Ix PROCEEDINGS OE THE GEOLOGICAL SOCIETY, [vol. Ixxviii, 



be a certain increment which will lead to fracture, earthquake, 

 and partial relief ; then Avith a further increment the process will 

 he repeated, and so we reach the concept of a mean strain - 

 interval for each shock, which may be regarded as constant, on 

 the average, for any given region, provided that the average is 

 taken over long enough a period. If, then, we divide the mean 

 increment of strain in a unit period of time by the mean number 

 of shocks occurring in the same period, we obtain a fraction which, 

 represents the mean stress-interval for each shock, a fraction which 

 should remain constant in the region under consideration ; and from 

 this it results that any variation in the rate of growth of strain 

 must be accompanied by a corresponding variation in the frequency 

 of earthquakes. We have, then, four quantities so inter-related 

 with each other that, if three of them were known, the fourth can 

 be determined. Two of these, namely, the mean frequency and the 

 variation from that mean in any chosen period, can be obtained 

 from observation ; and, if the variation from the mean rate of 

 growth of strain is also known for the selected portion of the 

 whole period, that mean rate, which is the object of search can be 

 obtained by a simple rule-of -three sum.^ 



The frequency of earthquakes is known to be subject to great 

 variation from time to time, and this variation indicates a corre- 

 sponding change in the rate of growth of strain. In the main, 

 this change may, and probably must, be attributed to causes acting 

 within the Earth, and directly related to the changes or processes 

 by which the strain is produced ; but it is evident that, if there 

 were any external cause, which acted periodically and alternately 

 in increase and decrease of the rate of growth of strain, and if it 

 were possible to disentangle the variations due to this from those 

 due to other causes, we should possess the means of framing a 

 numerical estimate of the general rate of growth of strain. 



One such cause of periodic variation is to be found in the tide- 



^ The argument may be put in a different form, simpler and more easily 

 intelligible to some. If S represent the mean increment of strain in a given 

 period and N the mean number of earthquakes recorded in the same period, 

 then S/N is the fraction representing the mean strain-interval corresponding 

 to an earthqu.ake. If the variation of the growth of strain in any particular 

 period is represented by v and that of the number of earthquakes by d, we 

 get the equation 



where d = v/S 



whence we obtain the simple ratio 



