April 25, 1918] 



I^ATURE 



159 



THE FREQUENCY OF EARTHQUAKES.^ 



THE publication of an abstract of twenty years' 

 record of earthquakes in Italy gives an oppor- 

 tunity for studying the effect of the gravitational attrac- 

 tion of the sun ; the period is so nearly coincident with 

 the lunar cytle of nineteen years that the effect of the 

 moon may be regarded as eliminated, the record is of 

 exceptional continuity and completeness, and the num- 

 ber of observations is large enough to allow of the ex- 

 traction of groups sufficiently numerous to give good 

 averages. 



The distribution of the stresses throughout each 

 liurnal period presents two peculiarities : first, the range 

 of stress is greater during the day than during the 

 night in summer, with an opposite variation during 

 winter ; secondly, the general effect of the vertical com- 

 ponent is towards a progressive diminution of the down- 

 ward pressure during the six hours preceding, and 

 towards an increase during the six hours following, the 

 meridian passages at noon and midnight. 



Investigating the first of these, a division of the year 

 into two parts, at the equinoxes, gives a proportion 

 of shocks during the day to those during the night, 

 somewhat greater than the average during the summer 

 half, and somewhat less during the winter. As this 

 result might be purely fortuitous it was tested by a 

 similar treatment of two other records which stood 

 ready for use — Milne's catalogue of Japanese earth- 

 quakes from 1885 to 1892, and the after-shocks of the 

 Indian earthquake of 1897. They show a variation iden- 

 tical in character with that of the Italian record. A second 

 test depends on the argument that, if the variation is 

 in any way seasonal, the divergence should be increased 

 at the height of each season ; the figures for the months 

 of January-February and of June-July were taken out, 

 as representing midwinter and midsummer respectively, 

 and found to show a divergence in each case greater 

 than, and in the same direction as, the respective half- 

 years. 



The actual figures are as follows, the frequency 

 being expressed as a ratio to the mean, of each group, 

 taken as 100 : — 



Distribution of Shocks by Day and Night. 

 Italy, 1891-1910. 



Japan, 1885-1892. 



Summer half 102 



Whole year 97 



Winter half ... ... 93 



Assam After-shocks. 



Summer ... ... ... 113 



Whole record 107 



Winter loi 



103 



Taken by itself the variation, as between any pair 

 of ratios, is as likely to be in one direction as in the 

 other, but the odds against a complete concordance 

 throughout the whole series are 31 to i ; it may, there- 

 fore, be taken that the variations are not fortuitous, 

 but due to some common cause which tends to increase 

 the frequency during the day and decrease it during 

 the night in summer, with the opposite in winter. 



' From a paper rntitled " SomeConsideration* arising from the Frequency 

 of Earthquakes," read before the Geological Society on February 6 by R. D. 

 Oldham, F.R.S. 



NO. 2530, VOL. lOl] 



For the second line of investigation a computation 

 was made of the mean amount of stress for the whole 

 of Italy and the whole year for each of the six hours 

 preceding and following the meridian passage. These 

 were plotted and compared with the corresponding 

 curve of frequency of earthquakes ; the result showed 

 no apparent relation between the frequency and the 

 total, or the horizontal, stress, though a close one 

 with the variation of the vertical stress, the greatest 

 number of earthquakes being in the period in which 

 there is the greatest increase of downward pressure. 

 As the rate of increase diminishes the frequency of shocks 

 is less, suffering a further diminution as the pressure 

 begins to decrease, and reaching its minimum in the 

 period where the decrease in pressure is greatest, in- 

 creasing again in the same way to the maximum. 



The Japanese record is not directly comparable with 

 the Italian, being dominated by the after-shocks of 

 great earthquakes of the world-shaking type, and 

 nearly half of the whole record consists of after-shocks 

 of the Mino-Owari earthquake of 189 1. Taking these 

 separately, we get a curve of frequency similar to the 

 Italian, except ihat the maximum and minimum are 

 reversed, the greatest number of shocks corresponding 

 with the period when the load is being lightened most 

 rapidly, indicating that these shocks were due to a 

 general movement of elevation rather than depression, 

 a conclusion in accord with field observations of other 

 great earthquakes. 



The actual figures of variation of stress, in Italy, 

 and the frequency of earthquakes are as follows : — 



Mean range of verti- 

 cal stress in each 

 two hours, Italy. 



Ratio of actual to 

 mean frequency of 

 each two-hour 

 period, Italy, 

 1891-1910 



After-shoqks of 

 Mino Owari, Oct. 

 28, 1 89 1, Japan. 



0*14 -o-27l-o'i3 4-0-I3+0-27 +0-14 



I -06 I "17 I I 01 090 088 0-99 



•01 0-95 0*96 0-97 I -08 I 1-03 



The principal point of interest in these figures is 

 that they give a means of estimating the rate of growth 

 of the strain which produces earthquakes. Accepting 

 the hypothesis that earthquakes are due to the relief 

 by fracture of a growing strain when this has 

 reached the breaking point, it can be shown that a 

 variable strain, acting alternately in increase or de- 

 crease of the general growth, while leaving the average 

 rate of growth unaltered, will give rise to a correspond- 

 ing variation in the frequency of shocks in each period, 

 and, besides that, there is a simple relation between 

 the magnitudes of the two stresses, to which the 

 strains are due, and the variations from the mean fre- 

 quency of earthquakes. .\ calculation based on this 

 shows that the growth of strain for Italy is such 

 that the breaking strain would be reached in about 

 three and a half years, starting from a condition of 

 no strain. The after-shocks of the Mino-Owari earth- 

 quake give about five to six months, if account is 

 taken of the difference between the resistance of rock 

 to tension and compression. These figures are given 

 for what they are worth; at the least they are of 

 interest as being the first authentic estimate which it 

 has been possible to make of the time required to pre- 

 pare for an earthquake, and, thence, of the rate of 

 growth of the particular tectonic process involved in 

 their production. 



