omission or 

 inclusion of slight shocks. 



The following results are obtained : (1) In both periods, the 

 amplitude is greater for slight than for strong shocks ; (2) there 

 appear to be two classes of slight shocks with an annual period, the 

 stronger having their maximum in winter, the weaker in summer ; 

 and (3) in the case of the semi-annual period, both strong and slight 

 shocks, as a rule, have nearly the same maximum epochs. 



Seismic Periodicity in relation to Geographical Position. The num- 

 ber of records examined is 62, 45 belonging to the northern hemi- 

 sphere, 14 to the southern, and 3 to equatorial countries. 



1. Annual Period. In every district, and in all but five records 

 (which are obviously incomplete), there is a fairly well-marked annual 

 period. As a rule, different records for the same district agree in 

 giving the same, or nearly the same, maximum epoch. Excluding, 

 however, those which disagree in this respect, we have left 34 records 

 for the northern hemisphere, 9 for the southern, and 2 for equatorial 

 countries. In the northern hemisphere, 4 records give the maximum 

 in November, 16 in December, and 6 in January; in the southern 

 hemisphere, 2 in April, 2 in May, 3 in July, and 2 in August ; the 

 end of the month being supposed in each case. As a rule, then, the 

 maximum epoch occurs in winter in both hemispheres. The ampli- 



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