part 2] IN THE FBEQUENCT OF EARTHQUAKES. 103 



records which had been previously available, it may not be without 

 interest to point out that the observed frequency is closely approxi- 

 mated by the formula 



N = 755-5-f212 sin. (/ 4-61° 45') + 122 sin. (2^ + 14°), . . . (1) 



where X represents the number of shocks occurring in an}' period 

 of two hours' length, and t the time of the middle of the two hours, 

 reckoned from midnight. This formula may be more conveniently 

 put in the form 



R = l-0 + -28 sin. (£ -h61° 45') + -13 sin. (2f + 14 c ) ; .... (2) 



where K represents the ratio of the actual to the mean number of 

 .shocks in a two-hour period, and from this we get the true 

 harmonic frequency 1 as 



F = l-04--28 sin. (f + 61°45') + -14 sin. (2^ + 14 c ) (3) 



In other words, we have a diurnal period with a maximum at 

 lh. 53m. after midnight and a minimum twelve hours later, 

 combined with a semidiurnal period having maxima at 2h. 32m. 

 after midnight and middav, and minima six hours later. The 

 semidiurnal period may be connected with the gravitational stresses 

 .set up by the sun, if the correlation is, as it should be, with the 

 rate of change, not with the actual amount, of the stress. The 

 diurnal period is less easy to explain ; there is no apparent con- 

 nexion with the distribution of the gravitational stresses, nor with 

 the diurnal variation in the height of the barometer ; there is 

 some apparent connexion with the diurnal variation in tempera- 

 ture, but it is difficult to see how this could affect the frequency of 

 earthquakes. The last named seems to have a real periodicity, for 

 each of the two decades gives a formula closely corresponding to 

 that of the whole jjeriod, and the variation in frequency cannot be 

 attributed, in any appreciable degree, to variation in the perfection 

 of the record, by feeble shocks being recorded at some times of the 

 day, and passing unnoticed at others. This is shown by the sepa- 

 rate tabulation of shocks of over Y° of the Mercalli scale, that is, 

 shocks of such a degree of violence that they could not pass un- 

 noticed and unrecorded, at whatever horn- of the day or night they 

 might occur, in a country where the observation of earthquakes 

 is so well organized as in Italy. This tabulation gives an harmonic 

 frequency of 



F = l-0+-28 sin. (£-t-61°15')4-'l7 sin. (2*4-19°), .... (4) 



which does not differ materially from (3). 



The seasonal variation in frequency dealt with in the paper 

 involves the introduction of a fourth term which makes the 

 approximate representation of the diurnal periodicity in each 

 half year 



F = r0-p28 sin. (f + 61° 45') + -14 sin. (2* + 14°) 



±•04 sin. (£+90°), (5) 



1 C. Davison, Phil. Trans. Roy. Soc. vol. clxxxiv (1893) p. 1111. 



